TSTP Solution File: NUM925+2 by iProverMo---2.5-0.1
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : iProverMo---2.5-0.1
% Problem : NUM925+2 : TPTP v8.1.0. Released v5.3.0.
% Transfm : none
% Format : tptp:raw
% Command : iprover_modulo %s %d
% Computer : n006.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 11:03:17 EDT 2022
% Result : Theorem 7.43s 7.62s
% Output : CNFRefutation 7.48s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 713
% Syntax : Number of formulae : 6221 (1569 unt; 0 def)
% Number of atoms : 14347 (4193 equ)
% Maximal formula atoms : 56 ( 2 avg)
% Number of connectives : 14224 (6098 ~;6404 |; 386 &)
% ( 390 <=>; 946 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 4 avg)
% Maximal term depth : 9 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 92 ( 92 usr; 22 con; 0-3 aty)
% Number of variables : 12059 ( 654 sgn4103 !; 24 ?)
% Comments :
%------------------------------------------------------------------------------
% Axioms transformation by autotheo
% Orienting (remaining) axiom formulas using strategy ClausalAll
% CNF of (remaining) axioms:
% Start CNF derivation
fof(c_0_0,axiom,
! [X3,X4] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(X3),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_int(power_power_int(X4),number_number_of_nat(bit0(bit1(pls)))))),zero_zero_int))
<=> ( X3 = zero_zero_int
& X4 = zero_zero_int ) ),
file('<stdin>',fact_606_sum__power2__le__zero__iff) ).
fof(c_0_1,axiom,
! [X3,X4] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(plus_plus_real(hAPP_nat_real(power_power_real(X3),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_real(power_power_real(X4),number_number_of_nat(bit0(bit1(pls)))))),zero_zero_real))
<=> ( X3 = zero_zero_real
& X4 = zero_zero_real ) ),
file('<stdin>',fact_605_sum__power2__le__zero__iff) ).
fof(c_0_2,axiom,
! [X43,X44] : ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(plus_plus_real(hAPP_nat_real(power_power_real(X43),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_real(power_power_real(X44),number_number_of_nat(bit0(bit1(pls)))))),zero_zero_real)),
file('<stdin>',fact_140_not__sum__power2__lt__zero) ).
fof(c_0_3,axiom,
! [X43,X44] : ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(X43),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_int(power_power_int(X44),number_number_of_nat(bit0(bit1(pls)))))),zero_zero_int)),
file('<stdin>',fact_139_not__sum__power2__lt__zero) ).
fof(c_0_4,axiom,
! [X29,X11,X249] :
( ! [X248,X90] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X248),X90))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(X249,X248)),hAPP_nat_nat(X249,X90))) )
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(X249,X29)),X11)),hAPP_nat_nat(X249,hAPP_nat_nat(plus_plus_nat(X29),X11)))) ),
file('<stdin>',fact_647_mono__nat__linear__lb) ).
fof(c_0_5,axiom,
! [X55,X250,X249] :
( ! [X56,X251] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X56),X251))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(X249,X56)),hAPP_nat_nat(X249,X251))) )
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X55),X250))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(X249,X55)),hAPP_nat_nat(X249,X250))) ) ),
file('<stdin>',fact_654_less__mono__imp__le__mono) ).
fof(c_0_6,axiom,
! [X8,X10] : hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),sqrt(hAPP_real_real(plus_plus_real(hAPP_nat_real(power_power_real(X8),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_real(power_power_real(X10),number_number_of_nat(bit0(bit1(pls)))))))),
file('<stdin>',fact_690_real__sqrt__sum__squares__ge__zero) ).
fof(c_0_7,axiom,
! [X3,X4] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),hAPP_real_real(plus_plus_real(hAPP_nat_real(power_power_real(X3),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_real(power_power_real(X4),number_number_of_nat(bit0(bit1(pls)))))))
<=> ( X3 != zero_zero_real
| X4 != zero_zero_real ) ),
file('<stdin>',fact_138_sum__power2__gt__zero__iff) ).
fof(c_0_8,axiom,
! [X3,X4] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(X3),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_int(power_power_int(X4),number_number_of_nat(bit0(bit1(pls)))))))
<=> ( X3 != zero_zero_int
| X4 != zero_zero_int ) ),
file('<stdin>',fact_137_sum__power2__gt__zero__iff) ).
fof(c_0_9,axiom,
! [X151,X282] : hAPP_nat_int(power_power_int(hAPP_int_int(plus_plus_int(X151),X282)),number_number_of_nat(bit0(bit1(pls)))) = hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(X151),number_number_of_nat(bit0(bit1(pls))))),times_times_int(times_times_int(number_number_of_int(bit0(bit1(pls))),X151),X282))),hAPP_nat_int(power_power_int(X282),number_number_of_nat(bit0(bit1(pls))))),
file('<stdin>',fact_691_zadd__power2) ).
fof(c_0_10,axiom,
! [X54,X11,X55] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X11),X55))
=> ( hBOOL(hAPP_int_bool(X54,hAPP_int_int(plus_plus_int(X11),one_one_int)))
=> ( ! [X56] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X11),X56))
=> ( hBOOL(hAPP_int_bool(X54,X56))
=> hBOOL(hAPP_int_bool(X54,hAPP_int_int(plus_plus_int(X56),one_one_int))) ) )
=> hBOOL(hAPP_int_bool(X54,X55)) ) ) ),
file('<stdin>',fact_169_int__gr__induct) ).
fof(c_0_11,axiom,
! [X54,X11,X55] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X11),X55))
=> ( hBOOL(hAPP_int_bool(X54,X11))
=> ( ! [X56] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X11),X56))
=> ( hBOOL(hAPP_int_bool(X54,X56))
=> hBOOL(hAPP_int_bool(X54,hAPP_int_int(plus_plus_int(X56),one_one_int))) ) )
=> hBOOL(hAPP_int_bool(X54,X55)) ) ) ),
file('<stdin>',fact_652_int__ge__induct) ).
fof(c_0_12,axiom,
! [X245,X246] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(X245),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_int(power_power_int(X246),number_number_of_nat(bit0(bit1(pls))))))),
file('<stdin>',fact_604_sum__power2__ge__zero) ).
fof(c_0_13,axiom,
! [X245,X246] : hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),hAPP_real_real(plus_plus_real(hAPP_nat_real(power_power_real(X245),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_real(power_power_real(X246),number_number_of_nat(bit0(bit1(pls))))))),
file('<stdin>',fact_603_sum__power2__ge__zero) ).
fof(c_0_14,axiom,
! [X243,X244] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_nat_int(power_power_int(X243),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_int(power_power_int(X244),number_number_of_nat(bit0(bit1(pls))))))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X244))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X243),X244)) ) ),
file('<stdin>',fact_602_power2__less__imp__less) ).
fof(c_0_15,axiom,
! [X243,X244] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(power_power_nat(X243),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_nat(power_power_nat(X244),number_number_of_nat(bit0(bit1(pls))))))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),X244))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X243),X244)) ) ),
file('<stdin>',fact_601_power2__less__imp__less) ).
fof(c_0_16,axiom,
! [X243,X244] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_nat_real(power_power_real(X243),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_real(power_power_real(X244),number_number_of_nat(bit0(bit1(pls))))))
=> ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X244))
=> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X243),X244)) ) ),
file('<stdin>',fact_600_power2__less__imp__less) ).
fof(c_0_17,axiom,
! [X238,X239] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_nat_int(power_power_int(X238),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_int(power_power_int(X239),number_number_of_nat(bit0(bit1(pls))))))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X239))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X238),X239)) ) ),
file('<stdin>',fact_594_power2__le__imp__le) ).
fof(c_0_18,axiom,
! [X238,X239] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(power_power_nat(X238),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_nat(power_power_nat(X239),number_number_of_nat(bit0(bit1(pls))))))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),X239))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X238),X239)) ) ),
file('<stdin>',fact_593_power2__le__imp__le) ).
fof(c_0_19,axiom,
! [X238,X239] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_nat_real(power_power_real(X238),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_real(power_power_real(X239),number_number_of_nat(bit0(bit1(pls))))))
=> ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X239))
=> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X238),X239)) ) ),
file('<stdin>',fact_592_power2__le__imp__le) ).
fof(c_0_20,axiom,
! [X30] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),X30)),X30)),zero_zero_int))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X30),zero_zero_int)) ),
file('<stdin>',fact_88_odd__less__0) ).
fof(c_0_21,axiom,
! [X42] : ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_nat_real(power_power_real(X42),number_number_of_nat(bit0(bit1(pls))))),zero_zero_real)),
file('<stdin>',fact_136_power2__less__0) ).
fof(c_0_22,axiom,
! [X42] : ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_nat_int(power_power_int(X42),number_number_of_nat(bit0(bit1(pls))))),zero_zero_int)),
file('<stdin>',fact_135_power2__less__0) ).
fof(c_0_23,axiom,
! [X225,X226,X227] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_nat_int(power_power_int(X225),X226)),hAPP_nat_int(power_power_int(X227),X226)))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X227))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X225),X227)) ) ),
file('<stdin>',fact_556_power__less__imp__less__base) ).
fof(c_0_24,axiom,
! [X225,X226,X227] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(power_power_nat(X225),X226)),hAPP_nat_nat(power_power_nat(X227),X226)))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),X227))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X225),X227)) ) ),
file('<stdin>',fact_555_power__less__imp__less__base) ).
fof(c_0_25,axiom,
! [X225,X226,X227] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_nat_real(power_power_real(X225),X226)),hAPP_nat_real(power_power_real(X227),X226)))
=> ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X227))
=> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X225),X227)) ) ),
file('<stdin>',fact_554_power__less__imp__less__base) ).
fof(c_0_26,axiom,
! [X177,X178,X179] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),X179))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_nat_int(power_power_int(X179),X177)),hAPP_nat_int(power_power_int(X179),X178)))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X177),X178)) ) ),
file('<stdin>',fact_462_power__le__imp__le__exp) ).
fof(c_0_27,axiom,
! [X177,X178,X179] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,one_one_nat),X179))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(power_power_nat(X179),X177)),hAPP_nat_nat(power_power_nat(X179),X178)))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X177),X178)) ) ),
file('<stdin>',fact_461_power__le__imp__le__exp) ).
fof(c_0_28,axiom,
! [X177,X178,X179] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,one_one_real),X179))
=> ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_nat_real(power_power_real(X179),X177)),hAPP_nat_real(power_power_real(X179),X178)))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X177),X178)) ) ),
file('<stdin>',fact_460_power__le__imp__le__exp) ).
fof(c_0_29,axiom,
! [X3,X4,X81] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),X81))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_nat_int(power_power_int(X81),X3)),hAPP_nat_int(power_power_int(X81),X4)))
<=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X3),X4)) ) ),
file('<stdin>',fact_459_power__increasing__iff) ).
fof(c_0_30,axiom,
! [X3,X4,X81] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,one_one_nat),X81))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(power_power_nat(X81),X3)),hAPP_nat_nat(power_power_nat(X81),X4)))
<=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X3),X4)) ) ),
file('<stdin>',fact_458_power__increasing__iff) ).
fof(c_0_31,axiom,
! [X3,X4,X81] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,one_one_real),X81))
=> ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_nat_real(power_power_real(X81),X3)),hAPP_nat_real(power_power_real(X81),X4)))
<=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X3),X4)) ) ),
file('<stdin>',fact_457_power__increasing__iff) ).
fof(c_0_32,axiom,
! [X82,X83,X84] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),X84))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_nat_int(power_power_int(X84),X82)),hAPP_nat_int(power_power_int(X84),X83)))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X82),X83)) ) ),
file('<stdin>',fact_279_power__less__imp__less__exp) ).
fof(c_0_33,axiom,
! [X82,X83,X84] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,one_one_nat),X84))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(power_power_nat(X84),X82)),hAPP_nat_nat(power_power_nat(X84),X83)))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X82),X83)) ) ),
file('<stdin>',fact_278_power__less__imp__less__exp) ).
fof(c_0_34,axiom,
! [X82,X83,X84] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,one_one_real),X84))
=> ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_nat_real(power_power_real(X84),X82)),hAPP_nat_real(power_power_real(X84),X83)))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X82),X83)) ) ),
file('<stdin>',fact_277_power__less__imp__less__exp) ).
fof(c_0_35,axiom,
! [X3,X4,X81] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),X81))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_nat_int(power_power_int(X81),X3)),hAPP_nat_int(power_power_int(X81),X4)))
<=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X3),X4)) ) ),
file('<stdin>',fact_276_power__strict__increasing__iff) ).
fof(c_0_36,axiom,
! [X3,X4,X81] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,one_one_nat),X81))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(power_power_nat(X81),X3)),hAPP_nat_nat(power_power_nat(X81),X4)))
<=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X3),X4)) ) ),
file('<stdin>',fact_275_power__strict__increasing__iff) ).
fof(c_0_37,axiom,
! [X3,X4,X81] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,one_one_real),X81))
=> ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_nat_real(power_power_real(X81),X3)),hAPP_nat_real(power_power_real(X81),X4)))
<=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X3),X4)) ) ),
file('<stdin>',fact_274_power__strict__increasing__iff) ).
fof(c_0_38,axiom,
! [X15,X16,X22] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X22))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(power_power_nat(X22),X15)),hAPP_nat_nat(power_power_nat(X22),X16)))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X15),X16)) ) ),
file('<stdin>',fact_197_nat__power__less__imp__less) ).
fof(c_0_39,axiom,
! [X174,X175,X176] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X175),X176))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X174))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X174),one_one_int))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_nat_int(power_power_int(X174),X176)),hAPP_nat_int(power_power_int(X174),X175))) ) ) ),
file('<stdin>',fact_456_power__decreasing) ).
fof(c_0_40,axiom,
! [X174,X175,X176] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X175),X176))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),X174))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X174),one_one_nat))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(power_power_nat(X174),X176)),hAPP_nat_nat(power_power_nat(X174),X175))) ) ) ),
file('<stdin>',fact_455_power__decreasing) ).
fof(c_0_41,axiom,
! [X174,X175,X176] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X175),X176))
=> ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X174))
=> ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X174),one_one_real))
=> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_nat_real(power_power_real(X174),X176)),hAPP_nat_real(power_power_real(X174),X175))) ) ) ),
file('<stdin>',fact_454_power__decreasing) ).
fof(c_0_42,axiom,
! [X51,X52,X53] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X52),X53))
=> ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X51))
=> ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X51),one_one_real))
=> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_nat_real(power_power_real(X51),X53)),hAPP_nat_real(power_power_real(X51),X52))) ) ) ),
file('<stdin>',fact_165_power__strict__decreasing) ).
fof(c_0_43,axiom,
! [X51,X52,X53] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X52),X53))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X51))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X51),one_one_nat))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(power_power_nat(X51),X53)),hAPP_nat_nat(power_power_nat(X51),X52))) ) ) ),
file('<stdin>',fact_164_power__strict__decreasing) ).
fof(c_0_44,axiom,
! [X51,X52,X53] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X52),X53))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X51))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X51),one_one_int))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_nat_int(power_power_int(X51),X53)),hAPP_nat_int(power_power_int(X51),X52))) ) ) ),
file('<stdin>',fact_163_power__strict__decreasing) ).
fof(c_0_45,axiom,
! [X234,X235,X236] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X235),X236))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X235))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X234))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_nat_int(power_power_int(X235),X234)),hAPP_nat_int(power_power_int(X236),X234))) ) ) ),
file('<stdin>',fact_587_power__strict__mono) ).
fof(c_0_46,axiom,
! [X234,X235,X236] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X235),X236))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),X235))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X234))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(power_power_nat(X235),X234)),hAPP_nat_nat(power_power_nat(X236),X234))) ) ) ),
file('<stdin>',fact_586_power__strict__mono) ).
fof(c_0_47,axiom,
! [X234,X235,X236] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X235),X236))
=> ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X235))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X234))
=> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_nat_real(power_power_real(X235),X234)),hAPP_nat_real(power_power_real(X236),X234))) ) ) ),
file('<stdin>',fact_585_power__strict__mono) ).
fof(c_0_48,axiom,
! [X11,X29,X18] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(X11),X29)),hAPP_nat_nat(plus_plus_nat(X11),X18)))
<=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X29),X18)) ),
file('<stdin>',fact_630_nat__add__left__cancel__le) ).
fof(c_0_49,axiom,
! [X168,X169,X170] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(plus_plus_int(X168),X169)),hAPP_int_int(plus_plus_int(X168),X170)))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X169),X170)) ),
file('<stdin>',fact_428_add__le__imp__le__left) ).
fof(c_0_50,axiom,
! [X168,X169,X170] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(X168),X169)),hAPP_nat_nat(plus_plus_nat(X168),X170)))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X169),X170)) ),
file('<stdin>',fact_427_add__le__imp__le__left) ).
fof(c_0_51,axiom,
! [X168,X169,X170] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(plus_plus_real(X168),X169)),hAPP_real_real(plus_plus_real(X168),X170)))
=> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X169),X170)) ),
file('<stdin>',fact_426_add__le__imp__le__left) ).
fof(c_0_52,axiom,
! [X165,X166,X167] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(plus_plus_int(X165),X166)),hAPP_int_int(plus_plus_int(X167),X166)))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X165),X167)) ),
file('<stdin>',fact_425_add__le__imp__le__right) ).
fof(c_0_53,axiom,
! [X165,X166,X167] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(X165),X166)),hAPP_nat_nat(plus_plus_nat(X167),X166)))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X165),X167)) ),
file('<stdin>',fact_424_add__le__imp__le__right) ).
fof(c_0_54,axiom,
! [X165,X166,X167] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(plus_plus_real(X165),X166)),hAPP_real_real(plus_plus_real(X167),X166)))
=> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X165),X167)) ),
file('<stdin>',fact_423_add__le__imp__le__right) ).
fof(c_0_55,axiom,
! [X106,X5,X81] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(plus_plus_int(X106),X5)),hAPP_int_int(plus_plus_int(X106),X81)))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X5),X81)) ),
file('<stdin>',fact_413_add__le__cancel__left) ).
fof(c_0_56,axiom,
! [X106,X5,X81] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(X106),X5)),hAPP_nat_nat(plus_plus_nat(X106),X81)))
<=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X5),X81)) ),
file('<stdin>',fact_412_add__le__cancel__left) ).
fof(c_0_57,axiom,
! [X106,X5,X81] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(plus_plus_real(X106),X5)),hAPP_real_real(plus_plus_real(X106),X81)))
<=> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X5),X81)) ),
file('<stdin>',fact_411_add__le__cancel__left) ).
fof(c_0_58,axiom,
! [X5,X106,X81] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(plus_plus_int(X5),X106)),hAPP_int_int(plus_plus_int(X81),X106)))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X5),X81)) ),
file('<stdin>',fact_410_add__le__cancel__right) ).
fof(c_0_59,axiom,
! [X5,X106,X81] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(X5),X106)),hAPP_nat_nat(plus_plus_nat(X81),X106)))
<=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X5),X81)) ),
file('<stdin>',fact_409_add__le__cancel__right) ).
fof(c_0_60,axiom,
! [X5,X106,X81] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(plus_plus_real(X5),X106)),hAPP_real_real(plus_plus_real(X81),X106)))
<=> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X5),X81)) ),
file('<stdin>',fact_408_add__le__cancel__right) ).
fof(c_0_61,axiom,
! [X5,X106,X81] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(X5),X106)),hAPP_int_int(plus_plus_int(X81),X106)))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X5),X81)) ),
file('<stdin>',fact_392_add__less__cancel__right) ).
fof(c_0_62,axiom,
! [X5,X106,X81] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(X5),X106)),hAPP_nat_nat(plus_plus_nat(X81),X106)))
<=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X5),X81)) ),
file('<stdin>',fact_391_add__less__cancel__right) ).
fof(c_0_63,axiom,
! [X5,X106,X81] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(plus_plus_real(X5),X106)),hAPP_real_real(plus_plus_real(X81),X106)))
<=> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X5),X81)) ),
file('<stdin>',fact_390_add__less__cancel__right) ).
fof(c_0_64,axiom,
! [X106,X5,X81] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(X106),X5)),hAPP_int_int(plus_plus_int(X106),X81)))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X5),X81)) ),
file('<stdin>',fact_389_add__less__cancel__left) ).
fof(c_0_65,axiom,
! [X106,X5,X81] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(X106),X5)),hAPP_nat_nat(plus_plus_nat(X106),X81)))
<=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X5),X81)) ),
file('<stdin>',fact_388_add__less__cancel__left) ).
fof(c_0_66,axiom,
! [X106,X5,X81] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(plus_plus_real(X106),X5)),hAPP_real_real(plus_plus_real(X106),X81)))
<=> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X5),X81)) ),
file('<stdin>',fact_387_add__less__cancel__left) ).
fof(c_0_67,axiom,
! [X133,X134,X135] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(X133),X134)),hAPP_int_int(plus_plus_int(X135),X134)))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X133),X135)) ),
file('<stdin>',fact_377_add__less__imp__less__right) ).
fof(c_0_68,axiom,
! [X133,X134,X135] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(X133),X134)),hAPP_nat_nat(plus_plus_nat(X135),X134)))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X133),X135)) ),
file('<stdin>',fact_376_add__less__imp__less__right) ).
fof(c_0_69,axiom,
! [X133,X134,X135] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(plus_plus_real(X133),X134)),hAPP_real_real(plus_plus_real(X135),X134)))
=> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X133),X135)) ),
file('<stdin>',fact_375_add__less__imp__less__right) ).
fof(c_0_70,axiom,
! [X130,X131,X132] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(X130),X131)),hAPP_int_int(plus_plus_int(X130),X132)))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X131),X132)) ),
file('<stdin>',fact_374_add__less__imp__less__left) ).
fof(c_0_71,axiom,
! [X130,X131,X132] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(X130),X131)),hAPP_nat_nat(plus_plus_nat(X130),X132)))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X131),X132)) ),
file('<stdin>',fact_373_add__less__imp__less__left) ).
fof(c_0_72,axiom,
! [X130,X131,X132] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(plus_plus_real(X130),X131)),hAPP_real_real(plus_plus_real(X130),X132)))
=> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X131),X132)) ),
file('<stdin>',fact_372_add__less__imp__less__left) ).
fof(c_0_73,axiom,
! [X11,X29,X18] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(X11),X29)),hAPP_nat_nat(plus_plus_nat(X11),X18)))
<=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X29),X18)) ),
file('<stdin>',fact_183_nat__add__left__cancel__less) ).
fof(c_0_74,axiom,
! [X21,X31,X22,X23] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X22),X23))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X21),X31))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(X22),X21)),hAPP_nat_nat(plus_plus_nat(X23),X31))) ) ),
file('<stdin>',fact_634_add__le__mono) ).
fof(c_0_75,axiom,
! [X207,X17,X208,X14] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X208),X14))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X207),X17))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(X208),X207)),hAPP_int_int(plus_plus_int(X14),X17))) ) ),
file('<stdin>',fact_523_zadd__zless__mono) ).
fof(c_0_76,axiom,
! [X194,X195,X196,X197] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X196),X197))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X194),X195))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(X196),X194)),hAPP_int_int(plus_plus_int(X197),X195))) ) ),
file('<stdin>',fact_491_add__le__less__mono) ).
fof(c_0_77,axiom,
! [X194,X195,X196,X197] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X196),X197))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X194),X195))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(X196),X194)),hAPP_nat_nat(plus_plus_nat(X197),X195))) ) ),
file('<stdin>',fact_490_add__le__less__mono) ).
fof(c_0_78,axiom,
! [X194,X195,X196,X197] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X196),X197))
=> ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X194),X195))
=> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(plus_plus_real(X196),X194)),hAPP_real_real(plus_plus_real(X197),X195))) ) ),
file('<stdin>',fact_489_add__le__less__mono) ).
fof(c_0_79,axiom,
! [X190,X191,X192,X193] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X192),X193))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X190),X191))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(X192),X190)),hAPP_int_int(plus_plus_int(X193),X191))) ) ),
file('<stdin>',fact_488_add__less__le__mono) ).
fof(c_0_80,axiom,
! [X190,X191,X192,X193] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X192),X193))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X190),X191))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(X192),X190)),hAPP_nat_nat(plus_plus_nat(X193),X191))) ) ),
file('<stdin>',fact_487_add__less__le__mono) ).
fof(c_0_81,axiom,
! [X190,X191,X192,X193] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X192),X193))
=> ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X190),X191))
=> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(plus_plus_real(X192),X190)),hAPP_real_real(plus_plus_real(X193),X191))) ) ),
file('<stdin>',fact_486_add__less__le__mono) ).
fof(c_0_82,axiom,
! [X161,X162,X163,X164] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X163),X164))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X161),X162))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(plus_plus_int(X163),X161)),hAPP_int_int(plus_plus_int(X164),X162))) ) ),
file('<stdin>',fact_422_add__mono) ).
fof(c_0_83,axiom,
! [X161,X162,X163,X164] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X163),X164))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X161),X162))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(X163),X161)),hAPP_nat_nat(plus_plus_nat(X164),X162))) ) ),
file('<stdin>',fact_421_add__mono) ).
fof(c_0_84,axiom,
! [X161,X162,X163,X164] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X163),X164))
=> ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X161),X162))
=> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(plus_plus_real(X163),X161)),hAPP_real_real(plus_plus_real(X164),X162))) ) ),
file('<stdin>',fact_420_add__mono) ).
fof(c_0_85,axiom,
! [X136,X137,X138,X139] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X138),X139))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X136),X137))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(X138),X136)),hAPP_int_int(plus_plus_int(X139),X137))) ) ),
file('<stdin>',fact_380_add__strict__mono) ).
fof(c_0_86,axiom,
! [X136,X137,X138,X139] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X138),X139))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X136),X137))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(X138),X136)),hAPP_nat_nat(plus_plus_nat(X139),X137))) ) ),
file('<stdin>',fact_379_add__strict__mono) ).
fof(c_0_87,axiom,
! [X136,X137,X138,X139] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X138),X139))
=> ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X136),X137))
=> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(plus_plus_real(X138),X136)),hAPP_real_real(plus_plus_real(X139),X137))) ) ),
file('<stdin>',fact_378_add__strict__mono) ).
fof(c_0_88,axiom,
! [X21,X31,X22,X23] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X22),X23))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X21),X31))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(X22),X21)),hAPP_nat_nat(plus_plus_nat(X23),X31))) ) ),
file('<stdin>',fact_191_add__less__mono) ).
fof(c_0_89,axiom,
! [X200,X201,X202] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X201),X202))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X201))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_nat_int(power_power_int(X201),X200)),hAPP_nat_int(power_power_int(X202),X200))) ) ),
file('<stdin>',fact_506_power__mono) ).
fof(c_0_90,axiom,
! [X200,X201,X202] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X201),X202))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),X201))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(power_power_nat(X201),X200)),hAPP_nat_nat(power_power_nat(X202),X200))) ) ),
file('<stdin>',fact_505_power__mono) ).
fof(c_0_91,axiom,
! [X200,X201,X202] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X201),X202))
=> ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X201))
=> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_nat_real(power_power_real(X201),X200)),hAPP_nat_real(power_power_real(X202),X200))) ) ),
file('<stdin>',fact_504_power__mono) ).
fof(c_0_92,axiom,
! [X171,X172,X173] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X172),X173))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),X171))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_nat_int(power_power_int(X171),X172)),hAPP_nat_int(power_power_int(X171),X173))) ) ),
file('<stdin>',fact_431_power__increasing) ).
fof(c_0_93,axiom,
! [X171,X172,X173] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X172),X173))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,one_one_nat),X171))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(power_power_nat(X171),X172)),hAPP_nat_nat(power_power_nat(X171),X173))) ) ),
file('<stdin>',fact_430_power__increasing) ).
fof(c_0_94,axiom,
! [X171,X172,X173] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X172),X173))
=> ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,one_one_real),X171))
=> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_nat_real(power_power_real(X171),X172)),hAPP_nat_real(power_power_real(X171),X173))) ) ),
file('<stdin>',fact_429_power__increasing) ).
fof(c_0_95,axiom,
! [X85,X86,X87] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X86),X87))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),X85))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_nat_int(power_power_int(X85),X86)),hAPP_nat_int(power_power_int(X85),X87))) ) ),
file('<stdin>',fact_282_power__strict__increasing) ).
fof(c_0_96,axiom,
! [X85,X86,X87] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X86),X87))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,one_one_nat),X85))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(power_power_nat(X85),X86)),hAPP_nat_nat(power_power_nat(X85),X87))) ) ),
file('<stdin>',fact_281_power__strict__increasing) ).
fof(c_0_97,axiom,
! [X85,X86,X87] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X86),X87))
=> ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,one_one_real),X85))
=> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_nat_real(power_power_real(X85),X86)),hAPP_nat_real(power_power_real(X85),X87))) ) ),
file('<stdin>',fact_280_power__strict__increasing) ).
fof(c_0_98,axiom,
! [X3,X4] :
( hAPP_real_real(plus_plus_real(hAPP_nat_real(power_power_real(X3),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_real(power_power_real(X4),number_number_of_nat(bit0(bit1(pls))))) = zero_zero_real
<=> ( X3 = zero_zero_real
& X4 = zero_zero_real ) ),
file('<stdin>',fact_153_realpow__two__sum__zero__iff) ).
fof(c_0_99,axiom,
! [X3,X4] :
( hAPP_real_real(plus_plus_real(hAPP_nat_real(power_power_real(X3),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_real(power_power_real(X4),number_number_of_nat(bit0(bit1(pls))))) = zero_zero_real
<=> ( X3 = zero_zero_real
& X4 = zero_zero_real ) ),
file('<stdin>',fact_3_sum__power2__eq__zero__iff) ).
fof(c_0_100,axiom,
! [X3,X4] :
( hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(X3),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_int(power_power_int(X4),number_number_of_nat(bit0(bit1(pls))))) = zero_zero_int
<=> ( X3 = zero_zero_int
& X4 = zero_zero_int ) ),
file('<stdin>',fact_2_sum__power2__eq__zero__iff) ).
fof(c_0_101,axiom,
! [X47] : hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_nat_real(semiri132038758t_real,X47)),hAPP_nat_real(power_power_real(number267125858f_real(bit0(bit1(pls)))),X47))),
file('<stdin>',fact_150_of__nat__less__two__power) ).
fof(c_0_102,axiom,
! [X47] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_nat_int(semiri1621563631at_int,X47)),hAPP_nat_int(power_power_int(number_number_of_int(bit0(bit1(pls)))),X47))),
file('<stdin>',fact_149_of__nat__less__two__power) ).
fof(c_0_103,axiom,
! [X54,X29,X18] :
( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X29),X18))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(X54,X18),X29)) )
=> ( ( X29 = X18
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(X54,X18),X29)) )
=> ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X18),X29))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(X54,X18),X29)) )
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(X54,X18),X29)) ) ) ),
file('<stdin>',fact_194_nat__less__cases) ).
fof(c_0_104,axiom,
! [X223,X224] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X224),zero_zero_int))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X223),zero_zero_int))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(X224),X223)),zero_zero_int)) ) ),
file('<stdin>',fact_553_add__nonpos__neg) ).
fof(c_0_105,axiom,
! [X223,X224] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X224),zero_zero_nat))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X223),zero_zero_nat))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(X224),X223)),zero_zero_nat)) ) ),
file('<stdin>',fact_552_add__nonpos__neg) ).
fof(c_0_106,axiom,
! [X223,X224] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X224),zero_zero_real))
=> ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X223),zero_zero_real))
=> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(plus_plus_real(X224),X223)),zero_zero_real)) ) ),
file('<stdin>',fact_551_add__nonpos__neg) ).
fof(c_0_107,axiom,
! [X221,X222] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X222),zero_zero_int))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X221),zero_zero_int))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(X222),X221)),zero_zero_int)) ) ),
file('<stdin>',fact_550_add__neg__nonpos) ).
fof(c_0_108,axiom,
! [X221,X222] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X222),zero_zero_nat))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X221),zero_zero_nat))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(X222),X221)),zero_zero_nat)) ) ),
file('<stdin>',fact_549_add__neg__nonpos) ).
fof(c_0_109,axiom,
! [X221,X222] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X222),zero_zero_real))
=> ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X221),zero_zero_real))
=> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(plus_plus_real(X222),X221)),zero_zero_real)) ) ),
file('<stdin>',fact_548_add__neg__nonpos) ).
fof(c_0_110,axiom,
! [X188,X189] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X189),zero_zero_int))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X188),zero_zero_int))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(plus_plus_int(X189),X188)),zero_zero_int)) ) ),
file('<stdin>',fact_485_add__nonpos__nonpos) ).
fof(c_0_111,axiom,
! [X188,X189] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X189),zero_zero_nat))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X188),zero_zero_nat))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(X189),X188)),zero_zero_nat)) ) ),
file('<stdin>',fact_484_add__nonpos__nonpos) ).
fof(c_0_112,axiom,
! [X188,X189] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X189),zero_zero_real))
=> ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X188),zero_zero_real))
=> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(plus_plus_real(X189),X188)),zero_zero_real)) ) ),
file('<stdin>',fact_483_add__nonpos__nonpos) ).
fof(c_0_113,axiom,
! [X147,X148] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X148),zero_zero_int))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X147),zero_zero_int))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(X148),X147)),zero_zero_int)) ) ),
file('<stdin>',fact_399_add__neg__neg) ).
fof(c_0_114,axiom,
! [X147,X148] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X148),zero_zero_nat))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X147),zero_zero_nat))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(X148),X147)),zero_zero_nat)) ) ),
file('<stdin>',fact_398_add__neg__neg) ).
fof(c_0_115,axiom,
! [X147,X148] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X148),zero_zero_real))
=> ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X147),zero_zero_real))
=> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(plus_plus_real(X148),X147)),zero_zero_real)) ) ),
file('<stdin>',fact_397_add__neg__neg) ).
fof(c_0_116,axiom,
! [X15,X21,X16] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(X15),X21)),X16))
=> ~ ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X15),X16))
=> ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X21),X16)) ) ),
file('<stdin>',fact_637_add__leE) ).
fof(c_0_117,axiom,
! [X15,X21,X16] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(X15),X21)),X16))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X15),X16)) ),
file('<stdin>',fact_636_add__leD1) ).
fof(c_0_118,axiom,
! [X15,X21,X16] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(X15),X21)),X16))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X21),X16)) ),
file('<stdin>',fact_635_add__leD2) ).
fof(c_0_119,axiom,
! [X22,X23,X21] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(X22),X23)),X21))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X22),X21)) ),
file('<stdin>',fact_193_add__lessD1) ).
fof(c_0_120,axiom,
! [X5] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(plus_plus_int(X5),X5)),zero_zero_int))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X5),zero_zero_int)) ),
file('<stdin>',fact_470_double__add__le__zero__iff__single__add__le__zero) ).
fof(c_0_121,axiom,
! [X5] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(plus_plus_real(X5),X5)),zero_zero_real))
<=> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X5),zero_zero_real)) ),
file('<stdin>',fact_469_double__add__le__zero__iff__single__add__le__zero) ).
fof(c_0_122,axiom,
! [X5] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(X5),X5)),zero_zero_int))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X5),zero_zero_int)) ),
file('<stdin>',fact_306_double__add__less__zero__iff__single__add__less__zero) ).
fof(c_0_123,axiom,
! [X5] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(plus_plus_real(X5),X5)),zero_zero_real))
<=> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X5),zero_zero_real)) ),
file('<stdin>',fact_305_double__add__less__zero__iff__single__add__less__zero) ).
fof(c_0_124,axiom,
! [X5] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(plus_plus_real(X5),X5)),zero_zero_real))
<=> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X5),zero_zero_real)) ),
file('<stdin>',fact_64_even__less__0__iff) ).
fof(c_0_125,axiom,
! [X5] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(X5),X5)),zero_zero_int))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X5),zero_zero_int)) ),
file('<stdin>',fact_63_even__less__0__iff) ).
fof(c_0_126,axiom,
! [X17,X8,X10] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X8),X10))
=> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(plus_plus_real(X17),X8)),hAPP_real_real(plus_plus_real(X17),X10))) ),
file('<stdin>',fact_638_real__add__left__mono) ).
fof(c_0_127,axiom,
! [X21,X22,X23] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X22),X23))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(X22),X21)),hAPP_nat_nat(plus_plus_nat(X23),X21))) ),
file('<stdin>',fact_633_add__le__mono1) ).
fof(c_0_128,axiom,
! [X21,X22,X23] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X22),X23))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(plus_plus_int(X21),X22)),hAPP_int_int(plus_plus_int(X21),X23))) ),
file('<stdin>',fact_448_zadd__left__mono) ).
fof(c_0_129,axiom,
! [X158,X159,X160] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X159),X160))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(plus_plus_int(X158),X159)),hAPP_int_int(plus_plus_int(X158),X160))) ),
file('<stdin>',fact_419_add__left__mono) ).
fof(c_0_130,axiom,
! [X158,X159,X160] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X159),X160))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(X158),X159)),hAPP_nat_nat(plus_plus_nat(X158),X160))) ),
file('<stdin>',fact_418_add__left__mono) ).
fof(c_0_131,axiom,
! [X158,X159,X160] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X159),X160))
=> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(plus_plus_real(X158),X159)),hAPP_real_real(plus_plus_real(X158),X160))) ),
file('<stdin>',fact_417_add__left__mono) ).
fof(c_0_132,axiom,
! [X155,X156,X157] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X156),X157))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(plus_plus_int(X156),X155)),hAPP_int_int(plus_plus_int(X157),X155))) ),
file('<stdin>',fact_416_add__right__mono) ).
fof(c_0_133,axiom,
! [X155,X156,X157] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X156),X157))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(X156),X155)),hAPP_nat_nat(plus_plus_nat(X157),X155))) ),
file('<stdin>',fact_415_add__right__mono) ).
fof(c_0_134,axiom,
! [X155,X156,X157] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X156),X157))
=> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(plus_plus_real(X156),X155)),hAPP_real_real(plus_plus_real(X157),X155))) ),
file('<stdin>',fact_414_add__right__mono) ).
fof(c_0_135,axiom,
! [X143,X144,X145] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X144),X145))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(X144),X143)),hAPP_int_int(plus_plus_int(X145),X143))) ),
file('<stdin>',fact_386_add__strict__right__mono) ).
fof(c_0_136,axiom,
! [X143,X144,X145] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X144),X145))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(X144),X143)),hAPP_nat_nat(plus_plus_nat(X145),X143))) ),
file('<stdin>',fact_385_add__strict__right__mono) ).
fof(c_0_137,axiom,
! [X143,X144,X145] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X144),X145))
=> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(plus_plus_real(X144),X143)),hAPP_real_real(plus_plus_real(X145),X143))) ),
file('<stdin>',fact_384_add__strict__right__mono) ).
fof(c_0_138,axiom,
! [X140,X141,X142] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X141),X142))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(X140),X141)),hAPP_int_int(plus_plus_int(X140),X142))) ),
file('<stdin>',fact_383_add__strict__left__mono) ).
fof(c_0_139,axiom,
! [X140,X141,X142] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X141),X142))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(X140),X141)),hAPP_nat_nat(plus_plus_nat(X140),X142))) ),
file('<stdin>',fact_382_add__strict__left__mono) ).
fof(c_0_140,axiom,
! [X140,X141,X142] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X141),X142))
=> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(plus_plus_real(X140),X141)),hAPP_real_real(plus_plus_real(X140),X142))) ),
file('<stdin>',fact_381_add__strict__left__mono) ).
fof(c_0_141,axiom,
! [X21,X22,X23] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X22),X23))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(X22),X21)),hAPP_nat_nat(plus_plus_nat(X23),X21))) ),
file('<stdin>',fact_190_add__less__mono1) ).
fof(c_0_142,axiom,
! [X21,X22,X23] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X22),X23))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(X22),X21)),hAPP_int_int(plus_plus_int(X23),X21))) ),
file('<stdin>',fact_51_zadd__strict__right__mono) ).
fof(c_0_143,axiom,
! [X5] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),hAPP_nat_real(power_power_real(X5),number_number_of_nat(bit0(bit1(pls))))))
<=> X5 != zero_zero_real ),
file('<stdin>',fact_134_zero__less__power2) ).
fof(c_0_144,axiom,
! [X5] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_nat_int(power_power_int(X5),number_number_of_nat(bit0(bit1(pls))))))
<=> X5 != zero_zero_int ),
file('<stdin>',fact_133_zero__less__power2) ).
fof(c_0_145,axiom,
! [X25,X30] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(plus_plus_int(X25),one_one_int)),X30))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X25),X30)) ),
file('<stdin>',fact_571_add1__zle__eq) ).
fof(c_0_146,axiom,
! [X15,X16,X17] : hAPP_int_int(plus_plus_int(hAPP_nat_int(semiri1621563631at_int,X15)),hAPP_int_int(plus_plus_int(hAPP_nat_int(semiri1621563631at_int,X16)),X17)) = hAPP_int_int(plus_plus_int(hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(plus_plus_nat(X15),X16))),X17),
file('<stdin>',fact_38_zadd__int__left) ).
fof(c_0_147,axiom,
! [X29,X18] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_nat_int(semiri1621563631at_int,X29)),hAPP_nat_int(semiri1621563631at_int,X18)))
<=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X29),X18)) ),
file('<stdin>',fact_640_zle__int) ).
fof(c_0_148,axiom,
! [X3,X4] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_nat_int(semiri1621563631at_int,X3)),hAPP_nat_int(semiri1621563631at_int,X4)))
<=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X3),X4)) ),
file('<stdin>',fact_639_Nat__Transfer_Otransfer__int__nat__relations_I3_J) ).
fof(c_0_149,axiom,
! [X29,X18] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_nat_int(semiri1621563631at_int,X29)),hAPP_nat_int(semiri1621563631at_int,X18)))
<=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X29),X18)) ),
file('<stdin>',fact_446_of__nat__le__iff) ).
fof(c_0_150,axiom,
! [X29,X18] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(semiri984289939at_nat,X29)),hAPP_nat_nat(semiri984289939at_nat,X18)))
<=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X29),X18)) ),
file('<stdin>',fact_445_of__nat__le__iff) ).
fof(c_0_151,axiom,
! [X29,X18] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_nat_real(semiri132038758t_real,X29)),hAPP_nat_real(semiri132038758t_real,X18)))
<=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X29),X18)) ),
file('<stdin>',fact_444_of__nat__le__iff) ).
fof(c_0_152,axiom,
! [X69,X70] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_nat_int(semiri1621563631at_int,X69)),hAPP_nat_int(semiri1621563631at_int,X70)))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X69),X70)) ),
file('<stdin>',fact_243_of__nat__less__imp__less) ).
fof(c_0_153,axiom,
! [X69,X70] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(semiri984289939at_nat,X69)),hAPP_nat_nat(semiri984289939at_nat,X70)))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X69),X70)) ),
file('<stdin>',fact_242_of__nat__less__imp__less) ).
fof(c_0_154,axiom,
! [X69,X70] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_nat_real(semiri132038758t_real,X69)),hAPP_nat_real(semiri132038758t_real,X70)))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X69),X70)) ),
file('<stdin>',fact_241_of__nat__less__imp__less) ).
fof(c_0_155,axiom,
! [X29,X18] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_nat_int(semiri1621563631at_int,X29)),hAPP_nat_int(semiri1621563631at_int,X18)))
<=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X29),X18)) ),
file('<stdin>',fact_237_of__nat__less__iff) ).
fof(c_0_156,axiom,
! [X29,X18] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(semiri984289939at_nat,X29)),hAPP_nat_nat(semiri984289939at_nat,X18)))
<=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X29),X18)) ),
file('<stdin>',fact_236_of__nat__less__iff) ).
fof(c_0_157,axiom,
! [X29,X18] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_nat_real(semiri132038758t_real,X29)),hAPP_nat_real(semiri132038758t_real,X18)))
<=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X29),X18)) ),
file('<stdin>',fact_235_of__nat__less__iff) ).
fof(c_0_158,axiom,
! [X29,X18] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_nat_int(semiri1621563631at_int,X29)),hAPP_nat_int(semiri1621563631at_int,X18)))
<=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X29),X18)) ),
file('<stdin>',fact_206_zless__int) ).
fof(c_0_159,axiom,
! [X3,X4] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_nat_int(semiri1621563631at_int,X3)),hAPP_nat_int(semiri1621563631at_int,X4)))
<=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X3),X4)) ),
file('<stdin>',fact_204_Nat__Transfer_Otransfer__int__nat__relations_I2_J) ).
fof(c_0_160,axiom,
! [X279,X280] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X280))
=> ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X279))
=> ? [X281] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X281))
& hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X281),X280))
& hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X281),X279)) ) ) ),
file('<stdin>',fact_689_real__lbound__gt__zero) ).
fof(c_0_161,axiom,
! [X228,X229,X230] :
( hAPP_nat_int(power_power_int(X228),X229) = hAPP_nat_int(power_power_int(X230),X229)
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X228))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X230))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X229))
=> X228 = X230 ) ) ) ),
file('<stdin>',fact_576_power__eq__imp__eq__base) ).
fof(c_0_162,axiom,
! [X228,X229,X230] :
( hAPP_nat_nat(power_power_nat(X228),X229) = hAPP_nat_nat(power_power_nat(X230),X229)
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),X228))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),X230))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X229))
=> X228 = X230 ) ) ) ),
file('<stdin>',fact_575_power__eq__imp__eq__base) ).
fof(c_0_163,axiom,
! [X228,X229,X230] :
( hAPP_nat_real(power_power_real(X228),X229) = hAPP_nat_real(power_power_real(X230),X229)
=> ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X228))
=> ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X230))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X229))
=> X228 = X230 ) ) ) ),
file('<stdin>',fact_574_power__eq__imp__eq__base) ).
fof(c_0_164,axiom,
! [X16] : hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,one_one_real),hAPP_nat_real(power_power_real(number267125858f_real(bit0(bit1(pls)))),X16))),
file('<stdin>',fact_642_two__realpow__ge__one) ).
fof(c_0_165,axiom,
! [X18,X54] :
( ~ hBOOL(hAPP_nat_bool(X54,zero_zero_nat))
=> ( hBOOL(hAPP_nat_bool(X54,X18))
=> ? [X91] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X91),X18))
& ! [X56] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X56),X91))
=> ~ hBOOL(hAPP_nat_bool(X54,X56)) )
& hBOOL(hAPP_nat_bool(X54,hAPP_nat_nat(plus_plus_nat(X91),one_one_nat))) ) ) ),
file('<stdin>',fact_645_ex__least__nat__less) ).
fof(c_0_166,axiom,
! [X218,X219,X220] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X220))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X218),X219))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X218),hAPP_int_int(plus_plus_int(X220),X219))) ) ),
file('<stdin>',fact_547_add__strict__increasing2) ).
fof(c_0_167,axiom,
! [X218,X219,X220] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),X220))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X218),X219))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X218),hAPP_nat_nat(plus_plus_nat(X220),X219))) ) ),
file('<stdin>',fact_546_add__strict__increasing2) ).
fof(c_0_168,axiom,
! [X218,X219,X220] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X220))
=> ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X218),X219))
=> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X218),hAPP_real_real(plus_plus_real(X220),X219))) ) ),
file('<stdin>',fact_545_add__strict__increasing2) ).
fof(c_0_169,axiom,
! [X215,X216,X217] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X217))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X215),X216))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X215),hAPP_int_int(plus_plus_int(X217),X216))) ) ),
file('<stdin>',fact_544_add__strict__increasing) ).
fof(c_0_170,axiom,
! [X215,X216,X217] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X217))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X215),X216))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X215),hAPP_nat_nat(plus_plus_nat(X217),X216))) ) ),
file('<stdin>',fact_543_add__strict__increasing) ).
fof(c_0_171,axiom,
! [X215,X216,X217] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X217))
=> ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X215),X216))
=> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X215),hAPP_real_real(plus_plus_real(X217),X216))) ) ),
file('<stdin>',fact_542_add__strict__increasing) ).
fof(c_0_172,axiom,
! [X185,X186,X187] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X187))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X185),X186))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X185),hAPP_int_int(plus_plus_int(X186),X187))) ) ),
file('<stdin>',fact_482_add__increasing2) ).
fof(c_0_173,axiom,
! [X185,X186,X187] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),X187))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X185),X186))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X185),hAPP_nat_nat(plus_plus_nat(X186),X187))) ) ),
file('<stdin>',fact_481_add__increasing2) ).
fof(c_0_174,axiom,
! [X185,X186,X187] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X187))
=> ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X185),X186))
=> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X185),hAPP_real_real(plus_plus_real(X186),X187))) ) ),
file('<stdin>',fact_480_add__increasing2) ).
fof(c_0_175,axiom,
! [X182,X183,X184] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X184))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X182),X183))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X182),hAPP_int_int(plus_plus_int(X184),X183))) ) ),
file('<stdin>',fact_479_add__increasing) ).
fof(c_0_176,axiom,
! [X182,X183,X184] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),X184))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X182),X183))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X182),hAPP_nat_nat(plus_plus_nat(X184),X183))) ) ),
file('<stdin>',fact_478_add__increasing) ).
fof(c_0_177,axiom,
! [X182,X183,X184] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X184))
=> ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X182),X183))
=> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X182),hAPP_real_real(plus_plus_real(X184),X183))) ) ),
file('<stdin>',fact_477_add__increasing) ).
fof(c_0_178,axiom,
! [X75,X76,X77] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X77))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X75),X76))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X75),hAPP_int_int(plus_plus_int(X77),X76))) ) ),
file('<stdin>',fact_258_pos__add__strict) ).
fof(c_0_179,axiom,
! [X75,X76,X77] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X77))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X75),X76))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X75),hAPP_nat_nat(plus_plus_nat(X77),X76))) ) ),
file('<stdin>',fact_257_pos__add__strict) ).
fof(c_0_180,axiom,
! [X75,X76,X77] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X77))
=> ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X75),X76))
=> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X75),hAPP_real_real(plus_plus_real(X77),X76))) ) ),
file('<stdin>',fact_256_pos__add__strict) ).
fof(c_0_181,axiom,
! [X240,X241] :
( hAPP_nat_int(power_power_int(X240),number_number_of_nat(bit0(bit1(pls)))) = hAPP_nat_int(power_power_int(X241),number_number_of_nat(bit0(bit1(pls))))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X240))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X241))
=> X240 = X241 ) ) ),
file('<stdin>',fact_597_power2__eq__imp__eq) ).
fof(c_0_182,axiom,
! [X240,X241] :
( hAPP_nat_nat(power_power_nat(X240),number_number_of_nat(bit0(bit1(pls)))) = hAPP_nat_nat(power_power_nat(X241),number_number_of_nat(bit0(bit1(pls))))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),X240))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),X241))
=> X240 = X241 ) ) ),
file('<stdin>',fact_596_power2__eq__imp__eq) ).
fof(c_0_183,axiom,
! [X240,X241] :
( hAPP_nat_real(power_power_real(X240),number_number_of_nat(bit0(bit1(pls)))) = hAPP_nat_real(power_power_real(X241),number_number_of_nat(bit0(bit1(pls))))
=> ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X240))
=> ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X241))
=> X240 = X241 ) ) ),
file('<stdin>',fact_595_power2__eq__imp__eq) ).
fof(c_0_184,axiom,
! [X151,X16] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X16))
=> ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X151))
=> ? [X152] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X152))
& hAPP_nat_real(power_power_real(X152),X16) = X151
& ! [X153] :
( ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X153))
& hAPP_nat_real(power_power_real(X153),X16) = X151 )
=> X153 = X152 ) ) ) ),
file('<stdin>',fact_403_realpow__pos__nth__unique) ).
fof(c_0_185,axiom,
! [X29,X18] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(plus_plus_nat(X29),X18)))
<=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X29))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X18)) ) ),
file('<stdin>',fact_200_add__gr__0) ).
fof(c_0_186,axiom,
! [X59,X60] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,number_number_of_nat(X59)),number_number_of_nat(X60)))
<=> ( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X59),X60))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),X60)) )
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X59),X60)) ) ),
file('<stdin>',fact_207_less__nat__number__of) ).
fof(c_0_187,axiom,
! [X213,X214] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X214))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X213))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_int_int(plus_plus_int(X214),X213))) ) ),
file('<stdin>',fact_541_add__nonneg__pos) ).
fof(c_0_188,axiom,
! [X213,X214] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),X214))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X213))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(plus_plus_nat(X214),X213))) ) ),
file('<stdin>',fact_540_add__nonneg__pos) ).
fof(c_0_189,axiom,
! [X213,X214] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X214))
=> ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X213))
=> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),hAPP_real_real(plus_plus_real(X214),X213))) ) ),
file('<stdin>',fact_539_add__nonneg__pos) ).
fof(c_0_190,axiom,
! [X211,X212] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X212))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X211))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_int_int(plus_plus_int(X212),X211))) ) ),
file('<stdin>',fact_538_add__pos__nonneg) ).
fof(c_0_191,axiom,
! [X211,X212] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X212))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),X211))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(plus_plus_nat(X212),X211))) ) ),
file('<stdin>',fact_537_add__pos__nonneg) ).
fof(c_0_192,axiom,
! [X211,X212] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X212))
=> ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X211))
=> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),hAPP_real_real(plus_plus_real(X212),X211))) ) ),
file('<stdin>',fact_536_add__pos__nonneg) ).
fof(c_0_193,axiom,
! [X10,X8] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X8))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X10))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_int_int(plus_plus_int(X8),X10))) ) ),
file('<stdin>',fact_522_Nat__Transfer_Otransfer__nat__int__function__closures_I1_J) ).
fof(c_0_194,axiom,
! [X180,X181] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X181))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X180))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_int_int(plus_plus_int(X181),X180))) ) ),
file('<stdin>',fact_473_add__nonneg__nonneg) ).
fof(c_0_195,axiom,
! [X180,X181] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),X181))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),X180))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),hAPP_nat_nat(plus_plus_nat(X181),X180))) ) ),
file('<stdin>',fact_472_add__nonneg__nonneg) ).
fof(c_0_196,axiom,
! [X180,X181] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X181))
=> ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X180))
=> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),hAPP_real_real(plus_plus_real(X181),X180))) ) ),
file('<stdin>',fact_471_add__nonneg__nonneg) ).
fof(c_0_197,axiom,
! [X149,X150] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X150))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X149))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_int_int(plus_plus_int(X150),X149))) ) ),
file('<stdin>',fact_402_add__pos__pos) ).
fof(c_0_198,axiom,
! [X149,X150] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X150))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X149))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(plus_plus_nat(X150),X149))) ) ),
file('<stdin>',fact_401_add__pos__pos) ).
fof(c_0_199,axiom,
! [X149,X150] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X150))
=> ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X149))
=> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),hAPP_real_real(plus_plus_real(X150),X149))) ) ),
file('<stdin>',fact_400_add__pos__pos) ).
fof(c_0_200,axiom,
! [X48,X49] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,one_one_real),X49))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X48))
=> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,one_one_real),hAPP_nat_real(power_power_real(X49),X48))) ) ),
file('<stdin>',fact_159_one__less__power) ).
fof(c_0_201,axiom,
! [X48,X49] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,one_one_nat),X49))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X48))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,one_one_nat),hAPP_nat_nat(power_power_nat(X49),X48))) ) ),
file('<stdin>',fact_158_one__less__power) ).
fof(c_0_202,axiom,
! [X48,X49] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),X49))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X48))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),hAPP_nat_int(power_power_int(X49),X48))) ) ),
file('<stdin>',fact_157_one__less__power) ).
fof(c_0_203,axiom,
! [X23,X22] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(X23),X22)),X22)),
file('<stdin>',fact_175_not__add__less2) ).
fof(c_0_204,axiom,
! [X22,X23] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(X22),X23)),X22)),
file('<stdin>',fact_174_not__add__less1) ).
fof(c_0_205,axiom,
! [X59,X25] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,number_number_of_int(X59)),number_number_of_int(X25)))
<=> ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(X25)),number_number_of_int(X59))) ),
file('<stdin>',fact_500_le__number__of__eq__not__less) ).
fof(c_0_206,axiom,
! [X59,X25] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,number_number_of_nat(X59)),number_number_of_nat(X25)))
<=> ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,number_number_of_nat(X25)),number_number_of_nat(X59))) ),
file('<stdin>',fact_499_le__number__of__eq__not__less) ).
fof(c_0_207,axiom,
! [X59,X25] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,number267125858f_real(X59)),number267125858f_real(X25)))
<=> ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,number267125858f_real(X25)),number267125858f_real(X59))) ),
file('<stdin>',fact_498_le__number__of__eq__not__less) ).
fof(c_0_208,axiom,
! [X3,X25] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(power_power_nat(X3),number_number_of_nat(X25))))
<=> ( number_number_of_nat(X25) = zero_zero_nat
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X3)) ) ),
file('<stdin>',fact_205_zero__less__power__nat__eq__number__of) ).
fof(c_0_209,axiom,
! [X151,X16] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X16))
=> ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X151))
=> ? [X154] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X154))
& hAPP_nat_real(power_power_real(X154),X16) = X151 ) ) ),
file('<stdin>',fact_404_realpow__pos__nth) ).
fof(c_0_210,axiom,
! [X14,X17] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X14),X17))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(plus_plus_int(X14),one_one_int)),X17)) ),
file('<stdin>',fact_572_zless__imp__add1__zle) ).
fof(c_0_211,axiom,
! [X8] : hAPP_nat_int(power_power_int(hAPP_nat_int(power_power_int(X8),number_number_of_nat(bit0(bit1(pls))))),number_number_of_nat(bit0(bit1(pls)))) = hAPP_nat_int(power_power_int(X8),number_number_of_nat(bit0(bit0(bit1(pls))))),
file('<stdin>',fact_21_quartic__square__square) ).
fof(c_0_212,axiom,
! [X67,X68] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X67),X68))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_nat_int(semiri1621563631at_int,X67)),hAPP_nat_int(semiri1621563631at_int,X68))) ),
file('<stdin>',fact_240_less__imp__of__nat__less) ).
fof(c_0_213,axiom,
! [X67,X68] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X67),X68))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(semiri984289939at_nat,X67)),hAPP_nat_nat(semiri984289939at_nat,X68))) ),
file('<stdin>',fact_239_less__imp__of__nat__less) ).
fof(c_0_214,axiom,
! [X67,X68] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X67),X68))
=> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_nat_real(semiri132038758t_real,X67)),hAPP_nat_real(semiri132038758t_real,X68))) ),
file('<stdin>',fact_238_less__imp__of__nat__less) ).
fof(c_0_215,axiom,
! [X8] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X8))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X8),number_number_of_int(bit0(bit1(pls)))))
=> ( X8 = zero_zero_int
| X8 = one_one_int ) ) ),
file('<stdin>',fact_607_int__pos__lt__two__imp__zero__or__one) ).
fof(c_0_216,axiom,
! [X59,X60] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,number_number_of_nat(X59)),number_number_of_nat(X60)))
<=> ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X59),X60))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X59),pls)) ) ),
file('<stdin>',fact_641_le__nat__number__of) ).
fof(c_0_217,axiom,
! [X18,X54] :
( ~ hBOOL(hAPP_nat_bool(X54,zero_zero_nat))
=> ( hBOOL(hAPP_nat_bool(X54,X18))
=> ? [X91] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X91),X18))
& ! [X56] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X56),X91))
=> ~ hBOOL(hAPP_nat_bool(X54,X56)) )
& hBOOL(hAPP_nat_bool(X54,X91)) ) ) ),
file('<stdin>',fact_653_ex__least__nat__le) ).
fof(c_0_218,axiom,
! [X260,X261,X262] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X261),X262))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X262),X260))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X261),X260)) ) ),
file('<stdin>',fact_669_order__trans) ).
fof(c_0_219,axiom,
! [X260,X261,X262] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X261),X262))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X262),X260))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X261),X260)) ) ),
file('<stdin>',fact_668_order__trans) ).
fof(c_0_220,axiom,
! [X260,X261,X262] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X261),X262))
=> ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X262),X260))
=> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X261),X260)) ) ),
file('<stdin>',fact_667_order__trans) ).
fof(c_0_221,axiom,
! [X255,X256,X257] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X256),X257))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X255),X256))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X255),X257)) ) ),
file('<stdin>',fact_663_xt1_I6_J) ).
fof(c_0_222,axiom,
! [X255,X256,X257] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X256),X257))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X255),X256))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X255),X257)) ) ),
file('<stdin>',fact_662_xt1_I6_J) ).
fof(c_0_223,axiom,
! [X255,X256,X257] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X256),X257))
=> ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X255),X256))
=> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X255),X257)) ) ),
file('<stdin>',fact_661_xt1_I6_J) ).
fof(c_0_224,axiom,
! [X21,X22,X23] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X22),X23))
=> ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X23),X21))
=> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X22),X21)) ) ),
file('<stdin>',fact_650_real__le__trans) ).
fof(c_0_225,axiom,
! [X21,X22,X23] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X22),X23))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X23),X21))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X22),X21)) ) ),
file('<stdin>',fact_623_le__trans) ).
fof(c_0_226,axiom,
! [X21,X22,X23] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X22),X23))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X23),X21))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X22),X21)) ) ),
file('<stdin>',fact_440_zle__trans) ).
fof(c_0_227,axiom,
! [X25,X30] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X25),hAPP_int_int(plus_plus_int(X30),one_one_int)))
<=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X25),X30))
| X25 = X30 ) ),
file('<stdin>',fact_82_zless__add1__eq) ).
fof(c_0_228,axiom,
! [X25,X30] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X25),hAPP_int_int(plus_plus_int(X30),one_one_int)))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X25),X30)) ),
file('<stdin>',fact_570_zle__add1__eq__le) ).
fof(c_0_229,axiom,
! [X3,X18] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(power_power_nat(X3),X18)))
<=> ( X18 = zero_zero_nat
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X3)) ) ),
file('<stdin>',fact_203_zero__less__power__nat__eq) ).
fof(c_0_230,axiom,
! [X3,X18] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(power_power_nat(X3),X18)))
<=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X3))
| X18 = zero_zero_nat ) ),
file('<stdin>',fact_199_nat__zero__less__power__iff) ).
fof(c_0_231,axiom,
! [X231,X232] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X232))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X231))
=> hAPP_int_int(plus_plus_int(number_number_of_int(X232)),number_number_of_int(X231)) = number_number_of_int(hAPP_int_int(plus_plus_int(X232),X231)) ) ),
file('<stdin>',fact_579_semiring__add__number__of) ).
fof(c_0_232,axiom,
! [X231,X232] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X232))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X231))
=> hAPP_nat_nat(plus_plus_nat(number_number_of_nat(X232)),number_number_of_nat(X231)) = number_number_of_nat(hAPP_int_int(plus_plus_int(X232),X231)) ) ),
file('<stdin>',fact_578_semiring__add__number__of) ).
fof(c_0_233,axiom,
! [X231,X232] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X232))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X231))
=> hAPP_real_real(plus_plus_real(number267125858f_real(X232)),number267125858f_real(X231)) = number267125858f_real(hAPP_int_int(plus_plus_int(X232),X231)) ) ),
file('<stdin>',fact_577_semiring__add__number__of) ).
fof(c_0_234,axiom,
! [X5] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_int_int(plus_plus_int(X5),X5)))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X5)) ),
file('<stdin>',fact_468_zero__le__double__add__iff__zero__le__single__add) ).
fof(c_0_235,axiom,
! [X5] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),hAPP_real_real(plus_plus_real(X5),X5)))
<=> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X5)) ),
file('<stdin>',fact_467_zero__le__double__add__iff__zero__le__single__add) ).
fof(c_0_236,axiom,
! [X5] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_int_int(plus_plus_int(X5),X5)))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X5)) ),
file('<stdin>',fact_304_zero__less__double__add__iff__zero__less__single__add) ).
fof(c_0_237,axiom,
! [X5] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),hAPP_real_real(plus_plus_real(X5),X5)))
<=> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X5)) ),
file('<stdin>',fact_303_zero__less__double__add__iff__zero__less__single__add) ).
fof(c_0_238,axiom,
! [X54] :
( ! [X152] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X152))
=> hBOOL(hAPP_int_bool(X54,X152)) )
<=> ! [X152] : hBOOL(hAPP_int_bool(X54,hAPP_nat_int(semiri1621563631at_int,X152))) ),
file('<stdin>',fact_526_transfer__int__nat__quantifiers_I1_J) ).
fof(c_0_239,axiom,
! [X34,X35,X36] : hAPP_real_real(plus_plus_real(number267125858f_real(X34)),hAPP_real_real(plus_plus_real(number267125858f_real(X35)),X36)) = hAPP_real_real(plus_plus_real(number267125858f_real(hAPP_int_int(plus_plus_int(X34),X35))),X36),
file('<stdin>',fact_121_add__number__of__left) ).
fof(c_0_240,axiom,
! [X34,X35,X36] : hAPP_int_int(plus_plus_int(number_number_of_int(X34)),hAPP_int_int(plus_plus_int(number_number_of_int(X35)),X36)) = hAPP_int_int(plus_plus_int(number_number_of_int(hAPP_int_int(plus_plus_int(X34),X35))),X36),
file('<stdin>',fact_120_add__number__of__left) ).
fof(c_0_241,axiom,
! [X8] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X8),hAPP_nat_int(power_power_int(X8),number_number_of_nat(bit0(bit1(pls)))))),
file('<stdin>',fact_589_power2__ge__self) ).
fof(c_0_242,axiom,
! [X15,X22,X23] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X22),X23))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X22),hAPP_nat_nat(plus_plus_nat(X15),X23))) ),
file('<stdin>',fact_632_trans__le__add2) ).
fof(c_0_243,axiom,
! [X15,X22,X23] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X22),X23))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X22),hAPP_nat_nat(plus_plus_nat(X23),X15))) ),
file('<stdin>',fact_631_trans__le__add1) ).
fof(c_0_244,axiom,
! [X15,X22,X23] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X22),X23))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X22),hAPP_nat_nat(plus_plus_nat(X15),X23))) ),
file('<stdin>',fact_189_trans__less__add2) ).
fof(c_0_245,axiom,
! [X15,X22,X23] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X22),X23))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X22),hAPP_nat_nat(plus_plus_nat(X23),X15))) ),
file('<stdin>',fact_188_trans__less__add1) ).
fof(c_0_246,axiom,
! [X102,X103,X104,X105] : hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(X102),X103)),hAPP_int_int(plus_plus_int(X104),X105)) = hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(X102),X104)),hAPP_int_int(plus_plus_int(X103),X105)),
file('<stdin>',fact_321_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J) ).
fof(c_0_247,axiom,
! [X102,X103,X104,X105] : hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(plus_plus_nat(X102),X103)),hAPP_nat_nat(plus_plus_nat(X104),X105)) = hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(plus_plus_nat(X102),X104)),hAPP_nat_nat(plus_plus_nat(X103),X105)),
file('<stdin>',fact_320_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J) ).
fof(c_0_248,axiom,
! [X102,X103,X104,X105] : hAPP_real_real(plus_plus_real(hAPP_real_real(plus_plus_real(X102),X103)),hAPP_real_real(plus_plus_real(X104),X105)) = hAPP_real_real(plus_plus_real(hAPP_real_real(plus_plus_real(X102),X104)),hAPP_real_real(plus_plus_real(X103),X105)),
file('<stdin>',fact_319_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J) ).
fof(c_0_249,axiom,
! [X237] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_nat_int(power_power_int(X237),number_number_of_nat(bit0(bit1(pls)))))),
file('<stdin>',fact_591_zero__le__power2) ).
fof(c_0_250,axiom,
! [X237] : hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),hAPP_nat_real(power_power_real(X237),number_number_of_nat(bit0(bit1(pls)))))),
file('<stdin>',fact_590_zero__le__power2) ).
fof(c_0_251,axiom,
! [X18] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_nat_int(semiri1621563631at_int,X18)),zero_zero_int))
<=> X18 = zero_zero_nat ),
file('<stdin>',fact_566_int__le__0__conv) ).
fof(c_0_252,axiom,
! [X15,X16,X21,X31] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X21),X31))
=> ( hAPP_nat_nat(plus_plus_nat(X15),X31) = hAPP_nat_nat(plus_plus_nat(X21),X16)
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X15),X16)) ) ),
file('<stdin>',fact_192_less__add__eq__less) ).
fof(c_0_253,axiom,
! [X54] :
( ? [X152] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X152))
& hBOOL(hAPP_int_bool(X54,X152)) )
<=> ? [X152] : hBOOL(hAPP_int_bool(X54,hAPP_nat_int(semiri1621563631at_int,X152))) ),
file('<stdin>',fact_525_transfer__int__nat__quantifiers_I2_J) ).
fof(c_0_254,axiom,
! [X88] : ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_nat_int(semiri1621563631at_int,X88)),zero_zero_int)),
file('<stdin>',fact_288_of__nat__less__0__iff) ).
fof(c_0_255,axiom,
! [X88] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(semiri984289939at_nat,X88)),zero_zero_nat)),
file('<stdin>',fact_287_of__nat__less__0__iff) ).
fof(c_0_256,axiom,
! [X88] : ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_nat_real(semiri132038758t_real,X88)),zero_zero_real)),
file('<stdin>',fact_286_of__nat__less__0__iff) ).
fof(c_0_257,axiom,
! [X21] : ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_nat_int(semiri1621563631at_int,X21)),zero_zero_int)),
file('<stdin>',fact_83_int__less__0__conv) ).
fof(c_0_258,axiom,
! [X247,X54,X3] :
( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X3))
=> ( hBOOL(X54)
<=> hBOOL(X247) ) )
=> ( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X3))
& hBOOL(X54) )
<=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X3))
& hBOOL(X247) ) ) ),
file('<stdin>',fact_643_conj__le__cong) ).
fof(c_0_259,axiom,
! [X16,X8] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X8))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_nat_int(power_power_int(X8),X16))) ),
file('<stdin>',fact_528_Nat__Transfer_Otransfer__nat__int__function__closures_I4_J) ).
fof(c_0_260,axiom,
! [X203,X204] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),X204))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),hAPP_nat_int(power_power_int(X204),X203))) ),
file('<stdin>',fact_509_one__le__power) ).
fof(c_0_261,axiom,
! [X203,X204] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,one_one_nat),X204))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,one_one_nat),hAPP_nat_nat(power_power_nat(X204),X203))) ),
file('<stdin>',fact_508_one__le__power) ).
fof(c_0_262,axiom,
! [X203,X204] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,one_one_real),X204))
=> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,one_one_real),hAPP_nat_real(power_power_real(X204),X203))) ),
file('<stdin>',fact_507_one__le__power) ).
fof(c_0_263,axiom,
! [X198,X199] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X199))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_nat_int(power_power_int(X199),X198))) ),
file('<stdin>',fact_503_zero__le__power) ).
fof(c_0_264,axiom,
! [X198,X199] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),X199))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),hAPP_nat_nat(power_power_nat(X199),X198))) ),
file('<stdin>',fact_502_zero__le__power) ).
fof(c_0_265,axiom,
! [X198,X199] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X199))
=> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),hAPP_nat_real(power_power_real(X199),X198))) ),
file('<stdin>',fact_501_zero__le__power) ).
fof(c_0_266,axiom,
! [X78,X79] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X79))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_nat_int(power_power_int(X79),X78))) ),
file('<stdin>',fact_267_zero__less__power) ).
fof(c_0_267,axiom,
! [X78,X79] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X79))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(power_power_nat(X79),X78))) ),
file('<stdin>',fact_266_zero__less__power) ).
fof(c_0_268,axiom,
! [X78,X79] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X79))
=> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),hAPP_nat_real(power_power_real(X79),X78))) ),
file('<stdin>',fact_265_zero__less__power) ).
fof(c_0_269,axiom,
! [X247,X54,X3] :
( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X3))
=> ( hBOOL(X54)
<=> hBOOL(X247) ) )
=> ( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X3))
=> hBOOL(X54) )
<=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X3))
=> hBOOL(X247) ) ) ),
file('<stdin>',fact_644_imp__le__cong) ).
fof(c_0_270,axiom,
! [X4,X3] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X3))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X4))
=> ( hAPP_int_int(plus_plus_int(X3),X4) = zero_zero_int
<=> ( X3 = zero_zero_int
& X4 = zero_zero_int ) ) ) ),
file('<stdin>',fact_476_add__nonneg__eq__0__iff) ).
fof(c_0_271,axiom,
! [X4,X3] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),X3))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),X4))
=> ( hAPP_nat_nat(plus_plus_nat(X3),X4) = zero_zero_nat
<=> ( X3 = zero_zero_nat
& X4 = zero_zero_nat ) ) ) ),
file('<stdin>',fact_475_add__nonneg__eq__0__iff) ).
fof(c_0_272,axiom,
! [X4,X3] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X3))
=> ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X4))
=> ( hAPP_real_real(plus_plus_real(X3),X4) = zero_zero_real
<=> ( X3 = zero_zero_real
& X4 = zero_zero_real ) ) ) ),
file('<stdin>',fact_474_add__nonneg__eq__0__iff) ).
fof(c_0_273,axiom,
! [X19,X20] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,bit1(X19)),bit0(X20)))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X19),X20)) ),
file('<stdin>',fact_564_less__eq__int__code_I15_J) ).
fof(c_0_274,axiom,
! [X11,X12] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,bit1(X11)),bit0(X12)))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X11),X12)) ),
file('<stdin>',fact_563_rel__simps_I33_J) ).
fof(c_0_275,axiom,
! [X19,X20] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit0(X19)),bit1(X20)))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X19),X20)) ),
file('<stdin>',fact_562_less__int__code_I14_J) ).
fof(c_0_276,axiom,
! [X11,X12] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit0(X11)),bit1(X12)))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X11),X12)) ),
file('<stdin>',fact_561_rel__simps_I15_J) ).
fof(c_0_277,axiom,
! [X19,X20] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,bit0(X19)),bit1(X20)))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X19),X20)) ),
file('<stdin>',fact_518_less__eq__int__code_I14_J) ).
fof(c_0_278,axiom,
! [X11,X12] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,bit0(X11)),bit1(X12)))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X11),X12)) ),
file('<stdin>',fact_517_rel__simps_I32_J) ).
fof(c_0_279,axiom,
! [X11,X12] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,number_number_of_int(X11)),number_number_of_int(X12)))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X11),X12)) ),
file('<stdin>',fact_449_less__eq__number__of__int__code) ).
fof(c_0_280,axiom,
! [X3,X4] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,number_number_of_int(X3)),number_number_of_int(X4)))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X3),X4)) ),
file('<stdin>',fact_443_le__number__of) ).
fof(c_0_281,axiom,
! [X3,X4] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,number267125858f_real(X3)),number267125858f_real(X4)))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X3),X4)) ),
file('<stdin>',fact_442_le__number__of) ).
fof(c_0_282,axiom,
! [X11,X12] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,bit0(X11)),bit0(X12)))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X11),X12)) ),
file('<stdin>',fact_436_rel__simps_I31_J) ).
fof(c_0_283,axiom,
! [X19,X20] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,bit0(X19)),bit0(X20)))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X19),X20)) ),
file('<stdin>',fact_435_less__eq__int__code_I13_J) ).
fof(c_0_284,axiom,
! [X11,X12] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,bit1(X11)),bit1(X12)))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X11),X12)) ),
file('<stdin>',fact_433_rel__simps_I34_J) ).
fof(c_0_285,axiom,
! [X19,X20] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,bit1(X19)),bit1(X20)))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X19),X20)) ),
file('<stdin>',fact_432_less__eq__int__code_I16_J) ).
fof(c_0_286,axiom,
! [X11,X12] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit1(X11)),bit0(X12)))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X11),X12)) ),
file('<stdin>',fact_75_rel__simps_I16_J) ).
fof(c_0_287,axiom,
! [X19,X20] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit1(X19)),bit0(X20)))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X19),X20)) ),
file('<stdin>',fact_74_less__int__code_I15_J) ).
fof(c_0_288,axiom,
! [X11,X12] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit0(X11)),bit0(X12)))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X11),X12)) ),
file('<stdin>',fact_50_rel__simps_I14_J) ).
fof(c_0_289,axiom,
! [X19,X20] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit0(X19)),bit0(X20)))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X19),X20)) ),
file('<stdin>',fact_49_less__int__code_I13_J) ).
fof(c_0_290,axiom,
! [X11,X12] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit1(X11)),bit1(X12)))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X11),X12)) ),
file('<stdin>',fact_47_rel__simps_I17_J) ).
fof(c_0_291,axiom,
! [X19,X20] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit1(X19)),bit1(X20)))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X19),X20)) ),
file('<stdin>',fact_46_less__int__code_I16_J) ).
fof(c_0_292,axiom,
! [X3,X4] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,number267125858f_real(X3)),number267125858f_real(X4)))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X3),X4)) ),
file('<stdin>',fact_34_less__number__of) ).
fof(c_0_293,axiom,
! [X3,X4] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(X3)),number_number_of_int(X4)))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X3),X4)) ),
file('<stdin>',fact_33_less__number__of) ).
fof(c_0_294,axiom,
! [X11,X12] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(X11)),number_number_of_int(X12)))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X11),X12)) ),
file('<stdin>',fact_31_less__number__of__int__code) ).
fof(c_0_295,axiom,
! [X18] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_nat_int(semiri1621563631at_int,X18)))
<=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X18)) ),
file('<stdin>',fact_223_zero__less__int__conv) ).
fof(c_0_296,axiom,
! [X18] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),hAPP_nat_real(semiri132038758t_real,X18)))
<=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X18)) ),
file('<stdin>',fact_156_of__nat__0__less__iff) ).
fof(c_0_297,axiom,
! [X18] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(semiri984289939at_nat,X18)))
<=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X18)) ),
file('<stdin>',fact_155_of__nat__0__less__iff) ).
fof(c_0_298,axiom,
! [X18] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_nat_int(semiri1621563631at_int,X18)))
<=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X18)) ),
file('<stdin>',fact_154_of__nat__0__less__iff) ).
fof(c_0_299,axiom,
! [X17] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X17))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_int_int(plus_plus_int(one_one_int),X17))) ),
file('<stdin>',fact_581_le__imp__0__less) ).
fof(c_0_300,axiom,
! [X4,X3] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X4),X3))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X3),X4))
<=> X3 = X4 ) ),
file('<stdin>',fact_687_order__antisym__conv) ).
fof(c_0_301,axiom,
! [X4,X3] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X4),X3))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X3),X4))
<=> X3 = X4 ) ),
file('<stdin>',fact_686_order__antisym__conv) ).
fof(c_0_302,axiom,
! [X4,X3] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X4),X3))
=> ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X3),X4))
<=> X3 = X4 ) ),
file('<stdin>',fact_685_order__antisym__conv) ).
fof(c_0_303,axiom,
! [X263,X264] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X263),X264))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X264),X263))
=> X263 = X264 ) ),
file('<stdin>',fact_672_order__antisym) ).
fof(c_0_304,axiom,
! [X263,X264] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X263),X264))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X264),X263))
=> X263 = X264 ) ),
file('<stdin>',fact_671_order__antisym) ).
fof(c_0_305,axiom,
! [X263,X264] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X263),X264))
=> ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X264),X263))
=> X263 = X264 ) ),
file('<stdin>',fact_670_order__antisym) ).
fof(c_0_306,axiom,
! [X258,X259] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X258),X259))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X259),X258))
=> X259 = X258 ) ),
file('<stdin>',fact_666_xt1_I5_J) ).
fof(c_0_307,axiom,
! [X258,X259] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X258),X259))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X259),X258))
=> X259 = X258 ) ),
file('<stdin>',fact_665_xt1_I5_J) ).
fof(c_0_308,axiom,
! [X258,X259] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X258),X259))
=> ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X259),X258))
=> X259 = X258 ) ),
file('<stdin>',fact_664_xt1_I5_J) ).
fof(c_0_309,axiom,
! [X17,X14] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X17),X14))
=> ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X14),X17))
=> X17 = X14 ) ),
file('<stdin>',fact_651_real__le__antisym) ).
fof(c_0_310,axiom,
! [X15,X16] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X15),X16))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X16),X15))
=> X15 = X16 ) ),
file('<stdin>',fact_624_le__antisym) ).
fof(c_0_311,axiom,
! [X17,X14] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X17),X14))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X14),X17))
=> X17 = X14 ) ),
file('<stdin>',fact_441_zle__antisym) ).
fof(c_0_312,axiom,
! [X22,X23] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X22),X23))
=> ? [X91] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X91))
& hAPP_nat_nat(plus_plus_nat(X22),X91) = X23 ) ),
file('<stdin>',fact_298_less__imp__add__positive) ).
fof(c_0_313,axiom,
! [X16] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),number_number_of_int(X16)))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),number_number_of_int(bit0(X16))))
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),number_number_of_int(bit1(X16)))) ) ),
file('<stdin>',fact_608_number__of1) ).
fof(c_0_314,axiom,
! [X3] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,number_number_of_int(X3)),one_one_int))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X3),bit1(pls))) ),
file('<stdin>',fact_466_le__special_I4_J) ).
fof(c_0_315,axiom,
! [X3] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,number267125858f_real(X3)),one_one_real))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X3),bit1(pls))) ),
file('<stdin>',fact_465_le__special_I4_J) ).
fof(c_0_316,axiom,
! [X3] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,number267125858f_real(X3)),one_one_real))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X3),bit1(pls))) ),
file('<stdin>',fact_85_less__special_I4_J) ).
fof(c_0_317,axiom,
! [X3] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(X3)),one_one_int))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X3),bit1(pls))) ),
file('<stdin>',fact_84_less__special_I4_J) ).
fof(c_0_318,axiom,
! [X24,X13] :
( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X13),pls))
=> hAPP_nat_nat(plus_plus_nat(number_number_of_nat(X13)),number_number_of_nat(X24)) = number_number_of_nat(X24) )
& ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X13),pls))
=> ( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X24),pls))
=> hAPP_nat_nat(plus_plus_nat(number_number_of_nat(X13)),number_number_of_nat(X24)) = number_number_of_nat(X13) )
& ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X24),pls))
=> hAPP_nat_nat(plus_plus_nat(number_number_of_nat(X13)),number_number_of_nat(X24)) = number_number_of_nat(hAPP_int_int(plus_plus_int(X13),X24)) ) ) ) ),
file('<stdin>',fact_52_add__nat__number__of) ).
fof(c_0_319,axiom,
! [X3] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,sqrt(X3)),one_one_real))
<=> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X3),one_one_real)) ),
file('<stdin>',fact_697_real__sqrt__lt__1__iff) ).
fof(c_0_320,axiom,
! [X3] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,sqrt(X3)),zero_zero_real))
<=> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X3),zero_zero_real)) ),
file('<stdin>',fact_695_real__sqrt__lt__0__iff) ).
fof(c_0_321,axiom,
! [X11] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,bit1(X11)),pls))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X11),pls)) ),
file('<stdin>',fact_560_rel__simps_I29_J) ).
fof(c_0_322,axiom,
! [X11] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,bit0(X11)),pls))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X11),pls)) ),
file('<stdin>',fact_520_rel__simps_I27_J) ).
fof(c_0_323,axiom,
! [X3] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,number_number_of_int(X3)),zero_zero_int))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X3),pls)) ),
file('<stdin>',fact_453_le__special_I3_J) ).
fof(c_0_324,axiom,
! [X3] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,number267125858f_real(X3)),zero_zero_real))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X3),pls)) ),
file('<stdin>',fact_452_le__special_I3_J) ).
fof(c_0_325,axiom,
! [X25] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit0(X25)),zero_zero_int))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X25),zero_zero_int)) ),
file('<stdin>',fact_80_bin__less__0__simps_I3_J) ).
fof(c_0_326,axiom,
! [X25] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit1(X25)),zero_zero_int))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X25),zero_zero_int)) ),
file('<stdin>',fact_78_bin__less__0__simps_I4_J) ).
fof(c_0_327,axiom,
! [X11] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit0(X11)),pls))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X11),pls)) ),
file('<stdin>',fact_76_rel__simps_I10_J) ).
fof(c_0_328,axiom,
! [X11] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit1(X11)),pls))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X11),pls)) ),
file('<stdin>',fact_73_rel__simps_I12_J) ).
fof(c_0_329,axiom,
! [X3] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,number267125858f_real(X3)),zero_zero_real))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X3),pls)) ),
file('<stdin>',fact_70_less__special_I3_J) ).
fof(c_0_330,axiom,
! [X3] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(X3)),zero_zero_int))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X3),pls)) ),
file('<stdin>',fact_69_less__special_I3_J) ).
fof(c_0_331,axiom,
! [X4] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),number_number_of_int(X4)))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,bit1(pls)),X4)) ),
file('<stdin>',fact_464_le__special_I2_J) ).
fof(c_0_332,axiom,
! [X4] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,one_one_real),number267125858f_real(X4)))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,bit1(pls)),X4)) ),
file('<stdin>',fact_463_le__special_I2_J) ).
fof(c_0_333,axiom,
! [X4] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,one_one_real),number267125858f_real(X4)))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit1(pls)),X4)) ),
file('<stdin>',fact_87_less__special_I2_J) ).
fof(c_0_334,axiom,
! [X4] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),number_number_of_int(X4)))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit1(pls)),X4)) ),
file('<stdin>',fact_86_less__special_I2_J) ).
fof(c_0_335,axiom,
! [X25,X30] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X25),X30))
<=> ? [X90] : X30 = hAPP_int_int(plus_plus_int(X25),hAPP_nat_int(semiri1621563631at_int,X90)) ),
file('<stdin>',fact_529_zle__iff__zadd) ).
fof(c_0_336,axiom,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,m1),hAPP_int_int(plus_plus_int(one_one_int),hAPP_nat_int(semiri1621563631at_int,n)))),
file('<stdin>',fact_148_mn) ).
fof(c_0_337,axiom,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_int_int(plus_plus_int(one_one_int),hAPP_nat_int(semiri1621563631at_int,n)))),
file('<stdin>',fact_0_n1pos) ).
fof(c_0_338,axiom,
! [X274,X275,X276] :
( X275 = X276
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X276),X274))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X275),X274)) ) ),
file('<stdin>',fact_684_ord__eq__le__trans) ).
fof(c_0_339,axiom,
! [X274,X275,X276] :
( X275 = X276
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X276),X274))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X275),X274)) ) ),
file('<stdin>',fact_683_ord__eq__le__trans) ).
fof(c_0_340,axiom,
! [X274,X275,X276] :
( X275 = X276
=> ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X276),X274))
=> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X275),X274)) ) ),
file('<stdin>',fact_682_ord__eq__le__trans) ).
fof(c_0_341,axiom,
! [X271,X272,X273] :
( X272 = X273
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X271),X273))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X271),X272)) ) ),
file('<stdin>',fact_681_xt1_I3_J) ).
fof(c_0_342,axiom,
! [X271,X272,X273] :
( X272 = X273
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X271),X273))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X271),X272)) ) ),
file('<stdin>',fact_680_xt1_I3_J) ).
fof(c_0_343,axiom,
! [X271,X272,X273] :
( X272 = X273
=> ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X271),X273))
=> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X271),X272)) ) ),
file('<stdin>',fact_679_xt1_I3_J) ).
fof(c_0_344,axiom,
! [X268,X269,X270] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X269),X270))
=> ( X270 = X268
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X269),X268)) ) ),
file('<stdin>',fact_678_ord__le__eq__trans) ).
fof(c_0_345,axiom,
! [X268,X269,X270] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X269),X270))
=> ( X270 = X268
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X269),X268)) ) ),
file('<stdin>',fact_677_ord__le__eq__trans) ).
fof(c_0_346,axiom,
! [X268,X269,X270] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X269),X270))
=> ( X270 = X268
=> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X269),X268)) ) ),
file('<stdin>',fact_676_ord__le__eq__trans) ).
fof(c_0_347,axiom,
! [X265,X266,X267] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X266),X267))
=> ( X266 = X265
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X265),X267)) ) ),
file('<stdin>',fact_675_xt1_I4_J) ).
fof(c_0_348,axiom,
! [X265,X266,X267] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X266),X267))
=> ( X266 = X265
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X265),X267)) ) ),
file('<stdin>',fact_674_xt1_I4_J) ).
fof(c_0_349,axiom,
! [X265,X266,X267] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X266),X267))
=> ( X266 = X265
=> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X265),X267)) ) ),
file('<stdin>',fact_673_xt1_I4_J) ).
fof(c_0_350,axiom,
! [X4] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,one_one_real),sqrt(X4)))
<=> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,one_one_real),X4)) ),
file('<stdin>',fact_698_real__sqrt__gt__1__iff) ).
fof(c_0_351,axiom,
! [X4] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),sqrt(X4)))
<=> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X4)) ),
file('<stdin>',fact_696_real__sqrt__gt__0__iff) ).
fof(c_0_352,axiom,
! [X11] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),bit1(X11)))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X11)) ),
file('<stdin>',fact_559_rel__simps_I5_J) ).
fof(c_0_353,axiom,
! [X11] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),bit0(X11)))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X11)) ),
file('<stdin>',fact_519_rel__simps_I21_J) ).
fof(c_0_354,axiom,
! [X11] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),bit1(X11)))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X11)) ),
file('<stdin>',fact_516_rel__simps_I22_J) ).
fof(c_0_355,axiom,
! [X4] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),number_number_of_int(X4)))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X4)) ),
file('<stdin>',fact_451_le__special_I1_J) ).
fof(c_0_356,axiom,
! [X4] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),number267125858f_real(X4)))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X4)) ),
file('<stdin>',fact_450_le__special_I1_J) ).
fof(c_0_357,axiom,
! [X59] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),number_number_of_nat(X59)))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),X59)) ),
file('<stdin>',fact_222_less__0__number__of) ).
fof(c_0_358,axiom,
! [X11] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),bit0(X11)))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),X11)) ),
file('<stdin>',fact_77_rel__simps_I4_J) ).
fof(c_0_359,axiom,
! [X4] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),number267125858f_real(X4)))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),X4)) ),
file('<stdin>',fact_72_less__special_I1_J) ).
fof(c_0_360,axiom,
! [X4] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),number_number_of_int(X4)))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),X4)) ),
file('<stdin>',fact_71_less__special_I1_J) ).
fof(c_0_361,axiom,
! [X3,X4] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X3),X4))
<=> ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X3),X4))
& X3 != X4 ) ),
file('<stdin>',fact_626_real__less__def) ).
fof(c_0_362,axiom,
! [X3,X4] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X3),X4))
<=> ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X3),X4))
| X3 = X4 ) ),
file('<stdin>',fact_625_less__eq__real__def) ).
fof(c_0_363,axiom,
! [X29,X18] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X29),X18))
<=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X29),X18))
& X29 != X18 ) ),
file('<stdin>',fact_619_nat__less__le) ).
fof(c_0_364,axiom,
! [X29,X18] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X29),X18))
<=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X29),X18))
| X29 = X18 ) ),
file('<stdin>',fact_618_le__eq__less__or__eq) ).
fof(c_0_365,axiom,
! [X15,X16] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X15),X16))
=> ( X15 != X16
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X15),X16)) ) ),
file('<stdin>',fact_616_le__neq__implies__less) ).
fof(c_0_366,axiom,
! [X30,X25] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X30),X25))
<=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X30),X25))
& X30 != X25 ) ),
file('<stdin>',fact_447_zless__le) ).
fof(c_0_367,axiom,
! [X15,X16] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X15),X16))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X15),X16)) ),
file('<stdin>',fact_617_less__imp__le__nat) ).
fof(c_0_368,axiom,
! [X15,X16] :
( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X15),X16))
| X15 = X16 )
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X15),X16)) ),
file('<stdin>',fact_615_less__or__eq__imp__le) ).
fof(c_0_369,axiom,
! [X107,X108,X109] : hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(X107),X108)),X109) = hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(X107),X109)),X108),
file('<stdin>',fact_330_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J) ).
fof(c_0_370,axiom,
! [X107,X108,X109] : hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(plus_plus_nat(X107),X108)),X109) = hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(plus_plus_nat(X107),X109)),X108),
file('<stdin>',fact_329_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J) ).
fof(c_0_371,axiom,
! [X107,X108,X109] : hAPP_real_real(plus_plus_real(hAPP_real_real(plus_plus_real(X107),X108)),X109) = hAPP_real_real(plus_plus_real(hAPP_real_real(plus_plus_real(X107),X109)),X108),
file('<stdin>',fact_328_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J) ).
fof(c_0_372,axiom,
! [X8] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X8))
=> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),sqrt(X8))) ),
file('<stdin>',fact_693_real__sqrt__gt__zero) ).
fof(c_0_373,axiom,
! [X21] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X21))
=> ? [X90] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X90))
& X21 = hAPP_nat_int(semiri1621563631at_int,X90) ) ),
file('<stdin>',fact_297_zero__less__imp__eq__int) ).
fof(c_0_374,axiom,
! [X30] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),X30))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X30)) ),
file('<stdin>',fact_565_int__one__le__iff__zero__less) ).
fof(c_0_375,axiom,
! [X29,X18,X5] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),X5))
=> ( hAPP_nat_int(power_power_int(X5),X29) = hAPP_nat_int(power_power_int(X5),X18)
<=> X29 = X18 ) ),
file('<stdin>',fact_273_power__inject__exp) ).
fof(c_0_376,axiom,
! [X29,X18,X5] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,one_one_nat),X5))
=> ( hAPP_nat_nat(power_power_nat(X5),X29) = hAPP_nat_nat(power_power_nat(X5),X18)
<=> X29 = X18 ) ),
file('<stdin>',fact_272_power__inject__exp) ).
fof(c_0_377,axiom,
! [X29,X18,X5] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,one_one_real),X5))
=> ( hAPP_nat_real(power_power_real(X5),X29) = hAPP_nat_real(power_power_real(X5),X18)
<=> X29 = X18 ) ),
file('<stdin>',fact_271_power__inject__exp) ).
fof(c_0_378,axiom,
! [X29,X18] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X29),X18))
<=> ? [X91] : X18 = hAPP_nat_nat(plus_plus_nat(X29),X91) ),
file('<stdin>',fact_629_le__iff__add) ).
fof(c_0_379,axiom,
! [X21,X31] : times_times_int(bit1(X21),X31) = hAPP_int_int(plus_plus_int(bit0(times_times_int(X21,X31))),X31),
file('<stdin>',fact_692_mult__Bit1) ).
fof(c_0_380,axiom,
! [X116,X117,X118] : hAPP_int_int(plus_plus_int(X116),hAPP_int_int(plus_plus_int(X117),X118)) = hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(X116),X117)),X118),
file('<stdin>',fact_339_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J) ).
fof(c_0_381,axiom,
! [X116,X117,X118] : hAPP_nat_nat(plus_plus_nat(X116),hAPP_nat_nat(plus_plus_nat(X117),X118)) = hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(plus_plus_nat(X116),X117)),X118),
file('<stdin>',fact_338_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J) ).
fof(c_0_382,axiom,
! [X116,X117,X118] : hAPP_real_real(plus_plus_real(X116),hAPP_real_real(plus_plus_real(X117),X118)) = hAPP_real_real(plus_plus_real(hAPP_real_real(plus_plus_real(X116),X117)),X118),
file('<stdin>',fact_337_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J) ).
fof(c_0_383,axiom,
! [X113,X114,X115] : hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(X113),X114)),X115) = hAPP_int_int(plus_plus_int(X113),hAPP_int_int(plus_plus_int(X114),X115)),
file('<stdin>',fact_336_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J) ).
fof(c_0_384,axiom,
! [X113,X114,X115] : hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(plus_plus_nat(X113),X114)),X115) = hAPP_nat_nat(plus_plus_nat(X113),hAPP_nat_nat(plus_plus_nat(X114),X115)),
file('<stdin>',fact_335_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J) ).
fof(c_0_385,axiom,
! [X113,X114,X115] : hAPP_real_real(plus_plus_real(hAPP_real_real(plus_plus_real(X113),X114)),X115) = hAPP_real_real(plus_plus_real(X113),hAPP_real_real(plus_plus_real(X114),X115)),
file('<stdin>',fact_334_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J) ).
fof(c_0_386,axiom,
! [X110,X111,X112] : hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(X110),X111)),X112) = hAPP_int_int(plus_plus_int(X110),hAPP_int_int(plus_plus_int(X111),X112)),
file('<stdin>',fact_333_ab__semigroup__add__class_Oadd__ac_I1_J) ).
fof(c_0_387,axiom,
! [X110,X111,X112] : hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(plus_plus_nat(X110),X111)),X112) = hAPP_nat_nat(plus_plus_nat(X110),hAPP_nat_nat(plus_plus_nat(X111),X112)),
file('<stdin>',fact_332_ab__semigroup__add__class_Oadd__ac_I1_J) ).
fof(c_0_388,axiom,
! [X110,X111,X112] : hAPP_real_real(plus_plus_real(hAPP_real_real(plus_plus_real(X110),X111)),X112) = hAPP_real_real(plus_plus_real(X110),hAPP_real_real(plus_plus_real(X111),X112)),
file('<stdin>',fact_331_ab__semigroup__add__class_Oadd__ac_I1_J) ).
fof(c_0_389,axiom,
! [X61,X62] :
( X61 != X62
=> ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X61),X62))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X62),X61)) ) ),
file('<stdin>',fact_209_linorder__neqE__linordered__idom) ).
fof(c_0_390,axiom,
! [X61,X62] :
( X61 != X62
=> ( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X61),X62))
=> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X62),X61)) ) ),
file('<stdin>',fact_208_linorder__neqE__linordered__idom) ).
fof(c_0_391,axiom,
! [X8,X10] :
( X8 != X10
=> ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X8),X10))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X10),X8)) ) ),
file('<stdin>',fact_184_linorder__neqE__nat) ).
fof(c_0_392,axiom,
! [X15,X16,X21] : hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(plus_plus_nat(X15),X16)),X21) = hAPP_nat_nat(plus_plus_nat(X15),hAPP_nat_nat(plus_plus_nat(X16),X21)),
file('<stdin>',fact_180_nat__add__assoc) ).
fof(c_0_393,axiom,
! [X29,X18] :
( X29 != X18
<=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X29),X18))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X18),X29)) ) ),
file('<stdin>',fact_177_nat__neq__iff) ).
fof(c_0_394,axiom,
! [X26,X27,X28] : hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(X26),X27)),X28) = hAPP_int_int(plus_plus_int(X26),hAPP_int_int(plus_plus_int(X27),X28)),
file('<stdin>',fact_65_zadd__assoc) ).
fof(c_0_395,axiom,
! [X8,X10] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X8),X10))
| X8 = X10
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X10),X8)) ),
file('<stdin>',fact_30_zless__linear) ).
fof(c_0_396,axiom,
! [X253,X254] :
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X253),X254))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X254),X253)) ),
file('<stdin>',fact_660_linorder__le__cases) ).
fof(c_0_397,axiom,
! [X253,X254] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X253),X254))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X254),X253)) ),
file('<stdin>',fact_659_linorder__le__cases) ).
fof(c_0_398,axiom,
! [X253,X254] :
( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X253),X254))
=> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X254),X253)) ),
file('<stdin>',fact_658_linorder__le__cases) ).
fof(c_0_399,axiom,
! [X17,X14] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X17),X14))
| hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X14),X17)) ),
file('<stdin>',fact_649_real__le__linear) ).
fof(c_0_400,axiom,
! [X16,X15] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X16),hAPP_nat_nat(plus_plus_nat(X16),X15))),
file('<stdin>',fact_628_le__add1) ).
fof(c_0_401,axiom,
! [X16,X15] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X16),hAPP_nat_nat(plus_plus_nat(X15),X16))),
file('<stdin>',fact_627_le__add2) ).
fof(c_0_402,axiom,
! [X15,X16] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X15),X16))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X16),X15)) ),
file('<stdin>',fact_621_nat__le__linear) ).
fof(c_0_403,axiom,
! [X17,X14] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X17),X14))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X14),X17)) ),
file('<stdin>',fact_439_zle__linear) ).
fof(c_0_404,axiom,
! [X242] :
( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),number_number_of_int(X242)))
=> hAPP_nat_int(semiri1621563631at_int,number_number_of_nat(X242)) = number_number_of_int(X242) )
& ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),number_number_of_int(X242)))
=> hAPP_nat_int(semiri1621563631at_int,number_number_of_nat(X242)) = zero_zero_int ) ),
file('<stdin>',fact_599_of__nat__number__of__lemma) ).
fof(c_0_405,axiom,
! [X242] :
( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),number_number_of_int(X242)))
=> hAPP_nat_real(semiri132038758t_real,number_number_of_nat(X242)) = number267125858f_real(X242) )
& ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),number_number_of_int(X242)))
=> hAPP_nat_real(semiri132038758t_real,number_number_of_nat(X242)) = zero_zero_real ) ),
file('<stdin>',fact_598_of__nat__number__of__lemma) ).
fof(c_0_406,axiom,
! [X210] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X210))
=> hAPP_int_int(plus_plus_int(number_number_of_int(X210)),one_one_int) = number_number_of_int(succ(X210)) ),
file('<stdin>',fact_535_semiring__number__of__add__1) ).
fof(c_0_407,axiom,
! [X210] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X210))
=> hAPP_nat_nat(plus_plus_nat(number_number_of_nat(X210)),one_one_nat) = number_number_of_nat(succ(X210)) ),
file('<stdin>',fact_534_semiring__number__of__add__1) ).
fof(c_0_408,axiom,
! [X210] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X210))
=> hAPP_real_real(plus_plus_real(number267125858f_real(X210)),one_one_real) = number267125858f_real(succ(X210)) ),
file('<stdin>',fact_533_semiring__number__of__add__1) ).
fof(c_0_409,axiom,
! [X80] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X80),hAPP_int_int(plus_plus_int(X80),one_one_int))),
file('<stdin>',fact_270_less__add__one) ).
fof(c_0_410,axiom,
! [X80] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X80),hAPP_nat_nat(plus_plus_nat(X80),one_one_nat))),
file('<stdin>',fact_269_less__add__one) ).
fof(c_0_411,axiom,
! [X80] : hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X80),hAPP_real_real(plus_plus_real(X80),one_one_real))),
file('<stdin>',fact_268_less__add__one) ).
fof(c_0_412,axiom,
! [X13] :
( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X13),pls))
=> hAPP_nat_nat(plus_plus_nat(number_number_of_nat(X13)),one_one_nat) = one_one_nat )
& ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X13),pls))
=> hAPP_nat_nat(plus_plus_nat(number_number_of_nat(X13)),one_one_nat) = number_number_of_nat(succ(X13)) ) ),
file('<stdin>',fact_406_nat__number__of__add__1) ).
fof(c_0_413,axiom,
! [X209] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X209))
=> hAPP_int_int(plus_plus_int(one_one_int),number_number_of_int(X209)) = number_number_of_int(succ(X209)) ),
file('<stdin>',fact_532_semiring__1__add__number__of) ).
fof(c_0_414,axiom,
! [X209] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X209))
=> hAPP_nat_nat(plus_plus_nat(one_one_nat),number_number_of_nat(X209)) = number_number_of_nat(succ(X209)) ),
file('<stdin>',fact_531_semiring__1__add__number__of) ).
fof(c_0_415,axiom,
! [X209] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X209))
=> hAPP_real_real(plus_plus_real(one_one_real),number267125858f_real(X209)) = number267125858f_real(succ(X209)) ),
file('<stdin>',fact_530_semiring__1__add__number__of) ).
fof(c_0_416,axiom,
! [X8,X10] : hAPP_int_int(plus_plus_int(hAPP_nat_int(semiri1621563631at_int,X8)),hAPP_nat_int(semiri1621563631at_int,X10)) = hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(plus_plus_nat(X8),X10)),
file('<stdin>',fact_254_Nat__Transfer_Otransfer__int__nat__functions_I1_J) ).
fof(c_0_417,axiom,
! [X71,X72] : hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(plus_plus_nat(X71),X72)) = hAPP_int_int(plus_plus_int(hAPP_nat_int(semiri1621563631at_int,X71)),hAPP_nat_int(semiri1621563631at_int,X72)),
file('<stdin>',fact_246_of__nat__add) ).
fof(c_0_418,axiom,
! [X71,X72] : hAPP_nat_nat(semiri984289939at_nat,hAPP_nat_nat(plus_plus_nat(X71),X72)) = hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(semiri984289939at_nat,X71)),hAPP_nat_nat(semiri984289939at_nat,X72)),
file('<stdin>',fact_245_of__nat__add) ).
fof(c_0_419,axiom,
! [X71,X72] : hAPP_nat_real(semiri132038758t_real,hAPP_nat_nat(plus_plus_nat(X71),X72)) = hAPP_real_real(plus_plus_real(hAPP_nat_real(semiri132038758t_real,X71)),hAPP_nat_real(semiri132038758t_real,X72)),
file('<stdin>',fact_244_of__nat__add) ).
fof(c_0_420,axiom,
! [X15,X16] : hAPP_int_int(plus_plus_int(hAPP_nat_int(semiri1621563631at_int,X15)),hAPP_nat_int(semiri1621563631at_int,X16)) = hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(plus_plus_nat(X15),X16)),
file('<stdin>',fact_39_zadd__int) ).
fof(c_0_421,axiom,
! [X13] :
( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X13),pls))
=> hAPP_nat_nat(plus_plus_nat(one_one_nat),number_number_of_nat(X13)) = one_one_nat )
& ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X13),pls))
=> hAPP_nat_nat(plus_plus_nat(one_one_nat),number_number_of_nat(X13)) = number_number_of_nat(succ(X13)) ) ),
file('<stdin>',fact_407_nat__1__add__number__of) ).
fof(c_0_422,axiom,
! [X17] : hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),X17)),X17) != zero_zero_int,
file('<stdin>',fact_129_odd__nonzero) ).
fof(c_0_423,axiom,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),number_number_of_int(bit0(bit1(pls))))),
file('<stdin>',fact_588_Nat__Transfer_Otransfer__nat__int__function__closures_I7_J) ).
fof(c_0_424,axiom,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),number_number_of_int(bit1(bit1(pls))))),
file('<stdin>',fact_580_Nat__Transfer_Otransfer__nat__int__function__closures_I8_J) ).
fof(c_0_425,axiom,
hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),number_number_of_nat(bit0(bit1(pls))))),
file('<stdin>',fact_296_pos2) ).
fof(c_0_426,axiom,
! [X17] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X17))
=> ~ ! [X248] : X17 != hAPP_nat_int(semiri1621563631at_int,X248) ),
file('<stdin>',fact_646_nonneg__eq__int) ).
fof(c_0_427,axiom,
! [X21] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X21))
=> ~ ! [X90] : X21 != hAPP_nat_int(semiri1621563631at_int,X90) ),
file('<stdin>',fact_611_nonneg__int__cases) ).
fof(c_0_428,axiom,
! [X21] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X21))
=> ? [X90] : X21 = hAPP_nat_int(semiri1621563631at_int,X90) ),
file('<stdin>',fact_610_zero__le__imp__eq__int) ).
fof(c_0_429,axiom,
hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),hAPP_real_real(plus_plus_real(one_one_real),one_one_real))),
file('<stdin>',fact_168_zero__less__two) ).
fof(c_0_430,axiom,
hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(plus_plus_nat(one_one_nat),one_one_nat))),
file('<stdin>',fact_167_zero__less__two) ).
fof(c_0_431,axiom,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_int_int(plus_plus_int(one_one_int),one_one_int))),
file('<stdin>',fact_166_zero__less__two) ).
fof(c_0_432,axiom,
! [X46] : number267125858f_real(bit1(X46)) = hAPP_real_real(plus_plus_real(hAPP_real_real(plus_plus_real(one_one_real),number267125858f_real(X46))),number267125858f_real(X46)),
file('<stdin>',fact_144_number__of__Bit1) ).
fof(c_0_433,axiom,
! [X46] : number_number_of_int(bit1(X46)) = hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),number_number_of_int(X46))),number_number_of_int(X46)),
file('<stdin>',fact_143_number__of__Bit1) ).
fof(c_0_434,axiom,
! [X45] : number267125858f_real(bit0(X45)) = hAPP_real_real(plus_plus_real(hAPP_real_real(plus_plus_real(zero_zero_real),number267125858f_real(X45))),number267125858f_real(X45)),
file('<stdin>',fact_142_number__of__Bit0) ).
fof(c_0_435,axiom,
! [X45] : number_number_of_int(bit0(X45)) = hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(zero_zero_int),number_number_of_int(X45))),number_number_of_int(X45)),
file('<stdin>',fact_141_number__of__Bit0) ).
fof(c_0_436,axiom,
! [X57,X58] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X57),X58))
=> X57 != X58 ),
file('<stdin>',fact_187_less__not__refl3) ).
fof(c_0_437,axiom,
! [X16,X15] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X16),X15))
=> X15 != X16 ),
file('<stdin>',fact_186_less__not__refl2) ).
fof(c_0_438,axiom,
! [X15,X16] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X15),X16))
=> X16 != zero_zero_nat ),
file('<stdin>',fact_196_gr__implies__not0) ).
fof(c_0_439,axiom,
! [X16] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X16),X16)),
file('<stdin>',fact_185_less__irrefl__nat) ).
fof(c_0_440,axiom,
! [X16] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X16),X16)),
file('<stdin>',fact_173_less__not__refl) ).
fof(c_0_441,axiom,
! [X59] :
( number_number_of_nat(X59) = zero_zero_nat
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X59),pls)) ),
file('<stdin>',fact_558_eq__number__of__0) ).
fof(c_0_442,axiom,
! [X59] :
( zero_zero_nat = number_number_of_nat(X59)
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X59),pls)) ),
file('<stdin>',fact_557_eq__0__number__of) ).
fof(c_0_443,axiom,
! [X8] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X8))
=> sqrt(X8) != zero_zero_real ),
file('<stdin>',fact_694_real__sqrt__not__eq__zero) ).
fof(c_0_444,axiom,
! [X119,X120,X121] : hAPP_int_int(plus_plus_int(X119),hAPP_int_int(plus_plus_int(X120),X121)) = hAPP_int_int(plus_plus_int(X120),hAPP_int_int(plus_plus_int(X119),X121)),
file('<stdin>',fact_342_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J) ).
fof(c_0_445,axiom,
! [X119,X120,X121] : hAPP_nat_nat(plus_plus_nat(X119),hAPP_nat_nat(plus_plus_nat(X120),X121)) = hAPP_nat_nat(plus_plus_nat(X120),hAPP_nat_nat(plus_plus_nat(X119),X121)),
file('<stdin>',fact_341_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J) ).
fof(c_0_446,axiom,
! [X119,X120,X121] : hAPP_real_real(plus_plus_real(X119),hAPP_real_real(plus_plus_real(X120),X121)) = hAPP_real_real(plus_plus_real(X120),hAPP_real_real(plus_plus_real(X119),X121)),
file('<stdin>',fact_340_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J) ).
fof(c_0_447,axiom,
! [X8,X16] : hAPP_nat_int(power_power_int(hAPP_nat_int(semiri1621563631at_int,X8)),X16) = hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(power_power_nat(X8),X16)),
file('<stdin>',fact_255_Nat__Transfer_Otransfer__int__nat__functions_I4_J) ).
fof(c_0_448,axiom,
! [X73,X74] : hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(power_power_nat(X73),X74)) = hAPP_nat_int(power_power_int(hAPP_nat_int(semiri1621563631at_int,X73)),X74),
file('<stdin>',fact_252_of__nat__power) ).
fof(c_0_449,axiom,
! [X73,X74] : hAPP_nat_nat(semiri984289939at_nat,hAPP_nat_nat(power_power_nat(X73),X74)) = hAPP_nat_nat(power_power_nat(hAPP_nat_nat(semiri984289939at_nat,X73)),X74),
file('<stdin>',fact_251_of__nat__power) ).
fof(c_0_450,axiom,
! [X73,X74] : hAPP_nat_real(semiri132038758t_real,hAPP_nat_nat(power_power_nat(X73),X74)) = hAPP_nat_real(power_power_real(hAPP_nat_real(semiri132038758t_real,X73)),X74),
file('<stdin>',fact_250_of__nat__power) ).
fof(c_0_451,axiom,
! [X8,X10,X17] : hAPP_nat_nat(plus_plus_nat(X8),hAPP_nat_nat(plus_plus_nat(X10),X17)) = hAPP_nat_nat(plus_plus_nat(X10),hAPP_nat_nat(plus_plus_nat(X8),X17)),
file('<stdin>',fact_179_nat__add__left__commute) ).
fof(c_0_452,axiom,
! [X8,X10,X17] : hAPP_int_int(plus_plus_int(X8),hAPP_int_int(plus_plus_int(X10),X17)) = hAPP_int_int(plus_plus_int(X10),hAPP_int_int(plus_plus_int(X8),X17)),
file('<stdin>',fact_66_zadd__left__commute) ).
fof(c_0_453,axiom,
! [X15,X16] : hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(power_power_nat(X15),X16)) = hAPP_nat_int(power_power_int(hAPP_nat_int(semiri1621563631at_int,X15)),X16),
file('<stdin>',fact_37_int__power) ).
fof(c_0_454,axiom,
! [X15,X16] : hAPP_nat_int(power_power_int(hAPP_nat_int(semiri1621563631at_int,X15)),X16) = hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(power_power_nat(X15),X16)),
file('<stdin>',fact_36_zpower__int) ).
fof(c_0_455,axiom,
! [X18] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X18),zero_zero_nat))
<=> X18 = zero_zero_nat ),
file('<stdin>',fact_614_le__0__eq) ).
fof(c_0_456,axiom,
! [X16] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_nat_int(semiri1621563631at_int,X16))),
file('<stdin>',fact_527_zero__zle__int) ).
fof(c_0_457,axiom,
! [X17] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_nat_int(semiri1621563631at_int,X17))),
file('<stdin>',fact_524_Nat__Transfer_Otransfer__nat__int__function__closures_I9_J) ).
fof(c_0_458,axiom,
! [X206] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_nat_int(semiri1621563631at_int,X206))),
file('<stdin>',fact_515_of__nat__0__le__iff) ).
fof(c_0_459,axiom,
! [X206] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),hAPP_nat_nat(semiri984289939at_nat,X206))),
file('<stdin>',fact_514_of__nat__0__le__iff) ).
fof(c_0_460,axiom,
! [X206] : hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),hAPP_nat_real(semiri132038758t_real,X206))),
file('<stdin>',fact_513_of__nat__0__le__iff) ).
fof(c_0_461,axiom,
! [X205] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_nat_int(semiri1621563631at_int,X205))),
file('<stdin>',fact_512_zero__le__imp__of__nat) ).
fof(c_0_462,axiom,
! [X205] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),hAPP_nat_nat(semiri984289939at_nat,X205))),
file('<stdin>',fact_511_zero__le__imp__of__nat) ).
fof(c_0_463,axiom,
! [X205] : hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),hAPP_nat_real(semiri132038758t_real,X205))),
file('<stdin>',fact_510_zero__le__imp__of__nat) ).
fof(c_0_464,axiom,
! [X16] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X16),zero_zero_nat)),
file('<stdin>',fact_202_not__less0) ).
fof(c_0_465,axiom,
! [X16] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X16),zero_zero_nat)),
file('<stdin>',fact_198_less__nat__zero__code) ).
fof(c_0_466,axiom,
! [X16] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X16),zero_zero_nat)),
file('<stdin>',fact_171_less__zeroE) ).
fof(c_0_467,axiom,
! [X18] :
( X18 != zero_zero_nat
<=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X18)) ),
file('<stdin>',fact_201_neq0__conv) ).
fof(c_0_468,axiom,
! [X3,X4,X54] :
( ( hBOOL(X54)
=> hAPP_nat_int(semiri1621563631at_int,X3) = hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(if_nat(X54,X3),X4)) )
& ( ~ hBOOL(X54)
=> hAPP_nat_int(semiri1621563631at_int,X4) = hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(if_nat(X54,X3),X4)) ) ),
file('<stdin>',fact_221_int__if__cong) ).
fof(c_0_469,axiom,
~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),zero_zero_int)),
file('<stdin>',fact_494_not__one__le__zero) ).
fof(c_0_470,axiom,
~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,one_one_nat),zero_zero_nat)),
file('<stdin>',fact_493_not__one__le__zero) ).
fof(c_0_471,axiom,
~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,one_one_real),zero_zero_real)),
file('<stdin>',fact_492_not__one__le__zero) ).
fof(c_0_472,axiom,
~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),zero_zero_int)),
file('<stdin>',fact_261_not__one__less__zero) ).
fof(c_0_473,axiom,
~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,one_one_nat),zero_zero_nat)),
file('<stdin>',fact_260_not__one__less__zero) ).
fof(c_0_474,axiom,
~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,one_one_real),zero_zero_real)),
file('<stdin>',fact_259_not__one__less__zero) ).
fof(c_0_475,axiom,
~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),zero_zero_int)),
file('<stdin>',fact_79_bin__less__0__simps_I1_J) ).
fof(c_0_476,axiom,
~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),pls)),
file('<stdin>',fact_48_rel__simps_I2_J) ).
fof(c_0_477,axiom,
! [X21,X31] : hAPP_int_int(plus_plus_int(bit1(X21)),bit1(X31)) = bit0(hAPP_int_int(plus_plus_int(X21),succ(X31))),
file('<stdin>',fact_584_add__Bit1__Bit1) ).
fof(c_0_478,axiom,
! [X21] : bit1(X21) = hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),X21)),X21),
file('<stdin>',fact_128_Bit1__def) ).
fof(c_0_479,axiom,
! [X5] :
( hAPP_nat_real(power_power_real(X5),number_number_of_nat(bit0(bit1(pls)))) = zero_zero_real
<=> X5 = zero_zero_real ),
file('<stdin>',fact_11_zero__eq__power2) ).
fof(c_0_480,axiom,
! [X5] :
( hAPP_nat_int(power_power_int(X5),number_number_of_nat(bit0(bit1(pls)))) = zero_zero_int
<=> X5 = zero_zero_int ),
file('<stdin>',fact_10_zero__eq__power2) ).
fof(c_0_481,axiom,
! [X21,X31] : hAPP_int_int(plus_plus_int(bit0(X21)),bit1(X31)) = bit1(hAPP_int_int(plus_plus_int(X21),X31)),
file('<stdin>',fact_127_add__Bit0__Bit1) ).
fof(c_0_482,axiom,
! [X21,X31] : hAPP_int_int(plus_plus_int(bit1(X21)),bit0(X31)) = bit1(hAPP_int_int(plus_plus_int(X21),X31)),
file('<stdin>',fact_126_add__Bit1__Bit0) ).
fof(c_0_483,axiom,
! [X39,X40] : number267125858f_real(hAPP_int_int(plus_plus_int(X39),X40)) = hAPP_real_real(plus_plus_real(number267125858f_real(X39)),number267125858f_real(X40)),
file('<stdin>',fact_125_number__of__add) ).
fof(c_0_484,axiom,
! [X39,X40] : number_number_of_int(hAPP_int_int(plus_plus_int(X39),X40)) = hAPP_int_int(plus_plus_int(number_number_of_int(X39)),number_number_of_int(X40)),
file('<stdin>',fact_124_number__of__add) ).
fof(c_0_485,axiom,
! [X37,X38] : hAPP_real_real(plus_plus_real(number267125858f_real(X37)),number267125858f_real(X38)) = number267125858f_real(hAPP_int_int(plus_plus_int(X37),X38)),
file('<stdin>',fact_123_add__number__of__eq) ).
fof(c_0_486,axiom,
! [X37,X38] : hAPP_int_int(plus_plus_int(number_number_of_int(X37)),number_number_of_int(X38)) = number_number_of_int(hAPP_int_int(plus_plus_int(X37),X38)),
file('<stdin>',fact_122_add__number__of__eq) ).
fof(c_0_487,axiom,
! [X21,X31] : hAPP_int_int(plus_plus_int(bit0(X21)),bit0(X31)) = bit0(hAPP_int_int(plus_plus_int(X21),X31)),
file('<stdin>',fact_102_add__Bit0__Bit0) ).
fof(c_0_488,axiom,
! [X13,X14] : hAPP_int_int(plus_plus_int(number_number_of_int(X13)),number_number_of_int(X14)) = number_number_of_int(hAPP_int_int(plus_plus_int(X13),X14)),
file('<stdin>',fact_32_plus__numeral__code_I9_J) ).
fof(c_0_489,axiom,
! [X277,X278] :
( X277 = X278
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X277),X278)) ),
file('<stdin>',fact_688_order__eq__refl) ).
fof(c_0_490,axiom,
! [X15,X16] :
( X15 = X16
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X15),X16)) ),
file('<stdin>',fact_622_eq__imp__le) ).
fof(c_0_491,axiom,
! [X7] : hAPP_real_real(plus_plus_real(number267125858f_real(X7)),one_one_real) = number267125858f_real(hAPP_int_int(plus_plus_int(X7),bit1(pls))),
file('<stdin>',fact_15_add__special_I3_J) ).
fof(c_0_492,axiom,
! [X7] : hAPP_int_int(plus_plus_int(number_number_of_int(X7)),one_one_int) = number_number_of_int(hAPP_int_int(plus_plus_int(X7),bit1(pls))),
file('<stdin>',fact_14_add__special_I3_J) ).
fof(c_0_493,axiom,
! [X6] : hAPP_real_real(plus_plus_real(one_one_real),number267125858f_real(X6)) = number267125858f_real(hAPP_int_int(plus_plus_int(bit1(pls)),X6)),
file('<stdin>',fact_13_add__special_I2_J) ).
fof(c_0_494,axiom,
! [X6] : hAPP_int_int(plus_plus_int(one_one_int),number_number_of_int(X6)) = number_number_of_int(hAPP_int_int(plus_plus_int(bit1(pls)),X6)),
file('<stdin>',fact_12_add__special_I2_J) ).
fof(c_0_495,axiom,
! [X252] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X252),X252)),
file('<stdin>',fact_657_order__refl) ).
fof(c_0_496,axiom,
! [X252] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X252),X252)),
file('<stdin>',fact_656_order__refl) ).
fof(c_0_497,axiom,
! [X252] : hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X252),X252)),
file('<stdin>',fact_655_order__refl) ).
fof(c_0_498,axiom,
! [X14] : hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X14),X14)),
file('<stdin>',fact_648_real__le__refl) ).
fof(c_0_499,axiom,
! [X16] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X16),X16)),
file('<stdin>',fact_620_le__refl) ).
fof(c_0_500,axiom,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),number_number_of_int(pls))),
file('<stdin>',fact_609_number__of2) ).
fof(c_0_501,axiom,
! [X14] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X14),X14)),
file('<stdin>',fact_438_zle__refl) ).
fof(c_0_502,axiom,
! [X16] :
( X16 != zero_zero_nat
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X16)) ),
file('<stdin>',fact_195_gr0I) ).
fof(c_0_503,axiom,
! [X16] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),X16)),
file('<stdin>',fact_613_less__eq__nat_Osimps_I1_J) ).
fof(c_0_504,axiom,
! [X16] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),X16)),
file('<stdin>',fact_612_le0) ).
fof(c_0_505,axiom,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),one_one_int)),
file('<stdin>',fact_521_Nat__Transfer_Otransfer__nat__int__function__closures_I6_J) ).
fof(c_0_506,axiom,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),one_one_int)),
file('<stdin>',fact_497_zero__le__one) ).
fof(c_0_507,axiom,
hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),one_one_nat)),
file('<stdin>',fact_496_zero__le__one) ).
fof(c_0_508,axiom,
hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),one_one_real)),
file('<stdin>',fact_495_zero__le__one) ).
fof(c_0_509,axiom,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),zero_zero_int)),
file('<stdin>',fact_437_Nat__Transfer_Otransfer__nat__int__function__closures_I5_J) ).
fof(c_0_510,axiom,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),pls)),
file('<stdin>',fact_434_rel__simps_I19_J) ).
fof(c_0_511,axiom,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),t)),
file('<stdin>',fact_405_tpos) ).
fof(c_0_512,axiom,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),one_one_int)),
file('<stdin>',fact_264_zero__less__one) ).
fof(c_0_513,axiom,
hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),one_one_nat)),
file('<stdin>',fact_263_zero__less__one) ).
fof(c_0_514,axiom,
hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),one_one_real)),
file('<stdin>',fact_262_zero__less__one) ).
fof(c_0_515,axiom,
hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),tn)),
file('<stdin>',fact_170_tn0) ).
fof(c_0_516,axiom,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),one_one_int)),
file('<stdin>',fact_81_int__0__less__1) ).
fof(c_0_517,axiom,
hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),n)),
file('<stdin>',fact_29_n0) ).
fof(c_0_518,axiom,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),t)),
file('<stdin>',fact_1_t1) ).
fof(c_0_519,axiom,
! [X5,X81,X106] :
( hAPP_int_int(plus_plus_int(X5),X81) = hAPP_int_int(plus_plus_int(X5),X106)
<=> X81 = X106 ),
file('<stdin>',fact_327_add__left__cancel) ).
fof(c_0_520,axiom,
! [X5,X81,X106] :
( hAPP_nat_nat(plus_plus_nat(X5),X81) = hAPP_nat_nat(plus_plus_nat(X5),X106)
<=> X81 = X106 ),
file('<stdin>',fact_326_add__left__cancel) ).
fof(c_0_521,axiom,
! [X5,X81,X106] :
( hAPP_real_real(plus_plus_real(X5),X81) = hAPP_real_real(plus_plus_real(X5),X106)
<=> X81 = X106 ),
file('<stdin>',fact_325_add__left__cancel) ).
fof(c_0_522,axiom,
! [X81,X5,X106] :
( hAPP_int_int(plus_plus_int(X81),X5) = hAPP_int_int(plus_plus_int(X106),X5)
<=> X81 = X106 ),
file('<stdin>',fact_324_add__right__cancel) ).
fof(c_0_523,axiom,
! [X81,X5,X106] :
( hAPP_nat_nat(plus_plus_nat(X81),X5) = hAPP_nat_nat(plus_plus_nat(X106),X5)
<=> X81 = X106 ),
file('<stdin>',fact_323_add__right__cancel) ).
fof(c_0_524,axiom,
! [X81,X5,X106] :
( hAPP_real_real(plus_plus_real(X81),X5) = hAPP_real_real(plus_plus_real(X106),X5)
<=> X81 = X106 ),
file('<stdin>',fact_322_add__right__cancel) ).
fof(c_0_525,axiom,
! [X99,X100,X101] :
( hAPP_int_int(plus_plus_int(X99),X100) = hAPP_int_int(plus_plus_int(X99),X101)
=> X100 = X101 ),
file('<stdin>',fact_318_add__left__imp__eq) ).
fof(c_0_526,axiom,
! [X99,X100,X101] :
( hAPP_nat_nat(plus_plus_nat(X99),X100) = hAPP_nat_nat(plus_plus_nat(X99),X101)
=> X100 = X101 ),
file('<stdin>',fact_317_add__left__imp__eq) ).
fof(c_0_527,axiom,
! [X99,X100,X101] :
( hAPP_real_real(plus_plus_real(X99),X100) = hAPP_real_real(plus_plus_real(X99),X101)
=> X100 = X101 ),
file('<stdin>',fact_316_add__left__imp__eq) ).
fof(c_0_528,axiom,
! [X96,X97,X98] :
( hAPP_int_int(plus_plus_int(X96),X97) = hAPP_int_int(plus_plus_int(X96),X98)
=> X97 = X98 ),
file('<stdin>',fact_315_add__imp__eq) ).
fof(c_0_529,axiom,
! [X96,X97,X98] :
( hAPP_nat_nat(plus_plus_nat(X96),X97) = hAPP_nat_nat(plus_plus_nat(X96),X98)
=> X97 = X98 ),
file('<stdin>',fact_314_add__imp__eq) ).
fof(c_0_530,axiom,
! [X96,X97,X98] :
( hAPP_real_real(plus_plus_real(X96),X97) = hAPP_real_real(plus_plus_real(X96),X98)
=> X97 = X98 ),
file('<stdin>',fact_313_add__imp__eq) ).
fof(c_0_531,axiom,
! [X93,X94,X95] :
( hAPP_int_int(plus_plus_int(X93),X94) = hAPP_int_int(plus_plus_int(X95),X94)
=> X93 = X95 ),
file('<stdin>',fact_312_add__right__imp__eq) ).
fof(c_0_532,axiom,
! [X93,X94,X95] :
( hAPP_nat_nat(plus_plus_nat(X93),X94) = hAPP_nat_nat(plus_plus_nat(X95),X94)
=> X93 = X95 ),
file('<stdin>',fact_311_add__right__imp__eq) ).
fof(c_0_533,axiom,
! [X93,X94,X95] :
( hAPP_real_real(plus_plus_real(X93),X94) = hAPP_real_real(plus_plus_real(X95),X94)
=> X93 = X95 ),
file('<stdin>',fact_310_add__right__imp__eq) ).
fof(c_0_534,axiom,
! [X29,X11,X18] :
( hAPP_nat_nat(plus_plus_nat(X29),X11) = hAPP_nat_nat(plus_plus_nat(X18),X11)
<=> X29 = X18 ),
file('<stdin>',fact_182_nat__add__right__cancel) ).
fof(c_0_535,axiom,
! [X11,X29,X18] :
( hAPP_nat_nat(plus_plus_nat(X11),X29) = hAPP_nat_nat(plus_plus_nat(X11),X18)
<=> X29 = X18 ),
file('<stdin>',fact_181_nat__add__left__cancel) ).
fof(c_0_536,axiom,
number_number_of_int(bit1(bit1(pls))) = hAPP_nat_int(semiri1621563631at_int,number_number_of_nat(bit1(bit1(pls)))),
file('<stdin>',fact_152_transfer__int__nat__numerals_I4_J) ).
fof(c_0_537,axiom,
number_number_of_int(bit0(bit1(pls))) = hAPP_nat_int(semiri1621563631at_int,number_number_of_nat(bit0(bit1(pls)))),
file('<stdin>',fact_151_transfer__int__nat__numerals_I3_J) ).
fof(c_0_538,axiom,
! [X5,X25] :
( hAPP_nat_real(power_power_real(X5),number_number_of_nat(X25)) = zero_zero_real
<=> ( X5 = zero_zero_real
& number_number_of_nat(X25) != zero_zero_nat ) ),
file('<stdin>',fact_119_power__eq__0__iff__number__of) ).
fof(c_0_539,axiom,
! [X5,X25] :
( hAPP_nat_nat(power_power_nat(X5),number_number_of_nat(X25)) = zero_zero_nat
<=> ( X5 = zero_zero_nat
& number_number_of_nat(X25) != zero_zero_nat ) ),
file('<stdin>',fact_118_power__eq__0__iff__number__of) ).
fof(c_0_540,axiom,
! [X5,X25] :
( hAPP_nat_int(power_power_int(X5),number_number_of_nat(X25)) = zero_zero_int
<=> ( X5 = zero_zero_int
& number_number_of_nat(X25) != zero_zero_nat ) ),
file('<stdin>',fact_117_power__eq__0__iff__number__of) ).
fof(c_0_541,axiom,
hAPP_nat_real(power_power_real(zero_zero_real),number_number_of_nat(bit0(bit1(pls)))) = zero_zero_real,
file('<stdin>',fact_9_zero__power2) ).
fof(c_0_542,axiom,
hAPP_nat_nat(power_power_nat(zero_zero_nat),number_number_of_nat(bit0(bit1(pls)))) = zero_zero_nat,
file('<stdin>',fact_8_zero__power2) ).
fof(c_0_543,axiom,
hAPP_nat_int(power_power_int(zero_zero_int),number_number_of_nat(bit0(bit1(pls)))) = zero_zero_int,
file('<stdin>',fact_7_zero__power2) ).
fof(c_0_544,axiom,
hAPP_nat_real(power_power_real(one_one_real),number_number_of_nat(bit0(bit1(pls)))) = one_one_real,
file('<stdin>',fact_6_one__power2) ).
fof(c_0_545,axiom,
hAPP_nat_nat(power_power_nat(one_one_nat),number_number_of_nat(bit0(bit1(pls)))) = one_one_nat,
file('<stdin>',fact_5_one__power2) ).
fof(c_0_546,axiom,
hAPP_nat_int(power_power_int(one_one_int),number_number_of_nat(bit0(bit1(pls)))) = one_one_int,
file('<stdin>',fact_4_one__power2) ).
fof(c_0_547,axiom,
! [X3,X4] :
( hAPP_nat_int(semiri1621563631at_int,X3) = hAPP_nat_int(semiri1621563631at_int,X4)
<=> X3 = X4 ),
file('<stdin>',fact_220_Nat__Transfer_Otransfer__int__nat__relations_I1_J) ).
fof(c_0_548,axiom,
! [X29,X18] :
( hAPP_nat_int(semiri1621563631at_int,X29) = hAPP_nat_int(semiri1621563631at_int,X18)
<=> X29 = X18 ),
file('<stdin>',fact_219_of__nat__eq__iff) ).
fof(c_0_549,axiom,
! [X29,X18] :
( hAPP_nat_nat(semiri984289939at_nat,X29) = hAPP_nat_nat(semiri984289939at_nat,X18)
<=> X29 = X18 ),
file('<stdin>',fact_218_of__nat__eq__iff) ).
fof(c_0_550,axiom,
! [X29,X18] :
( hAPP_nat_real(semiri132038758t_real,X29) = hAPP_nat_real(semiri132038758t_real,X18)
<=> X29 = X18 ),
file('<stdin>',fact_217_of__nat__eq__iff) ).
fof(c_0_551,axiom,
! [X29,X18] :
( hAPP_nat_int(semiri1621563631at_int,X29) = hAPP_nat_int(semiri1621563631at_int,X18)
<=> X29 = X18 ),
file('<stdin>',fact_68_int__int__eq) ).
fof(c_0_552,axiom,
! [X122,X123] : hAPP_int_int(plus_plus_int(X122),X123) = hAPP_int_int(plus_plus_int(X123),X122),
file('<stdin>',fact_345_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J) ).
fof(c_0_553,axiom,
! [X122,X123] : hAPP_nat_nat(plus_plus_nat(X122),X123) = hAPP_nat_nat(plus_plus_nat(X123),X122),
file('<stdin>',fact_344_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J) ).
fof(c_0_554,axiom,
! [X122,X123] : hAPP_real_real(plus_plus_real(X122),X123) = hAPP_real_real(plus_plus_real(X123),X122),
file('<stdin>',fact_343_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J) ).
fof(c_0_555,axiom,
! [X15,X16] : hAPP_nat_nat(plus_plus_nat(X15),X16) = hAPP_nat_nat(plus_plus_nat(X16),X15),
file('<stdin>',fact_178_nat__add__commute) ).
fof(c_0_556,axiom,
! [X17,X14] : hAPP_int_int(plus_plus_int(X17),X14) = hAPP_int_int(plus_plus_int(X14),X17),
file('<stdin>',fact_67_zadd__commute) ).
fof(c_0_557,axiom,
! [X41] : number267125858f_real(hAPP_nat_int(semiri1621563631at_int,X41)) = hAPP_nat_real(semiri132038758t_real,X41),
file('<stdin>',fact_132_number__of__int) ).
fof(c_0_558,axiom,
! [X41] : number_number_of_int(hAPP_nat_int(semiri1621563631at_int,X41)) = hAPP_nat_int(semiri1621563631at_int,X41),
file('<stdin>',fact_131_number__of__int) ).
fof(c_0_559,axiom,
! [X41] : number_number_of_nat(hAPP_nat_int(semiri1621563631at_int,X41)) = hAPP_nat_nat(semiri984289939at_nat,X41),
file('<stdin>',fact_130_number__of__int) ).
fof(c_0_560,axiom,
! [X8,X10] : hAPP_nat_nat(if_nat(fFalse,X8),X10) = X10,
file('<stdin>',help_If_2_1_If_000tc__Nat__Onat_T) ).
fof(c_0_561,axiom,
! [X8,X10] : hAPP_nat_nat(if_nat(fTrue,X8),X10) = X8,
file('<stdin>',help_If_1_1_If_000tc__Nat__Onat_T) ).
fof(c_0_562,axiom,
! [X3,X18] :
( hAPP_nat_nat(power_power_nat(X3),X18) = one_one_nat
<=> ( X3 = one_one_nat
| X18 = zero_zero_nat ) ),
file('<stdin>',fact_299_exp__eq__1) ).
fof(c_0_563,axiom,
! [X81,X5] :
( X81 = hAPP_int_int(plus_plus_int(X81),X5)
<=> X5 = zero_zero_int ),
file('<stdin>',fact_351_add__0__iff) ).
fof(c_0_564,axiom,
! [X81,X5] :
( X81 = hAPP_nat_nat(plus_plus_nat(X81),X5)
<=> X5 = zero_zero_nat ),
file('<stdin>',fact_350_add__0__iff) ).
fof(c_0_565,axiom,
! [X81,X5] :
( X81 = hAPP_real_real(plus_plus_real(X81),X5)
<=> X5 = zero_zero_real ),
file('<stdin>',fact_349_add__0__iff) ).
fof(c_0_566,axiom,
! [X15,X16] :
( hAPP_nat_nat(plus_plus_nat(X15),X16) = X15
=> X16 = zero_zero_nat ),
file('<stdin>',fact_210_add__eq__self__zero) ).
fof(c_0_567,axiom,
! [X29,X18] :
( hAPP_nat_nat(power_power_nat(X29),X18) = zero_zero_nat
<=> ( X18 != zero_zero_nat
& X29 = zero_zero_nat ) ),
file('<stdin>',fact_396_nat__power__eq__0__iff) ).
fof(c_0_568,axiom,
! [X5,X18] :
( hAPP_nat_int(power_power_int(X5),X18) = zero_zero_int
<=> ( X5 = zero_zero_int
& X18 != zero_zero_nat ) ),
file('<stdin>',fact_285_power__eq__0__iff) ).
fof(c_0_569,axiom,
! [X5,X18] :
( hAPP_nat_nat(power_power_nat(X5),X18) = zero_zero_nat
<=> ( X5 = zero_zero_nat
& X18 != zero_zero_nat ) ),
file('<stdin>',fact_284_power__eq__0__iff) ).
fof(c_0_570,axiom,
! [X5,X18] :
( hAPP_nat_real(power_power_real(X5),X18) = zero_zero_real
<=> ( X5 = zero_zero_real
& X18 != zero_zero_nat ) ),
file('<stdin>',fact_283_power__eq__0__iff) ).
fof(c_0_571,axiom,
! [X5] :
( zero_zero_int = hAPP_int_int(plus_plus_int(X5),X5)
<=> X5 = zero_zero_int ),
file('<stdin>',fact_362_double__zero__sym) ).
fof(c_0_572,axiom,
! [X5] :
( zero_zero_real = hAPP_real_real(plus_plus_real(X5),X5)
<=> X5 = zero_zero_real ),
file('<stdin>',fact_361_double__zero__sym) ).
fof(c_0_573,axiom,
! [X64,X65] :
( X65 != zero_zero_int
=> hAPP_nat_int(power_power_int(X65),X64) != zero_zero_int ),
file('<stdin>',fact_231_field__power__not__zero) ).
fof(c_0_574,axiom,
! [X64,X65] :
( X65 != zero_zero_real
=> hAPP_nat_real(power_power_real(X65),X64) != zero_zero_real ),
file('<stdin>',fact_230_field__power__not__zero) ).
fof(c_0_575,axiom,
! [X29,X18] :
( hAPP_nat_nat(plus_plus_nat(X29),X18) = zero_zero_nat
<=> ( X29 = zero_zero_nat
& X18 = zero_zero_nat ) ),
file('<stdin>',fact_211_add__is__0) ).
fof(c_0_576,axiom,
! [X5] :
( hAPP_real_real(plus_plus_real(X5),X5) = zero_zero_real
<=> X5 = zero_zero_real ),
file('<stdin>',fact_90_double__eq__0__iff) ).
fof(c_0_577,axiom,
! [X5] :
( hAPP_int_int(plus_plus_int(X5),X5) = zero_zero_int
<=> X5 = zero_zero_int ),
file('<stdin>',fact_89_double__eq__0__iff) ).
fof(c_0_578,axiom,
! [X233] : number_number_of_int(succ(X233)) = hAPP_int_int(plus_plus_int(one_one_int),number_number_of_int(X233)),
file('<stdin>',fact_583_number__of__succ) ).
fof(c_0_579,axiom,
! [X233] : number267125858f_real(succ(X233)) = hAPP_real_real(plus_plus_real(one_one_real),number267125858f_real(X233)),
file('<stdin>',fact_582_number__of__succ) ).
fof(c_0_580,axiom,
hAPP_nat_nat(plus_plus_nat(one_one_nat),one_one_nat) = number_number_of_nat(bit0(bit1(pls))),
file('<stdin>',fact_45_nat__1__add__1) ).
fof(c_0_581,axiom,
hAPP_real_real(plus_plus_real(one_one_real),one_one_real) = number267125858f_real(bit0(bit1(pls))),
file('<stdin>',fact_20_semiring__one__add__one__is__two) ).
fof(c_0_582,axiom,
hAPP_nat_nat(plus_plus_nat(one_one_nat),one_one_nat) = number_number_of_nat(bit0(bit1(pls))),
file('<stdin>',fact_19_semiring__one__add__one__is__two) ).
fof(c_0_583,axiom,
hAPP_int_int(plus_plus_int(one_one_int),one_one_int) = number_number_of_int(bit0(bit1(pls))),
file('<stdin>',fact_18_semiring__one__add__one__is__two) ).
fof(c_0_584,axiom,
hAPP_real_real(plus_plus_real(one_one_real),one_one_real) = number267125858f_real(bit0(bit1(pls))),
file('<stdin>',fact_17_one__add__one__is__two) ).
fof(c_0_585,axiom,
hAPP_int_int(plus_plus_int(one_one_int),one_one_int) = number_number_of_int(bit0(bit1(pls))),
file('<stdin>',fact_16_one__add__one__is__two) ).
fof(c_0_586,axiom,
! [X9] :
( ( number_number_of_nat(X9) = zero_zero_nat
=> hAPP_nat_real(power_power_real(zero_zero_real),number_number_of_nat(X9)) = one_one_real )
& ( number_number_of_nat(X9) != zero_zero_nat
=> hAPP_nat_real(power_power_real(zero_zero_real),number_number_of_nat(X9)) = zero_zero_real ) ),
file('<stdin>',fact_24_power__0__left__number__of) ).
fof(c_0_587,axiom,
! [X9] :
( ( number_number_of_nat(X9) = zero_zero_nat
=> hAPP_nat_nat(power_power_nat(zero_zero_nat),number_number_of_nat(X9)) = one_one_nat )
& ( number_number_of_nat(X9) != zero_zero_nat
=> hAPP_nat_nat(power_power_nat(zero_zero_nat),number_number_of_nat(X9)) = zero_zero_nat ) ),
file('<stdin>',fact_23_power__0__left__number__of) ).
fof(c_0_588,axiom,
! [X9] :
( ( number_number_of_nat(X9) = zero_zero_nat
=> hAPP_nat_int(power_power_int(zero_zero_int),number_number_of_nat(X9)) = one_one_int )
& ( number_number_of_nat(X9) != zero_zero_nat
=> hAPP_nat_int(power_power_int(zero_zero_int),number_number_of_nat(X9)) = zero_zero_int ) ),
file('<stdin>',fact_22_power__0__left__number__of) ).
fof(c_0_589,axiom,
! [X1,X2] : is_bool(hAPP_real_bool(X1,X2)),
file('<stdin>',gsy_c_hAPP_000tc__RealDef__Oreal_000tc__HOL__Obool) ).
fof(c_0_590,axiom,
! [X1,X2] : is_bool(hAPP_nat_bool(X1,X2)),
file('<stdin>',gsy_c_hAPP_000tc__Nat__Onat_000tc__HOL__Obool) ).
fof(c_0_591,axiom,
! [X1,X2] : is_bool(hAPP_int_bool(X1,X2)),
file('<stdin>',gsy_c_hAPP_000tc__Int__Oint_000tc__HOL__Obool) ).
fof(c_0_592,axiom,
! [X32] : hAPP_real_real(plus_plus_real(number267125858f_real(pls)),X32) = X32,
file('<stdin>',fact_114_add__numeral__0) ).
fof(c_0_593,axiom,
! [X32] : hAPP_int_int(plus_plus_int(number_number_of_int(pls)),X32) = X32,
file('<stdin>',fact_113_add__numeral__0) ).
fof(c_0_594,axiom,
! [X33] : hAPP_real_real(plus_plus_real(X33),number267125858f_real(pls)) = X33,
file('<stdin>',fact_116_add__numeral__0__right) ).
fof(c_0_595,axiom,
! [X33] : hAPP_int_int(plus_plus_int(X33),number_number_of_int(pls)) = X33,
file('<stdin>',fact_115_add__numeral__0__right) ).
fof(c_0_596,axiom,
! [X21] : bit0(X21) = hAPP_int_int(plus_plus_int(X21),X21),
file('<stdin>',fact_103_Bit0__def) ).
fof(c_0_597,axiom,
! [X21] : succ(X21) = hAPP_int_int(plus_plus_int(X21),one_one_int),
file('<stdin>',fact_573_succ__def) ).
fof(c_0_598,axiom,
! [X18] :
( hAPP_nat_int(semiri1621563631at_int,X18) = zero_zero_int
<=> X18 = zero_zero_nat ),
file('<stdin>',fact_43_int__eq__0__conv) ).
fof(c_0_599,axiom,
! [X21] : succ(bit1(X21)) = bit0(succ(X21)),
file('<stdin>',fact_569_succ__Bit1) ).
fof(c_0_600,axiom,
! [X50] :
( ( X50 = zero_zero_nat
=> hAPP_nat_real(power_power_real(zero_zero_real),X50) = one_one_real )
& ( X50 != zero_zero_nat
=> hAPP_nat_real(power_power_real(zero_zero_real),X50) = zero_zero_real ) ),
file('<stdin>',fact_162_power__0__left) ).
fof(c_0_601,axiom,
! [X50] :
( ( X50 = zero_zero_nat
=> hAPP_nat_nat(power_power_nat(zero_zero_nat),X50) = one_one_nat )
& ( X50 != zero_zero_nat
=> hAPP_nat_nat(power_power_nat(zero_zero_nat),X50) = zero_zero_nat ) ),
file('<stdin>',fact_161_power__0__left) ).
fof(c_0_602,axiom,
! [X50] :
( ( X50 = zero_zero_nat
=> hAPP_nat_int(power_power_int(zero_zero_int),X50) = one_one_int )
& ( X50 != zero_zero_nat
=> hAPP_nat_int(power_power_int(zero_zero_int),X50) = zero_zero_int ) ),
file('<stdin>',fact_160_power__0__left) ).
fof(c_0_603,axiom,
! [X146] : hAPP_nat_int(power_power_int(X146),one_one_nat) = X146,
file('<stdin>',fact_395_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J) ).
fof(c_0_604,axiom,
! [X146] : hAPP_nat_nat(power_power_nat(X146),one_one_nat) = X146,
file('<stdin>',fact_394_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J) ).
fof(c_0_605,axiom,
! [X146] : hAPP_nat_real(power_power_real(X146),one_one_nat) = X146,
file('<stdin>',fact_393_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J) ).
fof(c_0_606,axiom,
! [X126] : hAPP_int_int(plus_plus_int(X126),zero_zero_int) = X126,
file('<stdin>',fact_360_add__0__right) ).
fof(c_0_607,axiom,
! [X126] : hAPP_nat_nat(plus_plus_nat(X126),zero_zero_nat) = X126,
file('<stdin>',fact_359_add__0__right) ).
fof(c_0_608,axiom,
! [X126] : hAPP_real_real(plus_plus_real(X126),zero_zero_real) = X126,
file('<stdin>',fact_358_add__0__right) ).
fof(c_0_609,axiom,
! [X125] : hAPP_int_int(plus_plus_int(X125),zero_zero_int) = X125,
file('<stdin>',fact_357_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J) ).
fof(c_0_610,axiom,
! [X125] : hAPP_nat_nat(plus_plus_nat(X125),zero_zero_nat) = X125,
file('<stdin>',fact_356_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J) ).
fof(c_0_611,axiom,
! [X125] : hAPP_real_real(plus_plus_real(X125),zero_zero_real) = X125,
file('<stdin>',fact_355_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J) ).
fof(c_0_612,axiom,
! [X124] : hAPP_int_int(plus_plus_int(X124),zero_zero_int) = X124,
file('<stdin>',fact_354_add_Ocomm__neutral) ).
fof(c_0_613,axiom,
! [X124] : hAPP_nat_nat(plus_plus_nat(X124),zero_zero_nat) = X124,
file('<stdin>',fact_353_add_Ocomm__neutral) ).
fof(c_0_614,axiom,
! [X124] : hAPP_real_real(plus_plus_real(X124),zero_zero_real) = X124,
file('<stdin>',fact_352_add_Ocomm__neutral) ).
fof(c_0_615,axiom,
! [X63] : hAPP_nat_int(power_power_int(X63),one_one_nat) = X63,
file('<stdin>',fact_216_power__one__right) ).
fof(c_0_616,axiom,
! [X63] : hAPP_nat_nat(power_power_nat(X63),one_one_nat) = X63,
file('<stdin>',fact_215_power__one__right) ).
fof(c_0_617,axiom,
! [X63] : hAPP_nat_real(power_power_real(X63),one_one_nat) = X63,
file('<stdin>',fact_214_power__one__right) ).
fof(c_0_618,axiom,
! [X15] : hAPP_nat_nat(plus_plus_nat(X15),zero_zero_nat) = X15,
file('<stdin>',fact_212_Nat_Oadd__0__right) ).
fof(c_0_619,axiom,
! [X17] : hAPP_int_int(plus_plus_int(X17),zero_zero_int) = X17,
file('<stdin>',fact_104_zadd__0__right) ).
fof(c_0_620,axiom,
! [X21] : hAPP_int_int(plus_plus_int(X21),pls) = X21,
file('<stdin>',fact_100_add__Pls__right) ).
fof(c_0_621,axiom,
! [X92] : hAPP_nat_int(power_power_int(X92),zero_zero_nat) = one_one_int,
file('<stdin>',fact_302_comm__semiring__1__class_Onormalizing__semiring__rules_I32_J) ).
fof(c_0_622,axiom,
! [X92] : hAPP_nat_nat(power_power_nat(X92),zero_zero_nat) = one_one_nat,
file('<stdin>',fact_301_comm__semiring__1__class_Onormalizing__semiring__rules_I32_J) ).
fof(c_0_623,axiom,
! [X92] : hAPP_nat_real(power_power_real(X92),zero_zero_nat) = one_one_real,
file('<stdin>',fact_300_comm__semiring__1__class_Onormalizing__semiring__rules_I32_J) ).
fof(c_0_624,axiom,
! [X89] : hAPP_nat_int(power_power_int(X89),zero_zero_nat) = one_one_int,
file('<stdin>',fact_291_power__0) ).
fof(c_0_625,axiom,
! [X89] : hAPP_nat_nat(power_power_nat(X89),zero_zero_nat) = one_one_nat,
file('<stdin>',fact_290_power__0) ).
fof(c_0_626,axiom,
! [X89] : hAPP_nat_real(power_power_real(X89),zero_zero_nat) = one_one_real,
file('<stdin>',fact_289_power__0) ).
fof(c_0_627,axiom,
! [X129] : hAPP_int_int(plus_plus_int(zero_zero_int),X129) = X129,
file('<stdin>',fact_371_add__0__left) ).
fof(c_0_628,axiom,
! [X129] : hAPP_nat_nat(plus_plus_nat(zero_zero_nat),X129) = X129,
file('<stdin>',fact_370_add__0__left) ).
fof(c_0_629,axiom,
! [X129] : hAPP_real_real(plus_plus_real(zero_zero_real),X129) = X129,
file('<stdin>',fact_369_add__0__left) ).
fof(c_0_630,axiom,
! [X128] : hAPP_int_int(plus_plus_int(zero_zero_int),X128) = X128,
file('<stdin>',fact_368_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J) ).
fof(c_0_631,axiom,
! [X128] : hAPP_nat_nat(plus_plus_nat(zero_zero_nat),X128) = X128,
file('<stdin>',fact_367_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J) ).
fof(c_0_632,axiom,
! [X128] : hAPP_real_real(plus_plus_real(zero_zero_real),X128) = X128,
file('<stdin>',fact_366_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J) ).
fof(c_0_633,axiom,
! [X127] : hAPP_int_int(plus_plus_int(zero_zero_int),X127) = X127,
file('<stdin>',fact_365_add__0) ).
fof(c_0_634,axiom,
! [X127] : hAPP_nat_nat(plus_plus_nat(zero_zero_nat),X127) = X127,
file('<stdin>',fact_364_add__0) ).
fof(c_0_635,axiom,
! [X127] : hAPP_real_real(plus_plus_real(zero_zero_real),X127) = X127,
file('<stdin>',fact_363_add__0) ).
fof(c_0_636,axiom,
! [X16] : hAPP_nat_nat(plus_plus_nat(zero_zero_nat),X16) = X16,
file('<stdin>',fact_213_plus__nat_Oadd__0) ).
fof(c_0_637,axiom,
! [X17] : hAPP_int_int(plus_plus_int(zero_zero_int),X17) = X17,
file('<stdin>',fact_105_zadd__0) ).
fof(c_0_638,axiom,
! [X21] : hAPP_int_int(plus_plus_int(pls),X21) = X21,
file('<stdin>',fact_101_add__Pls) ).
fof(c_0_639,axiom,
! [X66] : hAPP_nat_int(power_power_int(one_one_int),X66) = one_one_int,
file('<stdin>',fact_234_power__one) ).
fof(c_0_640,axiom,
! [X66] : hAPP_nat_nat(power_power_nat(one_one_nat),X66) = one_one_nat,
file('<stdin>',fact_233_power__one) ).
fof(c_0_641,axiom,
! [X66] : hAPP_nat_real(power_power_real(one_one_real),X66) = one_one_real,
file('<stdin>',fact_232_power__one) ).
fof(c_0_642,axiom,
! [X11,X12] :
( bit0(X11) = bit0(X12)
<=> X11 = X12 ),
file('<stdin>',fact_62_rel__simps_I48_J) ).
fof(c_0_643,axiom,
! [X11,X12] :
( bit1(X11) = bit1(X12)
<=> X11 = X12 ),
file('<stdin>',fact_61_rel__simps_I51_J) ).
fof(c_0_644,axiom,
! [X3,X4] :
( number267125858f_real(X3) = number267125858f_real(X4)
<=> X3 = X4 ),
file('<stdin>',fact_57_eq__number__of) ).
fof(c_0_645,axiom,
! [X3,X4] :
( number_number_of_int(X3) = number_number_of_int(X4)
<=> X3 = X4 ),
file('<stdin>',fact_56_eq__number__of) ).
fof(c_0_646,axiom,
! [X21] : succ(bit0(X21)) = bit1(X21),
file('<stdin>',fact_568_succ__Bit0) ).
fof(c_0_647,axiom,
! [X25,X3] :
( number267125858f_real(X25) = X3
<=> X3 = number267125858f_real(X25) ),
file('<stdin>',fact_60_number__of__reorient) ).
fof(c_0_648,axiom,
! [X25,X3] :
( number_number_of_int(X25) = X3
<=> X3 = number_number_of_int(X25) ),
file('<stdin>',fact_59_number__of__reorient) ).
fof(c_0_649,axiom,
! [X25,X3] :
( number_number_of_nat(X25) = X3
<=> X3 = number_number_of_nat(X25) ),
file('<stdin>',fact_58_number__of__reorient) ).
fof(c_0_650,axiom,
! [X21,X31] : bit0(X21) != bit1(X31),
file('<stdin>',fact_94_rel__simps_I49_J) ).
fof(c_0_651,axiom,
! [X21,X31] : bit1(X21) != bit0(X31),
file('<stdin>',fact_93_rel__simps_I50_J) ).
fof(c_0_652,axiom,
zero_zero_int = hAPP_nat_int(semiri1621563631at_int,zero_zero_nat),
file('<stdin>',fact_295_transfer__int__nat__numerals_I1_J) ).
fof(c_0_653,axiom,
hAPP_nat_int(semiri1621563631at_int,zero_zero_nat) = zero_zero_int,
file('<stdin>',fact_294_of__nat__0) ).
fof(c_0_654,axiom,
hAPP_nat_nat(semiri984289939at_nat,zero_zero_nat) = zero_zero_nat,
file('<stdin>',fact_293_of__nat__0) ).
fof(c_0_655,axiom,
hAPP_nat_real(semiri132038758t_real,zero_zero_nat) = zero_zero_real,
file('<stdin>',fact_292_of__nat__0) ).
fof(c_0_656,axiom,
one_one_int = hAPP_nat_int(semiri1621563631at_int,one_one_nat),
file('<stdin>',fact_253_transfer__int__nat__numerals_I2_J) ).
fof(c_0_657,axiom,
hAPP_nat_int(semiri1621563631at_int,one_one_nat) = one_one_int,
file('<stdin>',fact_249_of__nat__1) ).
fof(c_0_658,axiom,
hAPP_nat_nat(semiri984289939at_nat,one_one_nat) = one_one_nat,
file('<stdin>',fact_248_of__nat__1) ).
fof(c_0_659,axiom,
hAPP_nat_real(semiri132038758t_real,one_one_nat) = one_one_real,
file('<stdin>',fact_247_of__nat__1) ).
fof(c_0_660,axiom,
hAPP_nat_int(semiri1621563631at_int,zero_zero_nat) = zero_zero_int,
file('<stdin>',fact_44_int__0) ).
fof(c_0_661,axiom,
hAPP_nat_int(semiri1621563631at_int,one_one_nat) = one_one_int,
file('<stdin>',fact_40_int__1) ).
fof(c_0_662,axiom,
! [X283] :
( is_bool(X283)
=> ( X283 = fTrue
| X283 = fFalse ) ),
file('<stdin>',help_If_3_1_If_000tc__Nat__Onat_T) ).
fof(c_0_663,axiom,
! [X12] :
( pls = bit0(X12)
<=> pls = X12 ),
file('<stdin>',fact_96_rel__simps_I38_J) ).
fof(c_0_664,axiom,
! [X11] :
( bit0(X11) = pls
<=> X11 = pls ),
file('<stdin>',fact_95_rel__simps_I44_J) ).
fof(c_0_665,axiom,
number267125858f_real(bit1(pls)) = one_one_real,
file('<stdin>',fact_147_semiring__numeral__1__eq__1) ).
fof(c_0_666,axiom,
number_number_of_nat(bit1(pls)) = one_one_nat,
file('<stdin>',fact_146_semiring__numeral__1__eq__1) ).
fof(c_0_667,axiom,
number_number_of_int(bit1(pls)) = one_one_int,
file('<stdin>',fact_145_semiring__numeral__1__eq__1) ).
fof(c_0_668,axiom,
one_one_nat = number_number_of_nat(bit1(pls)),
file('<stdin>',fact_55_Numeral1__eq1__nat) ).
fof(c_0_669,axiom,
number_number_of_nat(bit1(pls)) = one_one_nat,
file('<stdin>',fact_54_nat__numeral__1__eq__1) ).
fof(c_0_670,axiom,
one_one_int = number_number_of_int(bit1(pls)),
file('<stdin>',fact_53_one__is__num__one) ).
fof(c_0_671,axiom,
number267125858f_real(bit1(pls)) = one_one_real,
file('<stdin>',fact_28_numeral__1__eq__1) ).
fof(c_0_672,axiom,
number_number_of_int(bit1(pls)) = one_one_int,
file('<stdin>',fact_27_numeral__1__eq__1) ).
fof(c_0_673,axiom,
one_one_real = number267125858f_real(bit1(pls)),
file('<stdin>',fact_26_semiring__norm_I110_J) ).
fof(c_0_674,axiom,
one_one_int = number_number_of_int(bit1(pls)),
file('<stdin>',fact_25_semiring__norm_I110_J) ).
fof(c_0_675,axiom,
! [X31] : pls != bit1(X31),
file('<stdin>',fact_92_rel__simps_I39_J) ).
fof(c_0_676,axiom,
! [X21] : bit1(X21) != pls,
file('<stdin>',fact_91_rel__simps_I46_J) ).
fof(c_0_677,axiom,
succ(pls) = bit1(pls),
file('<stdin>',fact_567_succ__Pls) ).
fof(c_0_678,axiom,
! [X21] : number_number_of_int(X21) = X21,
file('<stdin>',fact_176_number__of__is__id) ).
fof(c_0_679,axiom,
! [X3] :
( one_one_int = X3
<=> X3 = one_one_int ),
file('<stdin>',fact_348_one__reorient) ).
fof(c_0_680,axiom,
! [X3] :
( one_one_nat = X3
<=> X3 = one_one_nat ),
file('<stdin>',fact_347_one__reorient) ).
fof(c_0_681,axiom,
! [X3] :
( one_one_real = X3
<=> X3 = one_one_real ),
file('<stdin>',fact_346_one__reorient) ).
fof(c_0_682,axiom,
! [X3] :
( zero_zero_int = X3
<=> X3 = zero_zero_int ),
file('<stdin>',fact_309_zero__reorient) ).
fof(c_0_683,axiom,
! [X3] :
( zero_zero_nat = X3
<=> X3 = zero_zero_nat ),
file('<stdin>',fact_308_zero__reorient) ).
fof(c_0_684,axiom,
! [X3] :
( zero_zero_real = X3
<=> X3 = zero_zero_real ),
file('<stdin>',fact_307_zero__reorient) ).
fof(c_0_685,axiom,
zero_zero_real = number267125858f_real(pls),
file('<stdin>',fact_112_semiring__norm_I112_J) ).
fof(c_0_686,axiom,
zero_zero_int = number_number_of_int(pls),
file('<stdin>',fact_111_semiring__norm_I112_J) ).
fof(c_0_687,axiom,
number267125858f_real(pls) = zero_zero_real,
file('<stdin>',fact_110_number__of__Pls) ).
fof(c_0_688,axiom,
number_number_of_int(pls) = zero_zero_int,
file('<stdin>',fact_109_number__of__Pls) ).
fof(c_0_689,axiom,
number267125858f_real(pls) = zero_zero_real,
file('<stdin>',fact_108_semiring__numeral__0__eq__0) ).
fof(c_0_690,axiom,
number_number_of_nat(pls) = zero_zero_nat,
file('<stdin>',fact_107_semiring__numeral__0__eq__0) ).
fof(c_0_691,axiom,
number_number_of_int(pls) = zero_zero_int,
file('<stdin>',fact_106_semiring__numeral__0__eq__0) ).
fof(c_0_692,axiom,
bit0(pls) = pls,
file('<stdin>',fact_97_Bit0__Pls) ).
fof(c_0_693,axiom,
zero_zero_nat = number_number_of_nat(pls),
file('<stdin>',fact_42_semiring__norm_I113_J) ).
fof(c_0_694,axiom,
number_number_of_nat(pls) = zero_zero_nat,
file('<stdin>',fact_41_nat__number__of__Pls) ).
fof(c_0_695,axiom,
zero_zero_int = number_number_of_int(pls),
file('<stdin>',fact_35_zero__is__num__zero) ).
fof(c_0_696,axiom,
is_bool(fTrue),
file('<stdin>',gsy_c_fTrue) ).
fof(c_0_697,axiom,
is_bool(fFalse),
file('<stdin>',gsy_c_fFalse) ).
fof(c_0_698,axiom,
zero_zero_int != one_one_int,
file('<stdin>',fact_229_zero__neq__one) ).
fof(c_0_699,axiom,
zero_zero_nat != one_one_nat,
file('<stdin>',fact_228_zero__neq__one) ).
fof(c_0_700,axiom,
zero_zero_real != one_one_real,
file('<stdin>',fact_227_zero__neq__one) ).
fof(c_0_701,axiom,
one_one_int != zero_zero_int,
file('<stdin>',fact_226_one__neq__zero) ).
fof(c_0_702,axiom,
one_one_nat != zero_zero_nat,
file('<stdin>',fact_225_one__neq__zero) ).
fof(c_0_703,axiom,
one_one_real != zero_zero_real,
file('<stdin>',fact_224_one__neq__zero) ).
fof(c_0_704,axiom,
zero_zero_real != one_one_real,
file('<stdin>',fact_172_real__zero__not__eq__one) ).
fof(c_0_705,axiom,
zero_zero_int != one_one_int,
file('<stdin>',fact_99_int__0__neq__1) ).
fof(c_0_706,axiom,
pls = zero_zero_int,
file('<stdin>',fact_98_Pls__def) ).
fof(c_0_707,axiom,
! [X3,X4] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(X3),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_int(power_power_int(X4),number_number_of_nat(bit0(bit1(pls)))))),zero_zero_int))
<=> ( X3 = zero_zero_int
& X4 = zero_zero_int ) ),
c_0_0 ).
fof(c_0_708,axiom,
! [X3,X4] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(plus_plus_real(hAPP_nat_real(power_power_real(X3),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_real(power_power_real(X4),number_number_of_nat(bit0(bit1(pls)))))),zero_zero_real))
<=> ( X3 = zero_zero_real
& X4 = zero_zero_real ) ),
c_0_1 ).
fof(c_0_709,plain,
! [X43,X44] : ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(plus_plus_real(hAPP_nat_real(power_power_real(X43),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_real(power_power_real(X44),number_number_of_nat(bit0(bit1(pls)))))),zero_zero_real)),
inference(fof_simplification,[status(thm)],[c_0_2]) ).
fof(c_0_710,plain,
! [X43,X44] : ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(X43),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_int(power_power_int(X44),number_number_of_nat(bit0(bit1(pls)))))),zero_zero_int)),
inference(fof_simplification,[status(thm)],[c_0_3]) ).
fof(c_0_711,axiom,
! [X29,X11,X249] :
( ! [X248,X90] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X248),X90))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(X249,X248)),hAPP_nat_nat(X249,X90))) )
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(X249,X29)),X11)),hAPP_nat_nat(X249,hAPP_nat_nat(plus_plus_nat(X29),X11)))) ),
c_0_4 ).
fof(c_0_712,axiom,
! [X55,X250,X249] :
( ! [X56,X251] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X56),X251))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(X249,X56)),hAPP_nat_nat(X249,X251))) )
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X55),X250))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(X249,X55)),hAPP_nat_nat(X249,X250))) ) ),
c_0_5 ).
fof(c_0_713,axiom,
! [X8,X10] : hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),sqrt(hAPP_real_real(plus_plus_real(hAPP_nat_real(power_power_real(X8),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_real(power_power_real(X10),number_number_of_nat(bit0(bit1(pls)))))))),
c_0_6 ).
fof(c_0_714,axiom,
! [X3,X4] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),hAPP_real_real(plus_plus_real(hAPP_nat_real(power_power_real(X3),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_real(power_power_real(X4),number_number_of_nat(bit0(bit1(pls)))))))
<=> ( X3 != zero_zero_real
| X4 != zero_zero_real ) ),
c_0_7 ).
fof(c_0_715,axiom,
! [X3,X4] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(X3),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_int(power_power_int(X4),number_number_of_nat(bit0(bit1(pls)))))))
<=> ( X3 != zero_zero_int
| X4 != zero_zero_int ) ),
c_0_8 ).
fof(c_0_716,axiom,
! [X151,X282] : hAPP_nat_int(power_power_int(hAPP_int_int(plus_plus_int(X151),X282)),number_number_of_nat(bit0(bit1(pls)))) = hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(X151),number_number_of_nat(bit0(bit1(pls))))),times_times_int(times_times_int(number_number_of_int(bit0(bit1(pls))),X151),X282))),hAPP_nat_int(power_power_int(X282),number_number_of_nat(bit0(bit1(pls))))),
c_0_9 ).
fof(c_0_717,axiom,
! [X54,X11,X55] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X11),X55))
=> ( hBOOL(hAPP_int_bool(X54,hAPP_int_int(plus_plus_int(X11),one_one_int)))
=> ( ! [X56] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X11),X56))
=> ( hBOOL(hAPP_int_bool(X54,X56))
=> hBOOL(hAPP_int_bool(X54,hAPP_int_int(plus_plus_int(X56),one_one_int))) ) )
=> hBOOL(hAPP_int_bool(X54,X55)) ) ) ),
c_0_10 ).
fof(c_0_718,axiom,
! [X54,X11,X55] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X11),X55))
=> ( hBOOL(hAPP_int_bool(X54,X11))
=> ( ! [X56] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X11),X56))
=> ( hBOOL(hAPP_int_bool(X54,X56))
=> hBOOL(hAPP_int_bool(X54,hAPP_int_int(plus_plus_int(X56),one_one_int))) ) )
=> hBOOL(hAPP_int_bool(X54,X55)) ) ) ),
c_0_11 ).
fof(c_0_719,axiom,
! [X245,X246] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(X245),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_int(power_power_int(X246),number_number_of_nat(bit0(bit1(pls))))))),
c_0_12 ).
fof(c_0_720,axiom,
! [X245,X246] : hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),hAPP_real_real(plus_plus_real(hAPP_nat_real(power_power_real(X245),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_real(power_power_real(X246),number_number_of_nat(bit0(bit1(pls))))))),
c_0_13 ).
fof(c_0_721,axiom,
! [X243,X244] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_nat_int(power_power_int(X243),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_int(power_power_int(X244),number_number_of_nat(bit0(bit1(pls))))))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X244))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X243),X244)) ) ),
c_0_14 ).
fof(c_0_722,axiom,
! [X243,X244] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(power_power_nat(X243),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_nat(power_power_nat(X244),number_number_of_nat(bit0(bit1(pls))))))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),X244))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X243),X244)) ) ),
c_0_15 ).
fof(c_0_723,axiom,
! [X243,X244] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_nat_real(power_power_real(X243),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_real(power_power_real(X244),number_number_of_nat(bit0(bit1(pls))))))
=> ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X244))
=> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X243),X244)) ) ),
c_0_16 ).
fof(c_0_724,axiom,
! [X238,X239] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_nat_int(power_power_int(X238),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_int(power_power_int(X239),number_number_of_nat(bit0(bit1(pls))))))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X239))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X238),X239)) ) ),
c_0_17 ).
fof(c_0_725,axiom,
! [X238,X239] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(power_power_nat(X238),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_nat(power_power_nat(X239),number_number_of_nat(bit0(bit1(pls))))))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),X239))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X238),X239)) ) ),
c_0_18 ).
fof(c_0_726,axiom,
! [X238,X239] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_nat_real(power_power_real(X238),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_real(power_power_real(X239),number_number_of_nat(bit0(bit1(pls))))))
=> ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X239))
=> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X238),X239)) ) ),
c_0_19 ).
fof(c_0_727,axiom,
! [X30] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),X30)),X30)),zero_zero_int))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X30),zero_zero_int)) ),
c_0_20 ).
fof(c_0_728,plain,
! [X42] : ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_nat_real(power_power_real(X42),number_number_of_nat(bit0(bit1(pls))))),zero_zero_real)),
inference(fof_simplification,[status(thm)],[c_0_21]) ).
fof(c_0_729,plain,
! [X42] : ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_nat_int(power_power_int(X42),number_number_of_nat(bit0(bit1(pls))))),zero_zero_int)),
inference(fof_simplification,[status(thm)],[c_0_22]) ).
fof(c_0_730,axiom,
! [X225,X226,X227] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_nat_int(power_power_int(X225),X226)),hAPP_nat_int(power_power_int(X227),X226)))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X227))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X225),X227)) ) ),
c_0_23 ).
fof(c_0_731,axiom,
! [X225,X226,X227] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(power_power_nat(X225),X226)),hAPP_nat_nat(power_power_nat(X227),X226)))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),X227))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X225),X227)) ) ),
c_0_24 ).
fof(c_0_732,axiom,
! [X225,X226,X227] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_nat_real(power_power_real(X225),X226)),hAPP_nat_real(power_power_real(X227),X226)))
=> ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X227))
=> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X225),X227)) ) ),
c_0_25 ).
fof(c_0_733,axiom,
! [X177,X178,X179] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),X179))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_nat_int(power_power_int(X179),X177)),hAPP_nat_int(power_power_int(X179),X178)))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X177),X178)) ) ),
c_0_26 ).
fof(c_0_734,axiom,
! [X177,X178,X179] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,one_one_nat),X179))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(power_power_nat(X179),X177)),hAPP_nat_nat(power_power_nat(X179),X178)))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X177),X178)) ) ),
c_0_27 ).
fof(c_0_735,axiom,
! [X177,X178,X179] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,one_one_real),X179))
=> ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_nat_real(power_power_real(X179),X177)),hAPP_nat_real(power_power_real(X179),X178)))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X177),X178)) ) ),
c_0_28 ).
fof(c_0_736,axiom,
! [X3,X4,X81] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),X81))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_nat_int(power_power_int(X81),X3)),hAPP_nat_int(power_power_int(X81),X4)))
<=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X3),X4)) ) ),
c_0_29 ).
fof(c_0_737,axiom,
! [X3,X4,X81] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,one_one_nat),X81))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(power_power_nat(X81),X3)),hAPP_nat_nat(power_power_nat(X81),X4)))
<=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X3),X4)) ) ),
c_0_30 ).
fof(c_0_738,axiom,
! [X3,X4,X81] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,one_one_real),X81))
=> ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_nat_real(power_power_real(X81),X3)),hAPP_nat_real(power_power_real(X81),X4)))
<=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X3),X4)) ) ),
c_0_31 ).
fof(c_0_739,axiom,
! [X82,X83,X84] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),X84))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_nat_int(power_power_int(X84),X82)),hAPP_nat_int(power_power_int(X84),X83)))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X82),X83)) ) ),
c_0_32 ).
fof(c_0_740,axiom,
! [X82,X83,X84] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,one_one_nat),X84))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(power_power_nat(X84),X82)),hAPP_nat_nat(power_power_nat(X84),X83)))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X82),X83)) ) ),
c_0_33 ).
fof(c_0_741,axiom,
! [X82,X83,X84] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,one_one_real),X84))
=> ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_nat_real(power_power_real(X84),X82)),hAPP_nat_real(power_power_real(X84),X83)))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X82),X83)) ) ),
c_0_34 ).
fof(c_0_742,axiom,
! [X3,X4,X81] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),X81))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_nat_int(power_power_int(X81),X3)),hAPP_nat_int(power_power_int(X81),X4)))
<=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X3),X4)) ) ),
c_0_35 ).
fof(c_0_743,axiom,
! [X3,X4,X81] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,one_one_nat),X81))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(power_power_nat(X81),X3)),hAPP_nat_nat(power_power_nat(X81),X4)))
<=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X3),X4)) ) ),
c_0_36 ).
fof(c_0_744,axiom,
! [X3,X4,X81] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,one_one_real),X81))
=> ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_nat_real(power_power_real(X81),X3)),hAPP_nat_real(power_power_real(X81),X4)))
<=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X3),X4)) ) ),
c_0_37 ).
fof(c_0_745,axiom,
! [X15,X16,X22] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X22))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(power_power_nat(X22),X15)),hAPP_nat_nat(power_power_nat(X22),X16)))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X15),X16)) ) ),
c_0_38 ).
fof(c_0_746,axiom,
! [X174,X175,X176] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X175),X176))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X174))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X174),one_one_int))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_nat_int(power_power_int(X174),X176)),hAPP_nat_int(power_power_int(X174),X175))) ) ) ),
c_0_39 ).
fof(c_0_747,axiom,
! [X174,X175,X176] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X175),X176))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),X174))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X174),one_one_nat))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(power_power_nat(X174),X176)),hAPP_nat_nat(power_power_nat(X174),X175))) ) ) ),
c_0_40 ).
fof(c_0_748,axiom,
! [X174,X175,X176] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X175),X176))
=> ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X174))
=> ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X174),one_one_real))
=> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_nat_real(power_power_real(X174),X176)),hAPP_nat_real(power_power_real(X174),X175))) ) ) ),
c_0_41 ).
fof(c_0_749,axiom,
! [X51,X52,X53] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X52),X53))
=> ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X51))
=> ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X51),one_one_real))
=> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_nat_real(power_power_real(X51),X53)),hAPP_nat_real(power_power_real(X51),X52))) ) ) ),
c_0_42 ).
fof(c_0_750,axiom,
! [X51,X52,X53] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X52),X53))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X51))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X51),one_one_nat))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(power_power_nat(X51),X53)),hAPP_nat_nat(power_power_nat(X51),X52))) ) ) ),
c_0_43 ).
fof(c_0_751,axiom,
! [X51,X52,X53] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X52),X53))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X51))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X51),one_one_int))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_nat_int(power_power_int(X51),X53)),hAPP_nat_int(power_power_int(X51),X52))) ) ) ),
c_0_44 ).
fof(c_0_752,axiom,
! [X234,X235,X236] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X235),X236))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X235))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X234))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_nat_int(power_power_int(X235),X234)),hAPP_nat_int(power_power_int(X236),X234))) ) ) ),
c_0_45 ).
fof(c_0_753,axiom,
! [X234,X235,X236] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X235),X236))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),X235))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X234))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(power_power_nat(X235),X234)),hAPP_nat_nat(power_power_nat(X236),X234))) ) ) ),
c_0_46 ).
fof(c_0_754,axiom,
! [X234,X235,X236] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X235),X236))
=> ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X235))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X234))
=> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_nat_real(power_power_real(X235),X234)),hAPP_nat_real(power_power_real(X236),X234))) ) ) ),
c_0_47 ).
fof(c_0_755,axiom,
! [X11,X29,X18] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(X11),X29)),hAPP_nat_nat(plus_plus_nat(X11),X18)))
<=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X29),X18)) ),
c_0_48 ).
fof(c_0_756,axiom,
! [X168,X169,X170] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(plus_plus_int(X168),X169)),hAPP_int_int(plus_plus_int(X168),X170)))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X169),X170)) ),
c_0_49 ).
fof(c_0_757,axiom,
! [X168,X169,X170] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(X168),X169)),hAPP_nat_nat(plus_plus_nat(X168),X170)))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X169),X170)) ),
c_0_50 ).
fof(c_0_758,axiom,
! [X168,X169,X170] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(plus_plus_real(X168),X169)),hAPP_real_real(plus_plus_real(X168),X170)))
=> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X169),X170)) ),
c_0_51 ).
fof(c_0_759,axiom,
! [X165,X166,X167] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(plus_plus_int(X165),X166)),hAPP_int_int(plus_plus_int(X167),X166)))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X165),X167)) ),
c_0_52 ).
fof(c_0_760,axiom,
! [X165,X166,X167] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(X165),X166)),hAPP_nat_nat(plus_plus_nat(X167),X166)))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X165),X167)) ),
c_0_53 ).
fof(c_0_761,axiom,
! [X165,X166,X167] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(plus_plus_real(X165),X166)),hAPP_real_real(plus_plus_real(X167),X166)))
=> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X165),X167)) ),
c_0_54 ).
fof(c_0_762,axiom,
! [X106,X5,X81] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(plus_plus_int(X106),X5)),hAPP_int_int(plus_plus_int(X106),X81)))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X5),X81)) ),
c_0_55 ).
fof(c_0_763,axiom,
! [X106,X5,X81] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(X106),X5)),hAPP_nat_nat(plus_plus_nat(X106),X81)))
<=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X5),X81)) ),
c_0_56 ).
fof(c_0_764,axiom,
! [X106,X5,X81] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(plus_plus_real(X106),X5)),hAPP_real_real(plus_plus_real(X106),X81)))
<=> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X5),X81)) ),
c_0_57 ).
fof(c_0_765,axiom,
! [X5,X106,X81] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(plus_plus_int(X5),X106)),hAPP_int_int(plus_plus_int(X81),X106)))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X5),X81)) ),
c_0_58 ).
fof(c_0_766,axiom,
! [X5,X106,X81] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(X5),X106)),hAPP_nat_nat(plus_plus_nat(X81),X106)))
<=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X5),X81)) ),
c_0_59 ).
fof(c_0_767,axiom,
! [X5,X106,X81] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(plus_plus_real(X5),X106)),hAPP_real_real(plus_plus_real(X81),X106)))
<=> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X5),X81)) ),
c_0_60 ).
fof(c_0_768,axiom,
! [X5,X106,X81] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(X5),X106)),hAPP_int_int(plus_plus_int(X81),X106)))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X5),X81)) ),
c_0_61 ).
fof(c_0_769,axiom,
! [X5,X106,X81] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(X5),X106)),hAPP_nat_nat(plus_plus_nat(X81),X106)))
<=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X5),X81)) ),
c_0_62 ).
fof(c_0_770,axiom,
! [X5,X106,X81] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(plus_plus_real(X5),X106)),hAPP_real_real(plus_plus_real(X81),X106)))
<=> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X5),X81)) ),
c_0_63 ).
fof(c_0_771,axiom,
! [X106,X5,X81] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(X106),X5)),hAPP_int_int(plus_plus_int(X106),X81)))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X5),X81)) ),
c_0_64 ).
fof(c_0_772,axiom,
! [X106,X5,X81] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(X106),X5)),hAPP_nat_nat(plus_plus_nat(X106),X81)))
<=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X5),X81)) ),
c_0_65 ).
fof(c_0_773,axiom,
! [X106,X5,X81] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(plus_plus_real(X106),X5)),hAPP_real_real(plus_plus_real(X106),X81)))
<=> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X5),X81)) ),
c_0_66 ).
fof(c_0_774,axiom,
! [X133,X134,X135] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(X133),X134)),hAPP_int_int(plus_plus_int(X135),X134)))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X133),X135)) ),
c_0_67 ).
fof(c_0_775,axiom,
! [X133,X134,X135] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(X133),X134)),hAPP_nat_nat(plus_plus_nat(X135),X134)))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X133),X135)) ),
c_0_68 ).
fof(c_0_776,axiom,
! [X133,X134,X135] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(plus_plus_real(X133),X134)),hAPP_real_real(plus_plus_real(X135),X134)))
=> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X133),X135)) ),
c_0_69 ).
fof(c_0_777,axiom,
! [X130,X131,X132] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(X130),X131)),hAPP_int_int(plus_plus_int(X130),X132)))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X131),X132)) ),
c_0_70 ).
fof(c_0_778,axiom,
! [X130,X131,X132] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(X130),X131)),hAPP_nat_nat(plus_plus_nat(X130),X132)))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X131),X132)) ),
c_0_71 ).
fof(c_0_779,axiom,
! [X130,X131,X132] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(plus_plus_real(X130),X131)),hAPP_real_real(plus_plus_real(X130),X132)))
=> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X131),X132)) ),
c_0_72 ).
fof(c_0_780,axiom,
! [X11,X29,X18] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(X11),X29)),hAPP_nat_nat(plus_plus_nat(X11),X18)))
<=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X29),X18)) ),
c_0_73 ).
fof(c_0_781,axiom,
! [X21,X31,X22,X23] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X22),X23))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X21),X31))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(X22),X21)),hAPP_nat_nat(plus_plus_nat(X23),X31))) ) ),
c_0_74 ).
fof(c_0_782,axiom,
! [X207,X17,X208,X14] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X208),X14))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X207),X17))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(X208),X207)),hAPP_int_int(plus_plus_int(X14),X17))) ) ),
c_0_75 ).
fof(c_0_783,axiom,
! [X194,X195,X196,X197] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X196),X197))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X194),X195))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(X196),X194)),hAPP_int_int(plus_plus_int(X197),X195))) ) ),
c_0_76 ).
fof(c_0_784,axiom,
! [X194,X195,X196,X197] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X196),X197))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X194),X195))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(X196),X194)),hAPP_nat_nat(plus_plus_nat(X197),X195))) ) ),
c_0_77 ).
fof(c_0_785,axiom,
! [X194,X195,X196,X197] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X196),X197))
=> ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X194),X195))
=> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(plus_plus_real(X196),X194)),hAPP_real_real(plus_plus_real(X197),X195))) ) ),
c_0_78 ).
fof(c_0_786,axiom,
! [X190,X191,X192,X193] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X192),X193))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X190),X191))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(X192),X190)),hAPP_int_int(plus_plus_int(X193),X191))) ) ),
c_0_79 ).
fof(c_0_787,axiom,
! [X190,X191,X192,X193] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X192),X193))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X190),X191))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(X192),X190)),hAPP_nat_nat(plus_plus_nat(X193),X191))) ) ),
c_0_80 ).
fof(c_0_788,axiom,
! [X190,X191,X192,X193] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X192),X193))
=> ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X190),X191))
=> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(plus_plus_real(X192),X190)),hAPP_real_real(plus_plus_real(X193),X191))) ) ),
c_0_81 ).
fof(c_0_789,axiom,
! [X161,X162,X163,X164] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X163),X164))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X161),X162))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(plus_plus_int(X163),X161)),hAPP_int_int(plus_plus_int(X164),X162))) ) ),
c_0_82 ).
fof(c_0_790,axiom,
! [X161,X162,X163,X164] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X163),X164))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X161),X162))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(X163),X161)),hAPP_nat_nat(plus_plus_nat(X164),X162))) ) ),
c_0_83 ).
fof(c_0_791,axiom,
! [X161,X162,X163,X164] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X163),X164))
=> ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X161),X162))
=> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(plus_plus_real(X163),X161)),hAPP_real_real(plus_plus_real(X164),X162))) ) ),
c_0_84 ).
fof(c_0_792,axiom,
! [X136,X137,X138,X139] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X138),X139))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X136),X137))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(X138),X136)),hAPP_int_int(plus_plus_int(X139),X137))) ) ),
c_0_85 ).
fof(c_0_793,axiom,
! [X136,X137,X138,X139] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X138),X139))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X136),X137))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(X138),X136)),hAPP_nat_nat(plus_plus_nat(X139),X137))) ) ),
c_0_86 ).
fof(c_0_794,axiom,
! [X136,X137,X138,X139] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X138),X139))
=> ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X136),X137))
=> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(plus_plus_real(X138),X136)),hAPP_real_real(plus_plus_real(X139),X137))) ) ),
c_0_87 ).
fof(c_0_795,axiom,
! [X21,X31,X22,X23] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X22),X23))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X21),X31))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(X22),X21)),hAPP_nat_nat(plus_plus_nat(X23),X31))) ) ),
c_0_88 ).
fof(c_0_796,axiom,
! [X200,X201,X202] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X201),X202))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X201))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_nat_int(power_power_int(X201),X200)),hAPP_nat_int(power_power_int(X202),X200))) ) ),
c_0_89 ).
fof(c_0_797,axiom,
! [X200,X201,X202] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X201),X202))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),X201))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(power_power_nat(X201),X200)),hAPP_nat_nat(power_power_nat(X202),X200))) ) ),
c_0_90 ).
fof(c_0_798,axiom,
! [X200,X201,X202] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X201),X202))
=> ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X201))
=> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_nat_real(power_power_real(X201),X200)),hAPP_nat_real(power_power_real(X202),X200))) ) ),
c_0_91 ).
fof(c_0_799,axiom,
! [X171,X172,X173] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X172),X173))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),X171))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_nat_int(power_power_int(X171),X172)),hAPP_nat_int(power_power_int(X171),X173))) ) ),
c_0_92 ).
fof(c_0_800,axiom,
! [X171,X172,X173] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X172),X173))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,one_one_nat),X171))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(power_power_nat(X171),X172)),hAPP_nat_nat(power_power_nat(X171),X173))) ) ),
c_0_93 ).
fof(c_0_801,axiom,
! [X171,X172,X173] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X172),X173))
=> ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,one_one_real),X171))
=> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_nat_real(power_power_real(X171),X172)),hAPP_nat_real(power_power_real(X171),X173))) ) ),
c_0_94 ).
fof(c_0_802,axiom,
! [X85,X86,X87] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X86),X87))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),X85))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_nat_int(power_power_int(X85),X86)),hAPP_nat_int(power_power_int(X85),X87))) ) ),
c_0_95 ).
fof(c_0_803,axiom,
! [X85,X86,X87] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X86),X87))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,one_one_nat),X85))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(power_power_nat(X85),X86)),hAPP_nat_nat(power_power_nat(X85),X87))) ) ),
c_0_96 ).
fof(c_0_804,axiom,
! [X85,X86,X87] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X86),X87))
=> ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,one_one_real),X85))
=> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_nat_real(power_power_real(X85),X86)),hAPP_nat_real(power_power_real(X85),X87))) ) ),
c_0_97 ).
fof(c_0_805,axiom,
! [X3,X4] :
( hAPP_real_real(plus_plus_real(hAPP_nat_real(power_power_real(X3),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_real(power_power_real(X4),number_number_of_nat(bit0(bit1(pls))))) = zero_zero_real
<=> ( X3 = zero_zero_real
& X4 = zero_zero_real ) ),
c_0_98 ).
fof(c_0_806,axiom,
! [X3,X4] :
( hAPP_real_real(plus_plus_real(hAPP_nat_real(power_power_real(X3),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_real(power_power_real(X4),number_number_of_nat(bit0(bit1(pls))))) = zero_zero_real
<=> ( X3 = zero_zero_real
& X4 = zero_zero_real ) ),
c_0_99 ).
fof(c_0_807,axiom,
! [X3,X4] :
( hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(X3),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_int(power_power_int(X4),number_number_of_nat(bit0(bit1(pls))))) = zero_zero_int
<=> ( X3 = zero_zero_int
& X4 = zero_zero_int ) ),
c_0_100 ).
fof(c_0_808,axiom,
! [X47] : hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_nat_real(semiri132038758t_real,X47)),hAPP_nat_real(power_power_real(number267125858f_real(bit0(bit1(pls)))),X47))),
c_0_101 ).
fof(c_0_809,axiom,
! [X47] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_nat_int(semiri1621563631at_int,X47)),hAPP_nat_int(power_power_int(number_number_of_int(bit0(bit1(pls)))),X47))),
c_0_102 ).
fof(c_0_810,axiom,
! [X54,X29,X18] :
( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X29),X18))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(X54,X18),X29)) )
=> ( ( X29 = X18
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(X54,X18),X29)) )
=> ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X18),X29))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(X54,X18),X29)) )
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(X54,X18),X29)) ) ) ),
c_0_103 ).
fof(c_0_811,axiom,
! [X223,X224] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X224),zero_zero_int))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X223),zero_zero_int))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(X224),X223)),zero_zero_int)) ) ),
c_0_104 ).
fof(c_0_812,axiom,
! [X223,X224] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X224),zero_zero_nat))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X223),zero_zero_nat))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(X224),X223)),zero_zero_nat)) ) ),
c_0_105 ).
fof(c_0_813,axiom,
! [X223,X224] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X224),zero_zero_real))
=> ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X223),zero_zero_real))
=> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(plus_plus_real(X224),X223)),zero_zero_real)) ) ),
c_0_106 ).
fof(c_0_814,axiom,
! [X221,X222] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X222),zero_zero_int))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X221),zero_zero_int))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(X222),X221)),zero_zero_int)) ) ),
c_0_107 ).
fof(c_0_815,axiom,
! [X221,X222] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X222),zero_zero_nat))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X221),zero_zero_nat))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(X222),X221)),zero_zero_nat)) ) ),
c_0_108 ).
fof(c_0_816,axiom,
! [X221,X222] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X222),zero_zero_real))
=> ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X221),zero_zero_real))
=> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(plus_plus_real(X222),X221)),zero_zero_real)) ) ),
c_0_109 ).
fof(c_0_817,axiom,
! [X188,X189] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X189),zero_zero_int))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X188),zero_zero_int))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(plus_plus_int(X189),X188)),zero_zero_int)) ) ),
c_0_110 ).
fof(c_0_818,axiom,
! [X188,X189] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X189),zero_zero_nat))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X188),zero_zero_nat))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(X189),X188)),zero_zero_nat)) ) ),
c_0_111 ).
fof(c_0_819,axiom,
! [X188,X189] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X189),zero_zero_real))
=> ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X188),zero_zero_real))
=> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(plus_plus_real(X189),X188)),zero_zero_real)) ) ),
c_0_112 ).
fof(c_0_820,axiom,
! [X147,X148] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X148),zero_zero_int))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X147),zero_zero_int))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(X148),X147)),zero_zero_int)) ) ),
c_0_113 ).
fof(c_0_821,axiom,
! [X147,X148] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X148),zero_zero_nat))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X147),zero_zero_nat))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(X148),X147)),zero_zero_nat)) ) ),
c_0_114 ).
fof(c_0_822,axiom,
! [X147,X148] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X148),zero_zero_real))
=> ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X147),zero_zero_real))
=> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(plus_plus_real(X148),X147)),zero_zero_real)) ) ),
c_0_115 ).
fof(c_0_823,plain,
! [X15,X21,X16] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(X15),X21)),X16))
=> ~ ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X15),X16))
=> ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X21),X16)) ) ),
inference(fof_simplification,[status(thm)],[c_0_116]) ).
fof(c_0_824,axiom,
! [X15,X21,X16] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(X15),X21)),X16))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X15),X16)) ),
c_0_117 ).
fof(c_0_825,axiom,
! [X15,X21,X16] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(X15),X21)),X16))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X21),X16)) ),
c_0_118 ).
fof(c_0_826,axiom,
! [X22,X23,X21] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(X22),X23)),X21))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X22),X21)) ),
c_0_119 ).
fof(c_0_827,axiom,
! [X5] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(plus_plus_int(X5),X5)),zero_zero_int))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X5),zero_zero_int)) ),
c_0_120 ).
fof(c_0_828,axiom,
! [X5] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(plus_plus_real(X5),X5)),zero_zero_real))
<=> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X5),zero_zero_real)) ),
c_0_121 ).
fof(c_0_829,axiom,
! [X5] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(X5),X5)),zero_zero_int))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X5),zero_zero_int)) ),
c_0_122 ).
fof(c_0_830,axiom,
! [X5] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(plus_plus_real(X5),X5)),zero_zero_real))
<=> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X5),zero_zero_real)) ),
c_0_123 ).
fof(c_0_831,axiom,
! [X5] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(plus_plus_real(X5),X5)),zero_zero_real))
<=> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X5),zero_zero_real)) ),
c_0_124 ).
fof(c_0_832,axiom,
! [X5] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(X5),X5)),zero_zero_int))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X5),zero_zero_int)) ),
c_0_125 ).
fof(c_0_833,axiom,
! [X17,X8,X10] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X8),X10))
=> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(plus_plus_real(X17),X8)),hAPP_real_real(plus_plus_real(X17),X10))) ),
c_0_126 ).
fof(c_0_834,axiom,
! [X21,X22,X23] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X22),X23))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(X22),X21)),hAPP_nat_nat(plus_plus_nat(X23),X21))) ),
c_0_127 ).
fof(c_0_835,axiom,
! [X21,X22,X23] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X22),X23))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(plus_plus_int(X21),X22)),hAPP_int_int(plus_plus_int(X21),X23))) ),
c_0_128 ).
fof(c_0_836,axiom,
! [X158,X159,X160] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X159),X160))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(plus_plus_int(X158),X159)),hAPP_int_int(plus_plus_int(X158),X160))) ),
c_0_129 ).
fof(c_0_837,axiom,
! [X158,X159,X160] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X159),X160))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(X158),X159)),hAPP_nat_nat(plus_plus_nat(X158),X160))) ),
c_0_130 ).
fof(c_0_838,axiom,
! [X158,X159,X160] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X159),X160))
=> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(plus_plus_real(X158),X159)),hAPP_real_real(plus_plus_real(X158),X160))) ),
c_0_131 ).
fof(c_0_839,axiom,
! [X155,X156,X157] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X156),X157))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(plus_plus_int(X156),X155)),hAPP_int_int(plus_plus_int(X157),X155))) ),
c_0_132 ).
fof(c_0_840,axiom,
! [X155,X156,X157] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X156),X157))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(X156),X155)),hAPP_nat_nat(plus_plus_nat(X157),X155))) ),
c_0_133 ).
fof(c_0_841,axiom,
! [X155,X156,X157] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X156),X157))
=> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(plus_plus_real(X156),X155)),hAPP_real_real(plus_plus_real(X157),X155))) ),
c_0_134 ).
fof(c_0_842,axiom,
! [X143,X144,X145] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X144),X145))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(X144),X143)),hAPP_int_int(plus_plus_int(X145),X143))) ),
c_0_135 ).
fof(c_0_843,axiom,
! [X143,X144,X145] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X144),X145))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(X144),X143)),hAPP_nat_nat(plus_plus_nat(X145),X143))) ),
c_0_136 ).
fof(c_0_844,axiom,
! [X143,X144,X145] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X144),X145))
=> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(plus_plus_real(X144),X143)),hAPP_real_real(plus_plus_real(X145),X143))) ),
c_0_137 ).
fof(c_0_845,axiom,
! [X140,X141,X142] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X141),X142))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(X140),X141)),hAPP_int_int(plus_plus_int(X140),X142))) ),
c_0_138 ).
fof(c_0_846,axiom,
! [X140,X141,X142] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X141),X142))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(X140),X141)),hAPP_nat_nat(plus_plus_nat(X140),X142))) ),
c_0_139 ).
fof(c_0_847,axiom,
! [X140,X141,X142] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X141),X142))
=> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(plus_plus_real(X140),X141)),hAPP_real_real(plus_plus_real(X140),X142))) ),
c_0_140 ).
fof(c_0_848,axiom,
! [X21,X22,X23] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X22),X23))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(X22),X21)),hAPP_nat_nat(plus_plus_nat(X23),X21))) ),
c_0_141 ).
fof(c_0_849,axiom,
! [X21,X22,X23] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X22),X23))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(X22),X21)),hAPP_int_int(plus_plus_int(X23),X21))) ),
c_0_142 ).
fof(c_0_850,axiom,
! [X5] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),hAPP_nat_real(power_power_real(X5),number_number_of_nat(bit0(bit1(pls))))))
<=> X5 != zero_zero_real ),
c_0_143 ).
fof(c_0_851,axiom,
! [X5] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_nat_int(power_power_int(X5),number_number_of_nat(bit0(bit1(pls))))))
<=> X5 != zero_zero_int ),
c_0_144 ).
fof(c_0_852,axiom,
! [X25,X30] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(plus_plus_int(X25),one_one_int)),X30))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X25),X30)) ),
c_0_145 ).
fof(c_0_853,axiom,
! [X15,X16,X17] : hAPP_int_int(plus_plus_int(hAPP_nat_int(semiri1621563631at_int,X15)),hAPP_int_int(plus_plus_int(hAPP_nat_int(semiri1621563631at_int,X16)),X17)) = hAPP_int_int(plus_plus_int(hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(plus_plus_nat(X15),X16))),X17),
c_0_146 ).
fof(c_0_854,axiom,
! [X29,X18] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_nat_int(semiri1621563631at_int,X29)),hAPP_nat_int(semiri1621563631at_int,X18)))
<=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X29),X18)) ),
c_0_147 ).
fof(c_0_855,axiom,
! [X3,X4] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_nat_int(semiri1621563631at_int,X3)),hAPP_nat_int(semiri1621563631at_int,X4)))
<=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X3),X4)) ),
c_0_148 ).
fof(c_0_856,axiom,
! [X29,X18] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_nat_int(semiri1621563631at_int,X29)),hAPP_nat_int(semiri1621563631at_int,X18)))
<=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X29),X18)) ),
c_0_149 ).
fof(c_0_857,axiom,
! [X29,X18] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(semiri984289939at_nat,X29)),hAPP_nat_nat(semiri984289939at_nat,X18)))
<=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X29),X18)) ),
c_0_150 ).
fof(c_0_858,axiom,
! [X29,X18] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_nat_real(semiri132038758t_real,X29)),hAPP_nat_real(semiri132038758t_real,X18)))
<=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X29),X18)) ),
c_0_151 ).
fof(c_0_859,axiom,
! [X69,X70] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_nat_int(semiri1621563631at_int,X69)),hAPP_nat_int(semiri1621563631at_int,X70)))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X69),X70)) ),
c_0_152 ).
fof(c_0_860,axiom,
! [X69,X70] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(semiri984289939at_nat,X69)),hAPP_nat_nat(semiri984289939at_nat,X70)))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X69),X70)) ),
c_0_153 ).
fof(c_0_861,axiom,
! [X69,X70] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_nat_real(semiri132038758t_real,X69)),hAPP_nat_real(semiri132038758t_real,X70)))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X69),X70)) ),
c_0_154 ).
fof(c_0_862,axiom,
! [X29,X18] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_nat_int(semiri1621563631at_int,X29)),hAPP_nat_int(semiri1621563631at_int,X18)))
<=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X29),X18)) ),
c_0_155 ).
fof(c_0_863,axiom,
! [X29,X18] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(semiri984289939at_nat,X29)),hAPP_nat_nat(semiri984289939at_nat,X18)))
<=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X29),X18)) ),
c_0_156 ).
fof(c_0_864,axiom,
! [X29,X18] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_nat_real(semiri132038758t_real,X29)),hAPP_nat_real(semiri132038758t_real,X18)))
<=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X29),X18)) ),
c_0_157 ).
fof(c_0_865,axiom,
! [X29,X18] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_nat_int(semiri1621563631at_int,X29)),hAPP_nat_int(semiri1621563631at_int,X18)))
<=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X29),X18)) ),
c_0_158 ).
fof(c_0_866,axiom,
! [X3,X4] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_nat_int(semiri1621563631at_int,X3)),hAPP_nat_int(semiri1621563631at_int,X4)))
<=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X3),X4)) ),
c_0_159 ).
fof(c_0_867,axiom,
! [X279,X280] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X280))
=> ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X279))
=> ? [X281] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X281))
& hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X281),X280))
& hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X281),X279)) ) ) ),
c_0_160 ).
fof(c_0_868,axiom,
! [X228,X229,X230] :
( hAPP_nat_int(power_power_int(X228),X229) = hAPP_nat_int(power_power_int(X230),X229)
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X228))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X230))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X229))
=> X228 = X230 ) ) ) ),
c_0_161 ).
fof(c_0_869,axiom,
! [X228,X229,X230] :
( hAPP_nat_nat(power_power_nat(X228),X229) = hAPP_nat_nat(power_power_nat(X230),X229)
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),X228))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),X230))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X229))
=> X228 = X230 ) ) ) ),
c_0_162 ).
fof(c_0_870,axiom,
! [X228,X229,X230] :
( hAPP_nat_real(power_power_real(X228),X229) = hAPP_nat_real(power_power_real(X230),X229)
=> ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X228))
=> ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X230))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X229))
=> X228 = X230 ) ) ) ),
c_0_163 ).
fof(c_0_871,axiom,
! [X16] : hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,one_one_real),hAPP_nat_real(power_power_real(number267125858f_real(bit0(bit1(pls)))),X16))),
c_0_164 ).
fof(c_0_872,plain,
! [X18,X54] :
( ~ hBOOL(hAPP_nat_bool(X54,zero_zero_nat))
=> ( hBOOL(hAPP_nat_bool(X54,X18))
=> ? [X91] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X91),X18))
& ! [X56] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X56),X91))
=> ~ hBOOL(hAPP_nat_bool(X54,X56)) )
& hBOOL(hAPP_nat_bool(X54,hAPP_nat_nat(plus_plus_nat(X91),one_one_nat))) ) ) ),
inference(fof_simplification,[status(thm)],[c_0_165]) ).
fof(c_0_873,axiom,
! [X218,X219,X220] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X220))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X218),X219))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X218),hAPP_int_int(plus_plus_int(X220),X219))) ) ),
c_0_166 ).
fof(c_0_874,axiom,
! [X218,X219,X220] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),X220))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X218),X219))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X218),hAPP_nat_nat(plus_plus_nat(X220),X219))) ) ),
c_0_167 ).
fof(c_0_875,axiom,
! [X218,X219,X220] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X220))
=> ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X218),X219))
=> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X218),hAPP_real_real(plus_plus_real(X220),X219))) ) ),
c_0_168 ).
fof(c_0_876,axiom,
! [X215,X216,X217] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X217))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X215),X216))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X215),hAPP_int_int(plus_plus_int(X217),X216))) ) ),
c_0_169 ).
fof(c_0_877,axiom,
! [X215,X216,X217] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X217))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X215),X216))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X215),hAPP_nat_nat(plus_plus_nat(X217),X216))) ) ),
c_0_170 ).
fof(c_0_878,axiom,
! [X215,X216,X217] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X217))
=> ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X215),X216))
=> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X215),hAPP_real_real(plus_plus_real(X217),X216))) ) ),
c_0_171 ).
fof(c_0_879,axiom,
! [X185,X186,X187] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X187))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X185),X186))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X185),hAPP_int_int(plus_plus_int(X186),X187))) ) ),
c_0_172 ).
fof(c_0_880,axiom,
! [X185,X186,X187] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),X187))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X185),X186))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X185),hAPP_nat_nat(plus_plus_nat(X186),X187))) ) ),
c_0_173 ).
fof(c_0_881,axiom,
! [X185,X186,X187] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X187))
=> ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X185),X186))
=> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X185),hAPP_real_real(plus_plus_real(X186),X187))) ) ),
c_0_174 ).
fof(c_0_882,axiom,
! [X182,X183,X184] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X184))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X182),X183))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X182),hAPP_int_int(plus_plus_int(X184),X183))) ) ),
c_0_175 ).
fof(c_0_883,axiom,
! [X182,X183,X184] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),X184))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X182),X183))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X182),hAPP_nat_nat(plus_plus_nat(X184),X183))) ) ),
c_0_176 ).
fof(c_0_884,axiom,
! [X182,X183,X184] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X184))
=> ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X182),X183))
=> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X182),hAPP_real_real(plus_plus_real(X184),X183))) ) ),
c_0_177 ).
fof(c_0_885,axiom,
! [X75,X76,X77] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X77))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X75),X76))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X75),hAPP_int_int(plus_plus_int(X77),X76))) ) ),
c_0_178 ).
fof(c_0_886,axiom,
! [X75,X76,X77] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X77))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X75),X76))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X75),hAPP_nat_nat(plus_plus_nat(X77),X76))) ) ),
c_0_179 ).
fof(c_0_887,axiom,
! [X75,X76,X77] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X77))
=> ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X75),X76))
=> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X75),hAPP_real_real(plus_plus_real(X77),X76))) ) ),
c_0_180 ).
fof(c_0_888,axiom,
! [X240,X241] :
( hAPP_nat_int(power_power_int(X240),number_number_of_nat(bit0(bit1(pls)))) = hAPP_nat_int(power_power_int(X241),number_number_of_nat(bit0(bit1(pls))))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X240))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X241))
=> X240 = X241 ) ) ),
c_0_181 ).
fof(c_0_889,axiom,
! [X240,X241] :
( hAPP_nat_nat(power_power_nat(X240),number_number_of_nat(bit0(bit1(pls)))) = hAPP_nat_nat(power_power_nat(X241),number_number_of_nat(bit0(bit1(pls))))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),X240))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),X241))
=> X240 = X241 ) ) ),
c_0_182 ).
fof(c_0_890,axiom,
! [X240,X241] :
( hAPP_nat_real(power_power_real(X240),number_number_of_nat(bit0(bit1(pls)))) = hAPP_nat_real(power_power_real(X241),number_number_of_nat(bit0(bit1(pls))))
=> ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X240))
=> ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X241))
=> X240 = X241 ) ) ),
c_0_183 ).
fof(c_0_891,axiom,
! [X151,X16] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X16))
=> ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X151))
=> ? [X152] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X152))
& hAPP_nat_real(power_power_real(X152),X16) = X151
& ! [X153] :
( ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X153))
& hAPP_nat_real(power_power_real(X153),X16) = X151 )
=> X153 = X152 ) ) ) ),
c_0_184 ).
fof(c_0_892,axiom,
! [X29,X18] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(plus_plus_nat(X29),X18)))
<=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X29))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X18)) ) ),
c_0_185 ).
fof(c_0_893,axiom,
! [X59,X60] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,number_number_of_nat(X59)),number_number_of_nat(X60)))
<=> ( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X59),X60))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),X60)) )
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X59),X60)) ) ),
c_0_186 ).
fof(c_0_894,axiom,
! [X213,X214] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X214))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X213))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_int_int(plus_plus_int(X214),X213))) ) ),
c_0_187 ).
fof(c_0_895,axiom,
! [X213,X214] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),X214))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X213))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(plus_plus_nat(X214),X213))) ) ),
c_0_188 ).
fof(c_0_896,axiom,
! [X213,X214] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X214))
=> ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X213))
=> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),hAPP_real_real(plus_plus_real(X214),X213))) ) ),
c_0_189 ).
fof(c_0_897,axiom,
! [X211,X212] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X212))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X211))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_int_int(plus_plus_int(X212),X211))) ) ),
c_0_190 ).
fof(c_0_898,axiom,
! [X211,X212] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X212))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),X211))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(plus_plus_nat(X212),X211))) ) ),
c_0_191 ).
fof(c_0_899,axiom,
! [X211,X212] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X212))
=> ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X211))
=> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),hAPP_real_real(plus_plus_real(X212),X211))) ) ),
c_0_192 ).
fof(c_0_900,axiom,
! [X10,X8] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X8))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X10))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_int_int(plus_plus_int(X8),X10))) ) ),
c_0_193 ).
fof(c_0_901,axiom,
! [X180,X181] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X181))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X180))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_int_int(plus_plus_int(X181),X180))) ) ),
c_0_194 ).
fof(c_0_902,axiom,
! [X180,X181] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),X181))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),X180))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),hAPP_nat_nat(plus_plus_nat(X181),X180))) ) ),
c_0_195 ).
fof(c_0_903,axiom,
! [X180,X181] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X181))
=> ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X180))
=> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),hAPP_real_real(plus_plus_real(X181),X180))) ) ),
c_0_196 ).
fof(c_0_904,axiom,
! [X149,X150] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X150))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X149))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_int_int(plus_plus_int(X150),X149))) ) ),
c_0_197 ).
fof(c_0_905,axiom,
! [X149,X150] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X150))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X149))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(plus_plus_nat(X150),X149))) ) ),
c_0_198 ).
fof(c_0_906,axiom,
! [X149,X150] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X150))
=> ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X149))
=> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),hAPP_real_real(plus_plus_real(X150),X149))) ) ),
c_0_199 ).
fof(c_0_907,axiom,
! [X48,X49] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,one_one_real),X49))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X48))
=> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,one_one_real),hAPP_nat_real(power_power_real(X49),X48))) ) ),
c_0_200 ).
fof(c_0_908,axiom,
! [X48,X49] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,one_one_nat),X49))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X48))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,one_one_nat),hAPP_nat_nat(power_power_nat(X49),X48))) ) ),
c_0_201 ).
fof(c_0_909,axiom,
! [X48,X49] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),X49))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X48))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),hAPP_nat_int(power_power_int(X49),X48))) ) ),
c_0_202 ).
fof(c_0_910,plain,
! [X23,X22] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(X23),X22)),X22)),
inference(fof_simplification,[status(thm)],[c_0_203]) ).
fof(c_0_911,plain,
! [X22,X23] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(X22),X23)),X22)),
inference(fof_simplification,[status(thm)],[c_0_204]) ).
fof(c_0_912,plain,
! [X59,X25] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,number_number_of_int(X59)),number_number_of_int(X25)))
<=> ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(X25)),number_number_of_int(X59))) ),
inference(fof_simplification,[status(thm)],[c_0_205]) ).
fof(c_0_913,plain,
! [X59,X25] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,number_number_of_nat(X59)),number_number_of_nat(X25)))
<=> ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,number_number_of_nat(X25)),number_number_of_nat(X59))) ),
inference(fof_simplification,[status(thm)],[c_0_206]) ).
fof(c_0_914,plain,
! [X59,X25] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,number267125858f_real(X59)),number267125858f_real(X25)))
<=> ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,number267125858f_real(X25)),number267125858f_real(X59))) ),
inference(fof_simplification,[status(thm)],[c_0_207]) ).
fof(c_0_915,axiom,
! [X3,X25] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(power_power_nat(X3),number_number_of_nat(X25))))
<=> ( number_number_of_nat(X25) = zero_zero_nat
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X3)) ) ),
c_0_208 ).
fof(c_0_916,axiom,
! [X151,X16] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X16))
=> ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X151))
=> ? [X154] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X154))
& hAPP_nat_real(power_power_real(X154),X16) = X151 ) ) ),
c_0_209 ).
fof(c_0_917,axiom,
! [X14,X17] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X14),X17))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(plus_plus_int(X14),one_one_int)),X17)) ),
c_0_210 ).
fof(c_0_918,axiom,
! [X8] : hAPP_nat_int(power_power_int(hAPP_nat_int(power_power_int(X8),number_number_of_nat(bit0(bit1(pls))))),number_number_of_nat(bit0(bit1(pls)))) = hAPP_nat_int(power_power_int(X8),number_number_of_nat(bit0(bit0(bit1(pls))))),
c_0_211 ).
fof(c_0_919,axiom,
! [X67,X68] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X67),X68))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_nat_int(semiri1621563631at_int,X67)),hAPP_nat_int(semiri1621563631at_int,X68))) ),
c_0_212 ).
fof(c_0_920,axiom,
! [X67,X68] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X67),X68))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(semiri984289939at_nat,X67)),hAPP_nat_nat(semiri984289939at_nat,X68))) ),
c_0_213 ).
fof(c_0_921,axiom,
! [X67,X68] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X67),X68))
=> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_nat_real(semiri132038758t_real,X67)),hAPP_nat_real(semiri132038758t_real,X68))) ),
c_0_214 ).
fof(c_0_922,axiom,
! [X8] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X8))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X8),number_number_of_int(bit0(bit1(pls)))))
=> ( X8 = zero_zero_int
| X8 = one_one_int ) ) ),
c_0_215 ).
fof(c_0_923,plain,
! [X59,X60] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,number_number_of_nat(X59)),number_number_of_nat(X60)))
<=> ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X59),X60))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X59),pls)) ) ),
inference(fof_simplification,[status(thm)],[c_0_216]) ).
fof(c_0_924,plain,
! [X18,X54] :
( ~ hBOOL(hAPP_nat_bool(X54,zero_zero_nat))
=> ( hBOOL(hAPP_nat_bool(X54,X18))
=> ? [X91] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X91),X18))
& ! [X56] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X56),X91))
=> ~ hBOOL(hAPP_nat_bool(X54,X56)) )
& hBOOL(hAPP_nat_bool(X54,X91)) ) ) ),
inference(fof_simplification,[status(thm)],[c_0_217]) ).
fof(c_0_925,axiom,
! [X260,X261,X262] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X261),X262))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X262),X260))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X261),X260)) ) ),
c_0_218 ).
fof(c_0_926,axiom,
! [X260,X261,X262] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X261),X262))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X262),X260))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X261),X260)) ) ),
c_0_219 ).
fof(c_0_927,axiom,
! [X260,X261,X262] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X261),X262))
=> ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X262),X260))
=> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X261),X260)) ) ),
c_0_220 ).
fof(c_0_928,axiom,
! [X255,X256,X257] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X256),X257))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X255),X256))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X255),X257)) ) ),
c_0_221 ).
fof(c_0_929,axiom,
! [X255,X256,X257] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X256),X257))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X255),X256))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X255),X257)) ) ),
c_0_222 ).
fof(c_0_930,axiom,
! [X255,X256,X257] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X256),X257))
=> ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X255),X256))
=> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X255),X257)) ) ),
c_0_223 ).
fof(c_0_931,axiom,
! [X21,X22,X23] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X22),X23))
=> ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X23),X21))
=> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X22),X21)) ) ),
c_0_224 ).
fof(c_0_932,axiom,
! [X21,X22,X23] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X22),X23))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X23),X21))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X22),X21)) ) ),
c_0_225 ).
fof(c_0_933,axiom,
! [X21,X22,X23] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X22),X23))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X23),X21))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X22),X21)) ) ),
c_0_226 ).
fof(c_0_934,axiom,
! [X25,X30] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X25),hAPP_int_int(plus_plus_int(X30),one_one_int)))
<=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X25),X30))
| X25 = X30 ) ),
c_0_227 ).
fof(c_0_935,axiom,
! [X25,X30] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X25),hAPP_int_int(plus_plus_int(X30),one_one_int)))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X25),X30)) ),
c_0_228 ).
fof(c_0_936,axiom,
! [X3,X18] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(power_power_nat(X3),X18)))
<=> ( X18 = zero_zero_nat
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X3)) ) ),
c_0_229 ).
fof(c_0_937,axiom,
! [X3,X18] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(power_power_nat(X3),X18)))
<=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X3))
| X18 = zero_zero_nat ) ),
c_0_230 ).
fof(c_0_938,axiom,
! [X231,X232] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X232))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X231))
=> hAPP_int_int(plus_plus_int(number_number_of_int(X232)),number_number_of_int(X231)) = number_number_of_int(hAPP_int_int(plus_plus_int(X232),X231)) ) ),
c_0_231 ).
fof(c_0_939,axiom,
! [X231,X232] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X232))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X231))
=> hAPP_nat_nat(plus_plus_nat(number_number_of_nat(X232)),number_number_of_nat(X231)) = number_number_of_nat(hAPP_int_int(plus_plus_int(X232),X231)) ) ),
c_0_232 ).
fof(c_0_940,axiom,
! [X231,X232] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X232))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X231))
=> hAPP_real_real(plus_plus_real(number267125858f_real(X232)),number267125858f_real(X231)) = number267125858f_real(hAPP_int_int(plus_plus_int(X232),X231)) ) ),
c_0_233 ).
fof(c_0_941,axiom,
! [X5] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_int_int(plus_plus_int(X5),X5)))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X5)) ),
c_0_234 ).
fof(c_0_942,axiom,
! [X5] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),hAPP_real_real(plus_plus_real(X5),X5)))
<=> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X5)) ),
c_0_235 ).
fof(c_0_943,axiom,
! [X5] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_int_int(plus_plus_int(X5),X5)))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X5)) ),
c_0_236 ).
fof(c_0_944,axiom,
! [X5] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),hAPP_real_real(plus_plus_real(X5),X5)))
<=> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X5)) ),
c_0_237 ).
fof(c_0_945,axiom,
! [X54] :
( ! [X152] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X152))
=> hBOOL(hAPP_int_bool(X54,X152)) )
<=> ! [X152] : hBOOL(hAPP_int_bool(X54,hAPP_nat_int(semiri1621563631at_int,X152))) ),
c_0_238 ).
fof(c_0_946,axiom,
! [X34,X35,X36] : hAPP_real_real(plus_plus_real(number267125858f_real(X34)),hAPP_real_real(plus_plus_real(number267125858f_real(X35)),X36)) = hAPP_real_real(plus_plus_real(number267125858f_real(hAPP_int_int(plus_plus_int(X34),X35))),X36),
c_0_239 ).
fof(c_0_947,axiom,
! [X34,X35,X36] : hAPP_int_int(plus_plus_int(number_number_of_int(X34)),hAPP_int_int(plus_plus_int(number_number_of_int(X35)),X36)) = hAPP_int_int(plus_plus_int(number_number_of_int(hAPP_int_int(plus_plus_int(X34),X35))),X36),
c_0_240 ).
fof(c_0_948,axiom,
! [X8] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X8),hAPP_nat_int(power_power_int(X8),number_number_of_nat(bit0(bit1(pls)))))),
c_0_241 ).
fof(c_0_949,axiom,
! [X15,X22,X23] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X22),X23))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X22),hAPP_nat_nat(plus_plus_nat(X15),X23))) ),
c_0_242 ).
fof(c_0_950,axiom,
! [X15,X22,X23] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X22),X23))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X22),hAPP_nat_nat(plus_plus_nat(X23),X15))) ),
c_0_243 ).
fof(c_0_951,axiom,
! [X15,X22,X23] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X22),X23))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X22),hAPP_nat_nat(plus_plus_nat(X15),X23))) ),
c_0_244 ).
fof(c_0_952,axiom,
! [X15,X22,X23] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X22),X23))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X22),hAPP_nat_nat(plus_plus_nat(X23),X15))) ),
c_0_245 ).
fof(c_0_953,axiom,
! [X102,X103,X104,X105] : hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(X102),X103)),hAPP_int_int(plus_plus_int(X104),X105)) = hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(X102),X104)),hAPP_int_int(plus_plus_int(X103),X105)),
c_0_246 ).
fof(c_0_954,axiom,
! [X102,X103,X104,X105] : hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(plus_plus_nat(X102),X103)),hAPP_nat_nat(plus_plus_nat(X104),X105)) = hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(plus_plus_nat(X102),X104)),hAPP_nat_nat(plus_plus_nat(X103),X105)),
c_0_247 ).
fof(c_0_955,axiom,
! [X102,X103,X104,X105] : hAPP_real_real(plus_plus_real(hAPP_real_real(plus_plus_real(X102),X103)),hAPP_real_real(plus_plus_real(X104),X105)) = hAPP_real_real(plus_plus_real(hAPP_real_real(plus_plus_real(X102),X104)),hAPP_real_real(plus_plus_real(X103),X105)),
c_0_248 ).
fof(c_0_956,axiom,
! [X237] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_nat_int(power_power_int(X237),number_number_of_nat(bit0(bit1(pls)))))),
c_0_249 ).
fof(c_0_957,axiom,
! [X237] : hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),hAPP_nat_real(power_power_real(X237),number_number_of_nat(bit0(bit1(pls)))))),
c_0_250 ).
fof(c_0_958,axiom,
! [X18] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_nat_int(semiri1621563631at_int,X18)),zero_zero_int))
<=> X18 = zero_zero_nat ),
c_0_251 ).
fof(c_0_959,axiom,
! [X15,X16,X21,X31] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X21),X31))
=> ( hAPP_nat_nat(plus_plus_nat(X15),X31) = hAPP_nat_nat(plus_plus_nat(X21),X16)
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X15),X16)) ) ),
c_0_252 ).
fof(c_0_960,axiom,
! [X54] :
( ? [X152] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X152))
& hBOOL(hAPP_int_bool(X54,X152)) )
<=> ? [X152] : hBOOL(hAPP_int_bool(X54,hAPP_nat_int(semiri1621563631at_int,X152))) ),
c_0_253 ).
fof(c_0_961,plain,
! [X88] : ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_nat_int(semiri1621563631at_int,X88)),zero_zero_int)),
inference(fof_simplification,[status(thm)],[c_0_254]) ).
fof(c_0_962,plain,
! [X88] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(semiri984289939at_nat,X88)),zero_zero_nat)),
inference(fof_simplification,[status(thm)],[c_0_255]) ).
fof(c_0_963,plain,
! [X88] : ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_nat_real(semiri132038758t_real,X88)),zero_zero_real)),
inference(fof_simplification,[status(thm)],[c_0_256]) ).
fof(c_0_964,plain,
! [X21] : ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_nat_int(semiri1621563631at_int,X21)),zero_zero_int)),
inference(fof_simplification,[status(thm)],[c_0_257]) ).
fof(c_0_965,axiom,
! [X247,X54,X3] :
( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X3))
=> ( hBOOL(X54)
<=> hBOOL(X247) ) )
=> ( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X3))
& hBOOL(X54) )
<=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X3))
& hBOOL(X247) ) ) ),
c_0_258 ).
fof(c_0_966,axiom,
! [X16,X8] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X8))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_nat_int(power_power_int(X8),X16))) ),
c_0_259 ).
fof(c_0_967,axiom,
! [X203,X204] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),X204))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),hAPP_nat_int(power_power_int(X204),X203))) ),
c_0_260 ).
fof(c_0_968,axiom,
! [X203,X204] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,one_one_nat),X204))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,one_one_nat),hAPP_nat_nat(power_power_nat(X204),X203))) ),
c_0_261 ).
fof(c_0_969,axiom,
! [X203,X204] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,one_one_real),X204))
=> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,one_one_real),hAPP_nat_real(power_power_real(X204),X203))) ),
c_0_262 ).
fof(c_0_970,axiom,
! [X198,X199] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X199))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_nat_int(power_power_int(X199),X198))) ),
c_0_263 ).
fof(c_0_971,axiom,
! [X198,X199] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),X199))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),hAPP_nat_nat(power_power_nat(X199),X198))) ),
c_0_264 ).
fof(c_0_972,axiom,
! [X198,X199] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X199))
=> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),hAPP_nat_real(power_power_real(X199),X198))) ),
c_0_265 ).
fof(c_0_973,axiom,
! [X78,X79] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X79))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_nat_int(power_power_int(X79),X78))) ),
c_0_266 ).
fof(c_0_974,axiom,
! [X78,X79] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X79))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(power_power_nat(X79),X78))) ),
c_0_267 ).
fof(c_0_975,axiom,
! [X78,X79] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X79))
=> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),hAPP_nat_real(power_power_real(X79),X78))) ),
c_0_268 ).
fof(c_0_976,axiom,
! [X247,X54,X3] :
( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X3))
=> ( hBOOL(X54)
<=> hBOOL(X247) ) )
=> ( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X3))
=> hBOOL(X54) )
<=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X3))
=> hBOOL(X247) ) ) ),
c_0_269 ).
fof(c_0_977,axiom,
! [X4,X3] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X3))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X4))
=> ( hAPP_int_int(plus_plus_int(X3),X4) = zero_zero_int
<=> ( X3 = zero_zero_int
& X4 = zero_zero_int ) ) ) ),
c_0_270 ).
fof(c_0_978,axiom,
! [X4,X3] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),X3))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),X4))
=> ( hAPP_nat_nat(plus_plus_nat(X3),X4) = zero_zero_nat
<=> ( X3 = zero_zero_nat
& X4 = zero_zero_nat ) ) ) ),
c_0_271 ).
fof(c_0_979,axiom,
! [X4,X3] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X3))
=> ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X4))
=> ( hAPP_real_real(plus_plus_real(X3),X4) = zero_zero_real
<=> ( X3 = zero_zero_real
& X4 = zero_zero_real ) ) ) ),
c_0_272 ).
fof(c_0_980,axiom,
! [X19,X20] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,bit1(X19)),bit0(X20)))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X19),X20)) ),
c_0_273 ).
fof(c_0_981,axiom,
! [X11,X12] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,bit1(X11)),bit0(X12)))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X11),X12)) ),
c_0_274 ).
fof(c_0_982,axiom,
! [X19,X20] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit0(X19)),bit1(X20)))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X19),X20)) ),
c_0_275 ).
fof(c_0_983,axiom,
! [X11,X12] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit0(X11)),bit1(X12)))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X11),X12)) ),
c_0_276 ).
fof(c_0_984,axiom,
! [X19,X20] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,bit0(X19)),bit1(X20)))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X19),X20)) ),
c_0_277 ).
fof(c_0_985,axiom,
! [X11,X12] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,bit0(X11)),bit1(X12)))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X11),X12)) ),
c_0_278 ).
fof(c_0_986,axiom,
! [X11,X12] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,number_number_of_int(X11)),number_number_of_int(X12)))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X11),X12)) ),
c_0_279 ).
fof(c_0_987,axiom,
! [X3,X4] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,number_number_of_int(X3)),number_number_of_int(X4)))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X3),X4)) ),
c_0_280 ).
fof(c_0_988,axiom,
! [X3,X4] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,number267125858f_real(X3)),number267125858f_real(X4)))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X3),X4)) ),
c_0_281 ).
fof(c_0_989,axiom,
! [X11,X12] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,bit0(X11)),bit0(X12)))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X11),X12)) ),
c_0_282 ).
fof(c_0_990,axiom,
! [X19,X20] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,bit0(X19)),bit0(X20)))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X19),X20)) ),
c_0_283 ).
fof(c_0_991,axiom,
! [X11,X12] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,bit1(X11)),bit1(X12)))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X11),X12)) ),
c_0_284 ).
fof(c_0_992,axiom,
! [X19,X20] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,bit1(X19)),bit1(X20)))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X19),X20)) ),
c_0_285 ).
fof(c_0_993,axiom,
! [X11,X12] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit1(X11)),bit0(X12)))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X11),X12)) ),
c_0_286 ).
fof(c_0_994,axiom,
! [X19,X20] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit1(X19)),bit0(X20)))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X19),X20)) ),
c_0_287 ).
fof(c_0_995,axiom,
! [X11,X12] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit0(X11)),bit0(X12)))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X11),X12)) ),
c_0_288 ).
fof(c_0_996,axiom,
! [X19,X20] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit0(X19)),bit0(X20)))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X19),X20)) ),
c_0_289 ).
fof(c_0_997,axiom,
! [X11,X12] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit1(X11)),bit1(X12)))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X11),X12)) ),
c_0_290 ).
fof(c_0_998,axiom,
! [X19,X20] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit1(X19)),bit1(X20)))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X19),X20)) ),
c_0_291 ).
fof(c_0_999,axiom,
! [X3,X4] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,number267125858f_real(X3)),number267125858f_real(X4)))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X3),X4)) ),
c_0_292 ).
fof(c_0_1000,axiom,
! [X3,X4] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(X3)),number_number_of_int(X4)))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X3),X4)) ),
c_0_293 ).
fof(c_0_1001,axiom,
! [X11,X12] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(X11)),number_number_of_int(X12)))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X11),X12)) ),
c_0_294 ).
fof(c_0_1002,axiom,
! [X18] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_nat_int(semiri1621563631at_int,X18)))
<=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X18)) ),
c_0_295 ).
fof(c_0_1003,axiom,
! [X18] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),hAPP_nat_real(semiri132038758t_real,X18)))
<=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X18)) ),
c_0_296 ).
fof(c_0_1004,axiom,
! [X18] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(semiri984289939at_nat,X18)))
<=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X18)) ),
c_0_297 ).
fof(c_0_1005,axiom,
! [X18] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_nat_int(semiri1621563631at_int,X18)))
<=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X18)) ),
c_0_298 ).
fof(c_0_1006,axiom,
! [X17] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X17))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_int_int(plus_plus_int(one_one_int),X17))) ),
c_0_299 ).
fof(c_0_1007,axiom,
! [X4,X3] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X4),X3))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X3),X4))
<=> X3 = X4 ) ),
c_0_300 ).
fof(c_0_1008,axiom,
! [X4,X3] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X4),X3))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X3),X4))
<=> X3 = X4 ) ),
c_0_301 ).
fof(c_0_1009,axiom,
! [X4,X3] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X4),X3))
=> ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X3),X4))
<=> X3 = X4 ) ),
c_0_302 ).
fof(c_0_1010,axiom,
! [X263,X264] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X263),X264))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X264),X263))
=> X263 = X264 ) ),
c_0_303 ).
fof(c_0_1011,axiom,
! [X263,X264] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X263),X264))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X264),X263))
=> X263 = X264 ) ),
c_0_304 ).
fof(c_0_1012,axiom,
! [X263,X264] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X263),X264))
=> ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X264),X263))
=> X263 = X264 ) ),
c_0_305 ).
fof(c_0_1013,axiom,
! [X258,X259] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X258),X259))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X259),X258))
=> X259 = X258 ) ),
c_0_306 ).
fof(c_0_1014,axiom,
! [X258,X259] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X258),X259))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X259),X258))
=> X259 = X258 ) ),
c_0_307 ).
fof(c_0_1015,axiom,
! [X258,X259] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X258),X259))
=> ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X259),X258))
=> X259 = X258 ) ),
c_0_308 ).
fof(c_0_1016,axiom,
! [X17,X14] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X17),X14))
=> ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X14),X17))
=> X17 = X14 ) ),
c_0_309 ).
fof(c_0_1017,axiom,
! [X15,X16] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X15),X16))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X16),X15))
=> X15 = X16 ) ),
c_0_310 ).
fof(c_0_1018,axiom,
! [X17,X14] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X17),X14))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X14),X17))
=> X17 = X14 ) ),
c_0_311 ).
fof(c_0_1019,axiom,
! [X22,X23] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X22),X23))
=> ? [X91] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X91))
& hAPP_nat_nat(plus_plus_nat(X22),X91) = X23 ) ),
c_0_312 ).
fof(c_0_1020,axiom,
! [X16] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),number_number_of_int(X16)))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),number_number_of_int(bit0(X16))))
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),number_number_of_int(bit1(X16)))) ) ),
c_0_313 ).
fof(c_0_1021,axiom,
! [X3] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,number_number_of_int(X3)),one_one_int))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X3),bit1(pls))) ),
c_0_314 ).
fof(c_0_1022,axiom,
! [X3] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,number267125858f_real(X3)),one_one_real))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X3),bit1(pls))) ),
c_0_315 ).
fof(c_0_1023,axiom,
! [X3] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,number267125858f_real(X3)),one_one_real))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X3),bit1(pls))) ),
c_0_316 ).
fof(c_0_1024,axiom,
! [X3] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(X3)),one_one_int))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X3),bit1(pls))) ),
c_0_317 ).
fof(c_0_1025,plain,
! [X24,X13] :
( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X13),pls))
=> hAPP_nat_nat(plus_plus_nat(number_number_of_nat(X13)),number_number_of_nat(X24)) = number_number_of_nat(X24) )
& ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X13),pls))
=> ( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X24),pls))
=> hAPP_nat_nat(plus_plus_nat(number_number_of_nat(X13)),number_number_of_nat(X24)) = number_number_of_nat(X13) )
& ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X24),pls))
=> hAPP_nat_nat(plus_plus_nat(number_number_of_nat(X13)),number_number_of_nat(X24)) = number_number_of_nat(hAPP_int_int(plus_plus_int(X13),X24)) ) ) ) ),
inference(fof_simplification,[status(thm)],[c_0_318]) ).
fof(c_0_1026,axiom,
! [X3] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,sqrt(X3)),one_one_real))
<=> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X3),one_one_real)) ),
c_0_319 ).
fof(c_0_1027,axiom,
! [X3] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,sqrt(X3)),zero_zero_real))
<=> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X3),zero_zero_real)) ),
c_0_320 ).
fof(c_0_1028,axiom,
! [X11] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,bit1(X11)),pls))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X11),pls)) ),
c_0_321 ).
fof(c_0_1029,axiom,
! [X11] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,bit0(X11)),pls))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X11),pls)) ),
c_0_322 ).
fof(c_0_1030,axiom,
! [X3] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,number_number_of_int(X3)),zero_zero_int))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X3),pls)) ),
c_0_323 ).
fof(c_0_1031,axiom,
! [X3] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,number267125858f_real(X3)),zero_zero_real))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X3),pls)) ),
c_0_324 ).
fof(c_0_1032,axiom,
! [X25] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit0(X25)),zero_zero_int))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X25),zero_zero_int)) ),
c_0_325 ).
fof(c_0_1033,axiom,
! [X25] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit1(X25)),zero_zero_int))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X25),zero_zero_int)) ),
c_0_326 ).
fof(c_0_1034,axiom,
! [X11] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit0(X11)),pls))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X11),pls)) ),
c_0_327 ).
fof(c_0_1035,axiom,
! [X11] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit1(X11)),pls))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X11),pls)) ),
c_0_328 ).
fof(c_0_1036,axiom,
! [X3] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,number267125858f_real(X3)),zero_zero_real))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X3),pls)) ),
c_0_329 ).
fof(c_0_1037,axiom,
! [X3] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(X3)),zero_zero_int))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X3),pls)) ),
c_0_330 ).
fof(c_0_1038,axiom,
! [X4] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),number_number_of_int(X4)))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,bit1(pls)),X4)) ),
c_0_331 ).
fof(c_0_1039,axiom,
! [X4] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,one_one_real),number267125858f_real(X4)))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,bit1(pls)),X4)) ),
c_0_332 ).
fof(c_0_1040,axiom,
! [X4] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,one_one_real),number267125858f_real(X4)))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit1(pls)),X4)) ),
c_0_333 ).
fof(c_0_1041,axiom,
! [X4] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),number_number_of_int(X4)))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit1(pls)),X4)) ),
c_0_334 ).
fof(c_0_1042,axiom,
! [X25,X30] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X25),X30))
<=> ? [X90] : X30 = hAPP_int_int(plus_plus_int(X25),hAPP_nat_int(semiri1621563631at_int,X90)) ),
c_0_335 ).
fof(c_0_1043,axiom,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,m1),hAPP_int_int(plus_plus_int(one_one_int),hAPP_nat_int(semiri1621563631at_int,n)))),
c_0_336 ).
fof(c_0_1044,axiom,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_int_int(plus_plus_int(one_one_int),hAPP_nat_int(semiri1621563631at_int,n)))),
c_0_337 ).
fof(c_0_1045,axiom,
! [X274,X275,X276] :
( X275 = X276
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X276),X274))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X275),X274)) ) ),
c_0_338 ).
fof(c_0_1046,axiom,
! [X274,X275,X276] :
( X275 = X276
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X276),X274))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X275),X274)) ) ),
c_0_339 ).
fof(c_0_1047,axiom,
! [X274,X275,X276] :
( X275 = X276
=> ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X276),X274))
=> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X275),X274)) ) ),
c_0_340 ).
fof(c_0_1048,axiom,
! [X271,X272,X273] :
( X272 = X273
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X271),X273))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X271),X272)) ) ),
c_0_341 ).
fof(c_0_1049,axiom,
! [X271,X272,X273] :
( X272 = X273
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X271),X273))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X271),X272)) ) ),
c_0_342 ).
fof(c_0_1050,axiom,
! [X271,X272,X273] :
( X272 = X273
=> ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X271),X273))
=> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X271),X272)) ) ),
c_0_343 ).
fof(c_0_1051,axiom,
! [X268,X269,X270] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X269),X270))
=> ( X270 = X268
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X269),X268)) ) ),
c_0_344 ).
fof(c_0_1052,axiom,
! [X268,X269,X270] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X269),X270))
=> ( X270 = X268
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X269),X268)) ) ),
c_0_345 ).
fof(c_0_1053,axiom,
! [X268,X269,X270] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X269),X270))
=> ( X270 = X268
=> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X269),X268)) ) ),
c_0_346 ).
fof(c_0_1054,axiom,
! [X265,X266,X267] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X266),X267))
=> ( X266 = X265
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X265),X267)) ) ),
c_0_347 ).
fof(c_0_1055,axiom,
! [X265,X266,X267] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X266),X267))
=> ( X266 = X265
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X265),X267)) ) ),
c_0_348 ).
fof(c_0_1056,axiom,
! [X265,X266,X267] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X266),X267))
=> ( X266 = X265
=> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X265),X267)) ) ),
c_0_349 ).
fof(c_0_1057,axiom,
! [X4] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,one_one_real),sqrt(X4)))
<=> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,one_one_real),X4)) ),
c_0_350 ).
fof(c_0_1058,axiom,
! [X4] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),sqrt(X4)))
<=> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X4)) ),
c_0_351 ).
fof(c_0_1059,axiom,
! [X11] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),bit1(X11)))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X11)) ),
c_0_352 ).
fof(c_0_1060,axiom,
! [X11] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),bit0(X11)))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X11)) ),
c_0_353 ).
fof(c_0_1061,axiom,
! [X11] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),bit1(X11)))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X11)) ),
c_0_354 ).
fof(c_0_1062,axiom,
! [X4] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),number_number_of_int(X4)))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X4)) ),
c_0_355 ).
fof(c_0_1063,axiom,
! [X4] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),number267125858f_real(X4)))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X4)) ),
c_0_356 ).
fof(c_0_1064,axiom,
! [X59] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),number_number_of_nat(X59)))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),X59)) ),
c_0_357 ).
fof(c_0_1065,axiom,
! [X11] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),bit0(X11)))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),X11)) ),
c_0_358 ).
fof(c_0_1066,axiom,
! [X4] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),number267125858f_real(X4)))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),X4)) ),
c_0_359 ).
fof(c_0_1067,axiom,
! [X4] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),number_number_of_int(X4)))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),X4)) ),
c_0_360 ).
fof(c_0_1068,axiom,
! [X3,X4] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X3),X4))
<=> ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X3),X4))
& X3 != X4 ) ),
c_0_361 ).
fof(c_0_1069,axiom,
! [X3,X4] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X3),X4))
<=> ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X3),X4))
| X3 = X4 ) ),
c_0_362 ).
fof(c_0_1070,axiom,
! [X29,X18] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X29),X18))
<=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X29),X18))
& X29 != X18 ) ),
c_0_363 ).
fof(c_0_1071,axiom,
! [X29,X18] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X29),X18))
<=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X29),X18))
| X29 = X18 ) ),
c_0_364 ).
fof(c_0_1072,axiom,
! [X15,X16] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X15),X16))
=> ( X15 != X16
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X15),X16)) ) ),
c_0_365 ).
fof(c_0_1073,axiom,
! [X30,X25] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X30),X25))
<=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X30),X25))
& X30 != X25 ) ),
c_0_366 ).
fof(c_0_1074,axiom,
! [X15,X16] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X15),X16))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X15),X16)) ),
c_0_367 ).
fof(c_0_1075,axiom,
! [X15,X16] :
( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X15),X16))
| X15 = X16 )
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X15),X16)) ),
c_0_368 ).
fof(c_0_1076,axiom,
! [X107,X108,X109] : hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(X107),X108)),X109) = hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(X107),X109)),X108),
c_0_369 ).
fof(c_0_1077,axiom,
! [X107,X108,X109] : hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(plus_plus_nat(X107),X108)),X109) = hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(plus_plus_nat(X107),X109)),X108),
c_0_370 ).
fof(c_0_1078,axiom,
! [X107,X108,X109] : hAPP_real_real(plus_plus_real(hAPP_real_real(plus_plus_real(X107),X108)),X109) = hAPP_real_real(plus_plus_real(hAPP_real_real(plus_plus_real(X107),X109)),X108),
c_0_371 ).
fof(c_0_1079,axiom,
! [X8] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X8))
=> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),sqrt(X8))) ),
c_0_372 ).
fof(c_0_1080,axiom,
! [X21] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X21))
=> ? [X90] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X90))
& X21 = hAPP_nat_int(semiri1621563631at_int,X90) ) ),
c_0_373 ).
fof(c_0_1081,axiom,
! [X30] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),X30))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X30)) ),
c_0_374 ).
fof(c_0_1082,axiom,
! [X29,X18,X5] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),X5))
=> ( hAPP_nat_int(power_power_int(X5),X29) = hAPP_nat_int(power_power_int(X5),X18)
<=> X29 = X18 ) ),
c_0_375 ).
fof(c_0_1083,axiom,
! [X29,X18,X5] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,one_one_nat),X5))
=> ( hAPP_nat_nat(power_power_nat(X5),X29) = hAPP_nat_nat(power_power_nat(X5),X18)
<=> X29 = X18 ) ),
c_0_376 ).
fof(c_0_1084,axiom,
! [X29,X18,X5] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,one_one_real),X5))
=> ( hAPP_nat_real(power_power_real(X5),X29) = hAPP_nat_real(power_power_real(X5),X18)
<=> X29 = X18 ) ),
c_0_377 ).
fof(c_0_1085,axiom,
! [X29,X18] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X29),X18))
<=> ? [X91] : X18 = hAPP_nat_nat(plus_plus_nat(X29),X91) ),
c_0_378 ).
fof(c_0_1086,axiom,
! [X21,X31] : times_times_int(bit1(X21),X31) = hAPP_int_int(plus_plus_int(bit0(times_times_int(X21,X31))),X31),
c_0_379 ).
fof(c_0_1087,axiom,
! [X116,X117,X118] : hAPP_int_int(plus_plus_int(X116),hAPP_int_int(plus_plus_int(X117),X118)) = hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(X116),X117)),X118),
c_0_380 ).
fof(c_0_1088,axiom,
! [X116,X117,X118] : hAPP_nat_nat(plus_plus_nat(X116),hAPP_nat_nat(plus_plus_nat(X117),X118)) = hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(plus_plus_nat(X116),X117)),X118),
c_0_381 ).
fof(c_0_1089,axiom,
! [X116,X117,X118] : hAPP_real_real(plus_plus_real(X116),hAPP_real_real(plus_plus_real(X117),X118)) = hAPP_real_real(plus_plus_real(hAPP_real_real(plus_plus_real(X116),X117)),X118),
c_0_382 ).
fof(c_0_1090,axiom,
! [X113,X114,X115] : hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(X113),X114)),X115) = hAPP_int_int(plus_plus_int(X113),hAPP_int_int(plus_plus_int(X114),X115)),
c_0_383 ).
fof(c_0_1091,axiom,
! [X113,X114,X115] : hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(plus_plus_nat(X113),X114)),X115) = hAPP_nat_nat(plus_plus_nat(X113),hAPP_nat_nat(plus_plus_nat(X114),X115)),
c_0_384 ).
fof(c_0_1092,axiom,
! [X113,X114,X115] : hAPP_real_real(plus_plus_real(hAPP_real_real(plus_plus_real(X113),X114)),X115) = hAPP_real_real(plus_plus_real(X113),hAPP_real_real(plus_plus_real(X114),X115)),
c_0_385 ).
fof(c_0_1093,axiom,
! [X110,X111,X112] : hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(X110),X111)),X112) = hAPP_int_int(plus_plus_int(X110),hAPP_int_int(plus_plus_int(X111),X112)),
c_0_386 ).
fof(c_0_1094,axiom,
! [X110,X111,X112] : hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(plus_plus_nat(X110),X111)),X112) = hAPP_nat_nat(plus_plus_nat(X110),hAPP_nat_nat(plus_plus_nat(X111),X112)),
c_0_387 ).
fof(c_0_1095,axiom,
! [X110,X111,X112] : hAPP_real_real(plus_plus_real(hAPP_real_real(plus_plus_real(X110),X111)),X112) = hAPP_real_real(plus_plus_real(X110),hAPP_real_real(plus_plus_real(X111),X112)),
c_0_388 ).
fof(c_0_1096,plain,
! [X61,X62] :
( X61 != X62
=> ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X61),X62))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X62),X61)) ) ),
inference(fof_simplification,[status(thm)],[c_0_389]) ).
fof(c_0_1097,plain,
! [X61,X62] :
( X61 != X62
=> ( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X61),X62))
=> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X62),X61)) ) ),
inference(fof_simplification,[status(thm)],[c_0_390]) ).
fof(c_0_1098,plain,
! [X8,X10] :
( X8 != X10
=> ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X8),X10))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X10),X8)) ) ),
inference(fof_simplification,[status(thm)],[c_0_391]) ).
fof(c_0_1099,axiom,
! [X15,X16,X21] : hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(plus_plus_nat(X15),X16)),X21) = hAPP_nat_nat(plus_plus_nat(X15),hAPP_nat_nat(plus_plus_nat(X16),X21)),
c_0_392 ).
fof(c_0_1100,axiom,
! [X29,X18] :
( X29 != X18
<=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X29),X18))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X18),X29)) ) ),
c_0_393 ).
fof(c_0_1101,axiom,
! [X26,X27,X28] : hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(X26),X27)),X28) = hAPP_int_int(plus_plus_int(X26),hAPP_int_int(plus_plus_int(X27),X28)),
c_0_394 ).
fof(c_0_1102,axiom,
! [X8,X10] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X8),X10))
| X8 = X10
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X10),X8)) ),
c_0_395 ).
fof(c_0_1103,plain,
! [X253,X254] :
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X253),X254))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X254),X253)) ),
inference(fof_simplification,[status(thm)],[c_0_396]) ).
fof(c_0_1104,plain,
! [X253,X254] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X253),X254))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X254),X253)) ),
inference(fof_simplification,[status(thm)],[c_0_397]) ).
fof(c_0_1105,plain,
! [X253,X254] :
( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X253),X254))
=> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X254),X253)) ),
inference(fof_simplification,[status(thm)],[c_0_398]) ).
fof(c_0_1106,axiom,
! [X17,X14] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X17),X14))
| hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X14),X17)) ),
c_0_399 ).
fof(c_0_1107,axiom,
! [X16,X15] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X16),hAPP_nat_nat(plus_plus_nat(X16),X15))),
c_0_400 ).
fof(c_0_1108,axiom,
! [X16,X15] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X16),hAPP_nat_nat(plus_plus_nat(X15),X16))),
c_0_401 ).
fof(c_0_1109,axiom,
! [X15,X16] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X15),X16))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X16),X15)) ),
c_0_402 ).
fof(c_0_1110,axiom,
! [X17,X14] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X17),X14))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X14),X17)) ),
c_0_403 ).
fof(c_0_1111,plain,
! [X242] :
( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),number_number_of_int(X242)))
=> hAPP_nat_int(semiri1621563631at_int,number_number_of_nat(X242)) = number_number_of_int(X242) )
& ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),number_number_of_int(X242)))
=> hAPP_nat_int(semiri1621563631at_int,number_number_of_nat(X242)) = zero_zero_int ) ),
inference(fof_simplification,[status(thm)],[c_0_404]) ).
fof(c_0_1112,plain,
! [X242] :
( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),number_number_of_int(X242)))
=> hAPP_nat_real(semiri132038758t_real,number_number_of_nat(X242)) = number267125858f_real(X242) )
& ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),number_number_of_int(X242)))
=> hAPP_nat_real(semiri132038758t_real,number_number_of_nat(X242)) = zero_zero_real ) ),
inference(fof_simplification,[status(thm)],[c_0_405]) ).
fof(c_0_1113,axiom,
! [X210] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X210))
=> hAPP_int_int(plus_plus_int(number_number_of_int(X210)),one_one_int) = number_number_of_int(succ(X210)) ),
c_0_406 ).
fof(c_0_1114,axiom,
! [X210] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X210))
=> hAPP_nat_nat(plus_plus_nat(number_number_of_nat(X210)),one_one_nat) = number_number_of_nat(succ(X210)) ),
c_0_407 ).
fof(c_0_1115,axiom,
! [X210] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X210))
=> hAPP_real_real(plus_plus_real(number267125858f_real(X210)),one_one_real) = number267125858f_real(succ(X210)) ),
c_0_408 ).
fof(c_0_1116,axiom,
! [X80] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X80),hAPP_int_int(plus_plus_int(X80),one_one_int))),
c_0_409 ).
fof(c_0_1117,axiom,
! [X80] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X80),hAPP_nat_nat(plus_plus_nat(X80),one_one_nat))),
c_0_410 ).
fof(c_0_1118,axiom,
! [X80] : hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X80),hAPP_real_real(plus_plus_real(X80),one_one_real))),
c_0_411 ).
fof(c_0_1119,plain,
! [X13] :
( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X13),pls))
=> hAPP_nat_nat(plus_plus_nat(number_number_of_nat(X13)),one_one_nat) = one_one_nat )
& ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X13),pls))
=> hAPP_nat_nat(plus_plus_nat(number_number_of_nat(X13)),one_one_nat) = number_number_of_nat(succ(X13)) ) ),
inference(fof_simplification,[status(thm)],[c_0_412]) ).
fof(c_0_1120,axiom,
! [X209] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X209))
=> hAPP_int_int(plus_plus_int(one_one_int),number_number_of_int(X209)) = number_number_of_int(succ(X209)) ),
c_0_413 ).
fof(c_0_1121,axiom,
! [X209] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X209))
=> hAPP_nat_nat(plus_plus_nat(one_one_nat),number_number_of_nat(X209)) = number_number_of_nat(succ(X209)) ),
c_0_414 ).
fof(c_0_1122,axiom,
! [X209] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X209))
=> hAPP_real_real(plus_plus_real(one_one_real),number267125858f_real(X209)) = number267125858f_real(succ(X209)) ),
c_0_415 ).
fof(c_0_1123,axiom,
! [X8,X10] : hAPP_int_int(plus_plus_int(hAPP_nat_int(semiri1621563631at_int,X8)),hAPP_nat_int(semiri1621563631at_int,X10)) = hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(plus_plus_nat(X8),X10)),
c_0_416 ).
fof(c_0_1124,axiom,
! [X71,X72] : hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(plus_plus_nat(X71),X72)) = hAPP_int_int(plus_plus_int(hAPP_nat_int(semiri1621563631at_int,X71)),hAPP_nat_int(semiri1621563631at_int,X72)),
c_0_417 ).
fof(c_0_1125,axiom,
! [X71,X72] : hAPP_nat_nat(semiri984289939at_nat,hAPP_nat_nat(plus_plus_nat(X71),X72)) = hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(semiri984289939at_nat,X71)),hAPP_nat_nat(semiri984289939at_nat,X72)),
c_0_418 ).
fof(c_0_1126,axiom,
! [X71,X72] : hAPP_nat_real(semiri132038758t_real,hAPP_nat_nat(plus_plus_nat(X71),X72)) = hAPP_real_real(plus_plus_real(hAPP_nat_real(semiri132038758t_real,X71)),hAPP_nat_real(semiri132038758t_real,X72)),
c_0_419 ).
fof(c_0_1127,axiom,
! [X15,X16] : hAPP_int_int(plus_plus_int(hAPP_nat_int(semiri1621563631at_int,X15)),hAPP_nat_int(semiri1621563631at_int,X16)) = hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(plus_plus_nat(X15),X16)),
c_0_420 ).
fof(c_0_1128,plain,
! [X13] :
( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X13),pls))
=> hAPP_nat_nat(plus_plus_nat(one_one_nat),number_number_of_nat(X13)) = one_one_nat )
& ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X13),pls))
=> hAPP_nat_nat(plus_plus_nat(one_one_nat),number_number_of_nat(X13)) = number_number_of_nat(succ(X13)) ) ),
inference(fof_simplification,[status(thm)],[c_0_421]) ).
fof(c_0_1129,axiom,
! [X17] : hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),X17)),X17) != zero_zero_int,
c_0_422 ).
fof(c_0_1130,axiom,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),number_number_of_int(bit0(bit1(pls))))),
c_0_423 ).
fof(c_0_1131,axiom,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),number_number_of_int(bit1(bit1(pls))))),
c_0_424 ).
fof(c_0_1132,axiom,
hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),number_number_of_nat(bit0(bit1(pls))))),
c_0_425 ).
fof(c_0_1133,axiom,
! [X17] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X17))
=> ~ ! [X248] : X17 != hAPP_nat_int(semiri1621563631at_int,X248) ),
c_0_426 ).
fof(c_0_1134,axiom,
! [X21] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X21))
=> ~ ! [X90] : X21 != hAPP_nat_int(semiri1621563631at_int,X90) ),
c_0_427 ).
fof(c_0_1135,axiom,
! [X21] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X21))
=> ? [X90] : X21 = hAPP_nat_int(semiri1621563631at_int,X90) ),
c_0_428 ).
fof(c_0_1136,axiom,
hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),hAPP_real_real(plus_plus_real(one_one_real),one_one_real))),
c_0_429 ).
fof(c_0_1137,axiom,
hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(plus_plus_nat(one_one_nat),one_one_nat))),
c_0_430 ).
fof(c_0_1138,axiom,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_int_int(plus_plus_int(one_one_int),one_one_int))),
c_0_431 ).
fof(c_0_1139,axiom,
! [X46] : number267125858f_real(bit1(X46)) = hAPP_real_real(plus_plus_real(hAPP_real_real(plus_plus_real(one_one_real),number267125858f_real(X46))),number267125858f_real(X46)),
c_0_432 ).
fof(c_0_1140,axiom,
! [X46] : number_number_of_int(bit1(X46)) = hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),number_number_of_int(X46))),number_number_of_int(X46)),
c_0_433 ).
fof(c_0_1141,axiom,
! [X45] : number267125858f_real(bit0(X45)) = hAPP_real_real(plus_plus_real(hAPP_real_real(plus_plus_real(zero_zero_real),number267125858f_real(X45))),number267125858f_real(X45)),
c_0_434 ).
fof(c_0_1142,axiom,
! [X45] : number_number_of_int(bit0(X45)) = hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(zero_zero_int),number_number_of_int(X45))),number_number_of_int(X45)),
c_0_435 ).
fof(c_0_1143,axiom,
! [X57,X58] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X57),X58))
=> X57 != X58 ),
c_0_436 ).
fof(c_0_1144,axiom,
! [X16,X15] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X16),X15))
=> X15 != X16 ),
c_0_437 ).
fof(c_0_1145,axiom,
! [X15,X16] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X15),X16))
=> X16 != zero_zero_nat ),
c_0_438 ).
fof(c_0_1146,plain,
! [X16] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X16),X16)),
inference(fof_simplification,[status(thm)],[c_0_439]) ).
fof(c_0_1147,plain,
! [X16] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X16),X16)),
inference(fof_simplification,[status(thm)],[c_0_440]) ).
fof(c_0_1148,axiom,
! [X59] :
( number_number_of_nat(X59) = zero_zero_nat
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X59),pls)) ),
c_0_441 ).
fof(c_0_1149,axiom,
! [X59] :
( zero_zero_nat = number_number_of_nat(X59)
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X59),pls)) ),
c_0_442 ).
fof(c_0_1150,axiom,
! [X8] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X8))
=> sqrt(X8) != zero_zero_real ),
c_0_443 ).
fof(c_0_1151,axiom,
! [X119,X120,X121] : hAPP_int_int(plus_plus_int(X119),hAPP_int_int(plus_plus_int(X120),X121)) = hAPP_int_int(plus_plus_int(X120),hAPP_int_int(plus_plus_int(X119),X121)),
c_0_444 ).
fof(c_0_1152,axiom,
! [X119,X120,X121] : hAPP_nat_nat(plus_plus_nat(X119),hAPP_nat_nat(plus_plus_nat(X120),X121)) = hAPP_nat_nat(plus_plus_nat(X120),hAPP_nat_nat(plus_plus_nat(X119),X121)),
c_0_445 ).
fof(c_0_1153,axiom,
! [X119,X120,X121] : hAPP_real_real(plus_plus_real(X119),hAPP_real_real(plus_plus_real(X120),X121)) = hAPP_real_real(plus_plus_real(X120),hAPP_real_real(plus_plus_real(X119),X121)),
c_0_446 ).
fof(c_0_1154,axiom,
! [X8,X16] : hAPP_nat_int(power_power_int(hAPP_nat_int(semiri1621563631at_int,X8)),X16) = hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(power_power_nat(X8),X16)),
c_0_447 ).
fof(c_0_1155,axiom,
! [X73,X74] : hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(power_power_nat(X73),X74)) = hAPP_nat_int(power_power_int(hAPP_nat_int(semiri1621563631at_int,X73)),X74),
c_0_448 ).
fof(c_0_1156,axiom,
! [X73,X74] : hAPP_nat_nat(semiri984289939at_nat,hAPP_nat_nat(power_power_nat(X73),X74)) = hAPP_nat_nat(power_power_nat(hAPP_nat_nat(semiri984289939at_nat,X73)),X74),
c_0_449 ).
fof(c_0_1157,axiom,
! [X73,X74] : hAPP_nat_real(semiri132038758t_real,hAPP_nat_nat(power_power_nat(X73),X74)) = hAPP_nat_real(power_power_real(hAPP_nat_real(semiri132038758t_real,X73)),X74),
c_0_450 ).
fof(c_0_1158,axiom,
! [X8,X10,X17] : hAPP_nat_nat(plus_plus_nat(X8),hAPP_nat_nat(plus_plus_nat(X10),X17)) = hAPP_nat_nat(plus_plus_nat(X10),hAPP_nat_nat(plus_plus_nat(X8),X17)),
c_0_451 ).
fof(c_0_1159,axiom,
! [X8,X10,X17] : hAPP_int_int(plus_plus_int(X8),hAPP_int_int(plus_plus_int(X10),X17)) = hAPP_int_int(plus_plus_int(X10),hAPP_int_int(plus_plus_int(X8),X17)),
c_0_452 ).
fof(c_0_1160,axiom,
! [X15,X16] : hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(power_power_nat(X15),X16)) = hAPP_nat_int(power_power_int(hAPP_nat_int(semiri1621563631at_int,X15)),X16),
c_0_453 ).
fof(c_0_1161,axiom,
! [X15,X16] : hAPP_nat_int(power_power_int(hAPP_nat_int(semiri1621563631at_int,X15)),X16) = hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(power_power_nat(X15),X16)),
c_0_454 ).
fof(c_0_1162,axiom,
! [X18] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X18),zero_zero_nat))
<=> X18 = zero_zero_nat ),
c_0_455 ).
fof(c_0_1163,axiom,
! [X16] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_nat_int(semiri1621563631at_int,X16))),
c_0_456 ).
fof(c_0_1164,axiom,
! [X17] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_nat_int(semiri1621563631at_int,X17))),
c_0_457 ).
fof(c_0_1165,axiom,
! [X206] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_nat_int(semiri1621563631at_int,X206))),
c_0_458 ).
fof(c_0_1166,axiom,
! [X206] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),hAPP_nat_nat(semiri984289939at_nat,X206))),
c_0_459 ).
fof(c_0_1167,axiom,
! [X206] : hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),hAPP_nat_real(semiri132038758t_real,X206))),
c_0_460 ).
fof(c_0_1168,axiom,
! [X205] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_nat_int(semiri1621563631at_int,X205))),
c_0_461 ).
fof(c_0_1169,axiom,
! [X205] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),hAPP_nat_nat(semiri984289939at_nat,X205))),
c_0_462 ).
fof(c_0_1170,axiom,
! [X205] : hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),hAPP_nat_real(semiri132038758t_real,X205))),
c_0_463 ).
fof(c_0_1171,plain,
! [X16] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X16),zero_zero_nat)),
inference(fof_simplification,[status(thm)],[c_0_464]) ).
fof(c_0_1172,plain,
! [X16] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X16),zero_zero_nat)),
inference(fof_simplification,[status(thm)],[c_0_465]) ).
fof(c_0_1173,plain,
! [X16] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X16),zero_zero_nat)),
inference(fof_simplification,[status(thm)],[c_0_466]) ).
fof(c_0_1174,axiom,
! [X18] :
( X18 != zero_zero_nat
<=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X18)) ),
c_0_467 ).
fof(c_0_1175,plain,
! [X3,X4,X54] :
( ( hBOOL(X54)
=> hAPP_nat_int(semiri1621563631at_int,X3) = hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(if_nat(X54,X3),X4)) )
& ( ~ hBOOL(X54)
=> hAPP_nat_int(semiri1621563631at_int,X4) = hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(if_nat(X54,X3),X4)) ) ),
inference(fof_simplification,[status(thm)],[c_0_468]) ).
fof(c_0_1176,plain,
~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),zero_zero_int)),
inference(fof_simplification,[status(thm)],[c_0_469]) ).
fof(c_0_1177,plain,
~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,one_one_nat),zero_zero_nat)),
inference(fof_simplification,[status(thm)],[c_0_470]) ).
fof(c_0_1178,plain,
~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,one_one_real),zero_zero_real)),
inference(fof_simplification,[status(thm)],[c_0_471]) ).
fof(c_0_1179,plain,
~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),zero_zero_int)),
inference(fof_simplification,[status(thm)],[c_0_472]) ).
fof(c_0_1180,plain,
~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,one_one_nat),zero_zero_nat)),
inference(fof_simplification,[status(thm)],[c_0_473]) ).
fof(c_0_1181,plain,
~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,one_one_real),zero_zero_real)),
inference(fof_simplification,[status(thm)],[c_0_474]) ).
fof(c_0_1182,plain,
~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),zero_zero_int)),
inference(fof_simplification,[status(thm)],[c_0_475]) ).
fof(c_0_1183,plain,
~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),pls)),
inference(fof_simplification,[status(thm)],[c_0_476]) ).
fof(c_0_1184,axiom,
! [X21,X31] : hAPP_int_int(plus_plus_int(bit1(X21)),bit1(X31)) = bit0(hAPP_int_int(plus_plus_int(X21),succ(X31))),
c_0_477 ).
fof(c_0_1185,axiom,
! [X21] : bit1(X21) = hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),X21)),X21),
c_0_478 ).
fof(c_0_1186,axiom,
! [X5] :
( hAPP_nat_real(power_power_real(X5),number_number_of_nat(bit0(bit1(pls)))) = zero_zero_real
<=> X5 = zero_zero_real ),
c_0_479 ).
fof(c_0_1187,axiom,
! [X5] :
( hAPP_nat_int(power_power_int(X5),number_number_of_nat(bit0(bit1(pls)))) = zero_zero_int
<=> X5 = zero_zero_int ),
c_0_480 ).
fof(c_0_1188,axiom,
! [X21,X31] : hAPP_int_int(plus_plus_int(bit0(X21)),bit1(X31)) = bit1(hAPP_int_int(plus_plus_int(X21),X31)),
c_0_481 ).
fof(c_0_1189,axiom,
! [X21,X31] : hAPP_int_int(plus_plus_int(bit1(X21)),bit0(X31)) = bit1(hAPP_int_int(plus_plus_int(X21),X31)),
c_0_482 ).
fof(c_0_1190,axiom,
! [X39,X40] : number267125858f_real(hAPP_int_int(plus_plus_int(X39),X40)) = hAPP_real_real(plus_plus_real(number267125858f_real(X39)),number267125858f_real(X40)),
c_0_483 ).
fof(c_0_1191,axiom,
! [X39,X40] : number_number_of_int(hAPP_int_int(plus_plus_int(X39),X40)) = hAPP_int_int(plus_plus_int(number_number_of_int(X39)),number_number_of_int(X40)),
c_0_484 ).
fof(c_0_1192,axiom,
! [X37,X38] : hAPP_real_real(plus_plus_real(number267125858f_real(X37)),number267125858f_real(X38)) = number267125858f_real(hAPP_int_int(plus_plus_int(X37),X38)),
c_0_485 ).
fof(c_0_1193,axiom,
! [X37,X38] : hAPP_int_int(plus_plus_int(number_number_of_int(X37)),number_number_of_int(X38)) = number_number_of_int(hAPP_int_int(plus_plus_int(X37),X38)),
c_0_486 ).
fof(c_0_1194,axiom,
! [X21,X31] : hAPP_int_int(plus_plus_int(bit0(X21)),bit0(X31)) = bit0(hAPP_int_int(plus_plus_int(X21),X31)),
c_0_487 ).
fof(c_0_1195,axiom,
! [X13,X14] : hAPP_int_int(plus_plus_int(number_number_of_int(X13)),number_number_of_int(X14)) = number_number_of_int(hAPP_int_int(plus_plus_int(X13),X14)),
c_0_488 ).
fof(c_0_1196,axiom,
! [X277,X278] :
( X277 = X278
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X277),X278)) ),
c_0_489 ).
fof(c_0_1197,axiom,
! [X15,X16] :
( X15 = X16
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X15),X16)) ),
c_0_490 ).
fof(c_0_1198,axiom,
! [X7] : hAPP_real_real(plus_plus_real(number267125858f_real(X7)),one_one_real) = number267125858f_real(hAPP_int_int(plus_plus_int(X7),bit1(pls))),
c_0_491 ).
fof(c_0_1199,axiom,
! [X7] : hAPP_int_int(plus_plus_int(number_number_of_int(X7)),one_one_int) = number_number_of_int(hAPP_int_int(plus_plus_int(X7),bit1(pls))),
c_0_492 ).
fof(c_0_1200,axiom,
! [X6] : hAPP_real_real(plus_plus_real(one_one_real),number267125858f_real(X6)) = number267125858f_real(hAPP_int_int(plus_plus_int(bit1(pls)),X6)),
c_0_493 ).
fof(c_0_1201,axiom,
! [X6] : hAPP_int_int(plus_plus_int(one_one_int),number_number_of_int(X6)) = number_number_of_int(hAPP_int_int(plus_plus_int(bit1(pls)),X6)),
c_0_494 ).
fof(c_0_1202,axiom,
! [X252] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X252),X252)),
c_0_495 ).
fof(c_0_1203,axiom,
! [X252] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X252),X252)),
c_0_496 ).
fof(c_0_1204,axiom,
! [X252] : hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X252),X252)),
c_0_497 ).
fof(c_0_1205,axiom,
! [X14] : hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X14),X14)),
c_0_498 ).
fof(c_0_1206,axiom,
! [X16] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X16),X16)),
c_0_499 ).
fof(c_0_1207,axiom,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),number_number_of_int(pls))),
c_0_500 ).
fof(c_0_1208,axiom,
! [X14] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X14),X14)),
c_0_501 ).
fof(c_0_1209,axiom,
! [X16] :
( X16 != zero_zero_nat
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X16)) ),
c_0_502 ).
fof(c_0_1210,axiom,
! [X16] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),X16)),
c_0_503 ).
fof(c_0_1211,axiom,
! [X16] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),X16)),
c_0_504 ).
fof(c_0_1212,axiom,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),one_one_int)),
c_0_505 ).
fof(c_0_1213,axiom,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),one_one_int)),
c_0_506 ).
fof(c_0_1214,axiom,
hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),one_one_nat)),
c_0_507 ).
fof(c_0_1215,axiom,
hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),one_one_real)),
c_0_508 ).
fof(c_0_1216,axiom,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),zero_zero_int)),
c_0_509 ).
fof(c_0_1217,axiom,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),pls)),
c_0_510 ).
fof(c_0_1218,axiom,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),t)),
c_0_511 ).
fof(c_0_1219,axiom,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),one_one_int)),
c_0_512 ).
fof(c_0_1220,axiom,
hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),one_one_nat)),
c_0_513 ).
fof(c_0_1221,axiom,
hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),one_one_real)),
c_0_514 ).
fof(c_0_1222,axiom,
hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),tn)),
c_0_515 ).
fof(c_0_1223,axiom,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),one_one_int)),
c_0_516 ).
fof(c_0_1224,axiom,
hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),n)),
c_0_517 ).
fof(c_0_1225,axiom,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),t)),
c_0_518 ).
fof(c_0_1226,axiom,
! [X5,X81,X106] :
( hAPP_int_int(plus_plus_int(X5),X81) = hAPP_int_int(plus_plus_int(X5),X106)
<=> X81 = X106 ),
c_0_519 ).
fof(c_0_1227,axiom,
! [X5,X81,X106] :
( hAPP_nat_nat(plus_plus_nat(X5),X81) = hAPP_nat_nat(plus_plus_nat(X5),X106)
<=> X81 = X106 ),
c_0_520 ).
fof(c_0_1228,axiom,
! [X5,X81,X106] :
( hAPP_real_real(plus_plus_real(X5),X81) = hAPP_real_real(plus_plus_real(X5),X106)
<=> X81 = X106 ),
c_0_521 ).
fof(c_0_1229,axiom,
! [X81,X5,X106] :
( hAPP_int_int(plus_plus_int(X81),X5) = hAPP_int_int(plus_plus_int(X106),X5)
<=> X81 = X106 ),
c_0_522 ).
fof(c_0_1230,axiom,
! [X81,X5,X106] :
( hAPP_nat_nat(plus_plus_nat(X81),X5) = hAPP_nat_nat(plus_plus_nat(X106),X5)
<=> X81 = X106 ),
c_0_523 ).
fof(c_0_1231,axiom,
! [X81,X5,X106] :
( hAPP_real_real(plus_plus_real(X81),X5) = hAPP_real_real(plus_plus_real(X106),X5)
<=> X81 = X106 ),
c_0_524 ).
fof(c_0_1232,axiom,
! [X99,X100,X101] :
( hAPP_int_int(plus_plus_int(X99),X100) = hAPP_int_int(plus_plus_int(X99),X101)
=> X100 = X101 ),
c_0_525 ).
fof(c_0_1233,axiom,
! [X99,X100,X101] :
( hAPP_nat_nat(plus_plus_nat(X99),X100) = hAPP_nat_nat(plus_plus_nat(X99),X101)
=> X100 = X101 ),
c_0_526 ).
fof(c_0_1234,axiom,
! [X99,X100,X101] :
( hAPP_real_real(plus_plus_real(X99),X100) = hAPP_real_real(plus_plus_real(X99),X101)
=> X100 = X101 ),
c_0_527 ).
fof(c_0_1235,axiom,
! [X96,X97,X98] :
( hAPP_int_int(plus_plus_int(X96),X97) = hAPP_int_int(plus_plus_int(X96),X98)
=> X97 = X98 ),
c_0_528 ).
fof(c_0_1236,axiom,
! [X96,X97,X98] :
( hAPP_nat_nat(plus_plus_nat(X96),X97) = hAPP_nat_nat(plus_plus_nat(X96),X98)
=> X97 = X98 ),
c_0_529 ).
fof(c_0_1237,axiom,
! [X96,X97,X98] :
( hAPP_real_real(plus_plus_real(X96),X97) = hAPP_real_real(plus_plus_real(X96),X98)
=> X97 = X98 ),
c_0_530 ).
fof(c_0_1238,axiom,
! [X93,X94,X95] :
( hAPP_int_int(plus_plus_int(X93),X94) = hAPP_int_int(plus_plus_int(X95),X94)
=> X93 = X95 ),
c_0_531 ).
fof(c_0_1239,axiom,
! [X93,X94,X95] :
( hAPP_nat_nat(plus_plus_nat(X93),X94) = hAPP_nat_nat(plus_plus_nat(X95),X94)
=> X93 = X95 ),
c_0_532 ).
fof(c_0_1240,axiom,
! [X93,X94,X95] :
( hAPP_real_real(plus_plus_real(X93),X94) = hAPP_real_real(plus_plus_real(X95),X94)
=> X93 = X95 ),
c_0_533 ).
fof(c_0_1241,axiom,
! [X29,X11,X18] :
( hAPP_nat_nat(plus_plus_nat(X29),X11) = hAPP_nat_nat(plus_plus_nat(X18),X11)
<=> X29 = X18 ),
c_0_534 ).
fof(c_0_1242,axiom,
! [X11,X29,X18] :
( hAPP_nat_nat(plus_plus_nat(X11),X29) = hAPP_nat_nat(plus_plus_nat(X11),X18)
<=> X29 = X18 ),
c_0_535 ).
fof(c_0_1243,axiom,
number_number_of_int(bit1(bit1(pls))) = hAPP_nat_int(semiri1621563631at_int,number_number_of_nat(bit1(bit1(pls)))),
c_0_536 ).
fof(c_0_1244,axiom,
number_number_of_int(bit0(bit1(pls))) = hAPP_nat_int(semiri1621563631at_int,number_number_of_nat(bit0(bit1(pls)))),
c_0_537 ).
fof(c_0_1245,axiom,
! [X5,X25] :
( hAPP_nat_real(power_power_real(X5),number_number_of_nat(X25)) = zero_zero_real
<=> ( X5 = zero_zero_real
& number_number_of_nat(X25) != zero_zero_nat ) ),
c_0_538 ).
fof(c_0_1246,axiom,
! [X5,X25] :
( hAPP_nat_nat(power_power_nat(X5),number_number_of_nat(X25)) = zero_zero_nat
<=> ( X5 = zero_zero_nat
& number_number_of_nat(X25) != zero_zero_nat ) ),
c_0_539 ).
fof(c_0_1247,axiom,
! [X5,X25] :
( hAPP_nat_int(power_power_int(X5),number_number_of_nat(X25)) = zero_zero_int
<=> ( X5 = zero_zero_int
& number_number_of_nat(X25) != zero_zero_nat ) ),
c_0_540 ).
fof(c_0_1248,axiom,
hAPP_nat_real(power_power_real(zero_zero_real),number_number_of_nat(bit0(bit1(pls)))) = zero_zero_real,
c_0_541 ).
fof(c_0_1249,axiom,
hAPP_nat_nat(power_power_nat(zero_zero_nat),number_number_of_nat(bit0(bit1(pls)))) = zero_zero_nat,
c_0_542 ).
fof(c_0_1250,axiom,
hAPP_nat_int(power_power_int(zero_zero_int),number_number_of_nat(bit0(bit1(pls)))) = zero_zero_int,
c_0_543 ).
fof(c_0_1251,axiom,
hAPP_nat_real(power_power_real(one_one_real),number_number_of_nat(bit0(bit1(pls)))) = one_one_real,
c_0_544 ).
fof(c_0_1252,axiom,
hAPP_nat_nat(power_power_nat(one_one_nat),number_number_of_nat(bit0(bit1(pls)))) = one_one_nat,
c_0_545 ).
fof(c_0_1253,axiom,
hAPP_nat_int(power_power_int(one_one_int),number_number_of_nat(bit0(bit1(pls)))) = one_one_int,
c_0_546 ).
fof(c_0_1254,axiom,
! [X3,X4] :
( hAPP_nat_int(semiri1621563631at_int,X3) = hAPP_nat_int(semiri1621563631at_int,X4)
<=> X3 = X4 ),
c_0_547 ).
fof(c_0_1255,axiom,
! [X29,X18] :
( hAPP_nat_int(semiri1621563631at_int,X29) = hAPP_nat_int(semiri1621563631at_int,X18)
<=> X29 = X18 ),
c_0_548 ).
fof(c_0_1256,axiom,
! [X29,X18] :
( hAPP_nat_nat(semiri984289939at_nat,X29) = hAPP_nat_nat(semiri984289939at_nat,X18)
<=> X29 = X18 ),
c_0_549 ).
fof(c_0_1257,axiom,
! [X29,X18] :
( hAPP_nat_real(semiri132038758t_real,X29) = hAPP_nat_real(semiri132038758t_real,X18)
<=> X29 = X18 ),
c_0_550 ).
fof(c_0_1258,axiom,
! [X29,X18] :
( hAPP_nat_int(semiri1621563631at_int,X29) = hAPP_nat_int(semiri1621563631at_int,X18)
<=> X29 = X18 ),
c_0_551 ).
fof(c_0_1259,axiom,
! [X122,X123] : hAPP_int_int(plus_plus_int(X122),X123) = hAPP_int_int(plus_plus_int(X123),X122),
c_0_552 ).
fof(c_0_1260,axiom,
! [X122,X123] : hAPP_nat_nat(plus_plus_nat(X122),X123) = hAPP_nat_nat(plus_plus_nat(X123),X122),
c_0_553 ).
fof(c_0_1261,axiom,
! [X122,X123] : hAPP_real_real(plus_plus_real(X122),X123) = hAPP_real_real(plus_plus_real(X123),X122),
c_0_554 ).
fof(c_0_1262,axiom,
! [X15,X16] : hAPP_nat_nat(plus_plus_nat(X15),X16) = hAPP_nat_nat(plus_plus_nat(X16),X15),
c_0_555 ).
fof(c_0_1263,axiom,
! [X17,X14] : hAPP_int_int(plus_plus_int(X17),X14) = hAPP_int_int(plus_plus_int(X14),X17),
c_0_556 ).
fof(c_0_1264,axiom,
! [X41] : number267125858f_real(hAPP_nat_int(semiri1621563631at_int,X41)) = hAPP_nat_real(semiri132038758t_real,X41),
c_0_557 ).
fof(c_0_1265,axiom,
! [X41] : number_number_of_int(hAPP_nat_int(semiri1621563631at_int,X41)) = hAPP_nat_int(semiri1621563631at_int,X41),
c_0_558 ).
fof(c_0_1266,axiom,
! [X41] : number_number_of_nat(hAPP_nat_int(semiri1621563631at_int,X41)) = hAPP_nat_nat(semiri984289939at_nat,X41),
c_0_559 ).
fof(c_0_1267,axiom,
! [X8,X10] : hAPP_nat_nat(if_nat(fFalse,X8),X10) = X10,
c_0_560 ).
fof(c_0_1268,axiom,
! [X8,X10] : hAPP_nat_nat(if_nat(fTrue,X8),X10) = X8,
c_0_561 ).
fof(c_0_1269,axiom,
! [X3,X18] :
( hAPP_nat_nat(power_power_nat(X3),X18) = one_one_nat
<=> ( X3 = one_one_nat
| X18 = zero_zero_nat ) ),
c_0_562 ).
fof(c_0_1270,axiom,
! [X81,X5] :
( X81 = hAPP_int_int(plus_plus_int(X81),X5)
<=> X5 = zero_zero_int ),
c_0_563 ).
fof(c_0_1271,axiom,
! [X81,X5] :
( X81 = hAPP_nat_nat(plus_plus_nat(X81),X5)
<=> X5 = zero_zero_nat ),
c_0_564 ).
fof(c_0_1272,axiom,
! [X81,X5] :
( X81 = hAPP_real_real(plus_plus_real(X81),X5)
<=> X5 = zero_zero_real ),
c_0_565 ).
fof(c_0_1273,axiom,
! [X15,X16] :
( hAPP_nat_nat(plus_plus_nat(X15),X16) = X15
=> X16 = zero_zero_nat ),
c_0_566 ).
fof(c_0_1274,axiom,
! [X29,X18] :
( hAPP_nat_nat(power_power_nat(X29),X18) = zero_zero_nat
<=> ( X18 != zero_zero_nat
& X29 = zero_zero_nat ) ),
c_0_567 ).
fof(c_0_1275,axiom,
! [X5,X18] :
( hAPP_nat_int(power_power_int(X5),X18) = zero_zero_int
<=> ( X5 = zero_zero_int
& X18 != zero_zero_nat ) ),
c_0_568 ).
fof(c_0_1276,axiom,
! [X5,X18] :
( hAPP_nat_nat(power_power_nat(X5),X18) = zero_zero_nat
<=> ( X5 = zero_zero_nat
& X18 != zero_zero_nat ) ),
c_0_569 ).
fof(c_0_1277,axiom,
! [X5,X18] :
( hAPP_nat_real(power_power_real(X5),X18) = zero_zero_real
<=> ( X5 = zero_zero_real
& X18 != zero_zero_nat ) ),
c_0_570 ).
fof(c_0_1278,axiom,
! [X5] :
( zero_zero_int = hAPP_int_int(plus_plus_int(X5),X5)
<=> X5 = zero_zero_int ),
c_0_571 ).
fof(c_0_1279,axiom,
! [X5] :
( zero_zero_real = hAPP_real_real(plus_plus_real(X5),X5)
<=> X5 = zero_zero_real ),
c_0_572 ).
fof(c_0_1280,axiom,
! [X64,X65] :
( X65 != zero_zero_int
=> hAPP_nat_int(power_power_int(X65),X64) != zero_zero_int ),
c_0_573 ).
fof(c_0_1281,axiom,
! [X64,X65] :
( X65 != zero_zero_real
=> hAPP_nat_real(power_power_real(X65),X64) != zero_zero_real ),
c_0_574 ).
fof(c_0_1282,axiom,
! [X29,X18] :
( hAPP_nat_nat(plus_plus_nat(X29),X18) = zero_zero_nat
<=> ( X29 = zero_zero_nat
& X18 = zero_zero_nat ) ),
c_0_575 ).
fof(c_0_1283,axiom,
! [X5] :
( hAPP_real_real(plus_plus_real(X5),X5) = zero_zero_real
<=> X5 = zero_zero_real ),
c_0_576 ).
fof(c_0_1284,axiom,
! [X5] :
( hAPP_int_int(plus_plus_int(X5),X5) = zero_zero_int
<=> X5 = zero_zero_int ),
c_0_577 ).
fof(c_0_1285,axiom,
! [X233] : number_number_of_int(succ(X233)) = hAPP_int_int(plus_plus_int(one_one_int),number_number_of_int(X233)),
c_0_578 ).
fof(c_0_1286,axiom,
! [X233] : number267125858f_real(succ(X233)) = hAPP_real_real(plus_plus_real(one_one_real),number267125858f_real(X233)),
c_0_579 ).
fof(c_0_1287,axiom,
hAPP_nat_nat(plus_plus_nat(one_one_nat),one_one_nat) = number_number_of_nat(bit0(bit1(pls))),
c_0_580 ).
fof(c_0_1288,axiom,
hAPP_real_real(plus_plus_real(one_one_real),one_one_real) = number267125858f_real(bit0(bit1(pls))),
c_0_581 ).
fof(c_0_1289,axiom,
hAPP_nat_nat(plus_plus_nat(one_one_nat),one_one_nat) = number_number_of_nat(bit0(bit1(pls))),
c_0_582 ).
fof(c_0_1290,axiom,
hAPP_int_int(plus_plus_int(one_one_int),one_one_int) = number_number_of_int(bit0(bit1(pls))),
c_0_583 ).
fof(c_0_1291,axiom,
hAPP_real_real(plus_plus_real(one_one_real),one_one_real) = number267125858f_real(bit0(bit1(pls))),
c_0_584 ).
fof(c_0_1292,axiom,
hAPP_int_int(plus_plus_int(one_one_int),one_one_int) = number_number_of_int(bit0(bit1(pls))),
c_0_585 ).
fof(c_0_1293,axiom,
! [X9] :
( ( number_number_of_nat(X9) = zero_zero_nat
=> hAPP_nat_real(power_power_real(zero_zero_real),number_number_of_nat(X9)) = one_one_real )
& ( number_number_of_nat(X9) != zero_zero_nat
=> hAPP_nat_real(power_power_real(zero_zero_real),number_number_of_nat(X9)) = zero_zero_real ) ),
c_0_586 ).
fof(c_0_1294,axiom,
! [X9] :
( ( number_number_of_nat(X9) = zero_zero_nat
=> hAPP_nat_nat(power_power_nat(zero_zero_nat),number_number_of_nat(X9)) = one_one_nat )
& ( number_number_of_nat(X9) != zero_zero_nat
=> hAPP_nat_nat(power_power_nat(zero_zero_nat),number_number_of_nat(X9)) = zero_zero_nat ) ),
c_0_587 ).
fof(c_0_1295,axiom,
! [X9] :
( ( number_number_of_nat(X9) = zero_zero_nat
=> hAPP_nat_int(power_power_int(zero_zero_int),number_number_of_nat(X9)) = one_one_int )
& ( number_number_of_nat(X9) != zero_zero_nat
=> hAPP_nat_int(power_power_int(zero_zero_int),number_number_of_nat(X9)) = zero_zero_int ) ),
c_0_588 ).
fof(c_0_1296,axiom,
! [X1,X2] : is_bool(hAPP_real_bool(X1,X2)),
c_0_589 ).
fof(c_0_1297,axiom,
! [X1,X2] : is_bool(hAPP_nat_bool(X1,X2)),
c_0_590 ).
fof(c_0_1298,axiom,
! [X1,X2] : is_bool(hAPP_int_bool(X1,X2)),
c_0_591 ).
fof(c_0_1299,axiom,
! [X32] : hAPP_real_real(plus_plus_real(number267125858f_real(pls)),X32) = X32,
c_0_592 ).
fof(c_0_1300,axiom,
! [X32] : hAPP_int_int(plus_plus_int(number_number_of_int(pls)),X32) = X32,
c_0_593 ).
fof(c_0_1301,axiom,
! [X33] : hAPP_real_real(plus_plus_real(X33),number267125858f_real(pls)) = X33,
c_0_594 ).
fof(c_0_1302,axiom,
! [X33] : hAPP_int_int(plus_plus_int(X33),number_number_of_int(pls)) = X33,
c_0_595 ).
fof(c_0_1303,axiom,
! [X21] : bit0(X21) = hAPP_int_int(plus_plus_int(X21),X21),
c_0_596 ).
fof(c_0_1304,axiom,
! [X21] : succ(X21) = hAPP_int_int(plus_plus_int(X21),one_one_int),
c_0_597 ).
fof(c_0_1305,axiom,
! [X18] :
( hAPP_nat_int(semiri1621563631at_int,X18) = zero_zero_int
<=> X18 = zero_zero_nat ),
c_0_598 ).
fof(c_0_1306,axiom,
! [X21] : succ(bit1(X21)) = bit0(succ(X21)),
c_0_599 ).
fof(c_0_1307,axiom,
! [X50] :
( ( X50 = zero_zero_nat
=> hAPP_nat_real(power_power_real(zero_zero_real),X50) = one_one_real )
& ( X50 != zero_zero_nat
=> hAPP_nat_real(power_power_real(zero_zero_real),X50) = zero_zero_real ) ),
c_0_600 ).
fof(c_0_1308,axiom,
! [X50] :
( ( X50 = zero_zero_nat
=> hAPP_nat_nat(power_power_nat(zero_zero_nat),X50) = one_one_nat )
& ( X50 != zero_zero_nat
=> hAPP_nat_nat(power_power_nat(zero_zero_nat),X50) = zero_zero_nat ) ),
c_0_601 ).
fof(c_0_1309,axiom,
! [X50] :
( ( X50 = zero_zero_nat
=> hAPP_nat_int(power_power_int(zero_zero_int),X50) = one_one_int )
& ( X50 != zero_zero_nat
=> hAPP_nat_int(power_power_int(zero_zero_int),X50) = zero_zero_int ) ),
c_0_602 ).
fof(c_0_1310,axiom,
! [X146] : hAPP_nat_int(power_power_int(X146),one_one_nat) = X146,
c_0_603 ).
fof(c_0_1311,axiom,
! [X146] : hAPP_nat_nat(power_power_nat(X146),one_one_nat) = X146,
c_0_604 ).
fof(c_0_1312,axiom,
! [X146] : hAPP_nat_real(power_power_real(X146),one_one_nat) = X146,
c_0_605 ).
fof(c_0_1313,axiom,
! [X126] : hAPP_int_int(plus_plus_int(X126),zero_zero_int) = X126,
c_0_606 ).
fof(c_0_1314,axiom,
! [X126] : hAPP_nat_nat(plus_plus_nat(X126),zero_zero_nat) = X126,
c_0_607 ).
fof(c_0_1315,axiom,
! [X126] : hAPP_real_real(plus_plus_real(X126),zero_zero_real) = X126,
c_0_608 ).
fof(c_0_1316,axiom,
! [X125] : hAPP_int_int(plus_plus_int(X125),zero_zero_int) = X125,
c_0_609 ).
fof(c_0_1317,axiom,
! [X125] : hAPP_nat_nat(plus_plus_nat(X125),zero_zero_nat) = X125,
c_0_610 ).
fof(c_0_1318,axiom,
! [X125] : hAPP_real_real(plus_plus_real(X125),zero_zero_real) = X125,
c_0_611 ).
fof(c_0_1319,axiom,
! [X124] : hAPP_int_int(plus_plus_int(X124),zero_zero_int) = X124,
c_0_612 ).
fof(c_0_1320,axiom,
! [X124] : hAPP_nat_nat(plus_plus_nat(X124),zero_zero_nat) = X124,
c_0_613 ).
fof(c_0_1321,axiom,
! [X124] : hAPP_real_real(plus_plus_real(X124),zero_zero_real) = X124,
c_0_614 ).
fof(c_0_1322,axiom,
! [X63] : hAPP_nat_int(power_power_int(X63),one_one_nat) = X63,
c_0_615 ).
fof(c_0_1323,axiom,
! [X63] : hAPP_nat_nat(power_power_nat(X63),one_one_nat) = X63,
c_0_616 ).
fof(c_0_1324,axiom,
! [X63] : hAPP_nat_real(power_power_real(X63),one_one_nat) = X63,
c_0_617 ).
fof(c_0_1325,axiom,
! [X15] : hAPP_nat_nat(plus_plus_nat(X15),zero_zero_nat) = X15,
c_0_618 ).
fof(c_0_1326,axiom,
! [X17] : hAPP_int_int(plus_plus_int(X17),zero_zero_int) = X17,
c_0_619 ).
fof(c_0_1327,axiom,
! [X21] : hAPP_int_int(plus_plus_int(X21),pls) = X21,
c_0_620 ).
fof(c_0_1328,axiom,
! [X92] : hAPP_nat_int(power_power_int(X92),zero_zero_nat) = one_one_int,
c_0_621 ).
fof(c_0_1329,axiom,
! [X92] : hAPP_nat_nat(power_power_nat(X92),zero_zero_nat) = one_one_nat,
c_0_622 ).
fof(c_0_1330,axiom,
! [X92] : hAPP_nat_real(power_power_real(X92),zero_zero_nat) = one_one_real,
c_0_623 ).
fof(c_0_1331,axiom,
! [X89] : hAPP_nat_int(power_power_int(X89),zero_zero_nat) = one_one_int,
c_0_624 ).
fof(c_0_1332,axiom,
! [X89] : hAPP_nat_nat(power_power_nat(X89),zero_zero_nat) = one_one_nat,
c_0_625 ).
fof(c_0_1333,axiom,
! [X89] : hAPP_nat_real(power_power_real(X89),zero_zero_nat) = one_one_real,
c_0_626 ).
fof(c_0_1334,axiom,
! [X129] : hAPP_int_int(plus_plus_int(zero_zero_int),X129) = X129,
c_0_627 ).
fof(c_0_1335,axiom,
! [X129] : hAPP_nat_nat(plus_plus_nat(zero_zero_nat),X129) = X129,
c_0_628 ).
fof(c_0_1336,axiom,
! [X129] : hAPP_real_real(plus_plus_real(zero_zero_real),X129) = X129,
c_0_629 ).
fof(c_0_1337,axiom,
! [X128] : hAPP_int_int(plus_plus_int(zero_zero_int),X128) = X128,
c_0_630 ).
fof(c_0_1338,axiom,
! [X128] : hAPP_nat_nat(plus_plus_nat(zero_zero_nat),X128) = X128,
c_0_631 ).
fof(c_0_1339,axiom,
! [X128] : hAPP_real_real(plus_plus_real(zero_zero_real),X128) = X128,
c_0_632 ).
fof(c_0_1340,axiom,
! [X127] : hAPP_int_int(plus_plus_int(zero_zero_int),X127) = X127,
c_0_633 ).
fof(c_0_1341,axiom,
! [X127] : hAPP_nat_nat(plus_plus_nat(zero_zero_nat),X127) = X127,
c_0_634 ).
fof(c_0_1342,axiom,
! [X127] : hAPP_real_real(plus_plus_real(zero_zero_real),X127) = X127,
c_0_635 ).
fof(c_0_1343,axiom,
! [X16] : hAPP_nat_nat(plus_plus_nat(zero_zero_nat),X16) = X16,
c_0_636 ).
fof(c_0_1344,axiom,
! [X17] : hAPP_int_int(plus_plus_int(zero_zero_int),X17) = X17,
c_0_637 ).
fof(c_0_1345,axiom,
! [X21] : hAPP_int_int(plus_plus_int(pls),X21) = X21,
c_0_638 ).
fof(c_0_1346,axiom,
! [X66] : hAPP_nat_int(power_power_int(one_one_int),X66) = one_one_int,
c_0_639 ).
fof(c_0_1347,axiom,
! [X66] : hAPP_nat_nat(power_power_nat(one_one_nat),X66) = one_one_nat,
c_0_640 ).
fof(c_0_1348,axiom,
! [X66] : hAPP_nat_real(power_power_real(one_one_real),X66) = one_one_real,
c_0_641 ).
fof(c_0_1349,axiom,
! [X11,X12] :
( bit0(X11) = bit0(X12)
<=> X11 = X12 ),
c_0_642 ).
fof(c_0_1350,axiom,
! [X11,X12] :
( bit1(X11) = bit1(X12)
<=> X11 = X12 ),
c_0_643 ).
fof(c_0_1351,axiom,
! [X3,X4] :
( number267125858f_real(X3) = number267125858f_real(X4)
<=> X3 = X4 ),
c_0_644 ).
fof(c_0_1352,axiom,
! [X3,X4] :
( number_number_of_int(X3) = number_number_of_int(X4)
<=> X3 = X4 ),
c_0_645 ).
fof(c_0_1353,axiom,
! [X21] : succ(bit0(X21)) = bit1(X21),
c_0_646 ).
fof(c_0_1354,axiom,
! [X25,X3] :
( number267125858f_real(X25) = X3
<=> X3 = number267125858f_real(X25) ),
c_0_647 ).
fof(c_0_1355,axiom,
! [X25,X3] :
( number_number_of_int(X25) = X3
<=> X3 = number_number_of_int(X25) ),
c_0_648 ).
fof(c_0_1356,axiom,
! [X25,X3] :
( number_number_of_nat(X25) = X3
<=> X3 = number_number_of_nat(X25) ),
c_0_649 ).
fof(c_0_1357,axiom,
! [X21,X31] : bit0(X21) != bit1(X31),
c_0_650 ).
fof(c_0_1358,axiom,
! [X21,X31] : bit1(X21) != bit0(X31),
c_0_651 ).
fof(c_0_1359,axiom,
zero_zero_int = hAPP_nat_int(semiri1621563631at_int,zero_zero_nat),
c_0_652 ).
fof(c_0_1360,axiom,
hAPP_nat_int(semiri1621563631at_int,zero_zero_nat) = zero_zero_int,
c_0_653 ).
fof(c_0_1361,axiom,
hAPP_nat_nat(semiri984289939at_nat,zero_zero_nat) = zero_zero_nat,
c_0_654 ).
fof(c_0_1362,axiom,
hAPP_nat_real(semiri132038758t_real,zero_zero_nat) = zero_zero_real,
c_0_655 ).
fof(c_0_1363,axiom,
one_one_int = hAPP_nat_int(semiri1621563631at_int,one_one_nat),
c_0_656 ).
fof(c_0_1364,axiom,
hAPP_nat_int(semiri1621563631at_int,one_one_nat) = one_one_int,
c_0_657 ).
fof(c_0_1365,axiom,
hAPP_nat_nat(semiri984289939at_nat,one_one_nat) = one_one_nat,
c_0_658 ).
fof(c_0_1366,axiom,
hAPP_nat_real(semiri132038758t_real,one_one_nat) = one_one_real,
c_0_659 ).
fof(c_0_1367,axiom,
hAPP_nat_int(semiri1621563631at_int,zero_zero_nat) = zero_zero_int,
c_0_660 ).
fof(c_0_1368,axiom,
hAPP_nat_int(semiri1621563631at_int,one_one_nat) = one_one_int,
c_0_661 ).
fof(c_0_1369,axiom,
! [X283] :
( is_bool(X283)
=> ( X283 = fTrue
| X283 = fFalse ) ),
c_0_662 ).
fof(c_0_1370,axiom,
! [X12] :
( pls = bit0(X12)
<=> pls = X12 ),
c_0_663 ).
fof(c_0_1371,axiom,
! [X11] :
( bit0(X11) = pls
<=> X11 = pls ),
c_0_664 ).
fof(c_0_1372,axiom,
number267125858f_real(bit1(pls)) = one_one_real,
c_0_665 ).
fof(c_0_1373,axiom,
number_number_of_nat(bit1(pls)) = one_one_nat,
c_0_666 ).
fof(c_0_1374,axiom,
number_number_of_int(bit1(pls)) = one_one_int,
c_0_667 ).
fof(c_0_1375,axiom,
one_one_nat = number_number_of_nat(bit1(pls)),
c_0_668 ).
fof(c_0_1376,axiom,
number_number_of_nat(bit1(pls)) = one_one_nat,
c_0_669 ).
fof(c_0_1377,axiom,
one_one_int = number_number_of_int(bit1(pls)),
c_0_670 ).
fof(c_0_1378,axiom,
number267125858f_real(bit1(pls)) = one_one_real,
c_0_671 ).
fof(c_0_1379,axiom,
number_number_of_int(bit1(pls)) = one_one_int,
c_0_672 ).
fof(c_0_1380,axiom,
one_one_real = number267125858f_real(bit1(pls)),
c_0_673 ).
fof(c_0_1381,axiom,
one_one_int = number_number_of_int(bit1(pls)),
c_0_674 ).
fof(c_0_1382,axiom,
! [X31] : pls != bit1(X31),
c_0_675 ).
fof(c_0_1383,axiom,
! [X21] : bit1(X21) != pls,
c_0_676 ).
fof(c_0_1384,axiom,
succ(pls) = bit1(pls),
c_0_677 ).
fof(c_0_1385,axiom,
! [X21] : number_number_of_int(X21) = X21,
c_0_678 ).
fof(c_0_1386,axiom,
! [X3] :
( one_one_int = X3
<=> X3 = one_one_int ),
c_0_679 ).
fof(c_0_1387,axiom,
! [X3] :
( one_one_nat = X3
<=> X3 = one_one_nat ),
c_0_680 ).
fof(c_0_1388,axiom,
! [X3] :
( one_one_real = X3
<=> X3 = one_one_real ),
c_0_681 ).
fof(c_0_1389,axiom,
! [X3] :
( zero_zero_int = X3
<=> X3 = zero_zero_int ),
c_0_682 ).
fof(c_0_1390,axiom,
! [X3] :
( zero_zero_nat = X3
<=> X3 = zero_zero_nat ),
c_0_683 ).
fof(c_0_1391,axiom,
! [X3] :
( zero_zero_real = X3
<=> X3 = zero_zero_real ),
c_0_684 ).
fof(c_0_1392,axiom,
zero_zero_real = number267125858f_real(pls),
c_0_685 ).
fof(c_0_1393,axiom,
zero_zero_int = number_number_of_int(pls),
c_0_686 ).
fof(c_0_1394,axiom,
number267125858f_real(pls) = zero_zero_real,
c_0_687 ).
fof(c_0_1395,axiom,
number_number_of_int(pls) = zero_zero_int,
c_0_688 ).
fof(c_0_1396,axiom,
number267125858f_real(pls) = zero_zero_real,
c_0_689 ).
fof(c_0_1397,axiom,
number_number_of_nat(pls) = zero_zero_nat,
c_0_690 ).
fof(c_0_1398,axiom,
number_number_of_int(pls) = zero_zero_int,
c_0_691 ).
fof(c_0_1399,axiom,
bit0(pls) = pls,
c_0_692 ).
fof(c_0_1400,axiom,
zero_zero_nat = number_number_of_nat(pls),
c_0_693 ).
fof(c_0_1401,axiom,
number_number_of_nat(pls) = zero_zero_nat,
c_0_694 ).
fof(c_0_1402,axiom,
zero_zero_int = number_number_of_int(pls),
c_0_695 ).
fof(c_0_1403,axiom,
is_bool(fTrue),
c_0_696 ).
fof(c_0_1404,axiom,
is_bool(fFalse),
c_0_697 ).
fof(c_0_1405,axiom,
zero_zero_int != one_one_int,
c_0_698 ).
fof(c_0_1406,axiom,
zero_zero_nat != one_one_nat,
c_0_699 ).
fof(c_0_1407,axiom,
zero_zero_real != one_one_real,
c_0_700 ).
fof(c_0_1408,axiom,
one_one_int != zero_zero_int,
c_0_701 ).
fof(c_0_1409,axiom,
one_one_nat != zero_zero_nat,
c_0_702 ).
fof(c_0_1410,axiom,
one_one_real != zero_zero_real,
c_0_703 ).
fof(c_0_1411,axiom,
zero_zero_real != one_one_real,
c_0_704 ).
fof(c_0_1412,axiom,
zero_zero_int != one_one_int,
c_0_705 ).
fof(c_0_1413,axiom,
pls = zero_zero_int,
c_0_706 ).
fof(c_0_1414,plain,
! [X5,X6,X7,X8] :
( ( X5 = zero_zero_int
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(X5),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_int(power_power_int(X6),number_number_of_nat(bit0(bit1(pls)))))),zero_zero_int)) )
& ( X6 = zero_zero_int
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(X5),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_int(power_power_int(X6),number_number_of_nat(bit0(bit1(pls)))))),zero_zero_int)) )
& ( X7 != zero_zero_int
| X8 != zero_zero_int
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(X7),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_int(power_power_int(X8),number_number_of_nat(bit0(bit1(pls)))))),zero_zero_int)) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_707])])])])]) ).
fof(c_0_1415,plain,
! [X5,X6,X7,X8] :
( ( X5 = zero_zero_real
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(plus_plus_real(hAPP_nat_real(power_power_real(X5),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_real(power_power_real(X6),number_number_of_nat(bit0(bit1(pls)))))),zero_zero_real)) )
& ( X6 = zero_zero_real
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(plus_plus_real(hAPP_nat_real(power_power_real(X5),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_real(power_power_real(X6),number_number_of_nat(bit0(bit1(pls)))))),zero_zero_real)) )
& ( X7 != zero_zero_real
| X8 != zero_zero_real
| hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(plus_plus_real(hAPP_nat_real(power_power_real(X7),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_real(power_power_real(X8),number_number_of_nat(bit0(bit1(pls)))))),zero_zero_real)) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_708])])])])]) ).
fof(c_0_1416,plain,
! [X45,X46] : ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(plus_plus_real(hAPP_nat_real(power_power_real(X45),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_real(power_power_real(X46),number_number_of_nat(bit0(bit1(pls)))))),zero_zero_real)),
inference(variable_rename,[status(thm)],[c_0_709]) ).
fof(c_0_1417,plain,
! [X45,X46] : ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(X45),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_int(power_power_int(X46),number_number_of_nat(bit0(bit1(pls)))))),zero_zero_int)),
inference(variable_rename,[status(thm)],[c_0_710]) ).
fof(c_0_1418,plain,
! [X250,X251,X252] :
( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,esk16_3(X250,X251,X252)),esk17_3(X250,X251,X252)))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(X252,X250)),X251)),hAPP_nat_nat(X252,hAPP_nat_nat(plus_plus_nat(X250),X251)))) )
& ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(X252,esk16_3(X250,X251,X252))),hAPP_nat_nat(X252,esk17_3(X250,X251,X252))))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(X252,X250)),X251)),hAPP_nat_nat(X252,hAPP_nat_nat(plus_plus_nat(X250),X251)))) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_711])])])]) ).
fof(c_0_1419,plain,
! [X252,X253,X254] :
( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,esk20_3(X252,X253,X254)),esk21_3(X252,X253,X254)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X252),X253))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(X254,X252)),hAPP_nat_nat(X254,X253))) )
& ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(X254,esk20_3(X252,X253,X254))),hAPP_nat_nat(X254,esk21_3(X252,X253,X254))))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X252),X253))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(X254,X252)),hAPP_nat_nat(X254,X253))) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_712])])])]) ).
fof(c_0_1420,plain,
! [X11,X12] : hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),sqrt(hAPP_real_real(plus_plus_real(hAPP_nat_real(power_power_real(X11),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_real(power_power_real(X12),number_number_of_nat(bit0(bit1(pls)))))))),
inference(variable_rename,[status(thm)],[c_0_713]) ).
fof(c_0_1421,plain,
! [X5,X6,X7,X8] :
( ( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),hAPP_real_real(plus_plus_real(hAPP_nat_real(power_power_real(X5),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_real(power_power_real(X6),number_number_of_nat(bit0(bit1(pls)))))))
| X5 != zero_zero_real
| X6 != zero_zero_real )
& ( X7 = zero_zero_real
| hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),hAPP_real_real(plus_plus_real(hAPP_nat_real(power_power_real(X7),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_real(power_power_real(X8),number_number_of_nat(bit0(bit1(pls))))))) )
& ( X8 = zero_zero_real
| hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),hAPP_real_real(plus_plus_real(hAPP_nat_real(power_power_real(X7),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_real(power_power_real(X8),number_number_of_nat(bit0(bit1(pls))))))) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_714])])])])]) ).
fof(c_0_1422,plain,
! [X5,X6,X7,X8] :
( ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(X5),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_int(power_power_int(X6),number_number_of_nat(bit0(bit1(pls)))))))
| X5 != zero_zero_int
| X6 != zero_zero_int )
& ( X7 = zero_zero_int
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(X7),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_int(power_power_int(X8),number_number_of_nat(bit0(bit1(pls))))))) )
& ( X8 = zero_zero_int
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(X7),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_int(power_power_int(X8),number_number_of_nat(bit0(bit1(pls))))))) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_715])])])])]) ).
fof(c_0_1423,plain,
! [X283,X284] : hAPP_nat_int(power_power_int(hAPP_int_int(plus_plus_int(X283),X284)),number_number_of_nat(bit0(bit1(pls)))) = hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(X283),number_number_of_nat(bit0(bit1(pls))))),times_times_int(times_times_int(number_number_of_int(bit0(bit1(pls))),X283),X284))),hAPP_nat_int(power_power_int(X284),number_number_of_nat(bit0(bit1(pls))))),
inference(variable_rename,[status(thm)],[c_0_716]) ).
fof(c_0_1424,plain,
! [X57,X58,X59] :
( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X58),esk1_3(X57,X58,X59)))
| hBOOL(hAPP_int_bool(X57,X59))
| ~ hBOOL(hAPP_int_bool(X57,hAPP_int_int(plus_plus_int(X58),one_one_int)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X58),X59)) )
& ( hBOOL(hAPP_int_bool(X57,esk1_3(X57,X58,X59)))
| hBOOL(hAPP_int_bool(X57,X59))
| ~ hBOOL(hAPP_int_bool(X57,hAPP_int_int(plus_plus_int(X58),one_one_int)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X58),X59)) )
& ( ~ hBOOL(hAPP_int_bool(X57,hAPP_int_int(plus_plus_int(esk1_3(X57,X58,X59)),one_one_int)))
| hBOOL(hAPP_int_bool(X57,X59))
| ~ hBOOL(hAPP_int_bool(X57,hAPP_int_int(plus_plus_int(X58),one_one_int)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X58),X59)) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_717])])])]) ).
fof(c_0_1425,plain,
! [X57,X58,X59] :
( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X58),esk18_3(X57,X58,X59)))
| hBOOL(hAPP_int_bool(X57,X59))
| ~ hBOOL(hAPP_int_bool(X57,X58))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X58),X59)) )
& ( hBOOL(hAPP_int_bool(X57,esk18_3(X57,X58,X59)))
| hBOOL(hAPP_int_bool(X57,X59))
| ~ hBOOL(hAPP_int_bool(X57,X58))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X58),X59)) )
& ( ~ hBOOL(hAPP_int_bool(X57,hAPP_int_int(plus_plus_int(esk18_3(X57,X58,X59)),one_one_int)))
| hBOOL(hAPP_int_bool(X57,X59))
| ~ hBOOL(hAPP_int_bool(X57,X58))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X58),X59)) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_718])])])]) ).
fof(c_0_1426,plain,
! [X247,X248] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(X247),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_int(power_power_int(X248),number_number_of_nat(bit0(bit1(pls))))))),
inference(variable_rename,[status(thm)],[c_0_719]) ).
fof(c_0_1427,plain,
! [X247,X248] : hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),hAPP_real_real(plus_plus_real(hAPP_nat_real(power_power_real(X247),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_real(power_power_real(X248),number_number_of_nat(bit0(bit1(pls))))))),
inference(variable_rename,[status(thm)],[c_0_720]) ).
fof(c_0_1428,plain,
! [X245,X246] :
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_nat_int(power_power_int(X245),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_int(power_power_int(X246),number_number_of_nat(bit0(bit1(pls))))))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X246))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X245),X246)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_721])]) ).
fof(c_0_1429,plain,
! [X245,X246] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(power_power_nat(X245),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_nat(power_power_nat(X246),number_number_of_nat(bit0(bit1(pls))))))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),X246))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X245),X246)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_722])]) ).
fof(c_0_1430,plain,
! [X245,X246] :
( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_nat_real(power_power_real(X245),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_real(power_power_real(X246),number_number_of_nat(bit0(bit1(pls))))))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X246))
| hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X245),X246)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_723])]) ).
fof(c_0_1431,plain,
! [X240,X241] :
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_nat_int(power_power_int(X240),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_int(power_power_int(X241),number_number_of_nat(bit0(bit1(pls))))))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X241))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X240),X241)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_724])]) ).
fof(c_0_1432,plain,
! [X240,X241] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(power_power_nat(X240),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_nat(power_power_nat(X241),number_number_of_nat(bit0(bit1(pls))))))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),X241))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X240),X241)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_725])]) ).
fof(c_0_1433,plain,
! [X240,X241] :
( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_nat_real(power_power_real(X240),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_real(power_power_real(X241),number_number_of_nat(bit0(bit1(pls))))))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X241))
| hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X240),X241)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_726])]) ).
fof(c_0_1434,plain,
! [X31,X32] :
( ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),X31)),X31)),zero_zero_int))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X31),zero_zero_int)) )
& ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X32),zero_zero_int))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),X32)),X32)),zero_zero_int)) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_727])])])]) ).
fof(c_0_1435,plain,
! [X43] : ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_nat_real(power_power_real(X43),number_number_of_nat(bit0(bit1(pls))))),zero_zero_real)),
inference(variable_rename,[status(thm)],[c_0_728]) ).
fof(c_0_1436,plain,
! [X43] : ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_nat_int(power_power_int(X43),number_number_of_nat(bit0(bit1(pls))))),zero_zero_int)),
inference(variable_rename,[status(thm)],[c_0_729]) ).
fof(c_0_1437,plain,
! [X228,X229,X230] :
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_nat_int(power_power_int(X228),X229)),hAPP_nat_int(power_power_int(X230),X229)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X230))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X228),X230)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_730])]) ).
fof(c_0_1438,plain,
! [X228,X229,X230] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(power_power_nat(X228),X229)),hAPP_nat_nat(power_power_nat(X230),X229)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),X230))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X228),X230)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_731])]) ).
fof(c_0_1439,plain,
! [X228,X229,X230] :
( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_nat_real(power_power_real(X228),X229)),hAPP_nat_real(power_power_real(X230),X229)))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X230))
| hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X228),X230)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_732])]) ).
fof(c_0_1440,plain,
! [X180,X181,X182] :
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),X182))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_nat_int(power_power_int(X182),X180)),hAPP_nat_int(power_power_int(X182),X181)))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X180),X181)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_733])]) ).
fof(c_0_1441,plain,
! [X180,X181,X182] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,one_one_nat),X182))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(power_power_nat(X182),X180)),hAPP_nat_nat(power_power_nat(X182),X181)))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X180),X181)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_734])]) ).
fof(c_0_1442,plain,
! [X180,X181,X182] :
( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,one_one_real),X182))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_nat_real(power_power_real(X182),X180)),hAPP_nat_real(power_power_real(X182),X181)))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X180),X181)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_735])]) ).
fof(c_0_1443,plain,
! [X82,X83,X84] :
( ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_nat_int(power_power_int(X84),X82)),hAPP_nat_int(power_power_int(X84),X83)))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X82),X83))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),X84)) )
& ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X82),X83))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_nat_int(power_power_int(X84),X82)),hAPP_nat_int(power_power_int(X84),X83)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),X84)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_736])])]) ).
fof(c_0_1444,plain,
! [X82,X83,X84] :
( ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(power_power_nat(X84),X82)),hAPP_nat_nat(power_power_nat(X84),X83)))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X82),X83))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,one_one_nat),X84)) )
& ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X82),X83))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(power_power_nat(X84),X82)),hAPP_nat_nat(power_power_nat(X84),X83)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,one_one_nat),X84)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_737])])]) ).
fof(c_0_1445,plain,
! [X82,X83,X84] :
( ( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_nat_real(power_power_real(X84),X82)),hAPP_nat_real(power_power_real(X84),X83)))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X82),X83))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,one_one_real),X84)) )
& ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X82),X83))
| hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_nat_real(power_power_real(X84),X82)),hAPP_nat_real(power_power_real(X84),X83)))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,one_one_real),X84)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_738])])]) ).
fof(c_0_1446,plain,
! [X85,X86,X87] :
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),X87))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_nat_int(power_power_int(X87),X85)),hAPP_nat_int(power_power_int(X87),X86)))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X85),X86)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_739])]) ).
fof(c_0_1447,plain,
! [X85,X86,X87] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,one_one_nat),X87))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(power_power_nat(X87),X85)),hAPP_nat_nat(power_power_nat(X87),X86)))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X85),X86)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_740])]) ).
fof(c_0_1448,plain,
! [X85,X86,X87] :
( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,one_one_real),X87))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_nat_real(power_power_real(X87),X85)),hAPP_nat_real(power_power_real(X87),X86)))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X85),X86)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_741])]) ).
fof(c_0_1449,plain,
! [X82,X83,X84] :
( ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_nat_int(power_power_int(X84),X82)),hAPP_nat_int(power_power_int(X84),X83)))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X82),X83))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),X84)) )
& ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X82),X83))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_nat_int(power_power_int(X84),X82)),hAPP_nat_int(power_power_int(X84),X83)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),X84)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_742])])]) ).
fof(c_0_1450,plain,
! [X82,X83,X84] :
( ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(power_power_nat(X84),X82)),hAPP_nat_nat(power_power_nat(X84),X83)))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X82),X83))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,one_one_nat),X84)) )
& ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X82),X83))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(power_power_nat(X84),X82)),hAPP_nat_nat(power_power_nat(X84),X83)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,one_one_nat),X84)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_743])])]) ).
fof(c_0_1451,plain,
! [X82,X83,X84] :
( ( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_nat_real(power_power_real(X84),X82)),hAPP_nat_real(power_power_real(X84),X83)))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X82),X83))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,one_one_real),X84)) )
& ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X82),X83))
| hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_nat_real(power_power_real(X84),X82)),hAPP_nat_real(power_power_real(X84),X83)))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,one_one_real),X84)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_744])])]) ).
fof(c_0_1452,plain,
! [X23,X24,X25] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X25))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(power_power_nat(X25),X23)),hAPP_nat_nat(power_power_nat(X25),X24)))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X23),X24)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_745])]) ).
fof(c_0_1453,plain,
! [X177,X178,X179] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X178),X179))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X177))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X177),one_one_int))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_nat_int(power_power_int(X177),X179)),hAPP_nat_int(power_power_int(X177),X178))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_746])]) ).
fof(c_0_1454,plain,
! [X177,X178,X179] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X178),X179))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),X177))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X177),one_one_nat))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(power_power_nat(X177),X179)),hAPP_nat_nat(power_power_nat(X177),X178))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_747])]) ).
fof(c_0_1455,plain,
! [X177,X178,X179] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X178),X179))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X177))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X177),one_one_real))
| hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_nat_real(power_power_real(X177),X179)),hAPP_nat_real(power_power_real(X177),X178))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_748])]) ).
fof(c_0_1456,plain,
! [X54,X55,X56] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X55),X56))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X54))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X54),one_one_real))
| hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_nat_real(power_power_real(X54),X56)),hAPP_nat_real(power_power_real(X54),X55))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_749])]) ).
fof(c_0_1457,plain,
! [X54,X55,X56] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X55),X56))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X54))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X54),one_one_nat))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(power_power_nat(X54),X56)),hAPP_nat_nat(power_power_nat(X54),X55))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_750])]) ).
fof(c_0_1458,plain,
! [X54,X55,X56] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X55),X56))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X54))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X54),one_one_int))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_nat_int(power_power_int(X54),X56)),hAPP_nat_int(power_power_int(X54),X55))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_751])]) ).
fof(c_0_1459,plain,
! [X237,X238,X239] :
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X238),X239))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X238))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X237))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_nat_int(power_power_int(X238),X237)),hAPP_nat_int(power_power_int(X239),X237))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_752])]) ).
fof(c_0_1460,plain,
! [X237,X238,X239] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X238),X239))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),X238))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X237))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(power_power_nat(X238),X237)),hAPP_nat_nat(power_power_nat(X239),X237))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_753])]) ).
fof(c_0_1461,plain,
! [X237,X238,X239] :
( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X238),X239))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X238))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X237))
| hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_nat_real(power_power_real(X238),X237)),hAPP_nat_real(power_power_real(X239),X237))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_754])]) ).
fof(c_0_1462,plain,
! [X30,X31,X32,X33,X34,X35] :
( ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(X30),X31)),hAPP_nat_nat(plus_plus_nat(X30),X32)))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X31),X32)) )
& ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X34),X35))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(X33),X34)),hAPP_nat_nat(plus_plus_nat(X33),X35))) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_755])])])]) ).
fof(c_0_1463,plain,
! [X171,X172,X173] :
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(plus_plus_int(X171),X172)),hAPP_int_int(plus_plus_int(X171),X173)))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X172),X173)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_756])]) ).
fof(c_0_1464,plain,
! [X171,X172,X173] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(X171),X172)),hAPP_nat_nat(plus_plus_nat(X171),X173)))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X172),X173)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_757])]) ).
fof(c_0_1465,plain,
! [X171,X172,X173] :
( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(plus_plus_real(X171),X172)),hAPP_real_real(plus_plus_real(X171),X173)))
| hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X172),X173)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_758])]) ).
fof(c_0_1466,plain,
! [X168,X169,X170] :
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(plus_plus_int(X168),X169)),hAPP_int_int(plus_plus_int(X170),X169)))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X168),X170)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_759])]) ).
fof(c_0_1467,plain,
! [X168,X169,X170] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(X168),X169)),hAPP_nat_nat(plus_plus_nat(X170),X169)))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X168),X170)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_760])]) ).
fof(c_0_1468,plain,
! [X168,X169,X170] :
( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(plus_plus_real(X168),X169)),hAPP_real_real(plus_plus_real(X170),X169)))
| hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X168),X170)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_761])]) ).
fof(c_0_1469,plain,
! [X107,X108,X109,X110,X111,X112] :
( ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(plus_plus_int(X107),X108)),hAPP_int_int(plus_plus_int(X107),X109)))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X108),X109)) )
& ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X111),X112))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(plus_plus_int(X110),X111)),hAPP_int_int(plus_plus_int(X110),X112))) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_762])])])]) ).
fof(c_0_1470,plain,
! [X107,X108,X109,X110,X111,X112] :
( ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(X107),X108)),hAPP_nat_nat(plus_plus_nat(X107),X109)))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X108),X109)) )
& ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X111),X112))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(X110),X111)),hAPP_nat_nat(plus_plus_nat(X110),X112))) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_763])])])]) ).
fof(c_0_1471,plain,
! [X107,X108,X109,X110,X111,X112] :
( ( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(plus_plus_real(X107),X108)),hAPP_real_real(plus_plus_real(X107),X109)))
| hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X108),X109)) )
& ( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X111),X112))
| hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(plus_plus_real(X110),X111)),hAPP_real_real(plus_plus_real(X110),X112))) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_764])])])]) ).
fof(c_0_1472,plain,
! [X107,X108,X109,X110,X111,X112] :
( ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(plus_plus_int(X107),X108)),hAPP_int_int(plus_plus_int(X109),X108)))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X107),X109)) )
& ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X110),X112))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(plus_plus_int(X110),X111)),hAPP_int_int(plus_plus_int(X112),X111))) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_765])])])]) ).
fof(c_0_1473,plain,
! [X107,X108,X109,X110,X111,X112] :
( ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(X107),X108)),hAPP_nat_nat(plus_plus_nat(X109),X108)))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X107),X109)) )
& ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X110),X112))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(X110),X111)),hAPP_nat_nat(plus_plus_nat(X112),X111))) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_766])])])]) ).
fof(c_0_1474,plain,
! [X107,X108,X109,X110,X111,X112] :
( ( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(plus_plus_real(X107),X108)),hAPP_real_real(plus_plus_real(X109),X108)))
| hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X107),X109)) )
& ( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X110),X112))
| hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(plus_plus_real(X110),X111)),hAPP_real_real(plus_plus_real(X112),X111))) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_767])])])]) ).
fof(c_0_1475,plain,
! [X107,X108,X109,X110,X111,X112] :
( ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(X107),X108)),hAPP_int_int(plus_plus_int(X109),X108)))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X107),X109)) )
& ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X110),X112))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(X110),X111)),hAPP_int_int(plus_plus_int(X112),X111))) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_768])])])]) ).
fof(c_0_1476,plain,
! [X107,X108,X109,X110,X111,X112] :
( ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(X107),X108)),hAPP_nat_nat(plus_plus_nat(X109),X108)))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X107),X109)) )
& ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X110),X112))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(X110),X111)),hAPP_nat_nat(plus_plus_nat(X112),X111))) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_769])])])]) ).
fof(c_0_1477,plain,
! [X107,X108,X109,X110,X111,X112] :
( ( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(plus_plus_real(X107),X108)),hAPP_real_real(plus_plus_real(X109),X108)))
| hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X107),X109)) )
& ( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X110),X112))
| hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(plus_plus_real(X110),X111)),hAPP_real_real(plus_plus_real(X112),X111))) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_770])])])]) ).
fof(c_0_1478,plain,
! [X107,X108,X109,X110,X111,X112] :
( ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(X107),X108)),hAPP_int_int(plus_plus_int(X107),X109)))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X108),X109)) )
& ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X111),X112))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(X110),X111)),hAPP_int_int(plus_plus_int(X110),X112))) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_771])])])]) ).
fof(c_0_1479,plain,
! [X107,X108,X109,X110,X111,X112] :
( ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(X107),X108)),hAPP_nat_nat(plus_plus_nat(X107),X109)))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X108),X109)) )
& ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X111),X112))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(X110),X111)),hAPP_nat_nat(plus_plus_nat(X110),X112))) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_772])])])]) ).
fof(c_0_1480,plain,
! [X107,X108,X109,X110,X111,X112] :
( ( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(plus_plus_real(X107),X108)),hAPP_real_real(plus_plus_real(X107),X109)))
| hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X108),X109)) )
& ( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X111),X112))
| hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(plus_plus_real(X110),X111)),hAPP_real_real(plus_plus_real(X110),X112))) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_773])])])]) ).
fof(c_0_1481,plain,
! [X136,X137,X138] :
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(X136),X137)),hAPP_int_int(plus_plus_int(X138),X137)))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X136),X138)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_774])]) ).
fof(c_0_1482,plain,
! [X136,X137,X138] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(X136),X137)),hAPP_nat_nat(plus_plus_nat(X138),X137)))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X136),X138)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_775])]) ).
fof(c_0_1483,plain,
! [X136,X137,X138] :
( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(plus_plus_real(X136),X137)),hAPP_real_real(plus_plus_real(X138),X137)))
| hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X136),X138)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_776])]) ).
fof(c_0_1484,plain,
! [X133,X134,X135] :
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(X133),X134)),hAPP_int_int(plus_plus_int(X133),X135)))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X134),X135)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_777])]) ).
fof(c_0_1485,plain,
! [X133,X134,X135] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(X133),X134)),hAPP_nat_nat(plus_plus_nat(X133),X135)))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X134),X135)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_778])]) ).
fof(c_0_1486,plain,
! [X133,X134,X135] :
( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(plus_plus_real(X133),X134)),hAPP_real_real(plus_plus_real(X133),X135)))
| hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X134),X135)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_779])]) ).
fof(c_0_1487,plain,
! [X30,X31,X32,X33,X34,X35] :
( ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(X30),X31)),hAPP_nat_nat(plus_plus_nat(X30),X32)))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X31),X32)) )
& ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X34),X35))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(X33),X34)),hAPP_nat_nat(plus_plus_nat(X33),X35))) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_780])])])]) ).
fof(c_0_1488,plain,
! [X32,X33,X34,X35] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X34),X35))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X32),X33))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(X34),X32)),hAPP_nat_nat(plus_plus_nat(X35),X33))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_781])]) ).
fof(c_0_1489,plain,
! [X209,X210,X211,X212] :
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X211),X212))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X209),X210))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(X211),X209)),hAPP_int_int(plus_plus_int(X212),X210))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_782])]) ).
fof(c_0_1490,plain,
! [X198,X199,X200,X201] :
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X200),X201))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X198),X199))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(X200),X198)),hAPP_int_int(plus_plus_int(X201),X199))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_783])]) ).
fof(c_0_1491,plain,
! [X198,X199,X200,X201] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X200),X201))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X198),X199))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(X200),X198)),hAPP_nat_nat(plus_plus_nat(X201),X199))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_784])]) ).
fof(c_0_1492,plain,
! [X198,X199,X200,X201] :
( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X200),X201))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X198),X199))
| hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(plus_plus_real(X200),X198)),hAPP_real_real(plus_plus_real(X201),X199))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_785])]) ).
fof(c_0_1493,plain,
! [X194,X195,X196,X197] :
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X196),X197))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X194),X195))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(X196),X194)),hAPP_int_int(plus_plus_int(X197),X195))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_786])]) ).
fof(c_0_1494,plain,
! [X194,X195,X196,X197] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X196),X197))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X194),X195))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(X196),X194)),hAPP_nat_nat(plus_plus_nat(X197),X195))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_787])]) ).
fof(c_0_1495,plain,
! [X194,X195,X196,X197] :
( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X196),X197))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X194),X195))
| hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(plus_plus_real(X196),X194)),hAPP_real_real(plus_plus_real(X197),X195))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_788])]) ).
fof(c_0_1496,plain,
! [X165,X166,X167,X168] :
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X167),X168))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X165),X166))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(plus_plus_int(X167),X165)),hAPP_int_int(plus_plus_int(X168),X166))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_789])]) ).
fof(c_0_1497,plain,
! [X165,X166,X167,X168] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X167),X168))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X165),X166))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(X167),X165)),hAPP_nat_nat(plus_plus_nat(X168),X166))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_790])]) ).
fof(c_0_1498,plain,
! [X165,X166,X167,X168] :
( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X167),X168))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X165),X166))
| hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(plus_plus_real(X167),X165)),hAPP_real_real(plus_plus_real(X168),X166))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_791])]) ).
fof(c_0_1499,plain,
! [X140,X141,X142,X143] :
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X142),X143))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X140),X141))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(X142),X140)),hAPP_int_int(plus_plus_int(X143),X141))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_792])]) ).
fof(c_0_1500,plain,
! [X140,X141,X142,X143] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X142),X143))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X140),X141))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(X142),X140)),hAPP_nat_nat(plus_plus_nat(X143),X141))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_793])]) ).
fof(c_0_1501,plain,
! [X140,X141,X142,X143] :
( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X142),X143))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X140),X141))
| hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(plus_plus_real(X142),X140)),hAPP_real_real(plus_plus_real(X143),X141))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_794])]) ).
fof(c_0_1502,plain,
! [X32,X33,X34,X35] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X34),X35))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X32),X33))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(X34),X32)),hAPP_nat_nat(plus_plus_nat(X35),X33))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_795])]) ).
fof(c_0_1503,plain,
! [X203,X204,X205] :
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X204),X205))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X204))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_nat_int(power_power_int(X204),X203)),hAPP_nat_int(power_power_int(X205),X203))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_796])]) ).
fof(c_0_1504,plain,
! [X203,X204,X205] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X204),X205))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),X204))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(power_power_nat(X204),X203)),hAPP_nat_nat(power_power_nat(X205),X203))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_797])]) ).
fof(c_0_1505,plain,
! [X203,X204,X205] :
( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X204),X205))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X204))
| hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_nat_real(power_power_real(X204),X203)),hAPP_nat_real(power_power_real(X205),X203))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_798])]) ).
fof(c_0_1506,plain,
! [X174,X175,X176] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X175),X176))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),X174))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_nat_int(power_power_int(X174),X175)),hAPP_nat_int(power_power_int(X174),X176))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_799])]) ).
fof(c_0_1507,plain,
! [X174,X175,X176] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X175),X176))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,one_one_nat),X174))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(power_power_nat(X174),X175)),hAPP_nat_nat(power_power_nat(X174),X176))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_800])]) ).
fof(c_0_1508,plain,
! [X174,X175,X176] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X175),X176))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,one_one_real),X174))
| hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_nat_real(power_power_real(X174),X175)),hAPP_nat_real(power_power_real(X174),X176))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_801])]) ).
fof(c_0_1509,plain,
! [X88,X89,X90] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X89),X90))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),X88))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_nat_int(power_power_int(X88),X89)),hAPP_nat_int(power_power_int(X88),X90))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_802])]) ).
fof(c_0_1510,plain,
! [X88,X89,X90] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X89),X90))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,one_one_nat),X88))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(power_power_nat(X88),X89)),hAPP_nat_nat(power_power_nat(X88),X90))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_803])]) ).
fof(c_0_1511,plain,
! [X88,X89,X90] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X89),X90))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,one_one_real),X88))
| hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_nat_real(power_power_real(X88),X89)),hAPP_nat_real(power_power_real(X88),X90))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_804])]) ).
fof(c_0_1512,plain,
! [X5,X6,X7,X8] :
( ( X5 = zero_zero_real
| hAPP_real_real(plus_plus_real(hAPP_nat_real(power_power_real(X5),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_real(power_power_real(X6),number_number_of_nat(bit0(bit1(pls))))) != zero_zero_real )
& ( X6 = zero_zero_real
| hAPP_real_real(plus_plus_real(hAPP_nat_real(power_power_real(X5),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_real(power_power_real(X6),number_number_of_nat(bit0(bit1(pls))))) != zero_zero_real )
& ( X7 != zero_zero_real
| X8 != zero_zero_real
| hAPP_real_real(plus_plus_real(hAPP_nat_real(power_power_real(X7),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_real(power_power_real(X8),number_number_of_nat(bit0(bit1(pls))))) = zero_zero_real ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_805])])])])]) ).
fof(c_0_1513,plain,
! [X5,X6,X7,X8] :
( ( X5 = zero_zero_real
| hAPP_real_real(plus_plus_real(hAPP_nat_real(power_power_real(X5),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_real(power_power_real(X6),number_number_of_nat(bit0(bit1(pls))))) != zero_zero_real )
& ( X6 = zero_zero_real
| hAPP_real_real(plus_plus_real(hAPP_nat_real(power_power_real(X5),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_real(power_power_real(X6),number_number_of_nat(bit0(bit1(pls))))) != zero_zero_real )
& ( X7 != zero_zero_real
| X8 != zero_zero_real
| hAPP_real_real(plus_plus_real(hAPP_nat_real(power_power_real(X7),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_real(power_power_real(X8),number_number_of_nat(bit0(bit1(pls))))) = zero_zero_real ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_806])])])])]) ).
fof(c_0_1514,plain,
! [X5,X6,X7,X8] :
( ( X5 = zero_zero_int
| hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(X5),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_int(power_power_int(X6),number_number_of_nat(bit0(bit1(pls))))) != zero_zero_int )
& ( X6 = zero_zero_int
| hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(X5),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_int(power_power_int(X6),number_number_of_nat(bit0(bit1(pls))))) != zero_zero_int )
& ( X7 != zero_zero_int
| X8 != zero_zero_int
| hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(X7),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_int(power_power_int(X8),number_number_of_nat(bit0(bit1(pls))))) = zero_zero_int ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_807])])])])]) ).
fof(c_0_1515,plain,
! [X48] : hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_nat_real(semiri132038758t_real,X48)),hAPP_nat_real(power_power_real(number267125858f_real(bit0(bit1(pls)))),X48))),
inference(variable_rename,[status(thm)],[c_0_808]) ).
fof(c_0_1516,plain,
! [X48] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_nat_int(semiri1621563631at_int,X48)),hAPP_nat_int(power_power_int(number_number_of_int(bit0(bit1(pls)))),X48))),
inference(variable_rename,[status(thm)],[c_0_809]) ).
fof(c_0_1517,plain,
! [X55,X56,X57] :
( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X57),X56))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(X55,X57),X56))
| X56 = X57
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X56),X57)) )
& ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(X55,X57),X56))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(X55,X57),X56))
| X56 = X57
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X56),X57)) )
& ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X57),X56))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(X55,X57),X56))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(X55,X57),X56))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X56),X57)) )
& ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(X55,X57),X56))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(X55,X57),X56))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(X55,X57),X56))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X56),X57)) )
& ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X57),X56))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(X55,X57),X56))
| X56 = X57
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(X55,X57),X56)) )
& ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(X55,X57),X56))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(X55,X57),X56))
| X56 = X57
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(X55,X57),X56)) )
& ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X57),X56))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(X55,X57),X56))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(X55,X57),X56))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(X55,X57),X56)) )
& ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(X55,X57),X56))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(X55,X57),X56))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(X55,X57),X56))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(X55,X57),X56)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_810])])]) ).
fof(c_0_1518,plain,
! [X225,X226] :
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X226),zero_zero_int))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X225),zero_zero_int))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(X226),X225)),zero_zero_int)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_811])]) ).
fof(c_0_1519,plain,
! [X225,X226] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X226),zero_zero_nat))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X225),zero_zero_nat))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(X226),X225)),zero_zero_nat)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_812])]) ).
fof(c_0_1520,plain,
! [X225,X226] :
( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X226),zero_zero_real))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X225),zero_zero_real))
| hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(plus_plus_real(X226),X225)),zero_zero_real)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_813])]) ).
fof(c_0_1521,plain,
! [X223,X224] :
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X224),zero_zero_int))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X223),zero_zero_int))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(X224),X223)),zero_zero_int)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_814])]) ).
fof(c_0_1522,plain,
! [X223,X224] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X224),zero_zero_nat))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X223),zero_zero_nat))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(X224),X223)),zero_zero_nat)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_815])]) ).
fof(c_0_1523,plain,
! [X223,X224] :
( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X224),zero_zero_real))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X223),zero_zero_real))
| hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(plus_plus_real(X224),X223)),zero_zero_real)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_816])]) ).
fof(c_0_1524,plain,
! [X190,X191] :
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X191),zero_zero_int))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X190),zero_zero_int))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(plus_plus_int(X191),X190)),zero_zero_int)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_817])]) ).
fof(c_0_1525,plain,
! [X190,X191] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X191),zero_zero_nat))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X190),zero_zero_nat))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(X191),X190)),zero_zero_nat)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_818])]) ).
fof(c_0_1526,plain,
! [X190,X191] :
( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X191),zero_zero_real))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X190),zero_zero_real))
| hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(plus_plus_real(X191),X190)),zero_zero_real)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_819])]) ).
fof(c_0_1527,plain,
! [X149,X150] :
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X150),zero_zero_int))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X149),zero_zero_int))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(X150),X149)),zero_zero_int)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_820])]) ).
fof(c_0_1528,plain,
! [X149,X150] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X150),zero_zero_nat))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X149),zero_zero_nat))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(X150),X149)),zero_zero_nat)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_821])]) ).
fof(c_0_1529,plain,
! [X149,X150] :
( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X150),zero_zero_real))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X149),zero_zero_real))
| hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(plus_plus_real(X150),X149)),zero_zero_real)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_822])]) ).
fof(c_0_1530,plain,
! [X22,X23,X24] :
( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X22),X24))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(X22),X23)),X24)) )
& ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X23),X24))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(X22),X23)),X24)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_823])])]) ).
fof(c_0_1531,plain,
! [X22,X23,X24] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(X22),X23)),X24))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X22),X24)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_824])]) ).
fof(c_0_1532,plain,
! [X22,X23,X24] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(X22),X23)),X24))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X23),X24)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_825])]) ).
fof(c_0_1533,plain,
! [X24,X25,X26] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(X24),X25)),X26))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X24),X26)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_826])]) ).
fof(c_0_1534,plain,
! [X6,X7] :
( ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(plus_plus_int(X6),X6)),zero_zero_int))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X6),zero_zero_int)) )
& ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X7),zero_zero_int))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(plus_plus_int(X7),X7)),zero_zero_int)) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_827])])])]) ).
fof(c_0_1535,plain,
! [X6,X7] :
( ( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(plus_plus_real(X6),X6)),zero_zero_real))
| hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X6),zero_zero_real)) )
& ( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X7),zero_zero_real))
| hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(plus_plus_real(X7),X7)),zero_zero_real)) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_828])])])]) ).
fof(c_0_1536,plain,
! [X6,X7] :
( ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(X6),X6)),zero_zero_int))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X6),zero_zero_int)) )
& ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X7),zero_zero_int))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(X7),X7)),zero_zero_int)) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_829])])])]) ).
fof(c_0_1537,plain,
! [X6,X7] :
( ( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(plus_plus_real(X6),X6)),zero_zero_real))
| hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X6),zero_zero_real)) )
& ( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X7),zero_zero_real))
| hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(plus_plus_real(X7),X7)),zero_zero_real)) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_830])])])]) ).
fof(c_0_1538,plain,
! [X6,X7] :
( ( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(plus_plus_real(X6),X6)),zero_zero_real))
| hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X6),zero_zero_real)) )
& ( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X7),zero_zero_real))
| hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(plus_plus_real(X7),X7)),zero_zero_real)) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_831])])])]) ).
fof(c_0_1539,plain,
! [X6,X7] :
( ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(X6),X6)),zero_zero_int))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X6),zero_zero_int)) )
& ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X7),zero_zero_int))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(X7),X7)),zero_zero_int)) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_832])])])]) ).
fof(c_0_1540,plain,
! [X18,X19,X20] :
( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X19),X20))
| hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(plus_plus_real(X18),X19)),hAPP_real_real(plus_plus_real(X18),X20))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_833])]) ).
fof(c_0_1541,plain,
! [X24,X25,X26] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X25),X26))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(X25),X24)),hAPP_nat_nat(plus_plus_nat(X26),X24))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_834])]) ).
fof(c_0_1542,plain,
! [X24,X25,X26] :
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X25),X26))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(plus_plus_int(X24),X25)),hAPP_int_int(plus_plus_int(X24),X26))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_835])]) ).
fof(c_0_1543,plain,
! [X161,X162,X163] :
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X162),X163))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(plus_plus_int(X161),X162)),hAPP_int_int(plus_plus_int(X161),X163))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_836])]) ).
fof(c_0_1544,plain,
! [X161,X162,X163] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X162),X163))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(X161),X162)),hAPP_nat_nat(plus_plus_nat(X161),X163))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_837])]) ).
fof(c_0_1545,plain,
! [X161,X162,X163] :
( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X162),X163))
| hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(plus_plus_real(X161),X162)),hAPP_real_real(plus_plus_real(X161),X163))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_838])]) ).
fof(c_0_1546,plain,
! [X158,X159,X160] :
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X159),X160))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(plus_plus_int(X159),X158)),hAPP_int_int(plus_plus_int(X160),X158))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_839])]) ).
fof(c_0_1547,plain,
! [X158,X159,X160] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X159),X160))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(X159),X158)),hAPP_nat_nat(plus_plus_nat(X160),X158))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_840])]) ).
fof(c_0_1548,plain,
! [X158,X159,X160] :
( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X159),X160))
| hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(plus_plus_real(X159),X158)),hAPP_real_real(plus_plus_real(X160),X158))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_841])]) ).
fof(c_0_1549,plain,
! [X146,X147,X148] :
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X147),X148))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(X147),X146)),hAPP_int_int(plus_plus_int(X148),X146))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_842])]) ).
fof(c_0_1550,plain,
! [X146,X147,X148] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X147),X148))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(X147),X146)),hAPP_nat_nat(plus_plus_nat(X148),X146))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_843])]) ).
fof(c_0_1551,plain,
! [X146,X147,X148] :
( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X147),X148))
| hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(plus_plus_real(X147),X146)),hAPP_real_real(plus_plus_real(X148),X146))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_844])]) ).
fof(c_0_1552,plain,
! [X143,X144,X145] :
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X144),X145))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(X143),X144)),hAPP_int_int(plus_plus_int(X143),X145))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_845])]) ).
fof(c_0_1553,plain,
! [X143,X144,X145] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X144),X145))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(X143),X144)),hAPP_nat_nat(plus_plus_nat(X143),X145))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_846])]) ).
fof(c_0_1554,plain,
! [X143,X144,X145] :
( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X144),X145))
| hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(plus_plus_real(X143),X144)),hAPP_real_real(plus_plus_real(X143),X145))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_847])]) ).
fof(c_0_1555,plain,
! [X24,X25,X26] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X25),X26))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(X25),X24)),hAPP_nat_nat(plus_plus_nat(X26),X24))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_848])]) ).
fof(c_0_1556,plain,
! [X24,X25,X26] :
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X25),X26))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(X25),X24)),hAPP_int_int(plus_plus_int(X26),X24))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_849])]) ).
fof(c_0_1557,plain,
! [X6,X7] :
( ( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),hAPP_nat_real(power_power_real(X6),number_number_of_nat(bit0(bit1(pls))))))
| X6 != zero_zero_real )
& ( X7 = zero_zero_real
| hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),hAPP_nat_real(power_power_real(X7),number_number_of_nat(bit0(bit1(pls)))))) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_850])])])]) ).
fof(c_0_1558,plain,
! [X6,X7] :
( ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_nat_int(power_power_int(X6),number_number_of_nat(bit0(bit1(pls))))))
| X6 != zero_zero_int )
& ( X7 = zero_zero_int
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_nat_int(power_power_int(X7),number_number_of_nat(bit0(bit1(pls)))))) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_851])])])]) ).
fof(c_0_1559,plain,
! [X31,X32,X33,X34] :
( ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(plus_plus_int(X31),one_one_int)),X32))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X31),X32)) )
& ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X33),X34))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(plus_plus_int(X33),one_one_int)),X34)) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_852])])])]) ).
fof(c_0_1560,plain,
! [X18,X19,X20] : hAPP_int_int(plus_plus_int(hAPP_nat_int(semiri1621563631at_int,X18)),hAPP_int_int(plus_plus_int(hAPP_nat_int(semiri1621563631at_int,X19)),X20)) = hAPP_int_int(plus_plus_int(hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(plus_plus_nat(X18),X19))),X20),
inference(variable_rename,[status(thm)],[c_0_853]) ).
fof(c_0_1561,plain,
! [X30,X31,X32,X33] :
( ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_nat_int(semiri1621563631at_int,X30)),hAPP_nat_int(semiri1621563631at_int,X31)))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X30),X31)) )
& ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X32),X33))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_nat_int(semiri1621563631at_int,X32)),hAPP_nat_int(semiri1621563631at_int,X33))) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_854])])])]) ).
fof(c_0_1562,plain,
! [X5,X6,X7,X8] :
( ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_nat_int(semiri1621563631at_int,X5)),hAPP_nat_int(semiri1621563631at_int,X6)))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X5),X6)) )
& ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X7),X8))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_nat_int(semiri1621563631at_int,X7)),hAPP_nat_int(semiri1621563631at_int,X8))) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_855])])])]) ).
fof(c_0_1563,plain,
! [X30,X31,X32,X33] :
( ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_nat_int(semiri1621563631at_int,X30)),hAPP_nat_int(semiri1621563631at_int,X31)))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X30),X31)) )
& ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X32),X33))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_nat_int(semiri1621563631at_int,X32)),hAPP_nat_int(semiri1621563631at_int,X33))) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_856])])])]) ).
fof(c_0_1564,plain,
! [X30,X31,X32,X33] :
( ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(semiri984289939at_nat,X30)),hAPP_nat_nat(semiri984289939at_nat,X31)))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X30),X31)) )
& ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X32),X33))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(semiri984289939at_nat,X32)),hAPP_nat_nat(semiri984289939at_nat,X33))) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_857])])])]) ).
fof(c_0_1565,plain,
! [X30,X31,X32,X33] :
( ( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_nat_real(semiri132038758t_real,X30)),hAPP_nat_real(semiri132038758t_real,X31)))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X30),X31)) )
& ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X32),X33))
| hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_nat_real(semiri132038758t_real,X32)),hAPP_nat_real(semiri132038758t_real,X33))) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_858])])])]) ).
fof(c_0_1566,plain,
! [X71,X72] :
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_nat_int(semiri1621563631at_int,X71)),hAPP_nat_int(semiri1621563631at_int,X72)))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X71),X72)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_859])]) ).
fof(c_0_1567,plain,
! [X71,X72] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(semiri984289939at_nat,X71)),hAPP_nat_nat(semiri984289939at_nat,X72)))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X71),X72)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_860])]) ).
fof(c_0_1568,plain,
! [X71,X72] :
( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_nat_real(semiri132038758t_real,X71)),hAPP_nat_real(semiri132038758t_real,X72)))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X71),X72)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_861])]) ).
fof(c_0_1569,plain,
! [X30,X31,X32,X33] :
( ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_nat_int(semiri1621563631at_int,X30)),hAPP_nat_int(semiri1621563631at_int,X31)))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X30),X31)) )
& ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X32),X33))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_nat_int(semiri1621563631at_int,X32)),hAPP_nat_int(semiri1621563631at_int,X33))) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_862])])])]) ).
fof(c_0_1570,plain,
! [X30,X31,X32,X33] :
( ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(semiri984289939at_nat,X30)),hAPP_nat_nat(semiri984289939at_nat,X31)))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X30),X31)) )
& ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X32),X33))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(semiri984289939at_nat,X32)),hAPP_nat_nat(semiri984289939at_nat,X33))) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_863])])])]) ).
fof(c_0_1571,plain,
! [X30,X31,X32,X33] :
( ( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_nat_real(semiri132038758t_real,X30)),hAPP_nat_real(semiri132038758t_real,X31)))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X30),X31)) )
& ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X32),X33))
| hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_nat_real(semiri132038758t_real,X32)),hAPP_nat_real(semiri132038758t_real,X33))) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_864])])])]) ).
fof(c_0_1572,plain,
! [X30,X31,X32,X33] :
( ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_nat_int(semiri1621563631at_int,X30)),hAPP_nat_int(semiri1621563631at_int,X31)))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X30),X31)) )
& ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X32),X33))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_nat_int(semiri1621563631at_int,X32)),hAPP_nat_int(semiri1621563631at_int,X33))) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_865])])])]) ).
fof(c_0_1573,plain,
! [X5,X6,X7,X8] :
( ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_nat_int(semiri1621563631at_int,X5)),hAPP_nat_int(semiri1621563631at_int,X6)))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X5),X6)) )
& ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X7),X8))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_nat_int(semiri1621563631at_int,X7)),hAPP_nat_int(semiri1621563631at_int,X8))) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_866])])])]) ).
fof(c_0_1574,plain,
! [X282,X283] :
( ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),esk22_2(X282,X283)))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X282))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X283)) )
& ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,esk22_2(X282,X283)),X283))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X282))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X283)) )
& ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,esk22_2(X282,X283)),X282))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X282))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X283)) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_867])])])]) ).
fof(c_0_1575,plain,
! [X231,X232,X233] :
( hAPP_nat_int(power_power_int(X231),X232) != hAPP_nat_int(power_power_int(X233),X232)
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X231))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X233))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X232))
| X231 = X233 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_868])]) ).
fof(c_0_1576,plain,
! [X231,X232,X233] :
( hAPP_nat_nat(power_power_nat(X231),X232) != hAPP_nat_nat(power_power_nat(X233),X232)
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),X231))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),X233))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X232))
| X231 = X233 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_869])]) ).
fof(c_0_1577,plain,
! [X231,X232,X233] :
( hAPP_nat_real(power_power_real(X231),X232) != hAPP_nat_real(power_power_real(X233),X232)
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X231))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X233))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X232))
| X231 = X233 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_870])]) ).
fof(c_0_1578,plain,
! [X17] : hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,one_one_real),hAPP_nat_real(power_power_real(number267125858f_real(bit0(bit1(pls)))),X17))),
inference(variable_rename,[status(thm)],[c_0_871]) ).
fof(c_0_1579,plain,
! [X92,X93,X95] :
( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,esk14_2(X92,X93)),X92))
| ~ hBOOL(hAPP_nat_bool(X93,X92))
| hBOOL(hAPP_nat_bool(X93,zero_zero_nat)) )
& ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X95),esk14_2(X92,X93)))
| ~ hBOOL(hAPP_nat_bool(X93,X95))
| ~ hBOOL(hAPP_nat_bool(X93,X92))
| hBOOL(hAPP_nat_bool(X93,zero_zero_nat)) )
& ( hBOOL(hAPP_nat_bool(X93,hAPP_nat_nat(plus_plus_nat(esk14_2(X92,X93)),one_one_nat)))
| ~ hBOOL(hAPP_nat_bool(X93,X92))
| hBOOL(hAPP_nat_bool(X93,zero_zero_nat)) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_872])])])])]) ).
fof(c_0_1580,plain,
! [X221,X222,X223] :
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X223))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X221),X222))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X221),hAPP_int_int(plus_plus_int(X223),X222))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_873])]) ).
fof(c_0_1581,plain,
! [X221,X222,X223] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),X223))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X221),X222))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X221),hAPP_nat_nat(plus_plus_nat(X223),X222))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_874])]) ).
fof(c_0_1582,plain,
! [X221,X222,X223] :
( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X223))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X221),X222))
| hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X221),hAPP_real_real(plus_plus_real(X223),X222))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_875])]) ).
fof(c_0_1583,plain,
! [X218,X219,X220] :
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X220))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X218),X219))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X218),hAPP_int_int(plus_plus_int(X220),X219))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_876])]) ).
fof(c_0_1584,plain,
! [X218,X219,X220] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X220))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X218),X219))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X218),hAPP_nat_nat(plus_plus_nat(X220),X219))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_877])]) ).
fof(c_0_1585,plain,
! [X218,X219,X220] :
( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X220))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X218),X219))
| hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X218),hAPP_real_real(plus_plus_real(X220),X219))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_878])]) ).
fof(c_0_1586,plain,
! [X188,X189,X190] :
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X190))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X188),X189))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X188),hAPP_int_int(plus_plus_int(X189),X190))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_879])]) ).
fof(c_0_1587,plain,
! [X188,X189,X190] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),X190))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X188),X189))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X188),hAPP_nat_nat(plus_plus_nat(X189),X190))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_880])]) ).
fof(c_0_1588,plain,
! [X188,X189,X190] :
( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X190))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X188),X189))
| hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X188),hAPP_real_real(plus_plus_real(X189),X190))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_881])]) ).
fof(c_0_1589,plain,
! [X185,X186,X187] :
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X187))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X185),X186))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X185),hAPP_int_int(plus_plus_int(X187),X186))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_882])]) ).
fof(c_0_1590,plain,
! [X185,X186,X187] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),X187))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X185),X186))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X185),hAPP_nat_nat(plus_plus_nat(X187),X186))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_883])]) ).
fof(c_0_1591,plain,
! [X185,X186,X187] :
( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X187))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X185),X186))
| hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X185),hAPP_real_real(plus_plus_real(X187),X186))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_884])]) ).
fof(c_0_1592,plain,
! [X78,X79,X80] :
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X80))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X78),X79))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X78),hAPP_int_int(plus_plus_int(X80),X79))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_885])]) ).
fof(c_0_1593,plain,
! [X78,X79,X80] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X80))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X78),X79))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X78),hAPP_nat_nat(plus_plus_nat(X80),X79))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_886])]) ).
fof(c_0_1594,plain,
! [X78,X79,X80] :
( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X80))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X78),X79))
| hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X78),hAPP_real_real(plus_plus_real(X80),X79))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_887])]) ).
fof(c_0_1595,plain,
! [X242,X243] :
( hAPP_nat_int(power_power_int(X242),number_number_of_nat(bit0(bit1(pls)))) != hAPP_nat_int(power_power_int(X243),number_number_of_nat(bit0(bit1(pls))))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X242))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X243))
| X242 = X243 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_888])]) ).
fof(c_0_1596,plain,
! [X242,X243] :
( hAPP_nat_nat(power_power_nat(X242),number_number_of_nat(bit0(bit1(pls)))) != hAPP_nat_nat(power_power_nat(X243),number_number_of_nat(bit0(bit1(pls))))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),X242))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),X243))
| X242 = X243 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_889])]) ).
fof(c_0_1597,plain,
! [X242,X243] :
( hAPP_nat_real(power_power_real(X242),number_number_of_nat(bit0(bit1(pls)))) != hAPP_nat_real(power_power_real(X243),number_number_of_nat(bit0(bit1(pls))))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X242))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X243))
| X242 = X243 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_890])]) ).
fof(c_0_1598,plain,
! [X154,X155,X157] :
( ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),esk4_2(X154,X155)))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X154))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X155)) )
& ( hAPP_nat_real(power_power_real(esk4_2(X154,X155)),X155) = X154
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X154))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X155)) )
& ( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X157))
| hAPP_nat_real(power_power_real(X157),X155) != X154
| X157 = esk4_2(X154,X155)
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X154))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X155)) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_891])])])])]) ).
fof(c_0_1599,plain,
! [X30,X31,X32,X33] :
( ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(plus_plus_nat(X30),X31)))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X30))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X31)) )
& ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X32))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(plus_plus_nat(X32),X33))) )
& ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X33))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(plus_plus_nat(X32),X33))) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_892])])])])]) ).
fof(c_0_1600,plain,
! [X61,X62,X63,X64] :
( ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X61),X62))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),X62))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,number_number_of_nat(X61)),number_number_of_nat(X62))) )
& ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X61),X62))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,number_number_of_nat(X61)),number_number_of_nat(X62))) )
& ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X63),X64))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X63),X64))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,number_number_of_nat(X63)),number_number_of_nat(X64))) )
& ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),X64))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X63),X64))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,number_number_of_nat(X63)),number_number_of_nat(X64))) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_893])])])])]) ).
fof(c_0_1601,plain,
! [X215,X216] :
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X216))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X215))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_int_int(plus_plus_int(X216),X215))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_894])]) ).
fof(c_0_1602,plain,
! [X215,X216] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),X216))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X215))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(plus_plus_nat(X216),X215))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_895])]) ).
fof(c_0_1603,plain,
! [X215,X216] :
( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X216))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X215))
| hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),hAPP_real_real(plus_plus_real(X216),X215))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_896])]) ).
fof(c_0_1604,plain,
! [X213,X214] :
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X214))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X213))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_int_int(plus_plus_int(X214),X213))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_897])]) ).
fof(c_0_1605,plain,
! [X213,X214] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X214))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),X213))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(plus_plus_nat(X214),X213))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_898])]) ).
fof(c_0_1606,plain,
! [X213,X214] :
( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X214))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X213))
| hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),hAPP_real_real(plus_plus_real(X214),X213))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_899])]) ).
fof(c_0_1607,plain,
! [X11,X12] :
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X12))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X11))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_int_int(plus_plus_int(X12),X11))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_900])]) ).
fof(c_0_1608,plain,
! [X182,X183] :
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X183))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X182))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_int_int(plus_plus_int(X183),X182))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_901])]) ).
fof(c_0_1609,plain,
! [X182,X183] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),X183))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),X182))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),hAPP_nat_nat(plus_plus_nat(X183),X182))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_902])]) ).
fof(c_0_1610,plain,
! [X182,X183] :
( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X183))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X182))
| hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),hAPP_real_real(plus_plus_real(X183),X182))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_903])]) ).
fof(c_0_1611,plain,
! [X151,X152] :
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X152))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X151))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_int_int(plus_plus_int(X152),X151))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_904])]) ).
fof(c_0_1612,plain,
! [X151,X152] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X152))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X151))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(plus_plus_nat(X152),X151))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_905])]) ).
fof(c_0_1613,plain,
! [X151,X152] :
( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X152))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X151))
| hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),hAPP_real_real(plus_plus_real(X152),X151))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_906])]) ).
fof(c_0_1614,plain,
! [X50,X51] :
( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,one_one_real),X51))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X50))
| hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,one_one_real),hAPP_nat_real(power_power_real(X51),X50))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_907])]) ).
fof(c_0_1615,plain,
! [X50,X51] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,one_one_nat),X51))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X50))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,one_one_nat),hAPP_nat_nat(power_power_nat(X51),X50))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_908])]) ).
fof(c_0_1616,plain,
! [X50,X51] :
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),X51))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X50))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),hAPP_nat_int(power_power_int(X51),X50))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_909])]) ).
fof(c_0_1617,plain,
! [X24,X25] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(X24),X25)),X25)),
inference(variable_rename,[status(thm)],[c_0_910]) ).
fof(c_0_1618,plain,
! [X24,X25] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(X24),X25)),X24)),
inference(variable_rename,[status(thm)],[c_0_911]) ).
fof(c_0_1619,plain,
! [X60,X61,X62,X63] :
( ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,number_number_of_int(X60)),number_number_of_int(X61)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(X61)),number_number_of_int(X60))) )
& ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(X63)),number_number_of_int(X62)))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,number_number_of_int(X62)),number_number_of_int(X63))) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_912])])])]) ).
fof(c_0_1620,plain,
! [X60,X61,X62,X63] :
( ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,number_number_of_nat(X60)),number_number_of_nat(X61)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,number_number_of_nat(X61)),number_number_of_nat(X60))) )
& ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,number_number_of_nat(X63)),number_number_of_nat(X62)))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,number_number_of_nat(X62)),number_number_of_nat(X63))) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_913])])])]) ).
fof(c_0_1621,plain,
! [X60,X61,X62,X63] :
( ( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,number267125858f_real(X60)),number267125858f_real(X61)))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,number267125858f_real(X61)),number267125858f_real(X60))) )
& ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,number267125858f_real(X63)),number267125858f_real(X62)))
| hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,number267125858f_real(X62)),number267125858f_real(X63))) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_914])])])]) ).
fof(c_0_1622,plain,
! [X26,X27,X28,X29] :
( ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(power_power_nat(X26),number_number_of_nat(X27))))
| number_number_of_nat(X27) = zero_zero_nat
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X26)) )
& ( number_number_of_nat(X29) != zero_zero_nat
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(power_power_nat(X28),number_number_of_nat(X29)))) )
& ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X28))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(power_power_nat(X28),number_number_of_nat(X29)))) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_915])])])])]) ).
fof(c_0_1623,plain,
! [X155,X156] :
( ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),esk5_2(X155,X156)))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X155))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X156)) )
& ( hAPP_nat_real(power_power_real(esk5_2(X155,X156)),X156) = X155
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X155))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X156)) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_916])])])]) ).
fof(c_0_1624,plain,
! [X18,X19] :
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X18),X19))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(plus_plus_int(X18),one_one_int)),X19)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_917])]) ).
fof(c_0_1625,plain,
! [X9] : hAPP_nat_int(power_power_int(hAPP_nat_int(power_power_int(X9),number_number_of_nat(bit0(bit1(pls))))),number_number_of_nat(bit0(bit1(pls)))) = hAPP_nat_int(power_power_int(X9),number_number_of_nat(bit0(bit0(bit1(pls))))),
inference(variable_rename,[status(thm)],[c_0_918]) ).
fof(c_0_1626,plain,
! [X69,X70] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X69),X70))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_nat_int(semiri1621563631at_int,X69)),hAPP_nat_int(semiri1621563631at_int,X70))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_919])]) ).
fof(c_0_1627,plain,
! [X69,X70] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X69),X70))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(semiri984289939at_nat,X69)),hAPP_nat_nat(semiri984289939at_nat,X70))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_920])]) ).
fof(c_0_1628,plain,
! [X69,X70] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X69),X70))
| hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_nat_real(semiri132038758t_real,X69)),hAPP_nat_real(semiri132038758t_real,X70))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_921])]) ).
fof(c_0_1629,plain,
! [X9] :
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X9))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X9),number_number_of_int(bit0(bit1(pls)))))
| X9 = zero_zero_int
| X9 = one_one_int ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_922])]) ).
fof(c_0_1630,plain,
! [X61,X62,X63,X64] :
( ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,number_number_of_nat(X61)),number_number_of_nat(X62)))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X61),X62))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X61),pls)) )
& ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X63),X64))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,number_number_of_nat(X63)),number_number_of_nat(X64))) )
& ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X63),pls))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,number_number_of_nat(X63)),number_number_of_nat(X64))) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_923])])])])]) ).
fof(c_0_1631,plain,
! [X92,X93,X95] :
( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,esk19_2(X92,X93)),X92))
| ~ hBOOL(hAPP_nat_bool(X93,X92))
| hBOOL(hAPP_nat_bool(X93,zero_zero_nat)) )
& ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X95),esk19_2(X92,X93)))
| ~ hBOOL(hAPP_nat_bool(X93,X95))
| ~ hBOOL(hAPP_nat_bool(X93,X92))
| hBOOL(hAPP_nat_bool(X93,zero_zero_nat)) )
& ( hBOOL(hAPP_nat_bool(X93,esk19_2(X92,X93)))
| ~ hBOOL(hAPP_nat_bool(X93,X92))
| hBOOL(hAPP_nat_bool(X93,zero_zero_nat)) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_924])])])])]) ).
fof(c_0_1632,plain,
! [X263,X264,X265] :
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X264),X265))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X265),X263))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X264),X263)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_925])]) ).
fof(c_0_1633,plain,
! [X263,X264,X265] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X264),X265))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X265),X263))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X264),X263)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_926])]) ).
fof(c_0_1634,plain,
! [X263,X264,X265] :
( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X264),X265))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X265),X263))
| hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X264),X263)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_927])]) ).
fof(c_0_1635,plain,
! [X258,X259,X260] :
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X259),X260))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X258),X259))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X258),X260)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_928])]) ).
fof(c_0_1636,plain,
! [X258,X259,X260] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X259),X260))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X258),X259))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X258),X260)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_929])]) ).
fof(c_0_1637,plain,
! [X258,X259,X260] :
( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X259),X260))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X258),X259))
| hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X258),X260)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_930])]) ).
fof(c_0_1638,plain,
! [X24,X25,X26] :
( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X25),X26))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X26),X24))
| hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X25),X24)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_931])]) ).
fof(c_0_1639,plain,
! [X24,X25,X26] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X25),X26))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X26),X24))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X25),X24)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_932])]) ).
fof(c_0_1640,plain,
! [X24,X25,X26] :
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X25),X26))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X26),X24))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X25),X24)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_933])]) ).
fof(c_0_1641,plain,
! [X31,X32,X33,X34] :
( ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X31),hAPP_int_int(plus_plus_int(X32),one_one_int)))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X31),X32))
| X31 = X32 )
& ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X33),X34))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X33),hAPP_int_int(plus_plus_int(X34),one_one_int))) )
& ( X33 != X34
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X33),hAPP_int_int(plus_plus_int(X34),one_one_int))) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_934])])])])]) ).
fof(c_0_1642,plain,
! [X31,X32,X33,X34] :
( ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X31),hAPP_int_int(plus_plus_int(X32),one_one_int)))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X31),X32)) )
& ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X33),X34))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X33),hAPP_int_int(plus_plus_int(X34),one_one_int))) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_935])])])]) ).
fof(c_0_1643,plain,
! [X19,X20,X21,X22] :
( ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(power_power_nat(X19),X20)))
| X20 = zero_zero_nat
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X19)) )
& ( X22 != zero_zero_nat
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(power_power_nat(X21),X22))) )
& ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X21))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(power_power_nat(X21),X22))) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_936])])])])]) ).
fof(c_0_1644,plain,
! [X19,X20,X21,X22] :
( ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(power_power_nat(X19),X20)))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X19))
| X20 = zero_zero_nat )
& ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X21))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(power_power_nat(X21),X22))) )
& ( X22 != zero_zero_nat
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(power_power_nat(X21),X22))) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_937])])])])]) ).
fof(c_0_1645,plain,
! [X233,X234] :
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X234))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X233))
| hAPP_int_int(plus_plus_int(number_number_of_int(X234)),number_number_of_int(X233)) = number_number_of_int(hAPP_int_int(plus_plus_int(X234),X233)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_938])]) ).
fof(c_0_1646,plain,
! [X233,X234] :
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X234))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X233))
| hAPP_nat_nat(plus_plus_nat(number_number_of_nat(X234)),number_number_of_nat(X233)) = number_number_of_nat(hAPP_int_int(plus_plus_int(X234),X233)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_939])]) ).
fof(c_0_1647,plain,
! [X233,X234] :
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X234))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X233))
| hAPP_real_real(plus_plus_real(number267125858f_real(X234)),number267125858f_real(X233)) = number267125858f_real(hAPP_int_int(plus_plus_int(X234),X233)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_940])]) ).
fof(c_0_1648,plain,
! [X6,X7] :
( ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_int_int(plus_plus_int(X6),X6)))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X6)) )
& ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X7))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_int_int(plus_plus_int(X7),X7))) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_941])])])]) ).
fof(c_0_1649,plain,
! [X6,X7] :
( ( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),hAPP_real_real(plus_plus_real(X6),X6)))
| hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X6)) )
& ( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X7))
| hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),hAPP_real_real(plus_plus_real(X7),X7))) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_942])])])]) ).
fof(c_0_1650,plain,
! [X6,X7] :
( ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_int_int(plus_plus_int(X6),X6)))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X6)) )
& ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X7))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_int_int(plus_plus_int(X7),X7))) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_943])])])]) ).
fof(c_0_1651,plain,
! [X6,X7] :
( ( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),hAPP_real_real(plus_plus_real(X6),X6)))
| hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X6)) )
& ( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X7))
| hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),hAPP_real_real(plus_plus_real(X7),X7))) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_944])])])]) ).
fof(c_0_1652,plain,
! [X153,X155,X156,X158] :
( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),esk8_1(X153)))
| hBOOL(hAPP_int_bool(X153,hAPP_nat_int(semiri1621563631at_int,X155))) )
& ( ~ hBOOL(hAPP_int_bool(X153,esk8_1(X153)))
| hBOOL(hAPP_int_bool(X153,hAPP_nat_int(semiri1621563631at_int,X155))) )
& ( ~ hBOOL(hAPP_int_bool(X156,hAPP_nat_int(semiri1621563631at_int,esk9_1(X156))))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X158))
| hBOOL(hAPP_int_bool(X156,X158)) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_945])])])])])]) ).
fof(c_0_1653,plain,
! [X37,X38,X39] : hAPP_real_real(plus_plus_real(number267125858f_real(X37)),hAPP_real_real(plus_plus_real(number267125858f_real(X38)),X39)) = hAPP_real_real(plus_plus_real(number267125858f_real(hAPP_int_int(plus_plus_int(X37),X38))),X39),
inference(variable_rename,[status(thm)],[c_0_946]) ).
fof(c_0_1654,plain,
! [X37,X38,X39] : hAPP_int_int(plus_plus_int(number_number_of_int(X37)),hAPP_int_int(plus_plus_int(number_number_of_int(X38)),X39)) = hAPP_int_int(plus_plus_int(number_number_of_int(hAPP_int_int(plus_plus_int(X37),X38))),X39),
inference(variable_rename,[status(thm)],[c_0_947]) ).
fof(c_0_1655,plain,
! [X9] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X9),hAPP_nat_int(power_power_int(X9),number_number_of_nat(bit0(bit1(pls)))))),
inference(variable_rename,[status(thm)],[c_0_948]) ).
fof(c_0_1656,plain,
! [X24,X25,X26] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X25),X26))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X25),hAPP_nat_nat(plus_plus_nat(X24),X26))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_949])]) ).
fof(c_0_1657,plain,
! [X24,X25,X26] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X25),X26))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X25),hAPP_nat_nat(plus_plus_nat(X26),X24))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_950])]) ).
fof(c_0_1658,plain,
! [X24,X25,X26] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X25),X26))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X25),hAPP_nat_nat(plus_plus_nat(X24),X26))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_951])]) ).
fof(c_0_1659,plain,
! [X24,X25,X26] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X25),X26))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X25),hAPP_nat_nat(plus_plus_nat(X26),X24))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_952])]) ).
fof(c_0_1660,plain,
! [X106,X107,X108,X109] : hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(X106),X107)),hAPP_int_int(plus_plus_int(X108),X109)) = hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(X106),X108)),hAPP_int_int(plus_plus_int(X107),X109)),
inference(variable_rename,[status(thm)],[c_0_953]) ).
fof(c_0_1661,plain,
! [X106,X107,X108,X109] : hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(plus_plus_nat(X106),X107)),hAPP_nat_nat(plus_plus_nat(X108),X109)) = hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(plus_plus_nat(X106),X108)),hAPP_nat_nat(plus_plus_nat(X107),X109)),
inference(variable_rename,[status(thm)],[c_0_954]) ).
fof(c_0_1662,plain,
! [X106,X107,X108,X109] : hAPP_real_real(plus_plus_real(hAPP_real_real(plus_plus_real(X106),X107)),hAPP_real_real(plus_plus_real(X108),X109)) = hAPP_real_real(plus_plus_real(hAPP_real_real(plus_plus_real(X106),X108)),hAPP_real_real(plus_plus_real(X107),X109)),
inference(variable_rename,[status(thm)],[c_0_955]) ).
fof(c_0_1663,plain,
! [X238] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_nat_int(power_power_int(X238),number_number_of_nat(bit0(bit1(pls)))))),
inference(variable_rename,[status(thm)],[c_0_956]) ).
fof(c_0_1664,plain,
! [X238] : hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),hAPP_nat_real(power_power_real(X238),number_number_of_nat(bit0(bit1(pls)))))),
inference(variable_rename,[status(thm)],[c_0_957]) ).
fof(c_0_1665,plain,
! [X19,X20] :
( ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_nat_int(semiri1621563631at_int,X19)),zero_zero_int))
| X19 = zero_zero_nat )
& ( X20 != zero_zero_nat
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_nat_int(semiri1621563631at_int,X20)),zero_zero_int)) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_958])])])]) ).
fof(c_0_1666,plain,
! [X32,X33,X34,X35] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X34),X35))
| hAPP_nat_nat(plus_plus_nat(X32),X35) != hAPP_nat_nat(plus_plus_nat(X34),X33)
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X32),X33)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_959])]) ).
fof(c_0_1667,plain,
! [X153,X154,X156,X157] :
( ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X154))
| ~ hBOOL(hAPP_int_bool(X153,X154))
| hBOOL(hAPP_int_bool(X153,hAPP_nat_int(semiri1621563631at_int,esk6_1(X153)))) )
& ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),esk7_1(X156)))
| ~ hBOOL(hAPP_int_bool(X156,hAPP_nat_int(semiri1621563631at_int,X157))) )
& ( hBOOL(hAPP_int_bool(X156,esk7_1(X156)))
| ~ hBOOL(hAPP_int_bool(X156,hAPP_nat_int(semiri1621563631at_int,X157))) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_960])])])])])]) ).
fof(c_0_1668,plain,
! [X89] : ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_nat_int(semiri1621563631at_int,X89)),zero_zero_int)),
inference(variable_rename,[status(thm)],[c_0_961]) ).
fof(c_0_1669,plain,
! [X89] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(semiri984289939at_nat,X89)),zero_zero_nat)),
inference(variable_rename,[status(thm)],[c_0_962]) ).
fof(c_0_1670,plain,
! [X89] : ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_nat_real(semiri132038758t_real,X89)),zero_zero_real)),
inference(variable_rename,[status(thm)],[c_0_963]) ).
fof(c_0_1671,plain,
! [X22] : ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_nat_int(semiri1621563631at_int,X22)),zero_zero_int)),
inference(variable_rename,[status(thm)],[c_0_964]) ).
fof(c_0_1672,plain,
! [X248,X249,X250] :
( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X250))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X250))
| ~ hBOOL(X249)
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X250)) )
& ( hBOOL(X248)
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X250))
| ~ hBOOL(X249)
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X250)) )
& ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X250))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X250))
| ~ hBOOL(X248)
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X250)) )
& ( hBOOL(X249)
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X250))
| ~ hBOOL(X248)
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X250)) )
& ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X250))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X250))
| ~ hBOOL(X249)
| ~ hBOOL(X249)
| ~ hBOOL(X248) )
& ( hBOOL(X248)
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X250))
| ~ hBOOL(X249)
| ~ hBOOL(X249)
| ~ hBOOL(X248) )
& ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X250))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X250))
| ~ hBOOL(X248)
| ~ hBOOL(X249)
| ~ hBOOL(X248) )
& ( hBOOL(X249)
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X250))
| ~ hBOOL(X248)
| ~ hBOOL(X249)
| ~ hBOOL(X248) )
& ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X250))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X250))
| ~ hBOOL(X249)
| hBOOL(X249)
| hBOOL(X248) )
& ( hBOOL(X248)
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X250))
| ~ hBOOL(X249)
| hBOOL(X249)
| hBOOL(X248) )
& ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X250))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X250))
| ~ hBOOL(X248)
| hBOOL(X249)
| hBOOL(X248) )
& ( hBOOL(X249)
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X250))
| ~ hBOOL(X248)
| hBOOL(X249)
| hBOOL(X248) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_965])])]) ).
fof(c_0_1673,plain,
! [X17,X18] :
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X18))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_nat_int(power_power_int(X18),X17))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_966])]) ).
fof(c_0_1674,plain,
! [X205,X206] :
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),X206))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),hAPP_nat_int(power_power_int(X206),X205))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_967])]) ).
fof(c_0_1675,plain,
! [X205,X206] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,one_one_nat),X206))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,one_one_nat),hAPP_nat_nat(power_power_nat(X206),X205))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_968])]) ).
fof(c_0_1676,plain,
! [X205,X206] :
( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,one_one_real),X206))
| hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,one_one_real),hAPP_nat_real(power_power_real(X206),X205))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_969])]) ).
fof(c_0_1677,plain,
! [X200,X201] :
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X201))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_nat_int(power_power_int(X201),X200))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_970])]) ).
fof(c_0_1678,plain,
! [X200,X201] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),X201))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),hAPP_nat_nat(power_power_nat(X201),X200))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_971])]) ).
fof(c_0_1679,plain,
! [X200,X201] :
( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X201))
| hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),hAPP_nat_real(power_power_real(X201),X200))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_972])]) ).
fof(c_0_1680,plain,
! [X80,X81] :
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X81))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_nat_int(power_power_int(X81),X80))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_973])]) ).
fof(c_0_1681,plain,
! [X80,X81] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X81))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(power_power_nat(X81),X80))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_974])]) ).
fof(c_0_1682,plain,
! [X80,X81] :
( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X81))
| hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),hAPP_nat_real(power_power_real(X81),X80))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_975])]) ).
fof(c_0_1683,plain,
! [X248,X249,X250] :
( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X250))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X250))
| hBOOL(X248)
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X250)) )
& ( ~ hBOOL(X249)
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X250))
| hBOOL(X248)
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X250)) )
& ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X250))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X250))
| hBOOL(X249)
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X250)) )
& ( ~ hBOOL(X248)
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X250))
| hBOOL(X249)
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X250)) )
& ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X250))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X250))
| hBOOL(X248)
| ~ hBOOL(X249)
| ~ hBOOL(X248) )
& ( ~ hBOOL(X249)
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X250))
| hBOOL(X248)
| ~ hBOOL(X249)
| ~ hBOOL(X248) )
& ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X250))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X250))
| hBOOL(X249)
| ~ hBOOL(X249)
| ~ hBOOL(X248) )
& ( ~ hBOOL(X248)
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X250))
| hBOOL(X249)
| ~ hBOOL(X249)
| ~ hBOOL(X248) )
& ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X250))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X250))
| hBOOL(X248)
| hBOOL(X249)
| hBOOL(X248) )
& ( ~ hBOOL(X249)
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X250))
| hBOOL(X248)
| hBOOL(X249)
| hBOOL(X248) )
& ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X250))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X250))
| hBOOL(X249)
| hBOOL(X249)
| hBOOL(X248) )
& ( ~ hBOOL(X248)
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X250))
| hBOOL(X249)
| hBOOL(X249)
| hBOOL(X248) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_976])])]) ).
fof(c_0_1684,plain,
! [X5,X6] :
( ( X6 = zero_zero_int
| hAPP_int_int(plus_plus_int(X6),X5) != zero_zero_int
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X5))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X6)) )
& ( X5 = zero_zero_int
| hAPP_int_int(plus_plus_int(X6),X5) != zero_zero_int
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X5))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X6)) )
& ( X6 != zero_zero_int
| X5 != zero_zero_int
| hAPP_int_int(plus_plus_int(X6),X5) = zero_zero_int
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X5))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X6)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_977])])]) ).
fof(c_0_1685,plain,
! [X5,X6] :
( ( X6 = zero_zero_nat
| hAPP_nat_nat(plus_plus_nat(X6),X5) != zero_zero_nat
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),X5))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),X6)) )
& ( X5 = zero_zero_nat
| hAPP_nat_nat(plus_plus_nat(X6),X5) != zero_zero_nat
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),X5))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),X6)) )
& ( X6 != zero_zero_nat
| X5 != zero_zero_nat
| hAPP_nat_nat(plus_plus_nat(X6),X5) = zero_zero_nat
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),X5))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),X6)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_978])])]) ).
fof(c_0_1686,plain,
! [X5,X6] :
( ( X6 = zero_zero_real
| hAPP_real_real(plus_plus_real(X6),X5) != zero_zero_real
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X5))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X6)) )
& ( X5 = zero_zero_real
| hAPP_real_real(plus_plus_real(X6),X5) != zero_zero_real
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X5))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X6)) )
& ( X6 != zero_zero_real
| X5 != zero_zero_real
| hAPP_real_real(plus_plus_real(X6),X5) = zero_zero_real
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X5))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X6)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_979])])]) ).
fof(c_0_1687,plain,
! [X21,X22,X23,X24] :
( ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,bit1(X21)),bit0(X22)))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X21),X22)) )
& ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X23),X24))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,bit1(X23)),bit0(X24))) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_980])])])]) ).
fof(c_0_1688,plain,
! [X13,X14,X15,X16] :
( ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,bit1(X13)),bit0(X14)))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X13),X14)) )
& ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X15),X16))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,bit1(X15)),bit0(X16))) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_981])])])]) ).
fof(c_0_1689,plain,
! [X21,X22,X23,X24] :
( ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit0(X21)),bit1(X22)))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X21),X22)) )
& ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X23),X24))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit0(X23)),bit1(X24))) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_982])])])]) ).
fof(c_0_1690,plain,
! [X13,X14,X15,X16] :
( ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit0(X13)),bit1(X14)))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X13),X14)) )
& ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X15),X16))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit0(X15)),bit1(X16))) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_983])])])]) ).
fof(c_0_1691,plain,
! [X21,X22,X23,X24] :
( ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,bit0(X21)),bit1(X22)))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X21),X22)) )
& ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X23),X24))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,bit0(X23)),bit1(X24))) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_984])])])]) ).
fof(c_0_1692,plain,
! [X13,X14,X15,X16] :
( ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,bit0(X13)),bit1(X14)))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X13),X14)) )
& ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X15),X16))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,bit0(X15)),bit1(X16))) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_985])])])]) ).
fof(c_0_1693,plain,
! [X13,X14,X15,X16] :
( ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,number_number_of_int(X13)),number_number_of_int(X14)))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X13),X14)) )
& ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X15),X16))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,number_number_of_int(X15)),number_number_of_int(X16))) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_986])])])]) ).
fof(c_0_1694,plain,
! [X5,X6,X7,X8] :
( ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,number_number_of_int(X5)),number_number_of_int(X6)))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X5),X6)) )
& ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X7),X8))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,number_number_of_int(X7)),number_number_of_int(X8))) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_987])])])]) ).
fof(c_0_1695,plain,
! [X5,X6,X7,X8] :
( ( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,number267125858f_real(X5)),number267125858f_real(X6)))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X5),X6)) )
& ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X7),X8))
| hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,number267125858f_real(X7)),number267125858f_real(X8))) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_988])])])]) ).
fof(c_0_1696,plain,
! [X13,X14,X15,X16] :
( ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,bit0(X13)),bit0(X14)))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X13),X14)) )
& ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X15),X16))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,bit0(X15)),bit0(X16))) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_989])])])]) ).
fof(c_0_1697,plain,
! [X21,X22,X23,X24] :
( ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,bit0(X21)),bit0(X22)))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X21),X22)) )
& ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X23),X24))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,bit0(X23)),bit0(X24))) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_990])])])]) ).
fof(c_0_1698,plain,
! [X13,X14,X15,X16] :
( ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,bit1(X13)),bit1(X14)))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X13),X14)) )
& ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X15),X16))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,bit1(X15)),bit1(X16))) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_991])])])]) ).
fof(c_0_1699,plain,
! [X21,X22,X23,X24] :
( ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,bit1(X21)),bit1(X22)))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X21),X22)) )
& ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X23),X24))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,bit1(X23)),bit1(X24))) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_992])])])]) ).
fof(c_0_1700,plain,
! [X13,X14,X15,X16] :
( ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit1(X13)),bit0(X14)))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X13),X14)) )
& ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X15),X16))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit1(X15)),bit0(X16))) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_993])])])]) ).
fof(c_0_1701,plain,
! [X21,X22,X23,X24] :
( ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit1(X21)),bit0(X22)))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X21),X22)) )
& ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X23),X24))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit1(X23)),bit0(X24))) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_994])])])]) ).
fof(c_0_1702,plain,
! [X13,X14,X15,X16] :
( ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit0(X13)),bit0(X14)))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X13),X14)) )
& ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X15),X16))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit0(X15)),bit0(X16))) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_995])])])]) ).
fof(c_0_1703,plain,
! [X21,X22,X23,X24] :
( ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit0(X21)),bit0(X22)))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X21),X22)) )
& ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X23),X24))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit0(X23)),bit0(X24))) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_996])])])]) ).
fof(c_0_1704,plain,
! [X13,X14,X15,X16] :
( ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit1(X13)),bit1(X14)))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X13),X14)) )
& ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X15),X16))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit1(X15)),bit1(X16))) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_997])])])]) ).
fof(c_0_1705,plain,
! [X21,X22,X23,X24] :
( ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit1(X21)),bit1(X22)))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X21),X22)) )
& ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X23),X24))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit1(X23)),bit1(X24))) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_998])])])]) ).
fof(c_0_1706,plain,
! [X5,X6,X7,X8] :
( ( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,number267125858f_real(X5)),number267125858f_real(X6)))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X5),X6)) )
& ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X7),X8))
| hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,number267125858f_real(X7)),number267125858f_real(X8))) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_999])])])]) ).
fof(c_0_1707,plain,
! [X5,X6,X7,X8] :
( ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(X5)),number_number_of_int(X6)))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X5),X6)) )
& ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X7),X8))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(X7)),number_number_of_int(X8))) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1000])])])]) ).
fof(c_0_1708,plain,
! [X13,X14,X15,X16] :
( ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(X13)),number_number_of_int(X14)))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X13),X14)) )
& ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X15),X16))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(X15)),number_number_of_int(X16))) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1001])])])]) ).
fof(c_0_1709,plain,
! [X19,X20] :
( ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_nat_int(semiri1621563631at_int,X19)))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X19)) )
& ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X20))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_nat_int(semiri1621563631at_int,X20))) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1002])])])]) ).
fof(c_0_1710,plain,
! [X19,X20] :
( ( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),hAPP_nat_real(semiri132038758t_real,X19)))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X19)) )
& ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X20))
| hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),hAPP_nat_real(semiri132038758t_real,X20))) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1003])])])]) ).
fof(c_0_1711,plain,
! [X19,X20] :
( ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(semiri984289939at_nat,X19)))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X19)) )
& ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X20))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(semiri984289939at_nat,X20))) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1004])])])]) ).
fof(c_0_1712,plain,
! [X19,X20] :
( ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_nat_int(semiri1621563631at_int,X19)))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X19)) )
& ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X20))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_nat_int(semiri1621563631at_int,X20))) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1005])])])]) ).
fof(c_0_1713,plain,
! [X18] :
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X18))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_int_int(plus_plus_int(one_one_int),X18))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1006])]) ).
fof(c_0_1714,plain,
! [X5,X6] :
( ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X6),X5))
| X6 = X5
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X5),X6)) )
& ( X6 != X5
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X6),X5))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X5),X6)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1007])])]) ).
fof(c_0_1715,plain,
! [X5,X6] :
( ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X6),X5))
| X6 = X5
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X5),X6)) )
& ( X6 != X5
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X6),X5))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X5),X6)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1008])])]) ).
fof(c_0_1716,plain,
! [X5,X6] :
( ( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X6),X5))
| X6 = X5
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X5),X6)) )
& ( X6 != X5
| hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X6),X5))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X5),X6)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1009])])]) ).
fof(c_0_1717,plain,
! [X265,X266] :
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X265),X266))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X266),X265))
| X265 = X266 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1010])]) ).
fof(c_0_1718,plain,
! [X265,X266] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X265),X266))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X266),X265))
| X265 = X266 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1011])]) ).
fof(c_0_1719,plain,
! [X265,X266] :
( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X265),X266))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X266),X265))
| X265 = X266 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1012])]) ).
fof(c_0_1720,plain,
! [X260,X261] :
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X260),X261))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X261),X260))
| X261 = X260 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1013])]) ).
fof(c_0_1721,plain,
! [X260,X261] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X260),X261))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X261),X260))
| X261 = X260 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1014])]) ).
fof(c_0_1722,plain,
! [X260,X261] :
( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X260),X261))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X261),X260))
| X261 = X260 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1015])]) ).
fof(c_0_1723,plain,
! [X18,X19] :
( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X18),X19))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X19),X18))
| X18 = X19 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1016])]) ).
fof(c_0_1724,plain,
! [X17,X18] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X17),X18))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X18),X17))
| X17 = X18 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1017])]) ).
fof(c_0_1725,plain,
! [X18,X19] :
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X18),X19))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X19),X18))
| X18 = X19 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1018])]) ).
fof(c_0_1726,plain,
! [X92,X93] :
( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),esk3_2(X92,X93)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X92),X93)) )
& ( hAPP_nat_nat(plus_plus_nat(X92),esk3_2(X92,X93)) = X93
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X92),X93)) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1019])])])]) ).
fof(c_0_1727,plain,
! [X17] :
( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),number_number_of_int(bit0(X17))))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),number_number_of_int(X17))) )
& ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),number_number_of_int(bit1(X17))))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),number_number_of_int(X17))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1020])])]) ).
fof(c_0_1728,plain,
! [X4,X5] :
( ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,number_number_of_int(X4)),one_one_int))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X4),bit1(pls))) )
& ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X5),bit1(pls)))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,number_number_of_int(X5)),one_one_int)) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1021])])])]) ).
fof(c_0_1729,plain,
! [X4,X5] :
( ( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,number267125858f_real(X4)),one_one_real))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X4),bit1(pls))) )
& ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X5),bit1(pls)))
| hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,number267125858f_real(X5)),one_one_real)) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1022])])])]) ).
fof(c_0_1730,plain,
! [X4,X5] :
( ( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,number267125858f_real(X4)),one_one_real))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X4),bit1(pls))) )
& ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X5),bit1(pls)))
| hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,number267125858f_real(X5)),one_one_real)) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1023])])])]) ).
fof(c_0_1731,plain,
! [X4,X5] :
( ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(X4)),one_one_int))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X4),bit1(pls))) )
& ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X5),bit1(pls)))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(X5)),one_one_int)) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1024])])])]) ).
fof(c_0_1732,plain,
! [X25,X26,X27,X28] :
( ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X26),pls))
| hAPP_nat_nat(plus_plus_nat(number_number_of_nat(X26)),number_number_of_nat(X25)) = number_number_of_nat(X25) )
& ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X27),pls))
| hAPP_nat_nat(plus_plus_nat(number_number_of_nat(X28)),number_number_of_nat(X27)) = number_number_of_nat(X28)
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X28),pls)) )
& ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X27),pls))
| hAPP_nat_nat(plus_plus_nat(number_number_of_nat(X28)),number_number_of_nat(X27)) = number_number_of_nat(hAPP_int_int(plus_plus_int(X28),X27))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X28),pls)) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1025])])])])]) ).
fof(c_0_1733,plain,
! [X4,X5] :
( ( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,sqrt(X4)),one_one_real))
| hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X4),one_one_real)) )
& ( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X5),one_one_real))
| hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,sqrt(X5)),one_one_real)) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1026])])])]) ).
fof(c_0_1734,plain,
! [X4,X5] :
( ( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,sqrt(X4)),zero_zero_real))
| hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X4),zero_zero_real)) )
& ( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X5),zero_zero_real))
| hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,sqrt(X5)),zero_zero_real)) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1027])])])]) ).
fof(c_0_1735,plain,
! [X12,X13] :
( ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,bit1(X12)),pls))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X12),pls)) )
& ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X13),pls))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,bit1(X13)),pls)) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1028])])])]) ).
fof(c_0_1736,plain,
! [X12,X13] :
( ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,bit0(X12)),pls))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X12),pls)) )
& ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X13),pls))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,bit0(X13)),pls)) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1029])])])]) ).
fof(c_0_1737,plain,
! [X4,X5] :
( ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,number_number_of_int(X4)),zero_zero_int))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X4),pls)) )
& ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X5),pls))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,number_number_of_int(X5)),zero_zero_int)) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1030])])])]) ).
fof(c_0_1738,plain,
! [X4,X5] :
( ( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,number267125858f_real(X4)),zero_zero_real))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X4),pls)) )
& ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X5),pls))
| hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,number267125858f_real(X5)),zero_zero_real)) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1031])])])]) ).
fof(c_0_1739,plain,
! [X26,X27] :
( ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit0(X26)),zero_zero_int))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X26),zero_zero_int)) )
& ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X27),zero_zero_int))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit0(X27)),zero_zero_int)) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1032])])])]) ).
fof(c_0_1740,plain,
! [X26,X27] :
( ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit1(X26)),zero_zero_int))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X26),zero_zero_int)) )
& ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X27),zero_zero_int))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit1(X27)),zero_zero_int)) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1033])])])]) ).
fof(c_0_1741,plain,
! [X12,X13] :
( ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit0(X12)),pls))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X12),pls)) )
& ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X13),pls))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit0(X13)),pls)) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1034])])])]) ).
fof(c_0_1742,plain,
! [X12,X13] :
( ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit1(X12)),pls))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X12),pls)) )
& ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X13),pls))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit1(X13)),pls)) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1035])])])]) ).
fof(c_0_1743,plain,
! [X4,X5] :
( ( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,number267125858f_real(X4)),zero_zero_real))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X4),pls)) )
& ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X5),pls))
| hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,number267125858f_real(X5)),zero_zero_real)) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1036])])])]) ).
fof(c_0_1744,plain,
! [X4,X5] :
( ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(X4)),zero_zero_int))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X4),pls)) )
& ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X5),pls))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(X5)),zero_zero_int)) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1037])])])]) ).
fof(c_0_1745,plain,
! [X5,X6] :
( ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),number_number_of_int(X5)))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,bit1(pls)),X5)) )
& ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,bit1(pls)),X6))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),number_number_of_int(X6))) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1038])])])]) ).
fof(c_0_1746,plain,
! [X5,X6] :
( ( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,one_one_real),number267125858f_real(X5)))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,bit1(pls)),X5)) )
& ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,bit1(pls)),X6))
| hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,one_one_real),number267125858f_real(X6))) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1039])])])]) ).
fof(c_0_1747,plain,
! [X5,X6] :
( ( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,one_one_real),number267125858f_real(X5)))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit1(pls)),X5)) )
& ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit1(pls)),X6))
| hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,one_one_real),number267125858f_real(X6))) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1040])])])]) ).
fof(c_0_1748,plain,
! [X5,X6] :
( ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),number_number_of_int(X5)))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit1(pls)),X5)) )
& ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit1(pls)),X6))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),number_number_of_int(X6))) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1041])])])]) ).
fof(c_0_1749,plain,
! [X91,X92,X94,X95,X96] :
( ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X91),X92))
| X92 = hAPP_int_int(plus_plus_int(X91),hAPP_nat_int(semiri1621563631at_int,esk10_2(X91,X92))) )
& ( X95 != hAPP_int_int(plus_plus_int(X94),hAPP_nat_int(semiri1621563631at_int,X96))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X94),X95)) ) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1042])])])])]) ).
fof(c_0_1750,axiom,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,m1),hAPP_int_int(plus_plus_int(one_one_int),hAPP_nat_int(semiri1621563631at_int,n)))),
c_0_1043 ).
fof(c_0_1751,axiom,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_int_int(plus_plus_int(one_one_int),hAPP_nat_int(semiri1621563631at_int,n)))),
c_0_1044 ).
fof(c_0_1752,plain,
! [X277,X278,X279] :
( X278 != X279
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X279),X277))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X278),X277)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1045])]) ).
fof(c_0_1753,plain,
! [X277,X278,X279] :
( X278 != X279
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X279),X277))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X278),X277)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1046])]) ).
fof(c_0_1754,plain,
! [X277,X278,X279] :
( X278 != X279
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X279),X277))
| hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X278),X277)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1047])]) ).
fof(c_0_1755,plain,
! [X274,X275,X276] :
( X275 != X276
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X274),X276))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X274),X275)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1048])]) ).
fof(c_0_1756,plain,
! [X274,X275,X276] :
( X275 != X276
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X274),X276))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X274),X275)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1049])]) ).
fof(c_0_1757,plain,
! [X274,X275,X276] :
( X275 != X276
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X274),X276))
| hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X274),X275)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1050])]) ).
fof(c_0_1758,plain,
! [X271,X272,X273] :
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X272),X273))
| X273 != X271
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X272),X271)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1051])]) ).
fof(c_0_1759,plain,
! [X271,X272,X273] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X272),X273))
| X273 != X271
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X272),X271)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1052])]) ).
fof(c_0_1760,plain,
! [X271,X272,X273] :
( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X272),X273))
| X273 != X271
| hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X272),X271)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1053])]) ).
fof(c_0_1761,plain,
! [X268,X269,X270] :
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X269),X270))
| X269 != X268
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X268),X270)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1054])]) ).
fof(c_0_1762,plain,
! [X268,X269,X270] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X269),X270))
| X269 != X268
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X268),X270)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1055])]) ).
fof(c_0_1763,plain,
! [X268,X269,X270] :
( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X269),X270))
| X269 != X268
| hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X268),X270)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1056])]) ).
fof(c_0_1764,plain,
! [X5,X6] :
( ( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,one_one_real),sqrt(X5)))
| hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,one_one_real),X5)) )
& ( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,one_one_real),X6))
| hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,one_one_real),sqrt(X6))) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1057])])])]) ).
fof(c_0_1765,plain,
! [X5,X6] :
( ( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),sqrt(X5)))
| hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X5)) )
& ( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X6))
| hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),sqrt(X6))) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1058])])])]) ).
fof(c_0_1766,plain,
! [X12,X13] :
( ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),bit1(X12)))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X12)) )
& ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X13))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),bit1(X13))) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1059])])])]) ).
fof(c_0_1767,plain,
! [X12,X13] :
( ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),bit0(X12)))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X12)) )
& ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X13))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),bit0(X13))) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1060])])])]) ).
fof(c_0_1768,plain,
! [X12,X13] :
( ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),bit1(X12)))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X12)) )
& ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X13))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),bit1(X13))) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1061])])])]) ).
fof(c_0_1769,plain,
! [X5,X6] :
( ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),number_number_of_int(X5)))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X5)) )
& ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X6))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),number_number_of_int(X6))) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1062])])])]) ).
fof(c_0_1770,plain,
! [X5,X6] :
( ( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),number267125858f_real(X5)))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X5)) )
& ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X6))
| hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),number267125858f_real(X6))) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1063])])])]) ).
fof(c_0_1771,plain,
! [X60,X61] :
( ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),number_number_of_nat(X60)))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),X60)) )
& ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),X61))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),number_number_of_nat(X61))) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1064])])])]) ).
fof(c_0_1772,plain,
! [X12,X13] :
( ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),bit0(X12)))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),X12)) )
& ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),X13))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),bit0(X13))) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1065])])])]) ).
fof(c_0_1773,plain,
! [X5,X6] :
( ( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),number267125858f_real(X5)))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),X5)) )
& ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),X6))
| hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),number267125858f_real(X6))) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1066])])])]) ).
fof(c_0_1774,plain,
! [X5,X6] :
( ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),number_number_of_int(X5)))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),X5)) )
& ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),X6))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),number_number_of_int(X6))) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1067])])])]) ).
fof(c_0_1775,plain,
! [X5,X6,X7,X8] :
( ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X5),X6))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X5),X6)) )
& ( X5 != X6
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X5),X6)) )
& ( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X7),X8))
| X7 = X8
| hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X7),X8)) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1068])])])])]) ).
fof(c_0_1776,plain,
! [X5,X6,X7,X8] :
( ( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X5),X6))
| hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X5),X6))
| X5 = X6 )
& ( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X7),X8))
| hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X7),X8)) )
& ( X7 != X8
| hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X7),X8)) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1069])])])])]) ).
fof(c_0_1777,plain,
! [X30,X31,X32,X33] :
( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X30),X31))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X30),X31)) )
& ( X30 != X31
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X30),X31)) )
& ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X32),X33))
| X32 = X33
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X32),X33)) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1070])])])])]) ).
fof(c_0_1778,plain,
! [X30,X31,X32,X33] :
( ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X30),X31))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X30),X31))
| X30 = X31 )
& ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X32),X33))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X32),X33)) )
& ( X32 != X33
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X32),X33)) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1071])])])])]) ).
fof(c_0_1779,plain,
! [X17,X18] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X17),X18))
| X17 = X18
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X17),X18)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1072])]) ).
fof(c_0_1780,plain,
! [X31,X32,X33,X34] :
( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X31),X32))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X31),X32)) )
& ( X31 != X32
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X31),X32)) )
& ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X33),X34))
| X33 = X34
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X33),X34)) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1073])])])])]) ).
fof(c_0_1781,plain,
! [X17,X18] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X17),X18))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X17),X18)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1074])]) ).
fof(c_0_1782,plain,
! [X17,X18] :
( ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X17),X18))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X17),X18)) )
& ( X17 != X18
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X17),X18)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1075])])]) ).
fof(c_0_1783,plain,
! [X110,X111,X112] : hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(X110),X111)),X112) = hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(X110),X112)),X111),
inference(variable_rename,[status(thm)],[c_0_1076]) ).
fof(c_0_1784,plain,
! [X110,X111,X112] : hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(plus_plus_nat(X110),X111)),X112) = hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(plus_plus_nat(X110),X112)),X111),
inference(variable_rename,[status(thm)],[c_0_1077]) ).
fof(c_0_1785,plain,
! [X110,X111,X112] : hAPP_real_real(plus_plus_real(hAPP_real_real(plus_plus_real(X110),X111)),X112) = hAPP_real_real(plus_plus_real(hAPP_real_real(plus_plus_real(X110),X112)),X111),
inference(variable_rename,[status(thm)],[c_0_1078]) ).
fof(c_0_1786,plain,
! [X9] :
( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X9))
| hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),sqrt(X9))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1079])]) ).
fof(c_0_1787,plain,
! [X91] :
( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),esk2_1(X91)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X91)) )
& ( X91 = hAPP_nat_int(semiri1621563631at_int,esk2_1(X91))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X91)) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1080])])])]) ).
fof(c_0_1788,plain,
! [X31,X32] :
( ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),X31))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X31)) )
& ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X32))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),X32)) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1081])])])]) ).
fof(c_0_1789,plain,
! [X30,X31,X32] :
( ( hAPP_nat_int(power_power_int(X32),X30) != hAPP_nat_int(power_power_int(X32),X31)
| X30 = X31
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),X32)) )
& ( X30 != X31
| hAPP_nat_int(power_power_int(X32),X30) = hAPP_nat_int(power_power_int(X32),X31)
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),X32)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1082])])]) ).
fof(c_0_1790,plain,
! [X30,X31,X32] :
( ( hAPP_nat_nat(power_power_nat(X32),X30) != hAPP_nat_nat(power_power_nat(X32),X31)
| X30 = X31
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,one_one_nat),X32)) )
& ( X30 != X31
| hAPP_nat_nat(power_power_nat(X32),X30) = hAPP_nat_nat(power_power_nat(X32),X31)
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,one_one_nat),X32)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1083])])]) ).
fof(c_0_1791,plain,
! [X30,X31,X32] :
( ( hAPP_nat_real(power_power_real(X32),X30) != hAPP_nat_real(power_power_real(X32),X31)
| X30 = X31
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,one_one_real),X32)) )
& ( X30 != X31
| hAPP_nat_real(power_power_real(X32),X30) = hAPP_nat_real(power_power_real(X32),X31)
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,one_one_real),X32)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1084])])]) ).
fof(c_0_1792,plain,
! [X92,X93,X95,X96,X97] :
( ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X92),X93))
| X93 = hAPP_nat_nat(plus_plus_nat(X92),esk13_2(X92,X93)) )
& ( X96 != hAPP_nat_nat(plus_plus_nat(X95),X97)
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X95),X96)) ) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1085])])])])]) ).
fof(c_0_1793,plain,
! [X32,X33] : times_times_int(bit1(X32),X33) = hAPP_int_int(plus_plus_int(bit0(times_times_int(X32,X33))),X33),
inference(variable_rename,[status(thm)],[c_0_1086]) ).
fof(c_0_1794,plain,
! [X119,X120,X121] : hAPP_int_int(plus_plus_int(X119),hAPP_int_int(plus_plus_int(X120),X121)) = hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(X119),X120)),X121),
inference(variable_rename,[status(thm)],[c_0_1087]) ).
fof(c_0_1795,plain,
! [X119,X120,X121] : hAPP_nat_nat(plus_plus_nat(X119),hAPP_nat_nat(plus_plus_nat(X120),X121)) = hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(plus_plus_nat(X119),X120)),X121),
inference(variable_rename,[status(thm)],[c_0_1088]) ).
fof(c_0_1796,plain,
! [X119,X120,X121] : hAPP_real_real(plus_plus_real(X119),hAPP_real_real(plus_plus_real(X120),X121)) = hAPP_real_real(plus_plus_real(hAPP_real_real(plus_plus_real(X119),X120)),X121),
inference(variable_rename,[status(thm)],[c_0_1089]) ).
fof(c_0_1797,plain,
! [X116,X117,X118] : hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(X116),X117)),X118) = hAPP_int_int(plus_plus_int(X116),hAPP_int_int(plus_plus_int(X117),X118)),
inference(variable_rename,[status(thm)],[c_0_1090]) ).
fof(c_0_1798,plain,
! [X116,X117,X118] : hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(plus_plus_nat(X116),X117)),X118) = hAPP_nat_nat(plus_plus_nat(X116),hAPP_nat_nat(plus_plus_nat(X117),X118)),
inference(variable_rename,[status(thm)],[c_0_1091]) ).
fof(c_0_1799,plain,
! [X116,X117,X118] : hAPP_real_real(plus_plus_real(hAPP_real_real(plus_plus_real(X116),X117)),X118) = hAPP_real_real(plus_plus_real(X116),hAPP_real_real(plus_plus_real(X117),X118)),
inference(variable_rename,[status(thm)],[c_0_1092]) ).
fof(c_0_1800,plain,
! [X113,X114,X115] : hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(X113),X114)),X115) = hAPP_int_int(plus_plus_int(X113),hAPP_int_int(plus_plus_int(X114),X115)),
inference(variable_rename,[status(thm)],[c_0_1093]) ).
fof(c_0_1801,plain,
! [X113,X114,X115] : hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(plus_plus_nat(X113),X114)),X115) = hAPP_nat_nat(plus_plus_nat(X113),hAPP_nat_nat(plus_plus_nat(X114),X115)),
inference(variable_rename,[status(thm)],[c_0_1094]) ).
fof(c_0_1802,plain,
! [X113,X114,X115] : hAPP_real_real(plus_plus_real(hAPP_real_real(plus_plus_real(X113),X114)),X115) = hAPP_real_real(plus_plus_real(X113),hAPP_real_real(plus_plus_real(X114),X115)),
inference(variable_rename,[status(thm)],[c_0_1095]) ).
fof(c_0_1803,plain,
! [X63,X64] :
( X63 = X64
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X63),X64))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X64),X63)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1096])]) ).
fof(c_0_1804,plain,
! [X63,X64] :
( X63 = X64
| hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X63),X64))
| hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X64),X63)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1097])]) ).
fof(c_0_1805,plain,
! [X11,X12] :
( X11 = X12
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X11),X12))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X12),X11)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1098])]) ).
fof(c_0_1806,plain,
! [X22,X23,X24] : hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(plus_plus_nat(X22),X23)),X24) = hAPP_nat_nat(plus_plus_nat(X22),hAPP_nat_nat(plus_plus_nat(X23),X24)),
inference(variable_rename,[status(thm)],[c_0_1099]) ).
fof(c_0_1807,plain,
! [X30,X31,X32,X33] :
( ( X30 = X31
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X30),X31))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X31),X30)) )
& ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X32),X33))
| X32 != X33 )
& ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X33),X32))
| X32 != X33 ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1100])])])])]) ).
fof(c_0_1808,plain,
! [X29,X30,X31] : hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(X29),X30)),X31) = hAPP_int_int(plus_plus_int(X29),hAPP_int_int(plus_plus_int(X30),X31)),
inference(variable_rename,[status(thm)],[c_0_1101]) ).
fof(c_0_1809,plain,
! [X11,X12] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X11),X12))
| X11 = X12
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X12),X11)) ),
inference(variable_rename,[status(thm)],[c_0_1102]) ).
fof(c_0_1810,plain,
! [X255,X256] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X255),X256))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X256),X255)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1103])]) ).
fof(c_0_1811,plain,
! [X255,X256] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X255),X256))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X256),X255)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1104])]) ).
fof(c_0_1812,plain,
! [X255,X256] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X255),X256))
| hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X256),X255)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1105])]) ).
fof(c_0_1813,plain,
! [X18,X19] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X18),X19))
| hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X19),X18)) ),
inference(variable_rename,[status(thm)],[c_0_1106]) ).
fof(c_0_1814,plain,
! [X17,X18] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X17),hAPP_nat_nat(plus_plus_nat(X17),X18))),
inference(variable_rename,[status(thm)],[c_0_1107]) ).
fof(c_0_1815,plain,
! [X17,X18] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X17),hAPP_nat_nat(plus_plus_nat(X18),X17))),
inference(variable_rename,[status(thm)],[c_0_1108]) ).
fof(c_0_1816,plain,
! [X17,X18] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X17),X18))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X18),X17)) ),
inference(variable_rename,[status(thm)],[c_0_1109]) ).
fof(c_0_1817,plain,
! [X18,X19] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X18),X19))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X19),X18)) ),
inference(variable_rename,[status(thm)],[c_0_1110]) ).
fof(c_0_1818,plain,
! [X243,X244] :
( ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),number_number_of_int(X243)))
| hAPP_nat_int(semiri1621563631at_int,number_number_of_nat(X243)) = number_number_of_int(X243) )
& ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),number_number_of_int(X244)))
| hAPP_nat_int(semiri1621563631at_int,number_number_of_nat(X244)) = zero_zero_int ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1111])])])]) ).
fof(c_0_1819,plain,
! [X243,X244] :
( ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),number_number_of_int(X243)))
| hAPP_nat_real(semiri132038758t_real,number_number_of_nat(X243)) = number267125858f_real(X243) )
& ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),number_number_of_int(X244)))
| hAPP_nat_real(semiri132038758t_real,number_number_of_nat(X244)) = zero_zero_real ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1112])])])]) ).
fof(c_0_1820,plain,
! [X211] :
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X211))
| hAPP_int_int(plus_plus_int(number_number_of_int(X211)),one_one_int) = number_number_of_int(succ(X211)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1113])]) ).
fof(c_0_1821,plain,
! [X211] :
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X211))
| hAPP_nat_nat(plus_plus_nat(number_number_of_nat(X211)),one_one_nat) = number_number_of_nat(succ(X211)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1114])]) ).
fof(c_0_1822,plain,
! [X211] :
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X211))
| hAPP_real_real(plus_plus_real(number267125858f_real(X211)),one_one_real) = number267125858f_real(succ(X211)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1115])]) ).
fof(c_0_1823,plain,
! [X81] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X81),hAPP_int_int(plus_plus_int(X81),one_one_int))),
inference(variable_rename,[status(thm)],[c_0_1116]) ).
fof(c_0_1824,plain,
! [X81] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X81),hAPP_nat_nat(plus_plus_nat(X81),one_one_nat))),
inference(variable_rename,[status(thm)],[c_0_1117]) ).
fof(c_0_1825,plain,
! [X81] : hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X81),hAPP_real_real(plus_plus_real(X81),one_one_real))),
inference(variable_rename,[status(thm)],[c_0_1118]) ).
fof(c_0_1826,plain,
! [X14,X15] :
( ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X14),pls))
| hAPP_nat_nat(plus_plus_nat(number_number_of_nat(X14)),one_one_nat) = one_one_nat )
& ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X15),pls))
| hAPP_nat_nat(plus_plus_nat(number_number_of_nat(X15)),one_one_nat) = number_number_of_nat(succ(X15)) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1119])])])]) ).
fof(c_0_1827,plain,
! [X210] :
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X210))
| hAPP_int_int(plus_plus_int(one_one_int),number_number_of_int(X210)) = number_number_of_int(succ(X210)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1120])]) ).
fof(c_0_1828,plain,
! [X210] :
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X210))
| hAPP_nat_nat(plus_plus_nat(one_one_nat),number_number_of_nat(X210)) = number_number_of_nat(succ(X210)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1121])]) ).
fof(c_0_1829,plain,
! [X210] :
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X210))
| hAPP_real_real(plus_plus_real(one_one_real),number267125858f_real(X210)) = number267125858f_real(succ(X210)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1122])]) ).
fof(c_0_1830,plain,
! [X11,X12] : hAPP_int_int(plus_plus_int(hAPP_nat_int(semiri1621563631at_int,X11)),hAPP_nat_int(semiri1621563631at_int,X12)) = hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(plus_plus_nat(X11),X12)),
inference(variable_rename,[status(thm)],[c_0_1123]) ).
fof(c_0_1831,plain,
! [X73,X74] : hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(plus_plus_nat(X73),X74)) = hAPP_int_int(plus_plus_int(hAPP_nat_int(semiri1621563631at_int,X73)),hAPP_nat_int(semiri1621563631at_int,X74)),
inference(variable_rename,[status(thm)],[c_0_1124]) ).
fof(c_0_1832,plain,
! [X73,X74] : hAPP_nat_nat(semiri984289939at_nat,hAPP_nat_nat(plus_plus_nat(X73),X74)) = hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(semiri984289939at_nat,X73)),hAPP_nat_nat(semiri984289939at_nat,X74)),
inference(variable_rename,[status(thm)],[c_0_1125]) ).
fof(c_0_1833,plain,
! [X73,X74] : hAPP_nat_real(semiri132038758t_real,hAPP_nat_nat(plus_plus_nat(X73),X74)) = hAPP_real_real(plus_plus_real(hAPP_nat_real(semiri132038758t_real,X73)),hAPP_nat_real(semiri132038758t_real,X74)),
inference(variable_rename,[status(thm)],[c_0_1126]) ).
fof(c_0_1834,plain,
! [X17,X18] : hAPP_int_int(plus_plus_int(hAPP_nat_int(semiri1621563631at_int,X17)),hAPP_nat_int(semiri1621563631at_int,X18)) = hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(plus_plus_nat(X17),X18)),
inference(variable_rename,[status(thm)],[c_0_1127]) ).
fof(c_0_1835,plain,
! [X14,X15] :
( ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X14),pls))
| hAPP_nat_nat(plus_plus_nat(one_one_nat),number_number_of_nat(X14)) = one_one_nat )
& ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X15),pls))
| hAPP_nat_nat(plus_plus_nat(one_one_nat),number_number_of_nat(X15)) = number_number_of_nat(succ(X15)) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1128])])])]) ).
fof(c_0_1836,plain,
! [X18] : hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),X18)),X18) != zero_zero_int,
inference(variable_rename,[status(thm)],[c_0_1129]) ).
fof(c_0_1837,axiom,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),number_number_of_int(bit0(bit1(pls))))),
c_0_1130 ).
fof(c_0_1838,axiom,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),number_number_of_int(bit1(bit1(pls))))),
c_0_1131 ).
fof(c_0_1839,axiom,
hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),number_number_of_nat(bit0(bit1(pls))))),
c_0_1132 ).
fof(c_0_1840,plain,
! [X249] :
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X249))
| X249 = hAPP_nat_int(semiri1621563631at_int,esk15_1(X249)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1133])])]) ).
fof(c_0_1841,plain,
! [X91] :
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X91))
| X91 = hAPP_nat_int(semiri1621563631at_int,esk12_1(X91)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1134])])]) ).
fof(c_0_1842,plain,
! [X91] :
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X91))
| X91 = hAPP_nat_int(semiri1621563631at_int,esk11_1(X91)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1135])])]) ).
fof(c_0_1843,axiom,
hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),hAPP_real_real(plus_plus_real(one_one_real),one_one_real))),
c_0_1136 ).
fof(c_0_1844,axiom,
hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(plus_plus_nat(one_one_nat),one_one_nat))),
c_0_1137 ).
fof(c_0_1845,axiom,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_int_int(plus_plus_int(one_one_int),one_one_int))),
c_0_1138 ).
fof(c_0_1846,plain,
! [X47] : number267125858f_real(bit1(X47)) = hAPP_real_real(plus_plus_real(hAPP_real_real(plus_plus_real(one_one_real),number267125858f_real(X47))),number267125858f_real(X47)),
inference(variable_rename,[status(thm)],[c_0_1139]) ).
fof(c_0_1847,plain,
! [X47] : number_number_of_int(bit1(X47)) = hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),number_number_of_int(X47))),number_number_of_int(X47)),
inference(variable_rename,[status(thm)],[c_0_1140]) ).
fof(c_0_1848,plain,
! [X46] : number267125858f_real(bit0(X46)) = hAPP_real_real(plus_plus_real(hAPP_real_real(plus_plus_real(zero_zero_real),number267125858f_real(X46))),number267125858f_real(X46)),
inference(variable_rename,[status(thm)],[c_0_1141]) ).
fof(c_0_1849,plain,
! [X46] : number_number_of_int(bit0(X46)) = hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(zero_zero_int),number_number_of_int(X46))),number_number_of_int(X46)),
inference(variable_rename,[status(thm)],[c_0_1142]) ).
fof(c_0_1850,plain,
! [X59,X60] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X59),X60))
| X59 != X60 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1143])]) ).
fof(c_0_1851,plain,
! [X17,X18] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X17),X18))
| X18 != X17 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1144])]) ).
fof(c_0_1852,plain,
! [X17,X18] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X17),X18))
| X18 != zero_zero_nat ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1145])]) ).
fof(c_0_1853,plain,
! [X17] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X17),X17)),
inference(variable_rename,[status(thm)],[c_0_1146]) ).
fof(c_0_1854,plain,
! [X17] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X17),X17)),
inference(variable_rename,[status(thm)],[c_0_1147]) ).
fof(c_0_1855,plain,
! [X60,X61] :
( ( number_number_of_nat(X60) != zero_zero_nat
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X60),pls)) )
& ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X61),pls))
| number_number_of_nat(X61) = zero_zero_nat ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1148])])])]) ).
fof(c_0_1856,plain,
! [X60,X61] :
( ( zero_zero_nat != number_number_of_nat(X60)
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X60),pls)) )
& ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X61),pls))
| zero_zero_nat = number_number_of_nat(X61) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1149])])])]) ).
fof(c_0_1857,plain,
! [X9] :
( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X9))
| sqrt(X9) != zero_zero_real ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1150])]) ).
fof(c_0_1858,plain,
! [X122,X123,X124] : hAPP_int_int(plus_plus_int(X122),hAPP_int_int(plus_plus_int(X123),X124)) = hAPP_int_int(plus_plus_int(X123),hAPP_int_int(plus_plus_int(X122),X124)),
inference(variable_rename,[status(thm)],[c_0_1151]) ).
fof(c_0_1859,plain,
! [X122,X123,X124] : hAPP_nat_nat(plus_plus_nat(X122),hAPP_nat_nat(plus_plus_nat(X123),X124)) = hAPP_nat_nat(plus_plus_nat(X123),hAPP_nat_nat(plus_plus_nat(X122),X124)),
inference(variable_rename,[status(thm)],[c_0_1152]) ).
fof(c_0_1860,plain,
! [X122,X123,X124] : hAPP_real_real(plus_plus_real(X122),hAPP_real_real(plus_plus_real(X123),X124)) = hAPP_real_real(plus_plus_real(X123),hAPP_real_real(plus_plus_real(X122),X124)),
inference(variable_rename,[status(thm)],[c_0_1153]) ).
fof(c_0_1861,plain,
! [X17,X18] : hAPP_nat_int(power_power_int(hAPP_nat_int(semiri1621563631at_int,X17)),X18) = hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(power_power_nat(X17),X18)),
inference(variable_rename,[status(thm)],[c_0_1154]) ).
fof(c_0_1862,plain,
! [X75,X76] : hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(power_power_nat(X75),X76)) = hAPP_nat_int(power_power_int(hAPP_nat_int(semiri1621563631at_int,X75)),X76),
inference(variable_rename,[status(thm)],[c_0_1155]) ).
fof(c_0_1863,plain,
! [X75,X76] : hAPP_nat_nat(semiri984289939at_nat,hAPP_nat_nat(power_power_nat(X75),X76)) = hAPP_nat_nat(power_power_nat(hAPP_nat_nat(semiri984289939at_nat,X75)),X76),
inference(variable_rename,[status(thm)],[c_0_1156]) ).
fof(c_0_1864,plain,
! [X75,X76] : hAPP_nat_real(semiri132038758t_real,hAPP_nat_nat(power_power_nat(X75),X76)) = hAPP_nat_real(power_power_real(hAPP_nat_real(semiri132038758t_real,X75)),X76),
inference(variable_rename,[status(thm)],[c_0_1157]) ).
fof(c_0_1865,plain,
! [X18,X19,X20] : hAPP_nat_nat(plus_plus_nat(X18),hAPP_nat_nat(plus_plus_nat(X19),X20)) = hAPP_nat_nat(plus_plus_nat(X19),hAPP_nat_nat(plus_plus_nat(X18),X20)),
inference(variable_rename,[status(thm)],[c_0_1158]) ).
fof(c_0_1866,plain,
! [X18,X19,X20] : hAPP_int_int(plus_plus_int(X18),hAPP_int_int(plus_plus_int(X19),X20)) = hAPP_int_int(plus_plus_int(X19),hAPP_int_int(plus_plus_int(X18),X20)),
inference(variable_rename,[status(thm)],[c_0_1159]) ).
fof(c_0_1867,plain,
! [X17,X18] : hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(power_power_nat(X17),X18)) = hAPP_nat_int(power_power_int(hAPP_nat_int(semiri1621563631at_int,X17)),X18),
inference(variable_rename,[status(thm)],[c_0_1160]) ).
fof(c_0_1868,plain,
! [X17,X18] : hAPP_nat_int(power_power_int(hAPP_nat_int(semiri1621563631at_int,X17)),X18) = hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(power_power_nat(X17),X18)),
inference(variable_rename,[status(thm)],[c_0_1161]) ).
fof(c_0_1869,plain,
! [X19,X20] :
( ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X19),zero_zero_nat))
| X19 = zero_zero_nat )
& ( X20 != zero_zero_nat
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X20),zero_zero_nat)) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1162])])])]) ).
fof(c_0_1870,plain,
! [X17] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_nat_int(semiri1621563631at_int,X17))),
inference(variable_rename,[status(thm)],[c_0_1163]) ).
fof(c_0_1871,plain,
! [X18] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_nat_int(semiri1621563631at_int,X18))),
inference(variable_rename,[status(thm)],[c_0_1164]) ).
fof(c_0_1872,plain,
! [X207] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_nat_int(semiri1621563631at_int,X207))),
inference(variable_rename,[status(thm)],[c_0_1165]) ).
fof(c_0_1873,plain,
! [X207] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),hAPP_nat_nat(semiri984289939at_nat,X207))),
inference(variable_rename,[status(thm)],[c_0_1166]) ).
fof(c_0_1874,plain,
! [X207] : hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),hAPP_nat_real(semiri132038758t_real,X207))),
inference(variable_rename,[status(thm)],[c_0_1167]) ).
fof(c_0_1875,plain,
! [X206] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_nat_int(semiri1621563631at_int,X206))),
inference(variable_rename,[status(thm)],[c_0_1168]) ).
fof(c_0_1876,plain,
! [X206] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),hAPP_nat_nat(semiri984289939at_nat,X206))),
inference(variable_rename,[status(thm)],[c_0_1169]) ).
fof(c_0_1877,plain,
! [X206] : hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),hAPP_nat_real(semiri132038758t_real,X206))),
inference(variable_rename,[status(thm)],[c_0_1170]) ).
fof(c_0_1878,plain,
! [X17] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X17),zero_zero_nat)),
inference(variable_rename,[status(thm)],[c_0_1171]) ).
fof(c_0_1879,plain,
! [X17] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X17),zero_zero_nat)),
inference(variable_rename,[status(thm)],[c_0_1172]) ).
fof(c_0_1880,plain,
! [X17] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X17),zero_zero_nat)),
inference(variable_rename,[status(thm)],[c_0_1173]) ).
fof(c_0_1881,plain,
! [X19,X20] :
( ( X19 = zero_zero_nat
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X19)) )
& ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X20))
| X20 != zero_zero_nat ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1174])])])]) ).
fof(c_0_1882,plain,
! [X55,X56,X57,X58,X59,X60] :
( ( ~ hBOOL(X57)
| hAPP_nat_int(semiri1621563631at_int,X55) = hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(if_nat(X57,X55),X56)) )
& ( hBOOL(X60)
| hAPP_nat_int(semiri1621563631at_int,X59) = hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(if_nat(X60,X58),X59)) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1175])])])]) ).
fof(c_0_1883,plain,
~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),zero_zero_int)),
c_0_1176 ).
fof(c_0_1884,plain,
~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,one_one_nat),zero_zero_nat)),
c_0_1177 ).
fof(c_0_1885,plain,
~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,one_one_real),zero_zero_real)),
c_0_1178 ).
fof(c_0_1886,plain,
~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),zero_zero_int)),
c_0_1179 ).
fof(c_0_1887,plain,
~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,one_one_nat),zero_zero_nat)),
c_0_1180 ).
fof(c_0_1888,plain,
~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,one_one_real),zero_zero_real)),
c_0_1181 ).
fof(c_0_1889,plain,
~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),zero_zero_int)),
c_0_1182 ).
fof(c_0_1890,plain,
~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),pls)),
c_0_1183 ).
fof(c_0_1891,plain,
! [X32,X33] : hAPP_int_int(plus_plus_int(bit1(X32)),bit1(X33)) = bit0(hAPP_int_int(plus_plus_int(X32),succ(X33))),
inference(variable_rename,[status(thm)],[c_0_1184]) ).
fof(c_0_1892,plain,
! [X22] : bit1(X22) = hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),X22)),X22),
inference(variable_rename,[status(thm)],[c_0_1185]) ).
fof(c_0_1893,plain,
! [X6,X7] :
( ( hAPP_nat_real(power_power_real(X6),number_number_of_nat(bit0(bit1(pls)))) != zero_zero_real
| X6 = zero_zero_real )
& ( X7 != zero_zero_real
| hAPP_nat_real(power_power_real(X7),number_number_of_nat(bit0(bit1(pls)))) = zero_zero_real ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1186])])])]) ).
fof(c_0_1894,plain,
! [X6,X7] :
( ( hAPP_nat_int(power_power_int(X6),number_number_of_nat(bit0(bit1(pls)))) != zero_zero_int
| X6 = zero_zero_int )
& ( X7 != zero_zero_int
| hAPP_nat_int(power_power_int(X7),number_number_of_nat(bit0(bit1(pls)))) = zero_zero_int ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1187])])])]) ).
fof(c_0_1895,plain,
! [X32,X33] : hAPP_int_int(plus_plus_int(bit0(X32)),bit1(X33)) = bit1(hAPP_int_int(plus_plus_int(X32),X33)),
inference(variable_rename,[status(thm)],[c_0_1188]) ).
fof(c_0_1896,plain,
! [X32,X33] : hAPP_int_int(plus_plus_int(bit1(X32)),bit0(X33)) = bit1(hAPP_int_int(plus_plus_int(X32),X33)),
inference(variable_rename,[status(thm)],[c_0_1189]) ).
fof(c_0_1897,plain,
! [X41,X42] : number267125858f_real(hAPP_int_int(plus_plus_int(X41),X42)) = hAPP_real_real(plus_plus_real(number267125858f_real(X41)),number267125858f_real(X42)),
inference(variable_rename,[status(thm)],[c_0_1190]) ).
fof(c_0_1898,plain,
! [X41,X42] : number_number_of_int(hAPP_int_int(plus_plus_int(X41),X42)) = hAPP_int_int(plus_plus_int(number_number_of_int(X41)),number_number_of_int(X42)),
inference(variable_rename,[status(thm)],[c_0_1191]) ).
fof(c_0_1899,plain,
! [X39,X40] : hAPP_real_real(plus_plus_real(number267125858f_real(X39)),number267125858f_real(X40)) = number267125858f_real(hAPP_int_int(plus_plus_int(X39),X40)),
inference(variable_rename,[status(thm)],[c_0_1192]) ).
fof(c_0_1900,plain,
! [X39,X40] : hAPP_int_int(plus_plus_int(number_number_of_int(X39)),number_number_of_int(X40)) = number_number_of_int(hAPP_int_int(plus_plus_int(X39),X40)),
inference(variable_rename,[status(thm)],[c_0_1193]) ).
fof(c_0_1901,plain,
! [X32,X33] : hAPP_int_int(plus_plus_int(bit0(X32)),bit0(X33)) = bit0(hAPP_int_int(plus_plus_int(X32),X33)),
inference(variable_rename,[status(thm)],[c_0_1194]) ).
fof(c_0_1902,plain,
! [X15,X16] : hAPP_int_int(plus_plus_int(number_number_of_int(X15)),number_number_of_int(X16)) = number_number_of_int(hAPP_int_int(plus_plus_int(X15),X16)),
inference(variable_rename,[status(thm)],[c_0_1195]) ).
fof(c_0_1903,plain,
! [X279,X280] :
( X279 != X280
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X279),X280)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1196])]) ).
fof(c_0_1904,plain,
! [X17,X18] :
( X17 != X18
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X17),X18)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1197])]) ).
fof(c_0_1905,plain,
! [X8] : hAPP_real_real(plus_plus_real(number267125858f_real(X8)),one_one_real) = number267125858f_real(hAPP_int_int(plus_plus_int(X8),bit1(pls))),
inference(variable_rename,[status(thm)],[c_0_1198]) ).
fof(c_0_1906,plain,
! [X8] : hAPP_int_int(plus_plus_int(number_number_of_int(X8)),one_one_int) = number_number_of_int(hAPP_int_int(plus_plus_int(X8),bit1(pls))),
inference(variable_rename,[status(thm)],[c_0_1199]) ).
fof(c_0_1907,plain,
! [X7] : hAPP_real_real(plus_plus_real(one_one_real),number267125858f_real(X7)) = number267125858f_real(hAPP_int_int(plus_plus_int(bit1(pls)),X7)),
inference(variable_rename,[status(thm)],[c_0_1200]) ).
fof(c_0_1908,plain,
! [X7] : hAPP_int_int(plus_plus_int(one_one_int),number_number_of_int(X7)) = number_number_of_int(hAPP_int_int(plus_plus_int(bit1(pls)),X7)),
inference(variable_rename,[status(thm)],[c_0_1201]) ).
fof(c_0_1909,plain,
! [X253] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X253),X253)),
inference(variable_rename,[status(thm)],[c_0_1202]) ).
fof(c_0_1910,plain,
! [X253] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X253),X253)),
inference(variable_rename,[status(thm)],[c_0_1203]) ).
fof(c_0_1911,plain,
! [X253] : hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X253),X253)),
inference(variable_rename,[status(thm)],[c_0_1204]) ).
fof(c_0_1912,plain,
! [X15] : hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X15),X15)),
inference(variable_rename,[status(thm)],[c_0_1205]) ).
fof(c_0_1913,plain,
! [X17] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X17),X17)),
inference(variable_rename,[status(thm)],[c_0_1206]) ).
fof(c_0_1914,axiom,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),number_number_of_int(pls))),
c_0_1207 ).
fof(c_0_1915,plain,
! [X15] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X15),X15)),
inference(variable_rename,[status(thm)],[c_0_1208]) ).
fof(c_0_1916,plain,
! [X17] :
( X17 = zero_zero_nat
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X17)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1209])]) ).
fof(c_0_1917,plain,
! [X17] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),X17)),
inference(variable_rename,[status(thm)],[c_0_1210]) ).
fof(c_0_1918,plain,
! [X17] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),X17)),
inference(variable_rename,[status(thm)],[c_0_1211]) ).
fof(c_0_1919,axiom,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),one_one_int)),
c_0_1212 ).
fof(c_0_1920,axiom,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),one_one_int)),
c_0_1213 ).
fof(c_0_1921,axiom,
hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),one_one_nat)),
c_0_1214 ).
fof(c_0_1922,axiom,
hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),one_one_real)),
c_0_1215 ).
fof(c_0_1923,axiom,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),zero_zero_int)),
c_0_1216 ).
fof(c_0_1924,axiom,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),pls)),
c_0_1217 ).
fof(c_0_1925,axiom,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),t)),
c_0_1218 ).
fof(c_0_1926,axiom,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),one_one_int)),
c_0_1219 ).
fof(c_0_1927,axiom,
hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),one_one_nat)),
c_0_1220 ).
fof(c_0_1928,axiom,
hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),one_one_real)),
c_0_1221 ).
fof(c_0_1929,axiom,
hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),tn)),
c_0_1222 ).
fof(c_0_1930,axiom,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),one_one_int)),
c_0_1223 ).
fof(c_0_1931,axiom,
hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),n)),
c_0_1224 ).
fof(c_0_1932,axiom,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),t)),
c_0_1225 ).
fof(c_0_1933,plain,
! [X107,X108,X109,X110,X111,X112] :
( ( hAPP_int_int(plus_plus_int(X107),X108) != hAPP_int_int(plus_plus_int(X107),X109)
| X108 = X109 )
& ( X111 != X112
| hAPP_int_int(plus_plus_int(X110),X111) = hAPP_int_int(plus_plus_int(X110),X112) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1226])])])]) ).
fof(c_0_1934,plain,
! [X107,X108,X109,X110,X111,X112] :
( ( hAPP_nat_nat(plus_plus_nat(X107),X108) != hAPP_nat_nat(plus_plus_nat(X107),X109)
| X108 = X109 )
& ( X111 != X112
| hAPP_nat_nat(plus_plus_nat(X110),X111) = hAPP_nat_nat(plus_plus_nat(X110),X112) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1227])])])]) ).
fof(c_0_1935,plain,
! [X107,X108,X109,X110,X111,X112] :
( ( hAPP_real_real(plus_plus_real(X107),X108) != hAPP_real_real(plus_plus_real(X107),X109)
| X108 = X109 )
& ( X111 != X112
| hAPP_real_real(plus_plus_real(X110),X111) = hAPP_real_real(plus_plus_real(X110),X112) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1228])])])]) ).
fof(c_0_1936,plain,
! [X107,X108,X109,X110,X111,X112] :
( ( hAPP_int_int(plus_plus_int(X107),X108) != hAPP_int_int(plus_plus_int(X109),X108)
| X107 = X109 )
& ( X110 != X112
| hAPP_int_int(plus_plus_int(X110),X111) = hAPP_int_int(plus_plus_int(X112),X111) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1229])])])]) ).
fof(c_0_1937,plain,
! [X107,X108,X109,X110,X111,X112] :
( ( hAPP_nat_nat(plus_plus_nat(X107),X108) != hAPP_nat_nat(plus_plus_nat(X109),X108)
| X107 = X109 )
& ( X110 != X112
| hAPP_nat_nat(plus_plus_nat(X110),X111) = hAPP_nat_nat(plus_plus_nat(X112),X111) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1230])])])]) ).
fof(c_0_1938,plain,
! [X107,X108,X109,X110,X111,X112] :
( ( hAPP_real_real(plus_plus_real(X107),X108) != hAPP_real_real(plus_plus_real(X109),X108)
| X107 = X109 )
& ( X110 != X112
| hAPP_real_real(plus_plus_real(X110),X111) = hAPP_real_real(plus_plus_real(X112),X111) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1231])])])]) ).
fof(c_0_1939,plain,
! [X102,X103,X104] :
( hAPP_int_int(plus_plus_int(X102),X103) != hAPP_int_int(plus_plus_int(X102),X104)
| X103 = X104 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1232])]) ).
fof(c_0_1940,plain,
! [X102,X103,X104] :
( hAPP_nat_nat(plus_plus_nat(X102),X103) != hAPP_nat_nat(plus_plus_nat(X102),X104)
| X103 = X104 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1233])]) ).
fof(c_0_1941,plain,
! [X102,X103,X104] :
( hAPP_real_real(plus_plus_real(X102),X103) != hAPP_real_real(plus_plus_real(X102),X104)
| X103 = X104 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1234])]) ).
fof(c_0_1942,plain,
! [X99,X100,X101] :
( hAPP_int_int(plus_plus_int(X99),X100) != hAPP_int_int(plus_plus_int(X99),X101)
| X100 = X101 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1235])]) ).
fof(c_0_1943,plain,
! [X99,X100,X101] :
( hAPP_nat_nat(plus_plus_nat(X99),X100) != hAPP_nat_nat(plus_plus_nat(X99),X101)
| X100 = X101 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1236])]) ).
fof(c_0_1944,plain,
! [X99,X100,X101] :
( hAPP_real_real(plus_plus_real(X99),X100) != hAPP_real_real(plus_plus_real(X99),X101)
| X100 = X101 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1237])]) ).
fof(c_0_1945,plain,
! [X96,X97,X98] :
( hAPP_int_int(plus_plus_int(X96),X97) != hAPP_int_int(plus_plus_int(X98),X97)
| X96 = X98 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1238])]) ).
fof(c_0_1946,plain,
! [X96,X97,X98] :
( hAPP_nat_nat(plus_plus_nat(X96),X97) != hAPP_nat_nat(plus_plus_nat(X98),X97)
| X96 = X98 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1239])]) ).
fof(c_0_1947,plain,
! [X96,X97,X98] :
( hAPP_real_real(plus_plus_real(X96),X97) != hAPP_real_real(plus_plus_real(X98),X97)
| X96 = X98 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1240])]) ).
fof(c_0_1948,plain,
! [X30,X31,X32,X33,X34,X35] :
( ( hAPP_nat_nat(plus_plus_nat(X30),X31) != hAPP_nat_nat(plus_plus_nat(X32),X31)
| X30 = X32 )
& ( X33 != X35
| hAPP_nat_nat(plus_plus_nat(X33),X34) = hAPP_nat_nat(plus_plus_nat(X35),X34) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1241])])])]) ).
fof(c_0_1949,plain,
! [X30,X31,X32,X33,X34,X35] :
( ( hAPP_nat_nat(plus_plus_nat(X30),X31) != hAPP_nat_nat(plus_plus_nat(X30),X32)
| X31 = X32 )
& ( X34 != X35
| hAPP_nat_nat(plus_plus_nat(X33),X34) = hAPP_nat_nat(plus_plus_nat(X33),X35) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1242])])])]) ).
fof(c_0_1950,axiom,
number_number_of_int(bit1(bit1(pls))) = hAPP_nat_int(semiri1621563631at_int,number_number_of_nat(bit1(bit1(pls)))),
c_0_1243 ).
fof(c_0_1951,axiom,
number_number_of_int(bit0(bit1(pls))) = hAPP_nat_int(semiri1621563631at_int,number_number_of_nat(bit0(bit1(pls)))),
c_0_1244 ).
fof(c_0_1952,plain,
! [X26,X27,X28,X29] :
( ( X26 = zero_zero_real
| hAPP_nat_real(power_power_real(X26),number_number_of_nat(X27)) != zero_zero_real )
& ( number_number_of_nat(X27) != zero_zero_nat
| hAPP_nat_real(power_power_real(X26),number_number_of_nat(X27)) != zero_zero_real )
& ( X28 != zero_zero_real
| number_number_of_nat(X29) = zero_zero_nat
| hAPP_nat_real(power_power_real(X28),number_number_of_nat(X29)) = zero_zero_real ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1245])])])])]) ).
fof(c_0_1953,plain,
! [X26,X27,X28,X29] :
( ( X26 = zero_zero_nat
| hAPP_nat_nat(power_power_nat(X26),number_number_of_nat(X27)) != zero_zero_nat )
& ( number_number_of_nat(X27) != zero_zero_nat
| hAPP_nat_nat(power_power_nat(X26),number_number_of_nat(X27)) != zero_zero_nat )
& ( X28 != zero_zero_nat
| number_number_of_nat(X29) = zero_zero_nat
| hAPP_nat_nat(power_power_nat(X28),number_number_of_nat(X29)) = zero_zero_nat ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1246])])])])]) ).
fof(c_0_1954,plain,
! [X26,X27,X28,X29] :
( ( X26 = zero_zero_int
| hAPP_nat_int(power_power_int(X26),number_number_of_nat(X27)) != zero_zero_int )
& ( number_number_of_nat(X27) != zero_zero_nat
| hAPP_nat_int(power_power_int(X26),number_number_of_nat(X27)) != zero_zero_int )
& ( X28 != zero_zero_int
| number_number_of_nat(X29) = zero_zero_nat
| hAPP_nat_int(power_power_int(X28),number_number_of_nat(X29)) = zero_zero_int ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1247])])])])]) ).
fof(c_0_1955,axiom,
hAPP_nat_real(power_power_real(zero_zero_real),number_number_of_nat(bit0(bit1(pls)))) = zero_zero_real,
c_0_1248 ).
fof(c_0_1956,axiom,
hAPP_nat_nat(power_power_nat(zero_zero_nat),number_number_of_nat(bit0(bit1(pls)))) = zero_zero_nat,
c_0_1249 ).
fof(c_0_1957,axiom,
hAPP_nat_int(power_power_int(zero_zero_int),number_number_of_nat(bit0(bit1(pls)))) = zero_zero_int,
c_0_1250 ).
fof(c_0_1958,axiom,
hAPP_nat_real(power_power_real(one_one_real),number_number_of_nat(bit0(bit1(pls)))) = one_one_real,
c_0_1251 ).
fof(c_0_1959,axiom,
hAPP_nat_nat(power_power_nat(one_one_nat),number_number_of_nat(bit0(bit1(pls)))) = one_one_nat,
c_0_1252 ).
fof(c_0_1960,axiom,
hAPP_nat_int(power_power_int(one_one_int),number_number_of_nat(bit0(bit1(pls)))) = one_one_int,
c_0_1253 ).
fof(c_0_1961,plain,
! [X5,X6,X7,X8] :
( ( hAPP_nat_int(semiri1621563631at_int,X5) != hAPP_nat_int(semiri1621563631at_int,X6)
| X5 = X6 )
& ( X7 != X8
| hAPP_nat_int(semiri1621563631at_int,X7) = hAPP_nat_int(semiri1621563631at_int,X8) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1254])])])]) ).
fof(c_0_1962,plain,
! [X30,X31,X32,X33] :
( ( hAPP_nat_int(semiri1621563631at_int,X30) != hAPP_nat_int(semiri1621563631at_int,X31)
| X30 = X31 )
& ( X32 != X33
| hAPP_nat_int(semiri1621563631at_int,X32) = hAPP_nat_int(semiri1621563631at_int,X33) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1255])])])]) ).
fof(c_0_1963,plain,
! [X30,X31,X32,X33] :
( ( hAPP_nat_nat(semiri984289939at_nat,X30) != hAPP_nat_nat(semiri984289939at_nat,X31)
| X30 = X31 )
& ( X32 != X33
| hAPP_nat_nat(semiri984289939at_nat,X32) = hAPP_nat_nat(semiri984289939at_nat,X33) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1256])])])]) ).
fof(c_0_1964,plain,
! [X30,X31,X32,X33] :
( ( hAPP_nat_real(semiri132038758t_real,X30) != hAPP_nat_real(semiri132038758t_real,X31)
| X30 = X31 )
& ( X32 != X33
| hAPP_nat_real(semiri132038758t_real,X32) = hAPP_nat_real(semiri132038758t_real,X33) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1257])])])]) ).
fof(c_0_1965,plain,
! [X30,X31,X32,X33] :
( ( hAPP_nat_int(semiri1621563631at_int,X30) != hAPP_nat_int(semiri1621563631at_int,X31)
| X30 = X31 )
& ( X32 != X33
| hAPP_nat_int(semiri1621563631at_int,X32) = hAPP_nat_int(semiri1621563631at_int,X33) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1258])])])]) ).
fof(c_0_1966,plain,
! [X124,X125] : hAPP_int_int(plus_plus_int(X124),X125) = hAPP_int_int(plus_plus_int(X125),X124),
inference(variable_rename,[status(thm)],[c_0_1259]) ).
fof(c_0_1967,plain,
! [X124,X125] : hAPP_nat_nat(plus_plus_nat(X124),X125) = hAPP_nat_nat(plus_plus_nat(X125),X124),
inference(variable_rename,[status(thm)],[c_0_1260]) ).
fof(c_0_1968,plain,
! [X124,X125] : hAPP_real_real(plus_plus_real(X124),X125) = hAPP_real_real(plus_plus_real(X125),X124),
inference(variable_rename,[status(thm)],[c_0_1261]) ).
fof(c_0_1969,plain,
! [X17,X18] : hAPP_nat_nat(plus_plus_nat(X17),X18) = hAPP_nat_nat(plus_plus_nat(X18),X17),
inference(variable_rename,[status(thm)],[c_0_1262]) ).
fof(c_0_1970,plain,
! [X18,X19] : hAPP_int_int(plus_plus_int(X18),X19) = hAPP_int_int(plus_plus_int(X19),X18),
inference(variable_rename,[status(thm)],[c_0_1263]) ).
fof(c_0_1971,plain,
! [X42] : number267125858f_real(hAPP_nat_int(semiri1621563631at_int,X42)) = hAPP_nat_real(semiri132038758t_real,X42),
inference(variable_rename,[status(thm)],[c_0_1264]) ).
fof(c_0_1972,plain,
! [X42] : number_number_of_int(hAPP_nat_int(semiri1621563631at_int,X42)) = hAPP_nat_int(semiri1621563631at_int,X42),
inference(variable_rename,[status(thm)],[c_0_1265]) ).
fof(c_0_1973,plain,
! [X42] : number_number_of_nat(hAPP_nat_int(semiri1621563631at_int,X42)) = hAPP_nat_nat(semiri984289939at_nat,X42),
inference(variable_rename,[status(thm)],[c_0_1266]) ).
fof(c_0_1974,plain,
! [X11,X12] : hAPP_nat_nat(if_nat(fFalse,X11),X12) = X12,
inference(variable_rename,[status(thm)],[c_0_1267]) ).
fof(c_0_1975,plain,
! [X11,X12] : hAPP_nat_nat(if_nat(fTrue,X11),X12) = X11,
inference(variable_rename,[status(thm)],[c_0_1268]) ).
fof(c_0_1976,plain,
! [X19,X20,X21,X22] :
( ( hAPP_nat_nat(power_power_nat(X19),X20) != one_one_nat
| X19 = one_one_nat
| X20 = zero_zero_nat )
& ( X21 != one_one_nat
| hAPP_nat_nat(power_power_nat(X21),X22) = one_one_nat )
& ( X22 != zero_zero_nat
| hAPP_nat_nat(power_power_nat(X21),X22) = one_one_nat ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1269])])])])]) ).
fof(c_0_1977,plain,
! [X82,X83,X84,X85] :
( ( X82 != hAPP_int_int(plus_plus_int(X82),X83)
| X83 = zero_zero_int )
& ( X85 != zero_zero_int
| X84 = hAPP_int_int(plus_plus_int(X84),X85) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1270])])])]) ).
fof(c_0_1978,plain,
! [X82,X83,X84,X85] :
( ( X82 != hAPP_nat_nat(plus_plus_nat(X82),X83)
| X83 = zero_zero_nat )
& ( X85 != zero_zero_nat
| X84 = hAPP_nat_nat(plus_plus_nat(X84),X85) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1271])])])]) ).
fof(c_0_1979,plain,
! [X82,X83,X84,X85] :
( ( X82 != hAPP_real_real(plus_plus_real(X82),X83)
| X83 = zero_zero_real )
& ( X85 != zero_zero_real
| X84 = hAPP_real_real(plus_plus_real(X84),X85) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1272])])])]) ).
fof(c_0_1980,plain,
! [X17,X18] :
( hAPP_nat_nat(plus_plus_nat(X17),X18) != X17
| X18 = zero_zero_nat ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1273])]) ).
fof(c_0_1981,plain,
! [X30,X31,X32,X33] :
( ( X31 != zero_zero_nat
| hAPP_nat_nat(power_power_nat(X30),X31) != zero_zero_nat )
& ( X30 = zero_zero_nat
| hAPP_nat_nat(power_power_nat(X30),X31) != zero_zero_nat )
& ( X33 = zero_zero_nat
| X32 != zero_zero_nat
| hAPP_nat_nat(power_power_nat(X32),X33) = zero_zero_nat ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1274])])])])]) ).
fof(c_0_1982,plain,
! [X19,X20,X21,X22] :
( ( X19 = zero_zero_int
| hAPP_nat_int(power_power_int(X19),X20) != zero_zero_int )
& ( X20 != zero_zero_nat
| hAPP_nat_int(power_power_int(X19),X20) != zero_zero_int )
& ( X21 != zero_zero_int
| X22 = zero_zero_nat
| hAPP_nat_int(power_power_int(X21),X22) = zero_zero_int ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1275])])])])]) ).
fof(c_0_1983,plain,
! [X19,X20,X21,X22] :
( ( X19 = zero_zero_nat
| hAPP_nat_nat(power_power_nat(X19),X20) != zero_zero_nat )
& ( X20 != zero_zero_nat
| hAPP_nat_nat(power_power_nat(X19),X20) != zero_zero_nat )
& ( X21 != zero_zero_nat
| X22 = zero_zero_nat
| hAPP_nat_nat(power_power_nat(X21),X22) = zero_zero_nat ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1276])])])])]) ).
fof(c_0_1984,plain,
! [X19,X20,X21,X22] :
( ( X19 = zero_zero_real
| hAPP_nat_real(power_power_real(X19),X20) != zero_zero_real )
& ( X20 != zero_zero_nat
| hAPP_nat_real(power_power_real(X19),X20) != zero_zero_real )
& ( X21 != zero_zero_real
| X22 = zero_zero_nat
| hAPP_nat_real(power_power_real(X21),X22) = zero_zero_real ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1277])])])])]) ).
fof(c_0_1985,plain,
! [X6,X7] :
( ( zero_zero_int != hAPP_int_int(plus_plus_int(X6),X6)
| X6 = zero_zero_int )
& ( X7 != zero_zero_int
| zero_zero_int = hAPP_int_int(plus_plus_int(X7),X7) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1278])])])]) ).
fof(c_0_1986,plain,
! [X6,X7] :
( ( zero_zero_real != hAPP_real_real(plus_plus_real(X6),X6)
| X6 = zero_zero_real )
& ( X7 != zero_zero_real
| zero_zero_real = hAPP_real_real(plus_plus_real(X7),X7) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1279])])])]) ).
fof(c_0_1987,plain,
! [X66,X67] :
( X67 = zero_zero_int
| hAPP_nat_int(power_power_int(X67),X66) != zero_zero_int ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1280])]) ).
fof(c_0_1988,plain,
! [X66,X67] :
( X67 = zero_zero_real
| hAPP_nat_real(power_power_real(X67),X66) != zero_zero_real ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1281])]) ).
fof(c_0_1989,plain,
! [X30,X31,X32,X33] :
( ( X30 = zero_zero_nat
| hAPP_nat_nat(plus_plus_nat(X30),X31) != zero_zero_nat )
& ( X31 = zero_zero_nat
| hAPP_nat_nat(plus_plus_nat(X30),X31) != zero_zero_nat )
& ( X32 != zero_zero_nat
| X33 != zero_zero_nat
| hAPP_nat_nat(plus_plus_nat(X32),X33) = zero_zero_nat ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1282])])])])]) ).
fof(c_0_1990,plain,
! [X6,X7] :
( ( hAPP_real_real(plus_plus_real(X6),X6) != zero_zero_real
| X6 = zero_zero_real )
& ( X7 != zero_zero_real
| hAPP_real_real(plus_plus_real(X7),X7) = zero_zero_real ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1283])])])]) ).
fof(c_0_1991,plain,
! [X6,X7] :
( ( hAPP_int_int(plus_plus_int(X6),X6) != zero_zero_int
| X6 = zero_zero_int )
& ( X7 != zero_zero_int
| hAPP_int_int(plus_plus_int(X7),X7) = zero_zero_int ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1284])])])]) ).
fof(c_0_1992,plain,
! [X234] : number_number_of_int(succ(X234)) = hAPP_int_int(plus_plus_int(one_one_int),number_number_of_int(X234)),
inference(variable_rename,[status(thm)],[c_0_1285]) ).
fof(c_0_1993,plain,
! [X234] : number267125858f_real(succ(X234)) = hAPP_real_real(plus_plus_real(one_one_real),number267125858f_real(X234)),
inference(variable_rename,[status(thm)],[c_0_1286]) ).
fof(c_0_1994,axiom,
hAPP_nat_nat(plus_plus_nat(one_one_nat),one_one_nat) = number_number_of_nat(bit0(bit1(pls))),
c_0_1287 ).
fof(c_0_1995,axiom,
hAPP_real_real(plus_plus_real(one_one_real),one_one_real) = number267125858f_real(bit0(bit1(pls))),
c_0_1288 ).
fof(c_0_1996,axiom,
hAPP_nat_nat(plus_plus_nat(one_one_nat),one_one_nat) = number_number_of_nat(bit0(bit1(pls))),
c_0_1289 ).
fof(c_0_1997,axiom,
hAPP_int_int(plus_plus_int(one_one_int),one_one_int) = number_number_of_int(bit0(bit1(pls))),
c_0_1290 ).
fof(c_0_1998,axiom,
hAPP_real_real(plus_plus_real(one_one_real),one_one_real) = number267125858f_real(bit0(bit1(pls))),
c_0_1291 ).
fof(c_0_1999,axiom,
hAPP_int_int(plus_plus_int(one_one_int),one_one_int) = number_number_of_int(bit0(bit1(pls))),
c_0_1292 ).
fof(c_0_2000,plain,
! [X10,X11] :
( ( number_number_of_nat(X10) != zero_zero_nat
| hAPP_nat_real(power_power_real(zero_zero_real),number_number_of_nat(X10)) = one_one_real )
& ( number_number_of_nat(X11) = zero_zero_nat
| hAPP_nat_real(power_power_real(zero_zero_real),number_number_of_nat(X11)) = zero_zero_real ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1293])])])]) ).
fof(c_0_2001,plain,
! [X10,X11] :
( ( number_number_of_nat(X10) != zero_zero_nat
| hAPP_nat_nat(power_power_nat(zero_zero_nat),number_number_of_nat(X10)) = one_one_nat )
& ( number_number_of_nat(X11) = zero_zero_nat
| hAPP_nat_nat(power_power_nat(zero_zero_nat),number_number_of_nat(X11)) = zero_zero_nat ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1294])])])]) ).
fof(c_0_2002,plain,
! [X10,X11] :
( ( number_number_of_nat(X10) != zero_zero_nat
| hAPP_nat_int(power_power_int(zero_zero_int),number_number_of_nat(X10)) = one_one_int )
& ( number_number_of_nat(X11) = zero_zero_nat
| hAPP_nat_int(power_power_int(zero_zero_int),number_number_of_nat(X11)) = zero_zero_int ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1295])])])]) ).
fof(c_0_2003,plain,
! [X3,X4] : is_bool(hAPP_real_bool(X3,X4)),
inference(variable_rename,[status(thm)],[c_0_1296]) ).
fof(c_0_2004,plain,
! [X3,X4] : is_bool(hAPP_nat_bool(X3,X4)),
inference(variable_rename,[status(thm)],[c_0_1297]) ).
fof(c_0_2005,plain,
! [X3,X4] : is_bool(hAPP_int_bool(X3,X4)),
inference(variable_rename,[status(thm)],[c_0_1298]) ).
fof(c_0_2006,plain,
! [X33] : hAPP_real_real(plus_plus_real(number267125858f_real(pls)),X33) = X33,
inference(variable_rename,[status(thm)],[c_0_1299]) ).
fof(c_0_2007,plain,
! [X33] : hAPP_int_int(plus_plus_int(number_number_of_int(pls)),X33) = X33,
inference(variable_rename,[status(thm)],[c_0_1300]) ).
fof(c_0_2008,plain,
! [X34] : hAPP_real_real(plus_plus_real(X34),number267125858f_real(pls)) = X34,
inference(variable_rename,[status(thm)],[c_0_1301]) ).
fof(c_0_2009,plain,
! [X34] : hAPP_int_int(plus_plus_int(X34),number_number_of_int(pls)) = X34,
inference(variable_rename,[status(thm)],[c_0_1302]) ).
fof(c_0_2010,plain,
! [X22] : bit0(X22) = hAPP_int_int(plus_plus_int(X22),X22),
inference(variable_rename,[status(thm)],[c_0_1303]) ).
fof(c_0_2011,plain,
! [X22] : succ(X22) = hAPP_int_int(plus_plus_int(X22),one_one_int),
inference(variable_rename,[status(thm)],[c_0_1304]) ).
fof(c_0_2012,plain,
! [X19,X20] :
( ( hAPP_nat_int(semiri1621563631at_int,X19) != zero_zero_int
| X19 = zero_zero_nat )
& ( X20 != zero_zero_nat
| hAPP_nat_int(semiri1621563631at_int,X20) = zero_zero_int ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1305])])])]) ).
fof(c_0_2013,plain,
! [X22] : succ(bit1(X22)) = bit0(succ(X22)),
inference(variable_rename,[status(thm)],[c_0_1306]) ).
fof(c_0_2014,plain,
! [X51,X52] :
( ( X51 != zero_zero_nat
| hAPP_nat_real(power_power_real(zero_zero_real),X51) = one_one_real )
& ( X52 = zero_zero_nat
| hAPP_nat_real(power_power_real(zero_zero_real),X52) = zero_zero_real ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1307])])])]) ).
fof(c_0_2015,plain,
! [X51,X52] :
( ( X51 != zero_zero_nat
| hAPP_nat_nat(power_power_nat(zero_zero_nat),X51) = one_one_nat )
& ( X52 = zero_zero_nat
| hAPP_nat_nat(power_power_nat(zero_zero_nat),X52) = zero_zero_nat ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1308])])])]) ).
fof(c_0_2016,plain,
! [X51,X52] :
( ( X51 != zero_zero_nat
| hAPP_nat_int(power_power_int(zero_zero_int),X51) = one_one_int )
& ( X52 = zero_zero_nat
| hAPP_nat_int(power_power_int(zero_zero_int),X52) = zero_zero_int ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1309])])])]) ).
fof(c_0_2017,plain,
! [X147] : hAPP_nat_int(power_power_int(X147),one_one_nat) = X147,
inference(variable_rename,[status(thm)],[c_0_1310]) ).
fof(c_0_2018,plain,
! [X147] : hAPP_nat_nat(power_power_nat(X147),one_one_nat) = X147,
inference(variable_rename,[status(thm)],[c_0_1311]) ).
fof(c_0_2019,plain,
! [X147] : hAPP_nat_real(power_power_real(X147),one_one_nat) = X147,
inference(variable_rename,[status(thm)],[c_0_1312]) ).
fof(c_0_2020,plain,
! [X127] : hAPP_int_int(plus_plus_int(X127),zero_zero_int) = X127,
inference(variable_rename,[status(thm)],[c_0_1313]) ).
fof(c_0_2021,plain,
! [X127] : hAPP_nat_nat(plus_plus_nat(X127),zero_zero_nat) = X127,
inference(variable_rename,[status(thm)],[c_0_1314]) ).
fof(c_0_2022,plain,
! [X127] : hAPP_real_real(plus_plus_real(X127),zero_zero_real) = X127,
inference(variable_rename,[status(thm)],[c_0_1315]) ).
fof(c_0_2023,plain,
! [X126] : hAPP_int_int(plus_plus_int(X126),zero_zero_int) = X126,
inference(variable_rename,[status(thm)],[c_0_1316]) ).
fof(c_0_2024,plain,
! [X126] : hAPP_nat_nat(plus_plus_nat(X126),zero_zero_nat) = X126,
inference(variable_rename,[status(thm)],[c_0_1317]) ).
fof(c_0_2025,plain,
! [X126] : hAPP_real_real(plus_plus_real(X126),zero_zero_real) = X126,
inference(variable_rename,[status(thm)],[c_0_1318]) ).
fof(c_0_2026,plain,
! [X125] : hAPP_int_int(plus_plus_int(X125),zero_zero_int) = X125,
inference(variable_rename,[status(thm)],[c_0_1319]) ).
fof(c_0_2027,plain,
! [X125] : hAPP_nat_nat(plus_plus_nat(X125),zero_zero_nat) = X125,
inference(variable_rename,[status(thm)],[c_0_1320]) ).
fof(c_0_2028,plain,
! [X125] : hAPP_real_real(plus_plus_real(X125),zero_zero_real) = X125,
inference(variable_rename,[status(thm)],[c_0_1321]) ).
fof(c_0_2029,plain,
! [X64] : hAPP_nat_int(power_power_int(X64),one_one_nat) = X64,
inference(variable_rename,[status(thm)],[c_0_1322]) ).
fof(c_0_2030,plain,
! [X64] : hAPP_nat_nat(power_power_nat(X64),one_one_nat) = X64,
inference(variable_rename,[status(thm)],[c_0_1323]) ).
fof(c_0_2031,plain,
! [X64] : hAPP_nat_real(power_power_real(X64),one_one_nat) = X64,
inference(variable_rename,[status(thm)],[c_0_1324]) ).
fof(c_0_2032,plain,
! [X16] : hAPP_nat_nat(plus_plus_nat(X16),zero_zero_nat) = X16,
inference(variable_rename,[status(thm)],[c_0_1325]) ).
fof(c_0_2033,plain,
! [X18] : hAPP_int_int(plus_plus_int(X18),zero_zero_int) = X18,
inference(variable_rename,[status(thm)],[c_0_1326]) ).
fof(c_0_2034,plain,
! [X22] : hAPP_int_int(plus_plus_int(X22),pls) = X22,
inference(variable_rename,[status(thm)],[c_0_1327]) ).
fof(c_0_2035,plain,
! [X93] : hAPP_nat_int(power_power_int(X93),zero_zero_nat) = one_one_int,
inference(variable_rename,[status(thm)],[c_0_1328]) ).
fof(c_0_2036,plain,
! [X93] : hAPP_nat_nat(power_power_nat(X93),zero_zero_nat) = one_one_nat,
inference(variable_rename,[status(thm)],[c_0_1329]) ).
fof(c_0_2037,plain,
! [X93] : hAPP_nat_real(power_power_real(X93),zero_zero_nat) = one_one_real,
inference(variable_rename,[status(thm)],[c_0_1330]) ).
fof(c_0_2038,plain,
! [X90] : hAPP_nat_int(power_power_int(X90),zero_zero_nat) = one_one_int,
inference(variable_rename,[status(thm)],[c_0_1331]) ).
fof(c_0_2039,plain,
! [X90] : hAPP_nat_nat(power_power_nat(X90),zero_zero_nat) = one_one_nat,
inference(variable_rename,[status(thm)],[c_0_1332]) ).
fof(c_0_2040,plain,
! [X90] : hAPP_nat_real(power_power_real(X90),zero_zero_nat) = one_one_real,
inference(variable_rename,[status(thm)],[c_0_1333]) ).
fof(c_0_2041,plain,
! [X130] : hAPP_int_int(plus_plus_int(zero_zero_int),X130) = X130,
inference(variable_rename,[status(thm)],[c_0_1334]) ).
fof(c_0_2042,plain,
! [X130] : hAPP_nat_nat(plus_plus_nat(zero_zero_nat),X130) = X130,
inference(variable_rename,[status(thm)],[c_0_1335]) ).
fof(c_0_2043,plain,
! [X130] : hAPP_real_real(plus_plus_real(zero_zero_real),X130) = X130,
inference(variable_rename,[status(thm)],[c_0_1336]) ).
fof(c_0_2044,plain,
! [X129] : hAPP_int_int(plus_plus_int(zero_zero_int),X129) = X129,
inference(variable_rename,[status(thm)],[c_0_1337]) ).
fof(c_0_2045,plain,
! [X129] : hAPP_nat_nat(plus_plus_nat(zero_zero_nat),X129) = X129,
inference(variable_rename,[status(thm)],[c_0_1338]) ).
fof(c_0_2046,plain,
! [X129] : hAPP_real_real(plus_plus_real(zero_zero_real),X129) = X129,
inference(variable_rename,[status(thm)],[c_0_1339]) ).
fof(c_0_2047,plain,
! [X128] : hAPP_int_int(plus_plus_int(zero_zero_int),X128) = X128,
inference(variable_rename,[status(thm)],[c_0_1340]) ).
fof(c_0_2048,plain,
! [X128] : hAPP_nat_nat(plus_plus_nat(zero_zero_nat),X128) = X128,
inference(variable_rename,[status(thm)],[c_0_1341]) ).
fof(c_0_2049,plain,
! [X128] : hAPP_real_real(plus_plus_real(zero_zero_real),X128) = X128,
inference(variable_rename,[status(thm)],[c_0_1342]) ).
fof(c_0_2050,plain,
! [X17] : hAPP_nat_nat(plus_plus_nat(zero_zero_nat),X17) = X17,
inference(variable_rename,[status(thm)],[c_0_1343]) ).
fof(c_0_2051,plain,
! [X18] : hAPP_int_int(plus_plus_int(zero_zero_int),X18) = X18,
inference(variable_rename,[status(thm)],[c_0_1344]) ).
fof(c_0_2052,plain,
! [X22] : hAPP_int_int(plus_plus_int(pls),X22) = X22,
inference(variable_rename,[status(thm)],[c_0_1345]) ).
fof(c_0_2053,plain,
! [X67] : hAPP_nat_int(power_power_int(one_one_int),X67) = one_one_int,
inference(variable_rename,[status(thm)],[c_0_1346]) ).
fof(c_0_2054,plain,
! [X67] : hAPP_nat_nat(power_power_nat(one_one_nat),X67) = one_one_nat,
inference(variable_rename,[status(thm)],[c_0_1347]) ).
fof(c_0_2055,plain,
! [X67] : hAPP_nat_real(power_power_real(one_one_real),X67) = one_one_real,
inference(variable_rename,[status(thm)],[c_0_1348]) ).
fof(c_0_2056,plain,
! [X13,X14,X15,X16] :
( ( bit0(X13) != bit0(X14)
| X13 = X14 )
& ( X15 != X16
| bit0(X15) = bit0(X16) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1349])])])]) ).
fof(c_0_2057,plain,
! [X13,X14,X15,X16] :
( ( bit1(X13) != bit1(X14)
| X13 = X14 )
& ( X15 != X16
| bit1(X15) = bit1(X16) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1350])])])]) ).
fof(c_0_2058,plain,
! [X5,X6,X7,X8] :
( ( number267125858f_real(X5) != number267125858f_real(X6)
| X5 = X6 )
& ( X7 != X8
| number267125858f_real(X7) = number267125858f_real(X8) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1351])])])]) ).
fof(c_0_2059,plain,
! [X5,X6,X7,X8] :
( ( number_number_of_int(X5) != number_number_of_int(X6)
| X5 = X6 )
& ( X7 != X8
| number_number_of_int(X7) = number_number_of_int(X8) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1352])])])]) ).
fof(c_0_2060,plain,
! [X22] : succ(bit0(X22)) = bit1(X22),
inference(variable_rename,[status(thm)],[c_0_1353]) ).
fof(c_0_2061,plain,
! [X26,X27,X28,X29] :
( ( number267125858f_real(X26) != X27
| X27 = number267125858f_real(X26) )
& ( X29 != number267125858f_real(X28)
| number267125858f_real(X28) = X29 ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1354])])])]) ).
fof(c_0_2062,plain,
! [X26,X27,X28,X29] :
( ( number_number_of_int(X26) != X27
| X27 = number_number_of_int(X26) )
& ( X29 != number_number_of_int(X28)
| number_number_of_int(X28) = X29 ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1355])])])]) ).
fof(c_0_2063,plain,
! [X26,X27,X28,X29] :
( ( number_number_of_nat(X26) != X27
| X27 = number_number_of_nat(X26) )
& ( X29 != number_number_of_nat(X28)
| number_number_of_nat(X28) = X29 ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1356])])])]) ).
fof(c_0_2064,plain,
! [X32,X33] : bit0(X32) != bit1(X33),
inference(variable_rename,[status(thm)],[c_0_1357]) ).
fof(c_0_2065,plain,
! [X32,X33] : bit1(X32) != bit0(X33),
inference(variable_rename,[status(thm)],[c_0_1358]) ).
fof(c_0_2066,axiom,
zero_zero_int = hAPP_nat_int(semiri1621563631at_int,zero_zero_nat),
c_0_1359 ).
fof(c_0_2067,axiom,
hAPP_nat_int(semiri1621563631at_int,zero_zero_nat) = zero_zero_int,
c_0_1360 ).
fof(c_0_2068,axiom,
hAPP_nat_nat(semiri984289939at_nat,zero_zero_nat) = zero_zero_nat,
c_0_1361 ).
fof(c_0_2069,axiom,
hAPP_nat_real(semiri132038758t_real,zero_zero_nat) = zero_zero_real,
c_0_1362 ).
fof(c_0_2070,axiom,
one_one_int = hAPP_nat_int(semiri1621563631at_int,one_one_nat),
c_0_1363 ).
fof(c_0_2071,axiom,
hAPP_nat_int(semiri1621563631at_int,one_one_nat) = one_one_int,
c_0_1364 ).
fof(c_0_2072,axiom,
hAPP_nat_nat(semiri984289939at_nat,one_one_nat) = one_one_nat,
c_0_1365 ).
fof(c_0_2073,axiom,
hAPP_nat_real(semiri132038758t_real,one_one_nat) = one_one_real,
c_0_1366 ).
fof(c_0_2074,axiom,
hAPP_nat_int(semiri1621563631at_int,zero_zero_nat) = zero_zero_int,
c_0_1367 ).
fof(c_0_2075,axiom,
hAPP_nat_int(semiri1621563631at_int,one_one_nat) = one_one_int,
c_0_1368 ).
fof(c_0_2076,plain,
! [X284] :
( ~ is_bool(X284)
| X284 = fTrue
| X284 = fFalse ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1369])]) ).
fof(c_0_2077,plain,
! [X13,X14] :
( ( pls != bit0(X13)
| pls = X13 )
& ( pls != X14
| pls = bit0(X14) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1370])])])]) ).
fof(c_0_2078,plain,
! [X12,X13] :
( ( bit0(X12) != pls
| X12 = pls )
& ( X13 != pls
| bit0(X13) = pls ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1371])])])]) ).
fof(c_0_2079,axiom,
number267125858f_real(bit1(pls)) = one_one_real,
c_0_1372 ).
fof(c_0_2080,axiom,
number_number_of_nat(bit1(pls)) = one_one_nat,
c_0_1373 ).
fof(c_0_2081,axiom,
number_number_of_int(bit1(pls)) = one_one_int,
c_0_1374 ).
fof(c_0_2082,axiom,
one_one_nat = number_number_of_nat(bit1(pls)),
c_0_1375 ).
fof(c_0_2083,axiom,
number_number_of_nat(bit1(pls)) = one_one_nat,
c_0_1376 ).
fof(c_0_2084,axiom,
one_one_int = number_number_of_int(bit1(pls)),
c_0_1377 ).
fof(c_0_2085,axiom,
number267125858f_real(bit1(pls)) = one_one_real,
c_0_1378 ).
fof(c_0_2086,axiom,
number_number_of_int(bit1(pls)) = one_one_int,
c_0_1379 ).
fof(c_0_2087,axiom,
one_one_real = number267125858f_real(bit1(pls)),
c_0_1380 ).
fof(c_0_2088,axiom,
one_one_int = number_number_of_int(bit1(pls)),
c_0_1381 ).
fof(c_0_2089,plain,
! [X32] : pls != bit1(X32),
inference(variable_rename,[status(thm)],[c_0_1382]) ).
fof(c_0_2090,plain,
! [X22] : bit1(X22) != pls,
inference(variable_rename,[status(thm)],[c_0_1383]) ).
fof(c_0_2091,axiom,
succ(pls) = bit1(pls),
c_0_1384 ).
fof(c_0_2092,plain,
! [X22] : number_number_of_int(X22) = X22,
inference(variable_rename,[status(thm)],[c_0_1385]) ).
fof(c_0_2093,plain,
! [X4,X5] :
( ( one_one_int != X4
| X4 = one_one_int )
& ( X5 != one_one_int
| one_one_int = X5 ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1386])])])]) ).
fof(c_0_2094,plain,
! [X4,X5] :
( ( one_one_nat != X4
| X4 = one_one_nat )
& ( X5 != one_one_nat
| one_one_nat = X5 ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1387])])])]) ).
fof(c_0_2095,plain,
! [X4,X5] :
( ( one_one_real != X4
| X4 = one_one_real )
& ( X5 != one_one_real
| one_one_real = X5 ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1388])])])]) ).
fof(c_0_2096,plain,
! [X4,X5] :
( ( zero_zero_int != X4
| X4 = zero_zero_int )
& ( X5 != zero_zero_int
| zero_zero_int = X5 ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1389])])])]) ).
fof(c_0_2097,plain,
! [X4,X5] :
( ( zero_zero_nat != X4
| X4 = zero_zero_nat )
& ( X5 != zero_zero_nat
| zero_zero_nat = X5 ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1390])])])]) ).
fof(c_0_2098,plain,
! [X4,X5] :
( ( zero_zero_real != X4
| X4 = zero_zero_real )
& ( X5 != zero_zero_real
| zero_zero_real = X5 ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1391])])])]) ).
fof(c_0_2099,axiom,
zero_zero_real = number267125858f_real(pls),
c_0_1392 ).
fof(c_0_2100,axiom,
zero_zero_int = number_number_of_int(pls),
c_0_1393 ).
fof(c_0_2101,axiom,
number267125858f_real(pls) = zero_zero_real,
c_0_1394 ).
fof(c_0_2102,axiom,
number_number_of_int(pls) = zero_zero_int,
c_0_1395 ).
fof(c_0_2103,axiom,
number267125858f_real(pls) = zero_zero_real,
c_0_1396 ).
fof(c_0_2104,axiom,
number_number_of_nat(pls) = zero_zero_nat,
c_0_1397 ).
fof(c_0_2105,axiom,
number_number_of_int(pls) = zero_zero_int,
c_0_1398 ).
fof(c_0_2106,axiom,
bit0(pls) = pls,
c_0_1399 ).
fof(c_0_2107,axiom,
zero_zero_nat = number_number_of_nat(pls),
c_0_1400 ).
fof(c_0_2108,axiom,
number_number_of_nat(pls) = zero_zero_nat,
c_0_1401 ).
fof(c_0_2109,axiom,
zero_zero_int = number_number_of_int(pls),
c_0_1402 ).
fof(c_0_2110,axiom,
is_bool(fTrue),
c_0_1403 ).
fof(c_0_2111,axiom,
is_bool(fFalse),
c_0_1404 ).
fof(c_0_2112,axiom,
zero_zero_int != one_one_int,
c_0_1405 ).
fof(c_0_2113,axiom,
zero_zero_nat != one_one_nat,
c_0_1406 ).
fof(c_0_2114,axiom,
zero_zero_real != one_one_real,
c_0_1407 ).
fof(c_0_2115,axiom,
one_one_int != zero_zero_int,
c_0_1408 ).
fof(c_0_2116,axiom,
one_one_nat != zero_zero_nat,
c_0_1409 ).
fof(c_0_2117,axiom,
one_one_real != zero_zero_real,
c_0_1410 ).
fof(c_0_2118,axiom,
zero_zero_real != one_one_real,
c_0_1411 ).
fof(c_0_2119,axiom,
zero_zero_int != one_one_int,
c_0_1412 ).
fof(c_0_2120,axiom,
pls = zero_zero_int,
c_0_1413 ).
cnf(c_0_2121,plain,
( X1 = zero_zero_int
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(X1),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_int(power_power_int(X2),number_number_of_nat(bit0(bit1(pls)))))),zero_zero_int)) ),
inference(split_conjunct,[status(thm)],[c_0_1414]) ).
cnf(c_0_2122,plain,
( X2 = zero_zero_int
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(X1),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_int(power_power_int(X2),number_number_of_nat(bit0(bit1(pls)))))),zero_zero_int)) ),
inference(split_conjunct,[status(thm)],[c_0_1414]) ).
cnf(c_0_2123,plain,
( X1 = zero_zero_real
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(plus_plus_real(hAPP_nat_real(power_power_real(X1),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_real(power_power_real(X2),number_number_of_nat(bit0(bit1(pls)))))),zero_zero_real)) ),
inference(split_conjunct,[status(thm)],[c_0_1415]) ).
cnf(c_0_2124,plain,
( X2 = zero_zero_real
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(plus_plus_real(hAPP_nat_real(power_power_real(X1),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_real(power_power_real(X2),number_number_of_nat(bit0(bit1(pls)))))),zero_zero_real)) ),
inference(split_conjunct,[status(thm)],[c_0_1415]) ).
cnf(c_0_2125,plain,
~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(plus_plus_real(hAPP_nat_real(power_power_real(X1),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_real(power_power_real(X2),number_number_of_nat(bit0(bit1(pls)))))),zero_zero_real)),
inference(split_conjunct,[status(thm)],[c_0_1416]) ).
cnf(c_0_2126,plain,
~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(X1),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_int(power_power_int(X2),number_number_of_nat(bit0(bit1(pls)))))),zero_zero_int)),
inference(split_conjunct,[status(thm)],[c_0_1417]) ).
cnf(c_0_2127,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(X1,X2)),X3)),hAPP_nat_nat(X1,hAPP_nat_nat(plus_plus_nat(X2),X3))))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(X1,esk16_3(X2,X3,X1))),hAPP_nat_nat(X1,esk17_3(X2,X3,X1)))) ),
inference(split_conjunct,[status(thm)],[c_0_1418]) ).
cnf(c_0_2128,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(X1,X2)),hAPP_nat_nat(X1,X3)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X3))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(X1,esk20_3(X2,X3,X1))),hAPP_nat_nat(X1,esk21_3(X2,X3,X1)))) ),
inference(split_conjunct,[status(thm)],[c_0_1419]) ).
cnf(c_0_2129,plain,
hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),sqrt(hAPP_real_real(plus_plus_real(hAPP_nat_real(power_power_real(X1),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_real(power_power_real(X2),number_number_of_nat(bit0(bit1(pls)))))))),
inference(split_conjunct,[status(thm)],[c_0_1420]) ).
cnf(c_0_2130,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(X1),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_int(power_power_int(X2),number_number_of_nat(bit0(bit1(pls)))))),zero_zero_int))
| X2 != zero_zero_int
| X1 != zero_zero_int ),
inference(split_conjunct,[status(thm)],[c_0_1414]) ).
cnf(c_0_2131,plain,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(plus_plus_real(hAPP_nat_real(power_power_real(X1),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_real(power_power_real(X2),number_number_of_nat(bit0(bit1(pls)))))),zero_zero_real))
| X2 != zero_zero_real
| X1 != zero_zero_real ),
inference(split_conjunct,[status(thm)],[c_0_1415]) ).
cnf(c_0_2132,plain,
( X1 != zero_zero_real
| X2 != zero_zero_real
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),hAPP_real_real(plus_plus_real(hAPP_nat_real(power_power_real(X2),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_real(power_power_real(X1),number_number_of_nat(bit0(bit1(pls))))))) ),
inference(split_conjunct,[status(thm)],[c_0_1421]) ).
cnf(c_0_2133,plain,
( X1 != zero_zero_int
| X2 != zero_zero_int
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(X2),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_int(power_power_int(X1),number_number_of_nat(bit0(bit1(pls))))))) ),
inference(split_conjunct,[status(thm)],[c_0_1422]) ).
cnf(c_0_2134,plain,
hAPP_nat_int(power_power_int(hAPP_int_int(plus_plus_int(X1),X2)),number_number_of_nat(bit0(bit1(pls)))) = hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(X1),number_number_of_nat(bit0(bit1(pls))))),times_times_int(times_times_int(number_number_of_int(bit0(bit1(pls))),X1),X2))),hAPP_nat_int(power_power_int(X2),number_number_of_nat(bit0(bit1(pls))))),
inference(split_conjunct,[status(thm)],[c_0_1423]) ).
cnf(c_0_2135,plain,
( hBOOL(hAPP_int_bool(X3,X2))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X2))
| ~ hBOOL(hAPP_int_bool(X3,hAPP_int_int(plus_plus_int(X1),one_one_int)))
| ~ hBOOL(hAPP_int_bool(X3,hAPP_int_int(plus_plus_int(esk1_3(X3,X1,X2)),one_one_int))) ),
inference(split_conjunct,[status(thm)],[c_0_1424]) ).
cnf(c_0_2136,plain,
( hBOOL(hAPP_int_bool(X3,X2))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2))
| ~ hBOOL(hAPP_int_bool(X3,X1))
| ~ hBOOL(hAPP_int_bool(X3,hAPP_int_int(plus_plus_int(esk18_3(X3,X1,X2)),one_one_int))) ),
inference(split_conjunct,[status(thm)],[c_0_1425]) ).
cnf(c_0_2137,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(X1,X2)),X3)),hAPP_nat_nat(X1,hAPP_nat_nat(plus_plus_nat(X2),X3))))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,esk16_3(X2,X3,X1)),esk17_3(X2,X3,X1))) ),
inference(split_conjunct,[status(thm)],[c_0_1418]) ).
cnf(c_0_2138,plain,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),hAPP_real_real(plus_plus_real(hAPP_nat_real(power_power_real(X1),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_real(power_power_real(X2),number_number_of_nat(bit0(bit1(pls)))))))
| X1 = zero_zero_real ),
inference(split_conjunct,[status(thm)],[c_0_1421]) ).
cnf(c_0_2139,plain,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),hAPP_real_real(plus_plus_real(hAPP_nat_real(power_power_real(X1),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_real(power_power_real(X2),number_number_of_nat(bit0(bit1(pls)))))))
| X2 = zero_zero_real ),
inference(split_conjunct,[status(thm)],[c_0_1421]) ).
cnf(c_0_2140,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(X1),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_int(power_power_int(X2),number_number_of_nat(bit0(bit1(pls)))))))
| X1 = zero_zero_int ),
inference(split_conjunct,[status(thm)],[c_0_1422]) ).
cnf(c_0_2141,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(X1),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_int(power_power_int(X2),number_number_of_nat(bit0(bit1(pls)))))))
| X2 = zero_zero_int ),
inference(split_conjunct,[status(thm)],[c_0_1422]) ).
cnf(c_0_2142,plain,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(X1),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_int(power_power_int(X2),number_number_of_nat(bit0(bit1(pls))))))),
inference(split_conjunct,[status(thm)],[c_0_1426]) ).
cnf(c_0_2143,plain,
hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),hAPP_real_real(plus_plus_real(hAPP_nat_real(power_power_real(X1),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_real(power_power_real(X2),number_number_of_nat(bit0(bit1(pls))))))),
inference(split_conjunct,[status(thm)],[c_0_1427]) ).
cnf(c_0_2144,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X2))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X2))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_nat_int(power_power_int(X1),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_int(power_power_int(X2),number_number_of_nat(bit0(bit1(pls)))))) ),
inference(split_conjunct,[status(thm)],[c_0_1428]) ).
cnf(c_0_2145,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(power_power_nat(X1),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_nat(power_power_nat(X2),number_number_of_nat(bit0(bit1(pls)))))) ),
inference(split_conjunct,[status(thm)],[c_0_1429]) ).
cnf(c_0_2146,plain,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X1),X2))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X2))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_nat_real(power_power_real(X1),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_real(power_power_real(X2),number_number_of_nat(bit0(bit1(pls)))))) ),
inference(split_conjunct,[status(thm)],[c_0_1430]) ).
cnf(c_0_2147,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X2))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_nat_int(power_power_int(X1),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_int(power_power_int(X2),number_number_of_nat(bit0(bit1(pls)))))) ),
inference(split_conjunct,[status(thm)],[c_0_1431]) ).
cnf(c_0_2148,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(power_power_nat(X1),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_nat(power_power_nat(X2),number_number_of_nat(bit0(bit1(pls)))))) ),
inference(split_conjunct,[status(thm)],[c_0_1432]) ).
cnf(c_0_2149,plain,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X1),X2))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X2))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_nat_real(power_power_real(X1),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_real(power_power_real(X2),number_number_of_nat(bit0(bit1(pls)))))) ),
inference(split_conjunct,[status(thm)],[c_0_1433]) ).
cnf(c_0_2150,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),zero_zero_int))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),X1)),X1)),zero_zero_int)) ),
inference(split_conjunct,[status(thm)],[c_0_1434]) ).
cnf(c_0_2151,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(X1,X2)),hAPP_nat_nat(X1,X3)))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,esk20_3(X2,X3,X1)),esk21_3(X2,X3,X1)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_1419]) ).
cnf(c_0_2152,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),X1)),X1)),zero_zero_int))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),zero_zero_int)) ),
inference(split_conjunct,[status(thm)],[c_0_1434]) ).
cnf(c_0_2153,plain,
~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_nat_real(power_power_real(X1),number_number_of_nat(bit0(bit1(pls))))),zero_zero_real)),
inference(split_conjunct,[status(thm)],[c_0_1435]) ).
cnf(c_0_2154,plain,
~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_nat_int(power_power_int(X1),number_number_of_nat(bit0(bit1(pls))))),zero_zero_int)),
inference(split_conjunct,[status(thm)],[c_0_1436]) ).
cnf(c_0_2155,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X2))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X2))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_nat_int(power_power_int(X1),X3)),hAPP_nat_int(power_power_int(X2),X3))) ),
inference(split_conjunct,[status(thm)],[c_0_1437]) ).
cnf(c_0_2156,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(power_power_nat(X1),X3)),hAPP_nat_nat(power_power_nat(X2),X3))) ),
inference(split_conjunct,[status(thm)],[c_0_1438]) ).
cnf(c_0_2157,plain,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X1),X2))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X2))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_nat_real(power_power_real(X1),X3)),hAPP_nat_real(power_power_real(X2),X3))) ),
inference(split_conjunct,[status(thm)],[c_0_1439]) ).
cnf(c_0_2158,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_nat_int(power_power_int(X3),X1)),hAPP_nat_int(power_power_int(X3),X2)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_1440]) ).
cnf(c_0_2159,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(power_power_nat(X3),X1)),hAPP_nat_nat(power_power_nat(X3),X2)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,one_one_nat),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_1441]) ).
cnf(c_0_2160,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_nat_real(power_power_real(X3),X1)),hAPP_nat_real(power_power_real(X3),X2)))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,one_one_real),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_1442]) ).
cnf(c_0_2161,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X3))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),X1))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_nat_int(power_power_int(X1),X2)),hAPP_nat_int(power_power_int(X1),X3))) ),
inference(split_conjunct,[status(thm)],[c_0_1443]) ).
cnf(c_0_2162,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X3))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,one_one_nat),X1))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(power_power_nat(X1),X2)),hAPP_nat_nat(power_power_nat(X1),X3))) ),
inference(split_conjunct,[status(thm)],[c_0_1444]) ).
cnf(c_0_2163,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X3))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,one_one_real),X1))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_nat_real(power_power_real(X1),X2)),hAPP_nat_real(power_power_real(X1),X3))) ),
inference(split_conjunct,[status(thm)],[c_0_1445]) ).
cnf(c_0_2164,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_nat_int(power_power_int(X3),X1)),hAPP_nat_int(power_power_int(X3),X2)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_1446]) ).
cnf(c_0_2165,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(power_power_nat(X3),X1)),hAPP_nat_nat(power_power_nat(X3),X2)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,one_one_nat),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_1447]) ).
cnf(c_0_2166,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_nat_real(power_power_real(X3),X1)),hAPP_nat_real(power_power_real(X3),X2)))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,one_one_real),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_1448]) ).
cnf(c_0_2167,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X2),X3))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),X1))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_nat_int(power_power_int(X1),X2)),hAPP_nat_int(power_power_int(X1),X3))) ),
inference(split_conjunct,[status(thm)],[c_0_1449]) ).
cnf(c_0_2168,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X2),X3))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,one_one_nat),X1))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(power_power_nat(X1),X2)),hAPP_nat_nat(power_power_nat(X1),X3))) ),
inference(split_conjunct,[status(thm)],[c_0_1450]) ).
cnf(c_0_2169,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X2),X3))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,one_one_real),X1))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_nat_real(power_power_real(X1),X2)),hAPP_nat_real(power_power_real(X1),X3))) ),
inference(split_conjunct,[status(thm)],[c_0_1451]) ).
cnf(c_0_2170,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(power_power_nat(X3),X1)),hAPP_nat_nat(power_power_nat(X3),X2)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_1452]) ).
cnf(c_0_2171,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_nat_int(power_power_int(X1),X2)),hAPP_nat_int(power_power_int(X1),X3)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),one_one_int))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X3),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_1453]) ).
cnf(c_0_2172,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(power_power_nat(X1),X2)),hAPP_nat_nat(power_power_nat(X1),X3)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),one_one_nat))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),X1))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X3),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_1454]) ).
cnf(c_0_2173,plain,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_nat_real(power_power_real(X1),X2)),hAPP_nat_real(power_power_real(X1),X3)))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X1),one_one_real))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X1))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X3),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_1455]) ).
cnf(c_0_2174,plain,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_nat_real(power_power_real(X1),X2)),hAPP_nat_real(power_power_real(X1),X3)))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X1),one_one_real))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X1))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X3),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_1456]) ).
cnf(c_0_2175,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(power_power_nat(X1),X2)),hAPP_nat_nat(power_power_nat(X1),X3)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),one_one_nat))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X3),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_1457]) ).
cnf(c_0_2176,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_nat_int(power_power_int(X1),X2)),hAPP_nat_int(power_power_int(X1),X3)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),one_one_int))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X1))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X3),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_1458]) ).
cnf(c_0_2177,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_nat_int(power_power_int(X1),X2)),hAPP_nat_int(power_power_int(X3),X2)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X2))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_1459]) ).
cnf(c_0_2178,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(power_power_nat(X1),X2)),hAPP_nat_nat(power_power_nat(X3),X2)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),X1))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_1460]) ).
cnf(c_0_2179,plain,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_nat_real(power_power_real(X1),X2)),hAPP_nat_real(power_power_real(X3),X2)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X2))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X1))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X1),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_1461]) ).
cnf(c_0_2180,plain,
( hBOOL(hAPP_int_bool(X3,X2))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),esk1_3(X3,X1,X2)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X2))
| ~ hBOOL(hAPP_int_bool(X3,hAPP_int_int(plus_plus_int(X1),one_one_int))) ),
inference(split_conjunct,[status(thm)],[c_0_1424]) ).
cnf(c_0_2181,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(X3),X1)),hAPP_nat_nat(plus_plus_nat(X3),X2))) ),
inference(split_conjunct,[status(thm)],[c_0_1462]) ).
cnf(c_0_2182,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(plus_plus_int(X3),X1)),hAPP_int_int(plus_plus_int(X3),X2))) ),
inference(split_conjunct,[status(thm)],[c_0_1463]) ).
cnf(c_0_2183,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(X3),X1)),hAPP_nat_nat(plus_plus_nat(X3),X2))) ),
inference(split_conjunct,[status(thm)],[c_0_1464]) ).
cnf(c_0_2184,plain,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X1),X2))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(plus_plus_real(X3),X1)),hAPP_real_real(plus_plus_real(X3),X2))) ),
inference(split_conjunct,[status(thm)],[c_0_1465]) ).
cnf(c_0_2185,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(plus_plus_int(X1),X3)),hAPP_int_int(plus_plus_int(X2),X3))) ),
inference(split_conjunct,[status(thm)],[c_0_1466]) ).
cnf(c_0_2186,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(X1),X3)),hAPP_nat_nat(plus_plus_nat(X2),X3))) ),
inference(split_conjunct,[status(thm)],[c_0_1467]) ).
cnf(c_0_2187,plain,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X1),X2))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(plus_plus_real(X1),X3)),hAPP_real_real(plus_plus_real(X2),X3))) ),
inference(split_conjunct,[status(thm)],[c_0_1468]) ).
cnf(c_0_2188,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(plus_plus_int(X3),X1)),hAPP_int_int(plus_plus_int(X3),X2))) ),
inference(split_conjunct,[status(thm)],[c_0_1469]) ).
cnf(c_0_2189,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(X3),X1)),hAPP_nat_nat(plus_plus_nat(X3),X2))) ),
inference(split_conjunct,[status(thm)],[c_0_1470]) ).
cnf(c_0_2190,plain,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X1),X2))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(plus_plus_real(X3),X1)),hAPP_real_real(plus_plus_real(X3),X2))) ),
inference(split_conjunct,[status(thm)],[c_0_1471]) ).
cnf(c_0_2191,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(plus_plus_int(X1),X3)),hAPP_int_int(plus_plus_int(X2),X3))) ),
inference(split_conjunct,[status(thm)],[c_0_1472]) ).
cnf(c_0_2192,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(X1),X3)),hAPP_nat_nat(plus_plus_nat(X2),X3))) ),
inference(split_conjunct,[status(thm)],[c_0_1473]) ).
cnf(c_0_2193,plain,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X1),X2))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(plus_plus_real(X1),X3)),hAPP_real_real(plus_plus_real(X2),X3))) ),
inference(split_conjunct,[status(thm)],[c_0_1474]) ).
cnf(c_0_2194,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X2))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(X1),X3)),hAPP_int_int(plus_plus_int(X2),X3))) ),
inference(split_conjunct,[status(thm)],[c_0_1475]) ).
cnf(c_0_2195,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(X1),X3)),hAPP_nat_nat(plus_plus_nat(X2),X3))) ),
inference(split_conjunct,[status(thm)],[c_0_1476]) ).
cnf(c_0_2196,plain,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X1),X2))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(plus_plus_real(X1),X3)),hAPP_real_real(plus_plus_real(X2),X3))) ),
inference(split_conjunct,[status(thm)],[c_0_1477]) ).
cnf(c_0_2197,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X2))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(X3),X1)),hAPP_int_int(plus_plus_int(X3),X2))) ),
inference(split_conjunct,[status(thm)],[c_0_1478]) ).
cnf(c_0_2198,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(X3),X1)),hAPP_nat_nat(plus_plus_nat(X3),X2))) ),
inference(split_conjunct,[status(thm)],[c_0_1479]) ).
cnf(c_0_2199,plain,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X1),X2))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(plus_plus_real(X3),X1)),hAPP_real_real(plus_plus_real(X3),X2))) ),
inference(split_conjunct,[status(thm)],[c_0_1480]) ).
cnf(c_0_2200,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X2))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(X1),X3)),hAPP_int_int(plus_plus_int(X2),X3))) ),
inference(split_conjunct,[status(thm)],[c_0_1481]) ).
cnf(c_0_2201,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(X1),X3)),hAPP_nat_nat(plus_plus_nat(X2),X3))) ),
inference(split_conjunct,[status(thm)],[c_0_1482]) ).
cnf(c_0_2202,plain,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X1),X2))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(plus_plus_real(X1),X3)),hAPP_real_real(plus_plus_real(X2),X3))) ),
inference(split_conjunct,[status(thm)],[c_0_1483]) ).
cnf(c_0_2203,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X2))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(X3),X1)),hAPP_int_int(plus_plus_int(X3),X2))) ),
inference(split_conjunct,[status(thm)],[c_0_1484]) ).
cnf(c_0_2204,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(X3),X1)),hAPP_nat_nat(plus_plus_nat(X3),X2))) ),
inference(split_conjunct,[status(thm)],[c_0_1485]) ).
cnf(c_0_2205,plain,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X1),X2))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(plus_plus_real(X3),X1)),hAPP_real_real(plus_plus_real(X3),X2))) ),
inference(split_conjunct,[status(thm)],[c_0_1486]) ).
cnf(c_0_2206,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(X3),X1)),hAPP_nat_nat(plus_plus_nat(X3),X2))) ),
inference(split_conjunct,[status(thm)],[c_0_1487]) ).
cnf(c_0_2207,plain,
( hBOOL(hAPP_int_bool(X3,X2))
| hBOOL(hAPP_int_bool(X3,esk1_3(X3,X1,X2)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X2))
| ~ hBOOL(hAPP_int_bool(X3,hAPP_int_int(plus_plus_int(X1),one_one_int))) ),
inference(split_conjunct,[status(thm)],[c_0_1424]) ).
cnf(c_0_2208,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(X1),X2)),hAPP_nat_nat(plus_plus_nat(X3),X4)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X4))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_1488]) ).
cnf(c_0_2209,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(X1),X2)),hAPP_int_int(plus_plus_int(X3),X4)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X2),X4))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_1489]) ).
cnf(c_0_2210,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(X1),X2)),hAPP_int_int(plus_plus_int(X3),X4)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X2),X4))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_1490]) ).
cnf(c_0_2211,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(X1),X2)),hAPP_nat_nat(plus_plus_nat(X3),X4)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X2),X4))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_1491]) ).
cnf(c_0_2212,plain,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(plus_plus_real(X1),X2)),hAPP_real_real(plus_plus_real(X3),X4)))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X2),X4))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X1),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_1492]) ).
cnf(c_0_2213,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(X1),X2)),hAPP_int_int(plus_plus_int(X3),X4)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X2),X4))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_1493]) ).
cnf(c_0_2214,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(X1),X2)),hAPP_nat_nat(plus_plus_nat(X3),X4)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X4))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_1494]) ).
cnf(c_0_2215,plain,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(plus_plus_real(X1),X2)),hAPP_real_real(plus_plus_real(X3),X4)))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X2),X4))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X1),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_1495]) ).
cnf(c_0_2216,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(plus_plus_int(X1),X2)),hAPP_int_int(plus_plus_int(X3),X4)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X2),X4))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_1496]) ).
cnf(c_0_2217,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(X1),X2)),hAPP_nat_nat(plus_plus_nat(X3),X4)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X4))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_1497]) ).
cnf(c_0_2218,plain,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(plus_plus_real(X1),X2)),hAPP_real_real(plus_plus_real(X3),X4)))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X2),X4))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X1),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_1498]) ).
cnf(c_0_2219,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(X1),X2)),hAPP_int_int(plus_plus_int(X3),X4)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X2),X4))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_1499]) ).
cnf(c_0_2220,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(X1),X2)),hAPP_nat_nat(plus_plus_nat(X3),X4)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X2),X4))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_1500]) ).
cnf(c_0_2221,plain,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(plus_plus_real(X1),X2)),hAPP_real_real(plus_plus_real(X3),X4)))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X2),X4))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X1),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_1501]) ).
cnf(c_0_2222,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(X1),X2)),hAPP_nat_nat(plus_plus_nat(X3),X4)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X2),X4))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_1502]) ).
cnf(c_0_2223,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_nat_int(power_power_int(X1),X2)),hAPP_nat_int(power_power_int(X3),X2)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_1503]) ).
cnf(c_0_2224,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(power_power_nat(X1),X2)),hAPP_nat_nat(power_power_nat(X3),X2)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),X1))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_1504]) ).
cnf(c_0_2225,plain,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_nat_real(power_power_real(X1),X2)),hAPP_nat_real(power_power_real(X3),X2)))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X1))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X1),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_1505]) ).
cnf(c_0_2226,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_nat_int(power_power_int(X1),X2)),hAPP_nat_int(power_power_int(X1),X3)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),X1))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_1443]) ).
cnf(c_0_2227,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(power_power_nat(X1),X2)),hAPP_nat_nat(power_power_nat(X1),X3)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,one_one_nat),X1))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_1444]) ).
cnf(c_0_2228,plain,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_nat_real(power_power_real(X1),X2)),hAPP_nat_real(power_power_real(X1),X3)))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,one_one_real),X1))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_1445]) ).
cnf(c_0_2229,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_nat_int(power_power_int(X1),X2)),hAPP_nat_int(power_power_int(X1),X3)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),X1))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_1506]) ).
cnf(c_0_2230,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(power_power_nat(X1),X2)),hAPP_nat_nat(power_power_nat(X1),X3)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,one_one_nat),X1))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_1507]) ).
cnf(c_0_2231,plain,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_nat_real(power_power_real(X1),X2)),hAPP_nat_real(power_power_real(X1),X3)))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,one_one_real),X1))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_1508]) ).
cnf(c_0_2232,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_nat_int(power_power_int(X1),X2)),hAPP_nat_int(power_power_int(X1),X3)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),X1))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X2),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_1509]) ).
cnf(c_0_2233,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(power_power_nat(X1),X2)),hAPP_nat_nat(power_power_nat(X1),X3)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,one_one_nat),X1))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X2),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_1510]) ).
cnf(c_0_2234,plain,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_nat_real(power_power_real(X1),X2)),hAPP_nat_real(power_power_real(X1),X3)))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,one_one_real),X1))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X2),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_1511]) ).
cnf(c_0_2235,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_nat_int(power_power_int(X1),X2)),hAPP_nat_int(power_power_int(X1),X3)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),X1))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X2),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_1449]) ).
cnf(c_0_2236,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(power_power_nat(X1),X2)),hAPP_nat_nat(power_power_nat(X1),X3)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,one_one_nat),X1))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X2),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_1450]) ).
cnf(c_0_2237,plain,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_nat_real(power_power_real(X1),X2)),hAPP_nat_real(power_power_real(X1),X3)))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,one_one_real),X1))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X2),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_1451]) ).
cnf(c_0_2238,plain,
( X1 = zero_zero_real
| hAPP_real_real(plus_plus_real(hAPP_nat_real(power_power_real(X1),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_real(power_power_real(X2),number_number_of_nat(bit0(bit1(pls))))) != zero_zero_real ),
inference(split_conjunct,[status(thm)],[c_0_1512]) ).
cnf(c_0_2239,plain,
( X2 = zero_zero_real
| hAPP_real_real(plus_plus_real(hAPP_nat_real(power_power_real(X1),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_real(power_power_real(X2),number_number_of_nat(bit0(bit1(pls))))) != zero_zero_real ),
inference(split_conjunct,[status(thm)],[c_0_1512]) ).
cnf(c_0_2240,plain,
( X1 = zero_zero_real
| hAPP_real_real(plus_plus_real(hAPP_nat_real(power_power_real(X1),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_real(power_power_real(X2),number_number_of_nat(bit0(bit1(pls))))) != zero_zero_real ),
inference(split_conjunct,[status(thm)],[c_0_1513]) ).
cnf(c_0_2241,plain,
( X2 = zero_zero_real
| hAPP_real_real(plus_plus_real(hAPP_nat_real(power_power_real(X1),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_real(power_power_real(X2),number_number_of_nat(bit0(bit1(pls))))) != zero_zero_real ),
inference(split_conjunct,[status(thm)],[c_0_1513]) ).
cnf(c_0_2242,plain,
( X1 = zero_zero_int
| hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(X1),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_int(power_power_int(X2),number_number_of_nat(bit0(bit1(pls))))) != zero_zero_int ),
inference(split_conjunct,[status(thm)],[c_0_1514]) ).
cnf(c_0_2243,plain,
( X2 = zero_zero_int
| hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(X1),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_int(power_power_int(X2),number_number_of_nat(bit0(bit1(pls))))) != zero_zero_int ),
inference(split_conjunct,[status(thm)],[c_0_1514]) ).
cnf(c_0_2244,plain,
( hBOOL(hAPP_int_bool(X3,X2))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),esk18_3(X3,X1,X2)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2))
| ~ hBOOL(hAPP_int_bool(X3,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_1425]) ).
cnf(c_0_2245,plain,
hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_nat_real(semiri132038758t_real,X1)),hAPP_nat_real(power_power_real(number267125858f_real(bit0(bit1(pls)))),X1))),
inference(split_conjunct,[status(thm)],[c_0_1515]) ).
cnf(c_0_2246,plain,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_nat_int(semiri1621563631at_int,X1)),hAPP_nat_int(power_power_int(number_number_of_int(bit0(bit1(pls)))),X1))),
inference(split_conjunct,[status(thm)],[c_0_1516]) ).
cnf(c_0_2247,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(X1,X2),X3))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(X1,X2),X3))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(X1,X2),X3))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(X1,X2),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_1517]) ).
cnf(c_0_2248,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(X1),X2)),zero_zero_int))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X2),zero_zero_int))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),zero_zero_int)) ),
inference(split_conjunct,[status(thm)],[c_0_1518]) ).
cnf(c_0_2249,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(X1),X2)),zero_zero_nat))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X2),zero_zero_nat))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),zero_zero_nat)) ),
inference(split_conjunct,[status(thm)],[c_0_1519]) ).
cnf(c_0_2250,plain,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(plus_plus_real(X1),X2)),zero_zero_real))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X2),zero_zero_real))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X1),zero_zero_real)) ),
inference(split_conjunct,[status(thm)],[c_0_1520]) ).
cnf(c_0_2251,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(X1),X2)),zero_zero_int))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X2),zero_zero_int))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),zero_zero_int)) ),
inference(split_conjunct,[status(thm)],[c_0_1521]) ).
cnf(c_0_2252,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(X1),X2)),zero_zero_nat))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),zero_zero_nat))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),zero_zero_nat)) ),
inference(split_conjunct,[status(thm)],[c_0_1522]) ).
cnf(c_0_2253,plain,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(plus_plus_real(X1),X2)),zero_zero_real))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X2),zero_zero_real))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X1),zero_zero_real)) ),
inference(split_conjunct,[status(thm)],[c_0_1523]) ).
cnf(c_0_2254,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(plus_plus_int(X1),X2)),zero_zero_int))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X2),zero_zero_int))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),zero_zero_int)) ),
inference(split_conjunct,[status(thm)],[c_0_1524]) ).
cnf(c_0_2255,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(X1),X2)),zero_zero_nat))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),zero_zero_nat))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),zero_zero_nat)) ),
inference(split_conjunct,[status(thm)],[c_0_1525]) ).
cnf(c_0_2256,plain,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(plus_plus_real(X1),X2)),zero_zero_real))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X2),zero_zero_real))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X1),zero_zero_real)) ),
inference(split_conjunct,[status(thm)],[c_0_1526]) ).
cnf(c_0_2257,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(X1),X2)),zero_zero_int))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X2),zero_zero_int))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),zero_zero_int)) ),
inference(split_conjunct,[status(thm)],[c_0_1527]) ).
cnf(c_0_2258,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(X1),X2)),zero_zero_nat))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X2),zero_zero_nat))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),zero_zero_nat)) ),
inference(split_conjunct,[status(thm)],[c_0_1528]) ).
cnf(c_0_2259,plain,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(plus_plus_real(X1),X2)),zero_zero_real))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X2),zero_zero_real))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X1),zero_zero_real)) ),
inference(split_conjunct,[status(thm)],[c_0_1529]) ).
cnf(c_0_2260,plain,
( hBOOL(hAPP_int_bool(X3,X2))
| hBOOL(hAPP_int_bool(X3,esk18_3(X3,X1,X2)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2))
| ~ hBOOL(hAPP_int_bool(X3,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_1425]) ).
cnf(c_0_2261,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X3))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(X1),X2)),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_1530]) ).
cnf(c_0_2262,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X3))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(X1),X2)),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_1530]) ).
cnf(c_0_2263,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(X1),X3)),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_1531]) ).
cnf(c_0_2264,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(X3),X1)),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_1532]) ).
cnf(c_0_2265,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(X1),X3)),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_1533]) ).
cnf(c_0_2266,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),zero_zero_int))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(plus_plus_int(X1),X1)),zero_zero_int)) ),
inference(split_conjunct,[status(thm)],[c_0_1534]) ).
cnf(c_0_2267,plain,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X1),zero_zero_real))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(plus_plus_real(X1),X1)),zero_zero_real)) ),
inference(split_conjunct,[status(thm)],[c_0_1535]) ).
cnf(c_0_2268,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),zero_zero_int))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(X1),X1)),zero_zero_int)) ),
inference(split_conjunct,[status(thm)],[c_0_1536]) ).
cnf(c_0_2269,plain,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X1),zero_zero_real))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(plus_plus_real(X1),X1)),zero_zero_real)) ),
inference(split_conjunct,[status(thm)],[c_0_1537]) ).
cnf(c_0_2270,plain,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X1),zero_zero_real))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(plus_plus_real(X1),X1)),zero_zero_real)) ),
inference(split_conjunct,[status(thm)],[c_0_1538]) ).
cnf(c_0_2271,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),zero_zero_int))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(X1),X1)),zero_zero_int)) ),
inference(split_conjunct,[status(thm)],[c_0_1539]) ).
cnf(c_0_2272,plain,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(plus_plus_real(X1),X2)),hAPP_real_real(plus_plus_real(X1),X3)))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X2),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_1540]) ).
cnf(c_0_2273,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(X1),X2)),hAPP_nat_nat(plus_plus_nat(X3),X2)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_1541]) ).
cnf(c_0_2274,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(X1),X2)),hAPP_nat_nat(plus_plus_nat(X1),X3)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_1462]) ).
cnf(c_0_2275,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(plus_plus_int(X1),X2)),hAPP_int_int(plus_plus_int(X1),X3)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X2),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_1542]) ).
cnf(c_0_2276,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(plus_plus_int(X1),X2)),hAPP_int_int(plus_plus_int(X1),X3)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X2),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_1543]) ).
cnf(c_0_2277,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(X1),X2)),hAPP_nat_nat(plus_plus_nat(X1),X3)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_1544]) ).
cnf(c_0_2278,plain,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(plus_plus_real(X1),X2)),hAPP_real_real(plus_plus_real(X1),X3)))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X2),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_1545]) ).
cnf(c_0_2279,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(plus_plus_int(X1),X2)),hAPP_int_int(plus_plus_int(X3),X2)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_1546]) ).
cnf(c_0_2280,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(X1),X2)),hAPP_nat_nat(plus_plus_nat(X3),X2)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_1547]) ).
cnf(c_0_2281,plain,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(plus_plus_real(X1),X2)),hAPP_real_real(plus_plus_real(X3),X2)))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X1),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_1548]) ).
cnf(c_0_2282,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(plus_plus_int(X1),X2)),hAPP_int_int(plus_plus_int(X1),X3)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X2),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_1469]) ).
cnf(c_0_2283,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(X1),X2)),hAPP_nat_nat(plus_plus_nat(X1),X3)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_1470]) ).
cnf(c_0_2284,plain,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(plus_plus_real(X1),X2)),hAPP_real_real(plus_plus_real(X1),X3)))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X2),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_1471]) ).
cnf(c_0_2285,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(plus_plus_int(X1),X2)),hAPP_int_int(plus_plus_int(X3),X2)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_1472]) ).
cnf(c_0_2286,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(X1),X2)),hAPP_nat_nat(plus_plus_nat(X3),X2)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_1473]) ).
cnf(c_0_2287,plain,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(plus_plus_real(X1),X2)),hAPP_real_real(plus_plus_real(X3),X2)))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X1),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_1474]) ).
cnf(c_0_2288,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(X1),X2)),hAPP_int_int(plus_plus_int(X3),X2)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_1475]) ).
cnf(c_0_2289,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(X1),X2)),hAPP_nat_nat(plus_plus_nat(X3),X2)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_1476]) ).
cnf(c_0_2290,plain,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(plus_plus_real(X1),X2)),hAPP_real_real(plus_plus_real(X3),X2)))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X1),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_1477]) ).
cnf(c_0_2291,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(X1),X2)),hAPP_int_int(plus_plus_int(X1),X3)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X2),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_1478]) ).
cnf(c_0_2292,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(X1),X2)),hAPP_nat_nat(plus_plus_nat(X1),X3)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X2),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_1479]) ).
cnf(c_0_2293,plain,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(plus_plus_real(X1),X2)),hAPP_real_real(plus_plus_real(X1),X3)))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X2),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_1480]) ).
cnf(c_0_2294,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(X1),X2)),hAPP_int_int(plus_plus_int(X3),X2)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_1549]) ).
cnf(c_0_2295,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(X1),X2)),hAPP_nat_nat(plus_plus_nat(X3),X2)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_1550]) ).
cnf(c_0_2296,plain,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(plus_plus_real(X1),X2)),hAPP_real_real(plus_plus_real(X3),X2)))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X1),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_1551]) ).
cnf(c_0_2297,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(X1),X2)),hAPP_int_int(plus_plus_int(X1),X3)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X2),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_1552]) ).
cnf(c_0_2298,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(X1),X2)),hAPP_nat_nat(plus_plus_nat(X1),X3)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X2),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_1553]) ).
cnf(c_0_2299,plain,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(plus_plus_real(X1),X2)),hAPP_real_real(plus_plus_real(X1),X3)))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X2),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_1554]) ).
cnf(c_0_2300,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(X1),X2)),hAPP_nat_nat(plus_plus_nat(X3),X2)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_1555]) ).
cnf(c_0_2301,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(X1),X2)),hAPP_nat_nat(plus_plus_nat(X1),X3)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X2),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_1487]) ).
cnf(c_0_2302,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(X1),X2)),hAPP_int_int(plus_plus_int(X3),X2)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_1556]) ).
cnf(c_0_2303,plain,
( X1 != zero_zero_real
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),hAPP_nat_real(power_power_real(X1),number_number_of_nat(bit0(bit1(pls)))))) ),
inference(split_conjunct,[status(thm)],[c_0_1557]) ).
cnf(c_0_2304,plain,
( X1 != zero_zero_int
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_nat_int(power_power_int(X1),number_number_of_nat(bit0(bit1(pls)))))) ),
inference(split_conjunct,[status(thm)],[c_0_1558]) ).
cnf(c_0_2305,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(X3,X2),X1))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(X3,X2),X1))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(X3,X2),X1)) ),
inference(split_conjunct,[status(thm)],[c_0_1517]) ).
cnf(c_0_2306,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(X1,X2),X3))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X2),X3))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(X1,X2),X3))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(X1,X2),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_1517]) ).
cnf(c_0_2307,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X2))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(plus_plus_int(X1),one_one_int)),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_1559]) ).
cnf(c_0_2308,plain,
hAPP_int_int(plus_plus_int(hAPP_nat_int(semiri1621563631at_int,X1)),hAPP_int_int(plus_plus_int(hAPP_nat_int(semiri1621563631at_int,X2)),X3)) = hAPP_int_int(plus_plus_int(hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(plus_plus_nat(X1),X2))),X3),
inference(split_conjunct,[status(thm)],[c_0_1560]) ).
cnf(c_0_2309,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_nat_int(semiri1621563631at_int,X1)),hAPP_nat_int(semiri1621563631at_int,X2))) ),
inference(split_conjunct,[status(thm)],[c_0_1561]) ).
cnf(c_0_2310,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_nat_int(semiri1621563631at_int,X1)),hAPP_nat_int(semiri1621563631at_int,X2))) ),
inference(split_conjunct,[status(thm)],[c_0_1562]) ).
cnf(c_0_2311,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_nat_int(semiri1621563631at_int,X1)),hAPP_nat_int(semiri1621563631at_int,X2))) ),
inference(split_conjunct,[status(thm)],[c_0_1563]) ).
cnf(c_0_2312,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(semiri984289939at_nat,X1)),hAPP_nat_nat(semiri984289939at_nat,X2))) ),
inference(split_conjunct,[status(thm)],[c_0_1564]) ).
cnf(c_0_2313,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_nat_real(semiri132038758t_real,X1)),hAPP_nat_real(semiri132038758t_real,X2))) ),
inference(split_conjunct,[status(thm)],[c_0_1565]) ).
cnf(c_0_2314,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_nat_int(semiri1621563631at_int,X1)),hAPP_nat_int(semiri1621563631at_int,X2))) ),
inference(split_conjunct,[status(thm)],[c_0_1566]) ).
cnf(c_0_2315,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(semiri984289939at_nat,X1)),hAPP_nat_nat(semiri984289939at_nat,X2))) ),
inference(split_conjunct,[status(thm)],[c_0_1567]) ).
cnf(c_0_2316,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_nat_real(semiri132038758t_real,X1)),hAPP_nat_real(semiri132038758t_real,X2))) ),
inference(split_conjunct,[status(thm)],[c_0_1568]) ).
cnf(c_0_2317,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_nat_int(semiri1621563631at_int,X1)),hAPP_nat_int(semiri1621563631at_int,X2))) ),
inference(split_conjunct,[status(thm)],[c_0_1569]) ).
cnf(c_0_2318,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(semiri984289939at_nat,X1)),hAPP_nat_nat(semiri984289939at_nat,X2))) ),
inference(split_conjunct,[status(thm)],[c_0_1570]) ).
cnf(c_0_2319,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_nat_real(semiri132038758t_real,X1)),hAPP_nat_real(semiri132038758t_real,X2))) ),
inference(split_conjunct,[status(thm)],[c_0_1571]) ).
cnf(c_0_2320,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_nat_int(semiri1621563631at_int,X1)),hAPP_nat_int(semiri1621563631at_int,X2))) ),
inference(split_conjunct,[status(thm)],[c_0_1572]) ).
cnf(c_0_2321,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_nat_int(semiri1621563631at_int,X1)),hAPP_nat_int(semiri1621563631at_int,X2))) ),
inference(split_conjunct,[status(thm)],[c_0_1573]) ).
cnf(c_0_2322,plain,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,esk22_2(X2,X1)),X1))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X1))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_1574]) ).
cnf(c_0_2323,plain,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,esk22_2(X2,X1)),X2))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X1))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_1574]) ).
cnf(c_0_2324,plain,
( X1 = X2
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X3))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X2))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1))
| hAPP_nat_int(power_power_int(X1),X3) != hAPP_nat_int(power_power_int(X2),X3) ),
inference(split_conjunct,[status(thm)],[c_0_1575]) ).
cnf(c_0_2325,plain,
( X1 = X2
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X3))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),X1))
| hAPP_nat_nat(power_power_nat(X1),X3) != hAPP_nat_nat(power_power_nat(X2),X3) ),
inference(split_conjunct,[status(thm)],[c_0_1576]) ).
cnf(c_0_2326,plain,
( X1 = X2
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X3))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X2))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X1))
| hAPP_nat_real(power_power_real(X1),X3) != hAPP_nat_real(power_power_real(X2),X3) ),
inference(split_conjunct,[status(thm)],[c_0_1577]) ).
cnf(c_0_2327,plain,
hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,one_one_real),hAPP_nat_real(power_power_real(number267125858f_real(bit0(bit1(pls)))),X1))),
inference(split_conjunct,[status(thm)],[c_0_1578]) ).
cnf(c_0_2328,plain,
( hBOOL(hAPP_nat_bool(X1,zero_zero_nat))
| hBOOL(hAPP_nat_bool(X1,hAPP_nat_nat(plus_plus_nat(esk14_2(X2,X1)),one_one_nat)))
| ~ hBOOL(hAPP_nat_bool(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_1579]) ).
cnf(c_0_2329,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),hAPP_int_int(plus_plus_int(X2),X3)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X3))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_1580]) ).
cnf(c_0_2330,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),hAPP_nat_nat(plus_plus_nat(X2),X3)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X3))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_1581]) ).
cnf(c_0_2331,plain,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X1),hAPP_real_real(plus_plus_real(X2),X3)))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X1),X3))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_1582]) ).
cnf(c_0_2332,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),hAPP_int_int(plus_plus_int(X2),X3)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X3))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_1583]) ).
cnf(c_0_2333,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),hAPP_nat_nat(plus_plus_nat(X2),X3)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X3))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_1584]) ).
cnf(c_0_2334,plain,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X1),hAPP_real_real(plus_plus_real(X2),X3)))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X1),X3))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_1585]) ).
cnf(c_0_2335,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),hAPP_int_int(plus_plus_int(X2),X3)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_1586]) ).
cnf(c_0_2336,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),hAPP_nat_nat(plus_plus_nat(X2),X3)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_1587]) ).
cnf(c_0_2337,plain,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X1),hAPP_real_real(plus_plus_real(X2),X3)))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X1),X2))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_1588]) ).
cnf(c_0_2338,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),hAPP_int_int(plus_plus_int(X2),X3)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X3))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_1589]) ).
cnf(c_0_2339,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),hAPP_nat_nat(plus_plus_nat(X2),X3)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X3))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_1590]) ).
cnf(c_0_2340,plain,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X1),hAPP_real_real(plus_plus_real(X2),X3)))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X1),X3))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_1591]) ).
cnf(c_0_2341,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),hAPP_int_int(plus_plus_int(X2),X3)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X3))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_1592]) ).
cnf(c_0_2342,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),hAPP_nat_nat(plus_plus_nat(X2),X3)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X3))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_1593]) ).
cnf(c_0_2343,plain,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X1),hAPP_real_real(plus_plus_real(X2),X3)))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X1),X3))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_1594]) ).
cnf(c_0_2344,plain,
( X1 = X2
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X2))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1))
| hAPP_nat_int(power_power_int(X1),number_number_of_nat(bit0(bit1(pls)))) != hAPP_nat_int(power_power_int(X2),number_number_of_nat(bit0(bit1(pls)))) ),
inference(split_conjunct,[status(thm)],[c_0_1595]) ).
cnf(c_0_2345,plain,
( X1 = X2
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),X1))
| hAPP_nat_nat(power_power_nat(X1),number_number_of_nat(bit0(bit1(pls)))) != hAPP_nat_nat(power_power_nat(X2),number_number_of_nat(bit0(bit1(pls)))) ),
inference(split_conjunct,[status(thm)],[c_0_1596]) ).
cnf(c_0_2346,plain,
( X1 = X2
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X2))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X1))
| hAPP_nat_real(power_power_real(X1),number_number_of_nat(bit0(bit1(pls)))) != hAPP_nat_real(power_power_real(X2),number_number_of_nat(bit0(bit1(pls)))) ),
inference(split_conjunct,[status(thm)],[c_0_1597]) ).
cnf(c_0_2347,plain,
( X3 = esk4_2(X2,X1)
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X2))
| hAPP_nat_real(power_power_real(X3),X1) != X2
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_1598]) ).
cnf(c_0_2348,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(plus_plus_nat(X2),X1))) ),
inference(split_conjunct,[status(thm)],[c_0_1599]) ).
cnf(c_0_2349,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,number_number_of_nat(X1)),number_number_of_nat(X2)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_1600]) ).
cnf(c_0_2350,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_int_int(plus_plus_int(X1),X2)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X2))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1)) ),
inference(split_conjunct,[status(thm)],[c_0_1601]) ).
cnf(c_0_2351,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(plus_plus_nat(X1),X2)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),X1)) ),
inference(split_conjunct,[status(thm)],[c_0_1602]) ).
cnf(c_0_2352,plain,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),hAPP_real_real(plus_plus_real(X1),X2)))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X2))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X1)) ),
inference(split_conjunct,[status(thm)],[c_0_1603]) ).
cnf(c_0_2353,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_int_int(plus_plus_int(X1),X2)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X2))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X1)) ),
inference(split_conjunct,[status(thm)],[c_0_1604]) ).
cnf(c_0_2354,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(plus_plus_nat(X1),X2)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1)) ),
inference(split_conjunct,[status(thm)],[c_0_1605]) ).
cnf(c_0_2355,plain,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),hAPP_real_real(plus_plus_real(X1),X2)))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X2))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X1)) ),
inference(split_conjunct,[status(thm)],[c_0_1606]) ).
cnf(c_0_2356,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_int_int(plus_plus_int(X1),X2)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X2))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1)) ),
inference(split_conjunct,[status(thm)],[c_0_1607]) ).
cnf(c_0_2357,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_int_int(plus_plus_int(X1),X2)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X2))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1)) ),
inference(split_conjunct,[status(thm)],[c_0_1608]) ).
cnf(c_0_2358,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),hAPP_nat_nat(plus_plus_nat(X1),X2)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),X1)) ),
inference(split_conjunct,[status(thm)],[c_0_1609]) ).
cnf(c_0_2359,plain,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),hAPP_real_real(plus_plus_real(X1),X2)))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X2))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X1)) ),
inference(split_conjunct,[status(thm)],[c_0_1610]) ).
cnf(c_0_2360,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_int_int(plus_plus_int(X1),X2)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X2))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X1)) ),
inference(split_conjunct,[status(thm)],[c_0_1611]) ).
cnf(c_0_2361,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(plus_plus_nat(X1),X2)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1)) ),
inference(split_conjunct,[status(thm)],[c_0_1612]) ).
cnf(c_0_2362,plain,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),hAPP_real_real(plus_plus_real(X1),X2)))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X2))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X1)) ),
inference(split_conjunct,[status(thm)],[c_0_1613]) ).
cnf(c_0_2363,plain,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,one_one_real),hAPP_nat_real(power_power_real(X1),X2)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X2))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,one_one_real),X1)) ),
inference(split_conjunct,[status(thm)],[c_0_1614]) ).
cnf(c_0_2364,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,one_one_nat),hAPP_nat_nat(power_power_nat(X1),X2)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,one_one_nat),X1)) ),
inference(split_conjunct,[status(thm)],[c_0_1615]) ).
cnf(c_0_2365,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),hAPP_nat_int(power_power_int(X1),X2)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X2))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),X1)) ),
inference(split_conjunct,[status(thm)],[c_0_1616]) ).
cnf(c_0_2366,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(X3,X2),X1))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X2),X1))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(X3,X2),X1)) ),
inference(split_conjunct,[status(thm)],[c_0_1517]) ).
cnf(c_0_2367,plain,
~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(X1),X2)),X2)),
inference(split_conjunct,[status(thm)],[c_0_1617]) ).
cnf(c_0_2368,plain,
~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(X1),X2)),X1)),
inference(split_conjunct,[status(thm)],[c_0_1618]) ).
cnf(c_0_2369,plain,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(X1)),number_number_of_int(X2)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,number_number_of_int(X2)),number_number_of_int(X1))) ),
inference(split_conjunct,[status(thm)],[c_0_1619]) ).
cnf(c_0_2370,plain,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,number_number_of_nat(X1)),number_number_of_nat(X2)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,number_number_of_nat(X2)),number_number_of_nat(X1))) ),
inference(split_conjunct,[status(thm)],[c_0_1620]) ).
cnf(c_0_2371,plain,
( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,number267125858f_real(X1)),number267125858f_real(X2)))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,number267125858f_real(X2)),number267125858f_real(X1))) ),
inference(split_conjunct,[status(thm)],[c_0_1621]) ).
cnf(c_0_2372,plain,
( X3 = X2
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(X1,X2),X3))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(X1,X2),X3))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(X1,X2),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_1517]) ).
cnf(c_0_2373,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1))
| number_number_of_nat(X2) = zero_zero_nat
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(power_power_nat(X1),number_number_of_nat(X2)))) ),
inference(split_conjunct,[status(thm)],[c_0_1622]) ).
cnf(c_0_2374,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,number_number_of_nat(X1)),number_number_of_nat(X2)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X2))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_1600]) ).
cnf(c_0_2375,plain,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),esk22_2(X2,X1)))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X1))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_1574]) ).
cnf(c_0_2376,plain,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),esk5_2(X2,X1)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_1623]) ).
cnf(c_0_2377,plain,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),esk4_2(X2,X1)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_1598]) ).
cnf(c_0_2378,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(plus_plus_int(X1),X1)),zero_zero_int))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),zero_zero_int)) ),
inference(split_conjunct,[status(thm)],[c_0_1534]) ).
cnf(c_0_2379,plain,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(plus_plus_real(X1),X1)),zero_zero_real))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X1),zero_zero_real)) ),
inference(split_conjunct,[status(thm)],[c_0_1535]) ).
cnf(c_0_2380,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(X1),X1)),zero_zero_int))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),zero_zero_int)) ),
inference(split_conjunct,[status(thm)],[c_0_1536]) ).
cnf(c_0_2381,plain,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(plus_plus_real(X1),X1)),zero_zero_real))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X1),zero_zero_real)) ),
inference(split_conjunct,[status(thm)],[c_0_1537]) ).
cnf(c_0_2382,plain,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(plus_plus_real(X1),X1)),zero_zero_real))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X1),zero_zero_real)) ),
inference(split_conjunct,[status(thm)],[c_0_1538]) ).
cnf(c_0_2383,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(X1),X1)),zero_zero_int))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),zero_zero_int)) ),
inference(split_conjunct,[status(thm)],[c_0_1539]) ).
cnf(c_0_2384,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(plus_plus_int(X1),one_one_int)),X2))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_1624]) ).
cnf(c_0_2385,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(plus_plus_int(X1),one_one_int)),X2))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_1559]) ).
cnf(c_0_2386,plain,
hAPP_nat_int(power_power_int(hAPP_nat_int(power_power_int(X1),number_number_of_nat(bit0(bit1(pls))))),number_number_of_nat(bit0(bit1(pls)))) = hAPP_nat_int(power_power_int(X1),number_number_of_nat(bit0(bit0(bit1(pls))))),
inference(split_conjunct,[status(thm)],[c_0_1625]) ).
cnf(c_0_2387,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_nat_int(semiri1621563631at_int,X1)),hAPP_nat_int(semiri1621563631at_int,X2)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_1561]) ).
cnf(c_0_2388,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_nat_int(semiri1621563631at_int,X1)),hAPP_nat_int(semiri1621563631at_int,X2)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_1562]) ).
cnf(c_0_2389,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_nat_int(semiri1621563631at_int,X1)),hAPP_nat_int(semiri1621563631at_int,X2)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_1563]) ).
cnf(c_0_2390,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(semiri984289939at_nat,X1)),hAPP_nat_nat(semiri984289939at_nat,X2)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_1564]) ).
cnf(c_0_2391,plain,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_nat_real(semiri132038758t_real,X1)),hAPP_nat_real(semiri132038758t_real,X2)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_1565]) ).
cnf(c_0_2392,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_nat_int(semiri1621563631at_int,X1)),hAPP_nat_int(semiri1621563631at_int,X2)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_1626]) ).
cnf(c_0_2393,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(semiri984289939at_nat,X1)),hAPP_nat_nat(semiri984289939at_nat,X2)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_1627]) ).
cnf(c_0_2394,plain,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_nat_real(semiri132038758t_real,X1)),hAPP_nat_real(semiri132038758t_real,X2)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_1628]) ).
cnf(c_0_2395,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_nat_int(semiri1621563631at_int,X1)),hAPP_nat_int(semiri1621563631at_int,X2)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_1569]) ).
cnf(c_0_2396,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(semiri984289939at_nat,X1)),hAPP_nat_nat(semiri984289939at_nat,X2)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_1570]) ).
cnf(c_0_2397,plain,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_nat_real(semiri132038758t_real,X1)),hAPP_nat_real(semiri132038758t_real,X2)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_1571]) ).
cnf(c_0_2398,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_nat_int(semiri1621563631at_int,X1)),hAPP_nat_int(semiri1621563631at_int,X2)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_1572]) ).
cnf(c_0_2399,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_nat_int(semiri1621563631at_int,X1)),hAPP_nat_int(semiri1621563631at_int,X2)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_1573]) ).
cnf(c_0_2400,plain,
( X1 = one_one_int
| X1 = zero_zero_int
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),number_number_of_int(bit0(bit1(pls)))))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1)) ),
inference(split_conjunct,[status(thm)],[c_0_1629]) ).
cnf(c_0_2401,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),pls))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,number_number_of_nat(X1)),number_number_of_nat(X2))) ),
inference(split_conjunct,[status(thm)],[c_0_1630]) ).
cnf(c_0_2402,plain,
( hBOOL(hAPP_nat_bool(X1,zero_zero_nat))
| ~ hBOOL(hAPP_nat_bool(X1,X2))
| ~ hBOOL(hAPP_nat_bool(X1,X3))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X3),esk19_2(X2,X1))) ),
inference(split_conjunct,[status(thm)],[c_0_1631]) ).
cnf(c_0_2403,plain,
( hBOOL(hAPP_nat_bool(X1,zero_zero_nat))
| ~ hBOOL(hAPP_nat_bool(X1,X2))
| ~ hBOOL(hAPP_nat_bool(X1,X3))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X3),esk14_2(X2,X1))) ),
inference(split_conjunct,[status(thm)],[c_0_1579]) ).
cnf(c_0_2404,plain,
( hAPP_real_real(plus_plus_real(hAPP_nat_real(power_power_real(X1),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_real(power_power_real(X2),number_number_of_nat(bit0(bit1(pls))))) = zero_zero_real
| X2 != zero_zero_real
| X1 != zero_zero_real ),
inference(split_conjunct,[status(thm)],[c_0_1512]) ).
cnf(c_0_2405,plain,
( hAPP_real_real(plus_plus_real(hAPP_nat_real(power_power_real(X1),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_real(power_power_real(X2),number_number_of_nat(bit0(bit1(pls))))) = zero_zero_real
| X2 != zero_zero_real
| X1 != zero_zero_real ),
inference(split_conjunct,[status(thm)],[c_0_1513]) ).
cnf(c_0_2406,plain,
( hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(X1),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_int(power_power_int(X2),number_number_of_nat(bit0(bit1(pls))))) = zero_zero_int
| X2 != zero_zero_int
| X1 != zero_zero_int ),
inference(split_conjunct,[status(thm)],[c_0_1514]) ).
cnf(c_0_2407,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X3),X2))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_1632]) ).
cnf(c_0_2408,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X3),X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_1633]) ).
cnf(c_0_2409,plain,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X1),X2))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X3),X2))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X1),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_1634]) ).
cnf(c_0_2410,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X3))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X3),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_1635]) ).
cnf(c_0_2411,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X3))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X3),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_1636]) ).
cnf(c_0_2412,plain,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X1),X2))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X1),X3))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X3),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_1637]) ).
cnf(c_0_2413,plain,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X1),X2))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X3),X2))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X1),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_1638]) ).
cnf(c_0_2414,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X3),X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_1639]) ).
cnf(c_0_2415,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X3),X2))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_1640]) ).
cnf(c_0_2416,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,number_number_of_nat(X1)),number_number_of_nat(X2)))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X2))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_1600]) ).
cnf(c_0_2417,plain,
( X1 = X2
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X2))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),hAPP_int_int(plus_plus_int(X2),one_one_int))) ),
inference(split_conjunct,[status(thm)],[c_0_1641]) ).
cnf(c_0_2418,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),hAPP_int_int(plus_plus_int(X2),one_one_int))) ),
inference(split_conjunct,[status(thm)],[c_0_1642]) ).
cnf(c_0_2419,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1))
| X2 = zero_zero_nat
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(power_power_nat(X1),X2))) ),
inference(split_conjunct,[status(thm)],[c_0_1643]) ).
cnf(c_0_2420,plain,
( X1 = zero_zero_nat
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(power_power_nat(X2),X1))) ),
inference(split_conjunct,[status(thm)],[c_0_1644]) ).
cnf(c_0_2421,plain,
( hAPP_int_int(plus_plus_int(number_number_of_int(X1)),number_number_of_int(X2)) = number_number_of_int(hAPP_int_int(plus_plus_int(X1),X2))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X2))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X1)) ),
inference(split_conjunct,[status(thm)],[c_0_1645]) ).
cnf(c_0_2422,plain,
( hAPP_nat_nat(plus_plus_nat(number_number_of_nat(X1)),number_number_of_nat(X2)) = number_number_of_nat(hAPP_int_int(plus_plus_int(X1),X2))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X2))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X1)) ),
inference(split_conjunct,[status(thm)],[c_0_1646]) ).
cnf(c_0_2423,plain,
( hAPP_real_real(plus_plus_real(number267125858f_real(X1)),number267125858f_real(X2)) = number267125858f_real(hAPP_int_int(plus_plus_int(X1),X2))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X2))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X1)) ),
inference(split_conjunct,[status(thm)],[c_0_1647]) ).
cnf(c_0_2424,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_int_int(plus_plus_int(X1),X1))) ),
inference(split_conjunct,[status(thm)],[c_0_1648]) ).
cnf(c_0_2425,plain,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X1))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),hAPP_real_real(plus_plus_real(X1),X1))) ),
inference(split_conjunct,[status(thm)],[c_0_1649]) ).
cnf(c_0_2426,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X1))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_int_int(plus_plus_int(X1),X1))) ),
inference(split_conjunct,[status(thm)],[c_0_1650]) ).
cnf(c_0_2427,plain,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X1))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),hAPP_real_real(plus_plus_real(X1),X1))) ),
inference(split_conjunct,[status(thm)],[c_0_1651]) ).
cnf(c_0_2428,plain,
( hBOOL(hAPP_int_bool(X1,X2))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X2))
| ~ hBOOL(hAPP_int_bool(X1,hAPP_nat_int(semiri1621563631at_int,esk9_1(X1)))) ),
inference(split_conjunct,[status(thm)],[c_0_1652]) ).
cnf(c_0_2429,plain,
( hAPP_nat_real(power_power_real(esk5_2(X2,X1)),X1) = X2
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_1623]) ).
cnf(c_0_2430,plain,
( hAPP_nat_real(power_power_real(esk4_2(X2,X1)),X1) = X2
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_1598]) ).
cnf(c_0_2431,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
| X1 = X2
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(X3,X2),X1))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(X3,X2),X1)) ),
inference(split_conjunct,[status(thm)],[c_0_1517]) ).
cnf(c_0_2432,plain,
( X3 = X2
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(X1,X2),X3))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X2),X3))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(X1,X2),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_1517]) ).
cnf(c_0_2433,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(power_power_nat(X1),number_number_of_nat(X2))))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1)) ),
inference(split_conjunct,[status(thm)],[c_0_1622]) ).
cnf(c_0_2434,plain,
hAPP_real_real(plus_plus_real(number267125858f_real(X1)),hAPP_real_real(plus_plus_real(number267125858f_real(X2)),X3)) = hAPP_real_real(plus_plus_real(number267125858f_real(hAPP_int_int(plus_plus_int(X1),X2))),X3),
inference(split_conjunct,[status(thm)],[c_0_1653]) ).
cnf(c_0_2435,plain,
hAPP_int_int(plus_plus_int(number_number_of_int(X1)),hAPP_int_int(plus_plus_int(number_number_of_int(X2)),X3)) = hAPP_int_int(plus_plus_int(number_number_of_int(hAPP_int_int(plus_plus_int(X1),X2))),X3),
inference(split_conjunct,[status(thm)],[c_0_1654]) ).
cnf(c_0_2436,plain,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),hAPP_nat_int(power_power_int(X1),number_number_of_nat(bit0(bit1(pls)))))),
inference(split_conjunct,[status(thm)],[c_0_1655]) ).
cnf(c_0_2437,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),hAPP_nat_nat(plus_plus_nat(X2),X3)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_1656]) ).
cnf(c_0_2438,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),hAPP_nat_nat(plus_plus_nat(X2),X3)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_1657]) ).
cnf(c_0_2439,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),hAPP_nat_nat(plus_plus_nat(X2),X3)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_1658]) ).
cnf(c_0_2440,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),hAPP_nat_nat(plus_plus_nat(X2),X3)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_1659]) ).
cnf(c_0_2441,plain,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),hAPP_nat_real(power_power_real(X1),number_number_of_nat(bit0(bit1(pls))))))
| X1 = zero_zero_real ),
inference(split_conjunct,[status(thm)],[c_0_1557]) ).
cnf(c_0_2442,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_nat_int(power_power_int(X1),number_number_of_nat(bit0(bit1(pls))))))
| X1 = zero_zero_int ),
inference(split_conjunct,[status(thm)],[c_0_1558]) ).
cnf(c_0_2443,plain,
hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(X1),X2)),hAPP_int_int(plus_plus_int(X3),X4)) = hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(X1),X3)),hAPP_int_int(plus_plus_int(X2),X4)),
inference(split_conjunct,[status(thm)],[c_0_1660]) ).
cnf(c_0_2444,plain,
hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(plus_plus_nat(X1),X2)),hAPP_nat_nat(plus_plus_nat(X3),X4)) = hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(plus_plus_nat(X1),X3)),hAPP_nat_nat(plus_plus_nat(X2),X4)),
inference(split_conjunct,[status(thm)],[c_0_1661]) ).
cnf(c_0_2445,plain,
hAPP_real_real(plus_plus_real(hAPP_real_real(plus_plus_real(X1),X2)),hAPP_real_real(plus_plus_real(X3),X4)) = hAPP_real_real(plus_plus_real(hAPP_real_real(plus_plus_real(X1),X3)),hAPP_real_real(plus_plus_real(X2),X4)),
inference(split_conjunct,[status(thm)],[c_0_1662]) ).
cnf(c_0_2446,plain,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_nat_int(power_power_int(X1),number_number_of_nat(bit0(bit1(pls)))))),
inference(split_conjunct,[status(thm)],[c_0_1663]) ).
cnf(c_0_2447,plain,
hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),hAPP_nat_real(power_power_real(X1),number_number_of_nat(bit0(bit1(pls)))))),
inference(split_conjunct,[status(thm)],[c_0_1664]) ).
cnf(c_0_2448,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),hAPP_int_int(plus_plus_int(X2),one_one_int)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_1642]) ).
cnf(c_0_2449,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),hAPP_int_int(plus_plus_int(X2),one_one_int)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_1641]) ).
cnf(c_0_2450,plain,
( X1 = zero_zero_nat
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_nat_int(semiri1621563631at_int,X1)),zero_zero_int)) ),
inference(split_conjunct,[status(thm)],[c_0_1665]) ).
cnf(c_0_2451,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
| hAPP_nat_nat(plus_plus_nat(X1),X3) != hAPP_nat_nat(plus_plus_nat(X4),X2)
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X4),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_1666]) ).
cnf(c_0_2452,plain,
( hBOOL(hAPP_int_bool(X1,hAPP_nat_int(semiri1621563631at_int,esk6_1(X1))))
| ~ hBOOL(hAPP_int_bool(X1,X2))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_1667]) ).
cnf(c_0_2453,plain,
~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_nat_int(semiri1621563631at_int,X1)),zero_zero_int)),
inference(split_conjunct,[status(thm)],[c_0_1668]) ).
cnf(c_0_2454,plain,
~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(semiri984289939at_nat,X1)),zero_zero_nat)),
inference(split_conjunct,[status(thm)],[c_0_1669]) ).
cnf(c_0_2455,plain,
~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_nat_real(semiri132038758t_real,X1)),zero_zero_real)),
inference(split_conjunct,[status(thm)],[c_0_1670]) ).
cnf(c_0_2456,plain,
~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_nat_int(semiri1621563631at_int,X1)),zero_zero_int)),
inference(split_conjunct,[status(thm)],[c_0_1671]) ).
cnf(c_0_2457,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1))
| ~ hBOOL(X2)
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1)) ),
inference(split_conjunct,[status(thm)],[c_0_1672]) ).
cnf(c_0_2458,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1))
| ~ hBOOL(X2)
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1)) ),
inference(split_conjunct,[status(thm)],[c_0_1672]) ).
cnf(c_0_2459,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_nat_int(power_power_int(X1),X2)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1)) ),
inference(split_conjunct,[status(thm)],[c_0_1673]) ).
cnf(c_0_2460,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),hAPP_nat_int(power_power_int(X1),X2)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),X1)) ),
inference(split_conjunct,[status(thm)],[c_0_1674]) ).
cnf(c_0_2461,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,one_one_nat),hAPP_nat_nat(power_power_nat(X1),X2)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,one_one_nat),X1)) ),
inference(split_conjunct,[status(thm)],[c_0_1675]) ).
cnf(c_0_2462,plain,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,one_one_real),hAPP_nat_real(power_power_real(X1),X2)))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,one_one_real),X1)) ),
inference(split_conjunct,[status(thm)],[c_0_1676]) ).
cnf(c_0_2463,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_nat_int(power_power_int(X1),X2)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1)) ),
inference(split_conjunct,[status(thm)],[c_0_1677]) ).
cnf(c_0_2464,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),hAPP_nat_nat(power_power_nat(X1),X2)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),X1)) ),
inference(split_conjunct,[status(thm)],[c_0_1678]) ).
cnf(c_0_2465,plain,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),hAPP_nat_real(power_power_real(X1),X2)))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X1)) ),
inference(split_conjunct,[status(thm)],[c_0_1679]) ).
cnf(c_0_2466,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_int_int(plus_plus_int(X1),X1)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1)) ),
inference(split_conjunct,[status(thm)],[c_0_1648]) ).
cnf(c_0_2467,plain,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),hAPP_real_real(plus_plus_real(X1),X1)))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X1)) ),
inference(split_conjunct,[status(thm)],[c_0_1649]) ).
cnf(c_0_2468,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_int_int(plus_plus_int(X1),X1)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X1)) ),
inference(split_conjunct,[status(thm)],[c_0_1650]) ).
cnf(c_0_2469,plain,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),hAPP_real_real(plus_plus_real(X1),X1)))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X1)) ),
inference(split_conjunct,[status(thm)],[c_0_1651]) ).
cnf(c_0_2470,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_nat_int(power_power_int(X1),X2)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X1)) ),
inference(split_conjunct,[status(thm)],[c_0_1680]) ).
cnf(c_0_2471,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(power_power_nat(X1),X2)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1)) ),
inference(split_conjunct,[status(thm)],[c_0_1681]) ).
cnf(c_0_2472,plain,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),hAPP_nat_real(power_power_real(X1),X2)))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X1)) ),
inference(split_conjunct,[status(thm)],[c_0_1682]) ).
cnf(c_0_2473,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(power_power_nat(X1),X2)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1)) ),
inference(split_conjunct,[status(thm)],[c_0_1643]) ).
cnf(c_0_2474,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(plus_plus_nat(X1),X2)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1)) ),
inference(split_conjunct,[status(thm)],[c_0_1599]) ).
cnf(c_0_2475,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(plus_plus_nat(X1),X2)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_1599]) ).
cnf(c_0_2476,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(power_power_nat(X1),X2)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1)) ),
inference(split_conjunct,[status(thm)],[c_0_1644]) ).
cnf(c_0_2477,plain,
( hBOOL(hAPP_nat_bool(X1,zero_zero_nat))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,esk19_2(X2,X1)),X2))
| ~ hBOOL(hAPP_nat_bool(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_1631]) ).
cnf(c_0_2478,plain,
( hBOOL(hAPP_nat_bool(X1,zero_zero_nat))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,esk14_2(X2,X1)),X2))
| ~ hBOOL(hAPP_nat_bool(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_1579]) ).
cnf(c_0_2479,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1))
| hBOOL(X2)
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1)) ),
inference(split_conjunct,[status(thm)],[c_0_1683]) ).
cnf(c_0_2480,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1))
| hBOOL(X2)
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1)) ),
inference(split_conjunct,[status(thm)],[c_0_1683]) ).
cnf(c_0_2481,plain,
( X1 = zero_zero_int
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X2))
| hAPP_int_int(plus_plus_int(X1),X2) != zero_zero_int ),
inference(split_conjunct,[status(thm)],[c_0_1684]) ).
cnf(c_0_2482,plain,
( X2 = zero_zero_int
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X2))
| hAPP_int_int(plus_plus_int(X1),X2) != zero_zero_int ),
inference(split_conjunct,[status(thm)],[c_0_1684]) ).
cnf(c_0_2483,plain,
( X1 = zero_zero_nat
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),X1))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),X2))
| hAPP_nat_nat(plus_plus_nat(X1),X2) != zero_zero_nat ),
inference(split_conjunct,[status(thm)],[c_0_1685]) ).
cnf(c_0_2484,plain,
( X2 = zero_zero_nat
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),X1))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),X2))
| hAPP_nat_nat(plus_plus_nat(X1),X2) != zero_zero_nat ),
inference(split_conjunct,[status(thm)],[c_0_1685]) ).
cnf(c_0_2485,plain,
( X1 = zero_zero_real
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X1))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X2))
| hAPP_real_real(plus_plus_real(X1),X2) != zero_zero_real ),
inference(split_conjunct,[status(thm)],[c_0_1686]) ).
cnf(c_0_2486,plain,
( X2 = zero_zero_real
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X1))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X2))
| hAPP_real_real(plus_plus_real(X1),X2) != zero_zero_real ),
inference(split_conjunct,[status(thm)],[c_0_1686]) ).
cnf(c_0_2487,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X2))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,bit1(X1)),bit0(X2))) ),
inference(split_conjunct,[status(thm)],[c_0_1687]) ).
cnf(c_0_2488,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X2))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,bit1(X1)),bit0(X2))) ),
inference(split_conjunct,[status(thm)],[c_0_1688]) ).
cnf(c_0_2489,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit0(X1)),bit1(X2))) ),
inference(split_conjunct,[status(thm)],[c_0_1689]) ).
cnf(c_0_2490,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit0(X1)),bit1(X2))) ),
inference(split_conjunct,[status(thm)],[c_0_1690]) ).
cnf(c_0_2491,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,bit0(X1)),bit1(X2))) ),
inference(split_conjunct,[status(thm)],[c_0_1691]) ).
cnf(c_0_2492,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,bit0(X1)),bit1(X2))) ),
inference(split_conjunct,[status(thm)],[c_0_1692]) ).
cnf(c_0_2493,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,number_number_of_int(X1)),number_number_of_int(X2))) ),
inference(split_conjunct,[status(thm)],[c_0_1693]) ).
cnf(c_0_2494,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,number_number_of_int(X1)),number_number_of_int(X2))) ),
inference(split_conjunct,[status(thm)],[c_0_1694]) ).
cnf(c_0_2495,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,number267125858f_real(X1)),number267125858f_real(X2))) ),
inference(split_conjunct,[status(thm)],[c_0_1695]) ).
cnf(c_0_2496,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,bit0(X1)),bit0(X2))) ),
inference(split_conjunct,[status(thm)],[c_0_1696]) ).
cnf(c_0_2497,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,bit0(X1)),bit0(X2))) ),
inference(split_conjunct,[status(thm)],[c_0_1697]) ).
cnf(c_0_2498,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,bit1(X1)),bit1(X2))) ),
inference(split_conjunct,[status(thm)],[c_0_1698]) ).
cnf(c_0_2499,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,bit1(X1)),bit1(X2))) ),
inference(split_conjunct,[status(thm)],[c_0_1699]) ).
cnf(c_0_2500,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,number_number_of_nat(X1)),number_number_of_nat(X2))) ),
inference(split_conjunct,[status(thm)],[c_0_1600]) ).
cnf(c_0_2501,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X2))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit1(X1)),bit0(X2))) ),
inference(split_conjunct,[status(thm)],[c_0_1700]) ).
cnf(c_0_2502,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X2))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit1(X1)),bit0(X2))) ),
inference(split_conjunct,[status(thm)],[c_0_1701]) ).
cnf(c_0_2503,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X2))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit0(X1)),bit0(X2))) ),
inference(split_conjunct,[status(thm)],[c_0_1702]) ).
cnf(c_0_2504,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X2))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit0(X1)),bit0(X2))) ),
inference(split_conjunct,[status(thm)],[c_0_1703]) ).
cnf(c_0_2505,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X2))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit1(X1)),bit1(X2))) ),
inference(split_conjunct,[status(thm)],[c_0_1704]) ).
cnf(c_0_2506,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X2))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit1(X1)),bit1(X2))) ),
inference(split_conjunct,[status(thm)],[c_0_1705]) ).
cnf(c_0_2507,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X2))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,number267125858f_real(X1)),number267125858f_real(X2))) ),
inference(split_conjunct,[status(thm)],[c_0_1706]) ).
cnf(c_0_2508,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X2))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(X1)),number_number_of_int(X2))) ),
inference(split_conjunct,[status(thm)],[c_0_1707]) ).
cnf(c_0_2509,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X2))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(X1)),number_number_of_int(X2))) ),
inference(split_conjunct,[status(thm)],[c_0_1708]) ).
cnf(c_0_2510,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_nat_int(semiri1621563631at_int,X1))) ),
inference(split_conjunct,[status(thm)],[c_0_1709]) ).
cnf(c_0_2511,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),hAPP_nat_real(semiri132038758t_real,X1))) ),
inference(split_conjunct,[status(thm)],[c_0_1710]) ).
cnf(c_0_2512,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(semiri984289939at_nat,X1))) ),
inference(split_conjunct,[status(thm)],[c_0_1711]) ).
cnf(c_0_2513,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_nat_int(semiri1621563631at_int,X1))) ),
inference(split_conjunct,[status(thm)],[c_0_1712]) ).
cnf(c_0_2514,plain,
( hAPP_int_int(plus_plus_int(X1),X2) = zero_zero_int
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X2))
| X2 != zero_zero_int
| X1 != zero_zero_int ),
inference(split_conjunct,[status(thm)],[c_0_1684]) ).
cnf(c_0_2515,plain,
( hAPP_nat_nat(plus_plus_nat(X1),X2) = zero_zero_nat
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),X1))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),X2))
| X2 != zero_zero_nat
| X1 != zero_zero_nat ),
inference(split_conjunct,[status(thm)],[c_0_1685]) ).
cnf(c_0_2516,plain,
( hAPP_real_real(plus_plus_real(X1),X2) = zero_zero_real
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X1))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X2))
| X2 != zero_zero_real
| X1 != zero_zero_real ),
inference(split_conjunct,[status(thm)],[c_0_1686]) ).
cnf(c_0_2517,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_int_int(plus_plus_int(one_one_int),X1)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1)) ),
inference(split_conjunct,[status(thm)],[c_0_1713]) ).
cnf(c_0_2518,plain,
( X2 = X1
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X2),X1)) ),
inference(split_conjunct,[status(thm)],[c_0_1714]) ).
cnf(c_0_2519,plain,
( X2 = X1
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X1)) ),
inference(split_conjunct,[status(thm)],[c_0_1715]) ).
cnf(c_0_2520,plain,
( X2 = X1
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X1),X2))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X2),X1)) ),
inference(split_conjunct,[status(thm)],[c_0_1716]) ).
cnf(c_0_2521,plain,
( X1 = X2
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X2),X1))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_1717]) ).
cnf(c_0_2522,plain,
( X1 = X2
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X1))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_1718]) ).
cnf(c_0_2523,plain,
( X1 = X2
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X2),X1))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X1),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_1719]) ).
cnf(c_0_2524,plain,
( X1 = X2
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X2),X1)) ),
inference(split_conjunct,[status(thm)],[c_0_1720]) ).
cnf(c_0_2525,plain,
( X1 = X2
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X1)) ),
inference(split_conjunct,[status(thm)],[c_0_1721]) ).
cnf(c_0_2526,plain,
( X1 = X2
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X1),X2))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X2),X1)) ),
inference(split_conjunct,[status(thm)],[c_0_1722]) ).
cnf(c_0_2527,plain,
( X1 = X2
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X2),X1))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X1),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_1723]) ).
cnf(c_0_2528,plain,
( X1 = X2
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X1))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_1724]) ).
cnf(c_0_2529,plain,
( X1 = X2
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X2),X1))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_1725]) ).
cnf(c_0_2530,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),esk3_2(X1,X2)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_1726]) ).
cnf(c_0_2531,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
| X1 = X2
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(X3,X2),X1))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X2),X1)) ),
inference(split_conjunct,[status(thm)],[c_0_1517]) ).
cnf(c_0_2532,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),number_number_of_int(bit0(X1))))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),number_number_of_int(X1))) ),
inference(split_conjunct,[status(thm)],[c_0_1727]) ).
cnf(c_0_2533,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),number_number_of_int(bit1(X1))))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),number_number_of_int(X1))) ),
inference(split_conjunct,[status(thm)],[c_0_1727]) ).
cnf(c_0_2534,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),bit1(pls)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,number_number_of_int(X1)),one_one_int)) ),
inference(split_conjunct,[status(thm)],[c_0_1728]) ).
cnf(c_0_2535,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),bit1(pls)))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,number267125858f_real(X1)),one_one_real)) ),
inference(split_conjunct,[status(thm)],[c_0_1729]) ).
cnf(c_0_2536,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),bit1(pls)))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,number267125858f_real(X1)),one_one_real)) ),
inference(split_conjunct,[status(thm)],[c_0_1730]) ).
cnf(c_0_2537,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),bit1(pls)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(X1)),one_one_int)) ),
inference(split_conjunct,[status(thm)],[c_0_1731]) ).
cnf(c_0_2538,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,number_number_of_nat(X1)),number_number_of_nat(X2)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_1630]) ).
cnf(c_0_2539,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,bit1(X1)),bit0(X2)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_1687]) ).
cnf(c_0_2540,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,bit1(X1)),bit0(X2)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_1688]) ).
cnf(c_0_2541,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit0(X1)),bit1(X2)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_1689]) ).
cnf(c_0_2542,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit0(X1)),bit1(X2)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_1690]) ).
cnf(c_0_2543,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,bit0(X1)),bit1(X2)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_1691]) ).
cnf(c_0_2544,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,bit0(X1)),bit1(X2)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_1692]) ).
cnf(c_0_2545,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,number_number_of_int(X1)),number_number_of_int(X2)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_1693]) ).
cnf(c_0_2546,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,number_number_of_int(X1)),number_number_of_int(X2)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_1694]) ).
cnf(c_0_2547,plain,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,number267125858f_real(X1)),number267125858f_real(X2)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_1695]) ).
cnf(c_0_2548,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,bit0(X1)),bit0(X2)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_1696]) ).
cnf(c_0_2549,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,bit0(X1)),bit0(X2)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_1697]) ).
cnf(c_0_2550,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,bit1(X1)),bit1(X2)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_1698]) ).
cnf(c_0_2551,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,bit1(X1)),bit1(X2)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_1699]) ).
cnf(c_0_2552,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit1(X1)),bit0(X2)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_1700]) ).
cnf(c_0_2553,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit1(X1)),bit0(X2)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_1701]) ).
cnf(c_0_2554,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit0(X1)),bit0(X2)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_1702]) ).
cnf(c_0_2555,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit0(X1)),bit0(X2)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_1703]) ).
cnf(c_0_2556,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit1(X1)),bit1(X2)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_1704]) ).
cnf(c_0_2557,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit1(X1)),bit1(X2)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_1705]) ).
cnf(c_0_2558,plain,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,number267125858f_real(X1)),number267125858f_real(X2)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_1706]) ).
cnf(c_0_2559,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(X1)),number_number_of_int(X2)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_1707]) ).
cnf(c_0_2560,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(X1)),number_number_of_int(X2)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_1708]) ).
cnf(c_0_2561,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),pls))
| hAPP_nat_nat(plus_plus_nat(number_number_of_nat(X1)),number_number_of_nat(X2)) = number_number_of_nat(X1)
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X2),pls)) ),
inference(split_conjunct,[status(thm)],[c_0_1732]) ).
cnf(c_0_2562,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,number_number_of_nat(X1)),number_number_of_nat(X2)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),pls)) ),
inference(split_conjunct,[status(thm)],[c_0_1630]) ).
cnf(c_0_2563,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),pls))
| hAPP_nat_nat(plus_plus_nat(number_number_of_nat(X1)),number_number_of_nat(X2)) = number_number_of_nat(hAPP_int_int(plus_plus_int(X1),X2))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X2),pls)) ),
inference(split_conjunct,[status(thm)],[c_0_1732]) ).
cnf(c_0_2564,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,number_number_of_int(X1)),one_one_int))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),bit1(pls))) ),
inference(split_conjunct,[status(thm)],[c_0_1728]) ).
cnf(c_0_2565,plain,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,number267125858f_real(X1)),one_one_real))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),bit1(pls))) ),
inference(split_conjunct,[status(thm)],[c_0_1729]) ).
cnf(c_0_2566,plain,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,number267125858f_real(X1)),one_one_real))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),bit1(pls))) ),
inference(split_conjunct,[status(thm)],[c_0_1730]) ).
cnf(c_0_2567,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(X1)),one_one_int))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),bit1(pls))) ),
inference(split_conjunct,[status(thm)],[c_0_1731]) ).
cnf(c_0_2568,plain,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X1),one_one_real))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,sqrt(X1)),one_one_real)) ),
inference(split_conjunct,[status(thm)],[c_0_1733]) ).
cnf(c_0_2569,plain,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X1),zero_zero_real))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,sqrt(X1)),zero_zero_real)) ),
inference(split_conjunct,[status(thm)],[c_0_1734]) ).
cnf(c_0_2570,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),pls))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,bit1(X1)),pls)) ),
inference(split_conjunct,[status(thm)],[c_0_1735]) ).
cnf(c_0_2571,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),pls))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,bit0(X1)),pls)) ),
inference(split_conjunct,[status(thm)],[c_0_1736]) ).
cnf(c_0_2572,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),pls))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,number_number_of_int(X1)),zero_zero_int)) ),
inference(split_conjunct,[status(thm)],[c_0_1737]) ).
cnf(c_0_2573,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),pls))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,number267125858f_real(X1)),zero_zero_real)) ),
inference(split_conjunct,[status(thm)],[c_0_1738]) ).
cnf(c_0_2574,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),zero_zero_int))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit0(X1)),zero_zero_int)) ),
inference(split_conjunct,[status(thm)],[c_0_1739]) ).
cnf(c_0_2575,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),zero_zero_int))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit1(X1)),zero_zero_int)) ),
inference(split_conjunct,[status(thm)],[c_0_1740]) ).
cnf(c_0_2576,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),pls))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit0(X1)),pls)) ),
inference(split_conjunct,[status(thm)],[c_0_1741]) ).
cnf(c_0_2577,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),pls))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit1(X1)),pls)) ),
inference(split_conjunct,[status(thm)],[c_0_1742]) ).
cnf(c_0_2578,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),pls))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,number267125858f_real(X1)),zero_zero_real)) ),
inference(split_conjunct,[status(thm)],[c_0_1743]) ).
cnf(c_0_2579,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),pls))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(X1)),zero_zero_int)) ),
inference(split_conjunct,[status(thm)],[c_0_1744]) ).
cnf(c_0_2580,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_nat_int(semiri1621563631at_int,X1)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1)) ),
inference(split_conjunct,[status(thm)],[c_0_1709]) ).
cnf(c_0_2581,plain,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),hAPP_nat_real(semiri132038758t_real,X1)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1)) ),
inference(split_conjunct,[status(thm)],[c_0_1710]) ).
cnf(c_0_2582,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(semiri984289939at_nat,X1)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1)) ),
inference(split_conjunct,[status(thm)],[c_0_1711]) ).
cnf(c_0_2583,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_nat_int(semiri1621563631at_int,X1)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1)) ),
inference(split_conjunct,[status(thm)],[c_0_1712]) ).
cnf(c_0_2584,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,number_number_of_int(X1)),number_number_of_int(X2)))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(X2)),number_number_of_int(X1))) ),
inference(split_conjunct,[status(thm)],[c_0_1619]) ).
cnf(c_0_2585,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,number_number_of_nat(X1)),number_number_of_nat(X2)))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,number_number_of_nat(X2)),number_number_of_nat(X1))) ),
inference(split_conjunct,[status(thm)],[c_0_1620]) ).
cnf(c_0_2586,plain,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,number267125858f_real(X1)),number267125858f_real(X2)))
| hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,number267125858f_real(X2)),number267125858f_real(X1))) ),
inference(split_conjunct,[status(thm)],[c_0_1621]) ).
cnf(c_0_2587,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),number_number_of_int(X1)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,bit1(pls)),X1)) ),
inference(split_conjunct,[status(thm)],[c_0_1745]) ).
cnf(c_0_2588,plain,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,one_one_real),number267125858f_real(X1)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,bit1(pls)),X1)) ),
inference(split_conjunct,[status(thm)],[c_0_1746]) ).
cnf(c_0_2589,plain,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,one_one_real),number267125858f_real(X1)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit1(pls)),X1)) ),
inference(split_conjunct,[status(thm)],[c_0_1747]) ).
cnf(c_0_2590,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),number_number_of_int(X1)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit1(pls)),X1)) ),
inference(split_conjunct,[status(thm)],[c_0_1748]) ).
cnf(c_0_2591,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,bit1(pls)),X1))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),number_number_of_int(X1))) ),
inference(split_conjunct,[status(thm)],[c_0_1745]) ).
cnf(c_0_2592,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,bit1(pls)),X1))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,one_one_real),number267125858f_real(X1))) ),
inference(split_conjunct,[status(thm)],[c_0_1746]) ).
cnf(c_0_2593,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit1(pls)),X1))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,one_one_real),number267125858f_real(X1))) ),
inference(split_conjunct,[status(thm)],[c_0_1747]) ).
cnf(c_0_2594,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit1(pls)),X1))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),number_number_of_int(X1))) ),
inference(split_conjunct,[status(thm)],[c_0_1748]) ).
cnf(c_0_2595,plain,
( X1 = hAPP_int_int(plus_plus_int(X2),hAPP_nat_int(semiri1621563631at_int,esk10_2(X2,X1)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X2),X1)) ),
inference(split_conjunct,[status(thm)],[c_0_1749]) ).
cnf(c_0_2596,plain,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,m1),hAPP_int_int(plus_plus_int(one_one_int),hAPP_nat_int(semiri1621563631at_int,n)))),
inference(split_conjunct,[status(thm)],[c_0_1750]) ).
cnf(c_0_2597,plain,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_int_int(plus_plus_int(one_one_int),hAPP_nat_int(semiri1621563631at_int,n)))),
inference(split_conjunct,[status(thm)],[c_0_1751]) ).
cnf(c_0_2598,plain,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,sqrt(X1)),one_one_real))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X1),one_one_real)) ),
inference(split_conjunct,[status(thm)],[c_0_1733]) ).
cnf(c_0_2599,plain,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,sqrt(X1)),zero_zero_real))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X1),zero_zero_real)) ),
inference(split_conjunct,[status(thm)],[c_0_1734]) ).
cnf(c_0_2600,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,bit1(X1)),pls))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),pls)) ),
inference(split_conjunct,[status(thm)],[c_0_1735]) ).
cnf(c_0_2601,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,bit0(X1)),pls))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),pls)) ),
inference(split_conjunct,[status(thm)],[c_0_1736]) ).
cnf(c_0_2602,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,number_number_of_int(X1)),zero_zero_int))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),pls)) ),
inference(split_conjunct,[status(thm)],[c_0_1737]) ).
cnf(c_0_2603,plain,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,number267125858f_real(X1)),zero_zero_real))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),pls)) ),
inference(split_conjunct,[status(thm)],[c_0_1738]) ).
cnf(c_0_2604,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit0(X1)),zero_zero_int))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),zero_zero_int)) ),
inference(split_conjunct,[status(thm)],[c_0_1739]) ).
cnf(c_0_2605,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit1(X1)),zero_zero_int))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),zero_zero_int)) ),
inference(split_conjunct,[status(thm)],[c_0_1740]) ).
cnf(c_0_2606,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit0(X1)),pls))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),pls)) ),
inference(split_conjunct,[status(thm)],[c_0_1741]) ).
cnf(c_0_2607,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit1(X1)),pls))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),pls)) ),
inference(split_conjunct,[status(thm)],[c_0_1742]) ).
cnf(c_0_2608,plain,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,number267125858f_real(X1)),zero_zero_real))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),pls)) ),
inference(split_conjunct,[status(thm)],[c_0_1743]) ).
cnf(c_0_2609,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(X1)),zero_zero_int))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),pls)) ),
inference(split_conjunct,[status(thm)],[c_0_1744]) ).
cnf(c_0_2610,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),esk7_1(X1)))
| ~ hBOOL(hAPP_int_bool(X1,hAPP_nat_int(semiri1621563631at_int,X2))) ),
inference(split_conjunct,[status(thm)],[c_0_1667]) ).
cnf(c_0_2611,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X3))
| ~ hBOOL(X1)
| ~ hBOOL(X2)
| ~ hBOOL(X2)
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_1672]) ).
cnf(c_0_2612,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X3))
| ~ hBOOL(X1)
| ~ hBOOL(X2)
| ~ hBOOL(X1)
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_1672]) ).
cnf(c_0_2613,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X2),X1))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2))
| X2 != X1 ),
inference(split_conjunct,[status(thm)],[c_0_1714]) ).
cnf(c_0_2614,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X1))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
| X2 != X1 ),
inference(split_conjunct,[status(thm)],[c_0_1715]) ).
cnf(c_0_2615,plain,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X2),X1))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X1),X2))
| X2 != X1 ),
inference(split_conjunct,[status(thm)],[c_0_1716]) ).
cnf(c_0_2616,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X3),X2))
| X1 != X3 ),
inference(split_conjunct,[status(thm)],[c_0_1752]) ).
cnf(c_0_2617,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X3),X2))
| X1 != X3 ),
inference(split_conjunct,[status(thm)],[c_0_1753]) ).
cnf(c_0_2618,plain,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X1),X2))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X3),X2))
| X1 != X3 ),
inference(split_conjunct,[status(thm)],[c_0_1754]) ).
cnf(c_0_2619,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X3))
| X2 != X3 ),
inference(split_conjunct,[status(thm)],[c_0_1755]) ).
cnf(c_0_2620,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X3))
| X2 != X3 ),
inference(split_conjunct,[status(thm)],[c_0_1756]) ).
cnf(c_0_2621,plain,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X1),X2))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X1),X3))
| X2 != X3 ),
inference(split_conjunct,[status(thm)],[c_0_1757]) ).
cnf(c_0_2622,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2))
| X3 != X2
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_1758]) ).
cnf(c_0_2623,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
| X3 != X2
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_1759]) ).
cnf(c_0_2624,plain,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X1),X2))
| X3 != X2
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X1),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_1760]) ).
cnf(c_0_2625,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2))
| X3 != X1
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X3),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_1761]) ).
cnf(c_0_2626,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
| X3 != X1
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X3),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_1762]) ).
cnf(c_0_2627,plain,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X1),X2))
| X3 != X1
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X3),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_1763]) ).
cnf(c_0_2628,plain,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,one_one_real),X1))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,one_one_real),sqrt(X1))) ),
inference(split_conjunct,[status(thm)],[c_0_1764]) ).
cnf(c_0_2629,plain,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X1))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),sqrt(X1))) ),
inference(split_conjunct,[status(thm)],[c_0_1765]) ).
cnf(c_0_2630,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X1))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),bit1(X1))) ),
inference(split_conjunct,[status(thm)],[c_0_1766]) ).
cnf(c_0_2631,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X1))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),bit0(X1))) ),
inference(split_conjunct,[status(thm)],[c_0_1767]) ).
cnf(c_0_2632,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X1))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),bit1(X1))) ),
inference(split_conjunct,[status(thm)],[c_0_1768]) ).
cnf(c_0_2633,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X1))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),number_number_of_int(X1))) ),
inference(split_conjunct,[status(thm)],[c_0_1769]) ).
cnf(c_0_2634,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X1))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),number267125858f_real(X1))) ),
inference(split_conjunct,[status(thm)],[c_0_1770]) ).
cnf(c_0_2635,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),X1))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),number_number_of_nat(X1))) ),
inference(split_conjunct,[status(thm)],[c_0_1771]) ).
cnf(c_0_2636,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),X1))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),bit0(X1))) ),
inference(split_conjunct,[status(thm)],[c_0_1772]) ).
cnf(c_0_2637,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),X1))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),number267125858f_real(X1))) ),
inference(split_conjunct,[status(thm)],[c_0_1773]) ).
cnf(c_0_2638,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),X1))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),number_number_of_int(X1))) ),
inference(split_conjunct,[status(thm)],[c_0_1774]) ).
cnf(c_0_2639,plain,
( hBOOL(X1)
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X3))
| ~ hBOOL(X1)
| ~ hBOOL(X2)
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_1683]) ).
cnf(c_0_2640,plain,
( hBOOL(X2)
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X3))
| ~ hBOOL(X1)
| ~ hBOOL(X2)
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_1683]) ).
cnf(c_0_2641,plain,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X1),X2))
| X1 = X2
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X1),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_1775]) ).
cnf(c_0_2642,plain,
( X1 = X2
| hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X1),X2))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X1),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_1776]) ).
cnf(c_0_2643,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
| X1 = X2
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_1777]) ).
cnf(c_0_2644,plain,
( X1 = X2
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_1778]) ).
cnf(c_0_2645,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
| X1 = X2
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_1779]) ).
cnf(c_0_2646,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X2))
| X1 = X2
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_1780]) ).
cnf(c_0_2647,plain,
( hBOOL(X1)
| hBOOL(X2)
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X3))
| ~ hBOOL(X2)
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_1672]) ).
cnf(c_0_2648,plain,
( hBOOL(X1)
| hBOOL(X2)
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X3))
| ~ hBOOL(X1)
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_1672]) ).
cnf(c_0_2649,plain,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X1),X2))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X1),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_1775]) ).
cnf(c_0_2650,plain,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X1),X2))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X1),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_1776]) ).
cnf(c_0_2651,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_1777]) ).
cnf(c_0_2652,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_1778]) ).
cnf(c_0_2653,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_1781]) ).
cnf(c_0_2654,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_1782]) ).
cnf(c_0_2655,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_1780]) ).
cnf(c_0_2656,plain,
( hBOOL(X1)
| hBOOL(X2)
| hBOOL(X1)
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X3))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_1683]) ).
cnf(c_0_2657,plain,
( hBOOL(X1)
| hBOOL(X2)
| hBOOL(X2)
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X3))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_1683]) ).
cnf(c_0_2658,plain,
hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(X1),X2)),X3) = hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(X1),X3)),X2),
inference(split_conjunct,[status(thm)],[c_0_1783]) ).
cnf(c_0_2659,plain,
hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(plus_plus_nat(X1),X2)),X3) = hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(plus_plus_nat(X1),X3)),X2),
inference(split_conjunct,[status(thm)],[c_0_1784]) ).
cnf(c_0_2660,plain,
hAPP_real_real(plus_plus_real(hAPP_real_real(plus_plus_real(X1),X2)),X3) = hAPP_real_real(plus_plus_real(hAPP_real_real(plus_plus_real(X1),X3)),X2),
inference(split_conjunct,[status(thm)],[c_0_1785]) ).
cnf(c_0_2661,plain,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,one_one_real),sqrt(X1)))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,one_one_real),X1)) ),
inference(split_conjunct,[status(thm)],[c_0_1764]) ).
cnf(c_0_2662,plain,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),sqrt(X1)))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X1)) ),
inference(split_conjunct,[status(thm)],[c_0_1765]) ).
cnf(c_0_2663,plain,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),sqrt(X1)))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X1)) ),
inference(split_conjunct,[status(thm)],[c_0_1786]) ).
cnf(c_0_2664,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),bit1(X1)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X1)) ),
inference(split_conjunct,[status(thm)],[c_0_1766]) ).
cnf(c_0_2665,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),bit0(X1)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X1)) ),
inference(split_conjunct,[status(thm)],[c_0_1767]) ).
cnf(c_0_2666,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),bit1(X1)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X1)) ),
inference(split_conjunct,[status(thm)],[c_0_1768]) ).
cnf(c_0_2667,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),number_number_of_int(X1)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X1)) ),
inference(split_conjunct,[status(thm)],[c_0_1769]) ).
cnf(c_0_2668,plain,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),number267125858f_real(X1)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X1)) ),
inference(split_conjunct,[status(thm)],[c_0_1770]) ).
cnf(c_0_2669,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),esk2_1(X1)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X1)) ),
inference(split_conjunct,[status(thm)],[c_0_1787]) ).
cnf(c_0_2670,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),number_number_of_nat(X1)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),X1)) ),
inference(split_conjunct,[status(thm)],[c_0_1771]) ).
cnf(c_0_2671,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),bit0(X1)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),X1)) ),
inference(split_conjunct,[status(thm)],[c_0_1772]) ).
cnf(c_0_2672,plain,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),number267125858f_real(X1)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),X1)) ),
inference(split_conjunct,[status(thm)],[c_0_1773]) ).
cnf(c_0_2673,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),number_number_of_int(X1)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),X1)) ),
inference(split_conjunct,[status(thm)],[c_0_1774]) ).
cnf(c_0_2674,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1))
| hBOOL(X2)
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1))
| ~ hBOOL(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1683]) ).
cnf(c_0_2675,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1))
| hBOOL(X2)
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1))
| ~ hBOOL(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1683]) ).
cnf(c_0_2676,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1))
| hBOOL(X3)
| ~ hBOOL(X2)
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1)) ),
inference(split_conjunct,[status(thm)],[c_0_1672]) ).
cnf(c_0_2677,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1))
| hBOOL(X3)
| ~ hBOOL(X2)
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1)) ),
inference(split_conjunct,[status(thm)],[c_0_1672]) ).
cnf(c_0_2678,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X1))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),X1)) ),
inference(split_conjunct,[status(thm)],[c_0_1788]) ).
cnf(c_0_2679,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),X1))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X1)) ),
inference(split_conjunct,[status(thm)],[c_0_1788]) ).
cnf(c_0_2680,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(power_power_nat(X1),number_number_of_nat(X2))))
| number_number_of_nat(X2) != zero_zero_nat ),
inference(split_conjunct,[status(thm)],[c_0_1622]) ).
cnf(c_0_2681,plain,
( X2 = X3
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),X1))
| hAPP_nat_int(power_power_int(X1),X2) != hAPP_nat_int(power_power_int(X1),X3) ),
inference(split_conjunct,[status(thm)],[c_0_1789]) ).
cnf(c_0_2682,plain,
( X2 = X3
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,one_one_nat),X1))
| hAPP_nat_nat(power_power_nat(X1),X2) != hAPP_nat_nat(power_power_nat(X1),X3) ),
inference(split_conjunct,[status(thm)],[c_0_1790]) ).
cnf(c_0_2683,plain,
( X2 = X3
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,one_one_real),X1))
| hAPP_nat_real(power_power_real(X1),X2) != hAPP_nat_real(power_power_real(X1),X3) ),
inference(split_conjunct,[status(thm)],[c_0_1791]) ).
cnf(c_0_2684,plain,
( X1 = hAPP_nat_nat(plus_plus_nat(X2),esk13_2(X2,X1))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X1)) ),
inference(split_conjunct,[status(thm)],[c_0_1792]) ).
cnf(c_0_2685,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_nat_int(semiri1621563631at_int,X1)),zero_zero_int))
| X1 != zero_zero_nat ),
inference(split_conjunct,[status(thm)],[c_0_1665]) ).
cnf(c_0_2686,plain,
( hAPP_nat_nat(plus_plus_nat(X1),esk3_2(X1,X2)) = X2
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_1726]) ).
cnf(c_0_2687,plain,
( hBOOL(hAPP_int_bool(X1,esk7_1(X1)))
| ~ hBOOL(hAPP_int_bool(X1,hAPP_nat_int(semiri1621563631at_int,X2))) ),
inference(split_conjunct,[status(thm)],[c_0_1667]) ).
cnf(c_0_2688,plain,
( hBOOL(hAPP_int_bool(X1,hAPP_nat_int(semiri1621563631at_int,X2)))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),esk8_1(X1))) ),
inference(split_conjunct,[status(thm)],[c_0_1652]) ).
cnf(c_0_2689,plain,
( hBOOL(hAPP_nat_bool(X1,zero_zero_nat))
| hBOOL(hAPP_nat_bool(X1,esk19_2(X2,X1)))
| ~ hBOOL(hAPP_nat_bool(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_1631]) ).
cnf(c_0_2690,plain,
( hAPP_nat_nat(plus_plus_nat(number_number_of_nat(X1)),number_number_of_nat(X2)) = number_number_of_nat(X2)
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),pls)) ),
inference(split_conjunct,[status(thm)],[c_0_1732]) ).
cnf(c_0_2691,plain,
times_times_int(bit1(X1),X2) = hAPP_int_int(plus_plus_int(bit0(times_times_int(X1,X2))),X2),
inference(split_conjunct,[status(thm)],[c_0_1793]) ).
cnf(c_0_2692,plain,
hAPP_int_int(plus_plus_int(X1),hAPP_int_int(plus_plus_int(X2),X3)) = hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(X1),X2)),X3),
inference(split_conjunct,[status(thm)],[c_0_1794]) ).
cnf(c_0_2693,plain,
hAPP_nat_nat(plus_plus_nat(X1),hAPP_nat_nat(plus_plus_nat(X2),X3)) = hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(plus_plus_nat(X1),X2)),X3),
inference(split_conjunct,[status(thm)],[c_0_1795]) ).
cnf(c_0_2694,plain,
hAPP_real_real(plus_plus_real(X1),hAPP_real_real(plus_plus_real(X2),X3)) = hAPP_real_real(plus_plus_real(hAPP_real_real(plus_plus_real(X1),X2)),X3),
inference(split_conjunct,[status(thm)],[c_0_1796]) ).
cnf(c_0_2695,plain,
hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(X1),X2)),X3) = hAPP_int_int(plus_plus_int(X1),hAPP_int_int(plus_plus_int(X2),X3)),
inference(split_conjunct,[status(thm)],[c_0_1797]) ).
cnf(c_0_2696,plain,
hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(plus_plus_nat(X1),X2)),X3) = hAPP_nat_nat(plus_plus_nat(X1),hAPP_nat_nat(plus_plus_nat(X2),X3)),
inference(split_conjunct,[status(thm)],[c_0_1798]) ).
cnf(c_0_2697,plain,
hAPP_real_real(plus_plus_real(hAPP_real_real(plus_plus_real(X1),X2)),X3) = hAPP_real_real(plus_plus_real(X1),hAPP_real_real(plus_plus_real(X2),X3)),
inference(split_conjunct,[status(thm)],[c_0_1799]) ).
cnf(c_0_2698,plain,
hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(X1),X2)),X3) = hAPP_int_int(plus_plus_int(X1),hAPP_int_int(plus_plus_int(X2),X3)),
inference(split_conjunct,[status(thm)],[c_0_1800]) ).
cnf(c_0_2699,plain,
hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(plus_plus_nat(X1),X2)),X3) = hAPP_nat_nat(plus_plus_nat(X1),hAPP_nat_nat(plus_plus_nat(X2),X3)),
inference(split_conjunct,[status(thm)],[c_0_1801]) ).
cnf(c_0_2700,plain,
hAPP_real_real(plus_plus_real(hAPP_real_real(plus_plus_real(X1),X2)),X3) = hAPP_real_real(plus_plus_real(X1),hAPP_real_real(plus_plus_real(X2),X3)),
inference(split_conjunct,[status(thm)],[c_0_1802]) ).
cnf(c_0_2701,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X2))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X2),X1))
| X2 = X1 ),
inference(split_conjunct,[status(thm)],[c_0_1803]) ).
cnf(c_0_2702,plain,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X1),X2))
| hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X2),X1))
| X2 = X1 ),
inference(split_conjunct,[status(thm)],[c_0_1804]) ).
cnf(c_0_2703,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X2),X1))
| X2 = X1 ),
inference(split_conjunct,[status(thm)],[c_0_1805]) ).
cnf(c_0_2704,plain,
hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(plus_plus_nat(X1),X2)),X3) = hAPP_nat_nat(plus_plus_nat(X1),hAPP_nat_nat(plus_plus_nat(X2),X3)),
inference(split_conjunct,[status(thm)],[c_0_1806]) ).
cnf(c_0_2705,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X2),X1))
| X2 = X1 ),
inference(split_conjunct,[status(thm)],[c_0_1807]) ).
cnf(c_0_2706,plain,
hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(X1),X2)),X3) = hAPP_int_int(plus_plus_int(X1),hAPP_int_int(plus_plus_int(X2),X3)),
inference(split_conjunct,[status(thm)],[c_0_1808]) ).
cnf(c_0_2707,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X2))
| X2 = X1
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X2),X1)) ),
inference(split_conjunct,[status(thm)],[c_0_1809]) ).
cnf(c_0_2708,plain,
( hAPP_nat_int(power_power_int(X1),X2) = hAPP_nat_int(power_power_int(X1),X3)
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),X1))
| X2 != X3 ),
inference(split_conjunct,[status(thm)],[c_0_1789]) ).
cnf(c_0_2709,plain,
( hAPP_nat_nat(power_power_nat(X1),X2) = hAPP_nat_nat(power_power_nat(X1),X3)
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,one_one_nat),X1))
| X2 != X3 ),
inference(split_conjunct,[status(thm)],[c_0_1790]) ).
cnf(c_0_2710,plain,
( hAPP_nat_real(power_power_real(X1),X2) = hAPP_nat_real(power_power_real(X1),X3)
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,one_one_real),X1))
| X2 != X3 ),
inference(split_conjunct,[status(thm)],[c_0_1791]) ).
cnf(c_0_2711,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X2),X1)) ),
inference(split_conjunct,[status(thm)],[c_0_1810]) ).
cnf(c_0_2712,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X1)) ),
inference(split_conjunct,[status(thm)],[c_0_1811]) ).
cnf(c_0_2713,plain,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X1),X2))
| hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X2),X1)) ),
inference(split_conjunct,[status(thm)],[c_0_1812]) ).
cnf(c_0_2714,plain,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X1),X2))
| hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X2),X1)) ),
inference(split_conjunct,[status(thm)],[c_0_1813]) ).
cnf(c_0_2715,plain,
hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),hAPP_nat_nat(plus_plus_nat(X1),X2))),
inference(split_conjunct,[status(thm)],[c_0_1814]) ).
cnf(c_0_2716,plain,
hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),hAPP_nat_nat(plus_plus_nat(X2),X1))),
inference(split_conjunct,[status(thm)],[c_0_1815]) ).
cnf(c_0_2717,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X1)) ),
inference(split_conjunct,[status(thm)],[c_0_1816]) ).
cnf(c_0_2718,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X2),X1)) ),
inference(split_conjunct,[status(thm)],[c_0_1817]) ).
cnf(c_0_2719,plain,
( hAPP_nat_int(semiri1621563631at_int,number_number_of_nat(X1)) = number_number_of_int(X1)
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),number_number_of_int(X1))) ),
inference(split_conjunct,[status(thm)],[c_0_1818]) ).
cnf(c_0_2720,plain,
( hAPP_nat_real(semiri132038758t_real,number_number_of_nat(X1)) = number267125858f_real(X1)
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),number_number_of_int(X1))) ),
inference(split_conjunct,[status(thm)],[c_0_1819]) ).
cnf(c_0_2721,plain,
( hAPP_int_int(plus_plus_int(number_number_of_int(X1)),one_one_int) = number_number_of_int(succ(X1))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X1)) ),
inference(split_conjunct,[status(thm)],[c_0_1820]) ).
cnf(c_0_2722,plain,
( hAPP_nat_nat(plus_plus_nat(number_number_of_nat(X1)),one_one_nat) = number_number_of_nat(succ(X1))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X1)) ),
inference(split_conjunct,[status(thm)],[c_0_1821]) ).
cnf(c_0_2723,plain,
( hAPP_real_real(plus_plus_real(number267125858f_real(X1)),one_one_real) = number267125858f_real(succ(X1))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X1)) ),
inference(split_conjunct,[status(thm)],[c_0_1822]) ).
cnf(c_0_2724,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),hAPP_int_int(plus_plus_int(X2),one_one_int)))
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[c_0_1641]) ).
cnf(c_0_2725,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(power_power_nat(X1),X2)))
| X2 != zero_zero_nat ),
inference(split_conjunct,[status(thm)],[c_0_1643]) ).
cnf(c_0_2726,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(power_power_nat(X1),X2)))
| X2 != zero_zero_nat ),
inference(split_conjunct,[status(thm)],[c_0_1644]) ).
cnf(c_0_2727,plain,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),hAPP_int_int(plus_plus_int(X1),one_one_int))),
inference(split_conjunct,[status(thm)],[c_0_1823]) ).
cnf(c_0_2728,plain,
hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),hAPP_nat_nat(plus_plus_nat(X1),one_one_nat))),
inference(split_conjunct,[status(thm)],[c_0_1824]) ).
cnf(c_0_2729,plain,
hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X1),hAPP_real_real(plus_plus_real(X1),one_one_real))),
inference(split_conjunct,[status(thm)],[c_0_1825]) ).
cnf(c_0_2730,plain,
( hAPP_nat_nat(plus_plus_nat(number_number_of_nat(X1)),one_one_nat) = one_one_nat
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),pls)) ),
inference(split_conjunct,[status(thm)],[c_0_1826]) ).
cnf(c_0_2731,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2))
| X2 != hAPP_int_int(plus_plus_int(X1),hAPP_nat_int(semiri1621563631at_int,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_1749]) ).
cnf(c_0_2732,plain,
( hAPP_int_int(plus_plus_int(one_one_int),number_number_of_int(X1)) = number_number_of_int(succ(X1))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X1)) ),
inference(split_conjunct,[status(thm)],[c_0_1827]) ).
cnf(c_0_2733,plain,
( hAPP_nat_nat(plus_plus_nat(one_one_nat),number_number_of_nat(X1)) = number_number_of_nat(succ(X1))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X1)) ),
inference(split_conjunct,[status(thm)],[c_0_1828]) ).
cnf(c_0_2734,plain,
( hAPP_real_real(plus_plus_real(one_one_real),number267125858f_real(X1)) = number267125858f_real(succ(X1))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X1)) ),
inference(split_conjunct,[status(thm)],[c_0_1829]) ).
cnf(c_0_2735,plain,
( hBOOL(hAPP_int_bool(X1,hAPP_nat_int(semiri1621563631at_int,X2)))
| ~ hBOOL(hAPP_int_bool(X1,esk8_1(X1))) ),
inference(split_conjunct,[status(thm)],[c_0_1652]) ).
cnf(c_0_2736,plain,
hAPP_int_int(plus_plus_int(hAPP_nat_int(semiri1621563631at_int,X1)),hAPP_nat_int(semiri1621563631at_int,X2)) = hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(plus_plus_nat(X1),X2)),
inference(split_conjunct,[status(thm)],[c_0_1830]) ).
cnf(c_0_2737,plain,
hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(plus_plus_nat(X1),X2)) = hAPP_int_int(plus_plus_int(hAPP_nat_int(semiri1621563631at_int,X1)),hAPP_nat_int(semiri1621563631at_int,X2)),
inference(split_conjunct,[status(thm)],[c_0_1831]) ).
cnf(c_0_2738,plain,
hAPP_nat_nat(semiri984289939at_nat,hAPP_nat_nat(plus_plus_nat(X1),X2)) = hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(semiri984289939at_nat,X1)),hAPP_nat_nat(semiri984289939at_nat,X2)),
inference(split_conjunct,[status(thm)],[c_0_1832]) ).
cnf(c_0_2739,plain,
hAPP_nat_real(semiri132038758t_real,hAPP_nat_nat(plus_plus_nat(X1),X2)) = hAPP_real_real(plus_plus_real(hAPP_nat_real(semiri132038758t_real,X1)),hAPP_nat_real(semiri132038758t_real,X2)),
inference(split_conjunct,[status(thm)],[c_0_1833]) ).
cnf(c_0_2740,plain,
hAPP_int_int(plus_plus_int(hAPP_nat_int(semiri1621563631at_int,X1)),hAPP_nat_int(semiri1621563631at_int,X2)) = hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(plus_plus_nat(X1),X2)),
inference(split_conjunct,[status(thm)],[c_0_1834]) ).
cnf(c_0_2741,plain,
( hAPP_nat_nat(plus_plus_nat(one_one_nat),number_number_of_nat(X1)) = one_one_nat
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),pls)) ),
inference(split_conjunct,[status(thm)],[c_0_1835]) ).
cnf(c_0_2742,plain,
( hBOOL(X1)
| ~ hBOOL(X1)
| ~ hBOOL(X2)
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X3))
| ~ hBOOL(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1683]) ).
cnf(c_0_2743,plain,
( hBOOL(X2)
| ~ hBOOL(X1)
| ~ hBOOL(X2)
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X3))
| ~ hBOOL(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1683]) ).
cnf(c_0_2744,plain,
( hBOOL(X1)
| ~ hBOOL(X1)
| ~ hBOOL(X2)
| ~ hBOOL(X2)
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_1672]) ).
cnf(c_0_2745,plain,
( hBOOL(X2)
| ~ hBOOL(X1)
| ~ hBOOL(X2)
| ~ hBOOL(X1)
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_1672]) ).
cnf(c_0_2746,plain,
hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),X1)),X1) != zero_zero_int,
inference(split_conjunct,[status(thm)],[c_0_1836]) ).
cnf(c_0_2747,plain,
( hBOOL(X1)
| hBOOL(X2)
| hBOOL(X1)
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X3))
| ~ hBOOL(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1683]) ).
cnf(c_0_2748,plain,
( hBOOL(X1)
| hBOOL(X2)
| hBOOL(X2)
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X3))
| ~ hBOOL(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1683]) ).
cnf(c_0_2749,plain,
( hBOOL(X1)
| hBOOL(X2)
| hBOOL(X1)
| ~ hBOOL(X2)
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_1672]) ).
cnf(c_0_2750,plain,
( hBOOL(X1)
| hBOOL(X2)
| hBOOL(X2)
| ~ hBOOL(X1)
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_1672]) ).
cnf(c_0_2751,plain,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),number_number_of_int(bit0(bit1(pls))))),
inference(split_conjunct,[status(thm)],[c_0_1837]) ).
cnf(c_0_2752,plain,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),number_number_of_int(bit1(bit1(pls))))),
inference(split_conjunct,[status(thm)],[c_0_1838]) ).
cnf(c_0_2753,plain,
hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),number_number_of_nat(bit0(bit1(pls))))),
inference(split_conjunct,[status(thm)],[c_0_1839]) ).
cnf(c_0_2754,plain,
( X1 = hAPP_nat_int(semiri1621563631at_int,esk15_1(X1))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1)) ),
inference(split_conjunct,[status(thm)],[c_0_1840]) ).
cnf(c_0_2755,plain,
( X1 = hAPP_nat_int(semiri1621563631at_int,esk12_1(X1))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1)) ),
inference(split_conjunct,[status(thm)],[c_0_1841]) ).
cnf(c_0_2756,plain,
( X1 = hAPP_nat_int(semiri1621563631at_int,esk11_1(X1))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1)) ),
inference(split_conjunct,[status(thm)],[c_0_1842]) ).
cnf(c_0_2757,plain,
( X1 = hAPP_nat_int(semiri1621563631at_int,esk2_1(X1))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X1)) ),
inference(split_conjunct,[status(thm)],[c_0_1787]) ).
cnf(c_0_2758,plain,
hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),hAPP_real_real(plus_plus_real(one_one_real),one_one_real))),
inference(split_conjunct,[status(thm)],[c_0_1843]) ).
cnf(c_0_2759,plain,
hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(plus_plus_nat(one_one_nat),one_one_nat))),
inference(split_conjunct,[status(thm)],[c_0_1844]) ).
cnf(c_0_2760,plain,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_int_int(plus_plus_int(one_one_int),one_one_int))),
inference(split_conjunct,[status(thm)],[c_0_1845]) ).
cnf(c_0_2761,plain,
number267125858f_real(bit1(X1)) = hAPP_real_real(plus_plus_real(hAPP_real_real(plus_plus_real(one_one_real),number267125858f_real(X1))),number267125858f_real(X1)),
inference(split_conjunct,[status(thm)],[c_0_1846]) ).
cnf(c_0_2762,plain,
number_number_of_int(bit1(X1)) = hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),number_number_of_int(X1))),number_number_of_int(X1)),
inference(split_conjunct,[status(thm)],[c_0_1847]) ).
cnf(c_0_2763,plain,
number267125858f_real(bit0(X1)) = hAPP_real_real(plus_plus_real(hAPP_real_real(plus_plus_real(zero_zero_real),number267125858f_real(X1))),number267125858f_real(X1)),
inference(split_conjunct,[status(thm)],[c_0_1848]) ).
cnf(c_0_2764,plain,
number_number_of_int(bit0(X1)) = hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(zero_zero_int),number_number_of_int(X1))),number_number_of_int(X1)),
inference(split_conjunct,[status(thm)],[c_0_1849]) ).
cnf(c_0_2765,plain,
( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X1),X2))
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[c_0_1775]) ).
cnf(c_0_2766,plain,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[c_0_1777]) ).
cnf(c_0_2767,plain,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X2))
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[c_0_1780]) ).
cnf(c_0_2768,plain,
( X1 != X2
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_1850]) ).
cnf(c_0_2769,plain,
( X1 != X2
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X2),X1)) ),
inference(split_conjunct,[status(thm)],[c_0_1851]) ).
cnf(c_0_2770,plain,
( X1 != X2
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_1807]) ).
cnf(c_0_2771,plain,
( X1 != X2
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X2),X1)) ),
inference(split_conjunct,[status(thm)],[c_0_1807]) ).
cnf(c_0_2772,plain,
( X1 != zero_zero_nat
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X2),X1)) ),
inference(split_conjunct,[status(thm)],[c_0_1852]) ).
cnf(c_0_2773,plain,
~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X1)),
inference(split_conjunct,[status(thm)],[c_0_1853]) ).
cnf(c_0_2774,plain,
~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X1)),
inference(split_conjunct,[status(thm)],[c_0_1854]) ).
cnf(c_0_2775,plain,
( number_number_of_nat(X1) = zero_zero_nat
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),pls)) ),
inference(split_conjunct,[status(thm)],[c_0_1855]) ).
cnf(c_0_2776,plain,
( zero_zero_nat = number_number_of_nat(X1)
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),pls)) ),
inference(split_conjunct,[status(thm)],[c_0_1856]) ).
cnf(c_0_2777,plain,
( sqrt(X1) != zero_zero_real
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X1)) ),
inference(split_conjunct,[status(thm)],[c_0_1857]) ).
cnf(c_0_2778,plain,
hAPP_int_int(plus_plus_int(X1),hAPP_int_int(plus_plus_int(X2),X3)) = hAPP_int_int(plus_plus_int(X2),hAPP_int_int(plus_plus_int(X1),X3)),
inference(split_conjunct,[status(thm)],[c_0_1858]) ).
cnf(c_0_2779,plain,
hAPP_nat_nat(plus_plus_nat(X1),hAPP_nat_nat(plus_plus_nat(X2),X3)) = hAPP_nat_nat(plus_plus_nat(X2),hAPP_nat_nat(plus_plus_nat(X1),X3)),
inference(split_conjunct,[status(thm)],[c_0_1859]) ).
cnf(c_0_2780,plain,
hAPP_real_real(plus_plus_real(X1),hAPP_real_real(plus_plus_real(X2),X3)) = hAPP_real_real(plus_plus_real(X2),hAPP_real_real(plus_plus_real(X1),X3)),
inference(split_conjunct,[status(thm)],[c_0_1860]) ).
cnf(c_0_2781,plain,
hAPP_nat_int(power_power_int(hAPP_nat_int(semiri1621563631at_int,X1)),X2) = hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(power_power_nat(X1),X2)),
inference(split_conjunct,[status(thm)],[c_0_1861]) ).
cnf(c_0_2782,plain,
hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(power_power_nat(X1),X2)) = hAPP_nat_int(power_power_int(hAPP_nat_int(semiri1621563631at_int,X1)),X2),
inference(split_conjunct,[status(thm)],[c_0_1862]) ).
cnf(c_0_2783,plain,
hAPP_nat_nat(semiri984289939at_nat,hAPP_nat_nat(power_power_nat(X1),X2)) = hAPP_nat_nat(power_power_nat(hAPP_nat_nat(semiri984289939at_nat,X1)),X2),
inference(split_conjunct,[status(thm)],[c_0_1863]) ).
cnf(c_0_2784,plain,
hAPP_nat_real(semiri132038758t_real,hAPP_nat_nat(power_power_nat(X1),X2)) = hAPP_nat_real(power_power_real(hAPP_nat_real(semiri132038758t_real,X1)),X2),
inference(split_conjunct,[status(thm)],[c_0_1864]) ).
cnf(c_0_2785,plain,
hAPP_nat_nat(plus_plus_nat(X1),hAPP_nat_nat(plus_plus_nat(X2),X3)) = hAPP_nat_nat(plus_plus_nat(X2),hAPP_nat_nat(plus_plus_nat(X1),X3)),
inference(split_conjunct,[status(thm)],[c_0_1865]) ).
cnf(c_0_2786,plain,
hAPP_int_int(plus_plus_int(X1),hAPP_int_int(plus_plus_int(X2),X3)) = hAPP_int_int(plus_plus_int(X2),hAPP_int_int(plus_plus_int(X1),X3)),
inference(split_conjunct,[status(thm)],[c_0_1866]) ).
cnf(c_0_2787,plain,
hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(power_power_nat(X1),X2)) = hAPP_nat_int(power_power_int(hAPP_nat_int(semiri1621563631at_int,X1)),X2),
inference(split_conjunct,[status(thm)],[c_0_1867]) ).
cnf(c_0_2788,plain,
hAPP_nat_int(power_power_int(hAPP_nat_int(semiri1621563631at_int,X1)),X2) = hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(power_power_nat(X1),X2)),
inference(split_conjunct,[status(thm)],[c_0_1868]) ).
cnf(c_0_2789,plain,
( X1 = zero_zero_nat
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),zero_zero_nat)) ),
inference(split_conjunct,[status(thm)],[c_0_1869]) ).
cnf(c_0_2790,plain,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_nat_int(semiri1621563631at_int,X1))),
inference(split_conjunct,[status(thm)],[c_0_1870]) ).
cnf(c_0_2791,plain,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_nat_int(semiri1621563631at_int,X1))),
inference(split_conjunct,[status(thm)],[c_0_1871]) ).
cnf(c_0_2792,plain,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_nat_int(semiri1621563631at_int,X1))),
inference(split_conjunct,[status(thm)],[c_0_1872]) ).
cnf(c_0_2793,plain,
hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),hAPP_nat_nat(semiri984289939at_nat,X1))),
inference(split_conjunct,[status(thm)],[c_0_1873]) ).
cnf(c_0_2794,plain,
hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),hAPP_nat_real(semiri132038758t_real,X1))),
inference(split_conjunct,[status(thm)],[c_0_1874]) ).
cnf(c_0_2795,plain,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_nat_int(semiri1621563631at_int,X1))),
inference(split_conjunct,[status(thm)],[c_0_1875]) ).
cnf(c_0_2796,plain,
hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),hAPP_nat_nat(semiri984289939at_nat,X1))),
inference(split_conjunct,[status(thm)],[c_0_1876]) ).
cnf(c_0_2797,plain,
hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),hAPP_nat_real(semiri132038758t_real,X1))),
inference(split_conjunct,[status(thm)],[c_0_1877]) ).
cnf(c_0_2798,plain,
~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),zero_zero_nat)),
inference(split_conjunct,[status(thm)],[c_0_1878]) ).
cnf(c_0_2799,plain,
~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),zero_zero_nat)),
inference(split_conjunct,[status(thm)],[c_0_1879]) ).
cnf(c_0_2800,plain,
~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),zero_zero_nat)),
inference(split_conjunct,[status(thm)],[c_0_1880]) ).
cnf(c_0_2801,plain,
( hAPP_nat_nat(plus_plus_nat(number_number_of_nat(X1)),one_one_nat) = number_number_of_nat(succ(X1))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),pls)) ),
inference(split_conjunct,[status(thm)],[c_0_1826]) ).
cnf(c_0_2802,plain,
( X1 != zero_zero_nat
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1)) ),
inference(split_conjunct,[status(thm)],[c_0_1881]) ).
cnf(c_0_2803,plain,
( hAPP_nat_int(semiri1621563631at_int,X1) = hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(if_nat(X2,X1),X3))
| ~ hBOOL(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1882]) ).
cnf(c_0_2804,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
| X2 != hAPP_nat_nat(plus_plus_nat(X1),X3) ),
inference(split_conjunct,[status(thm)],[c_0_1792]) ).
cnf(c_0_2805,plain,
( hAPP_nat_int(semiri1621563631at_int,X1) = hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(if_nat(X2,X3),X1))
| hBOOL(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1882]) ).
cnf(c_0_2806,plain,
( hAPP_nat_nat(plus_plus_nat(one_one_nat),number_number_of_nat(X1)) = number_number_of_nat(succ(X1))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),pls)) ),
inference(split_conjunct,[status(thm)],[c_0_1835]) ).
cnf(c_0_2807,plain,
~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),zero_zero_int)),
inference(split_conjunct,[status(thm)],[c_0_1883]) ).
cnf(c_0_2808,plain,
~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,one_one_nat),zero_zero_nat)),
inference(split_conjunct,[status(thm)],[c_0_1884]) ).
cnf(c_0_2809,plain,
~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,one_one_real),zero_zero_real)),
inference(split_conjunct,[status(thm)],[c_0_1885]) ).
cnf(c_0_2810,plain,
~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),zero_zero_int)),
inference(split_conjunct,[status(thm)],[c_0_1886]) ).
cnf(c_0_2811,plain,
~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,one_one_nat),zero_zero_nat)),
inference(split_conjunct,[status(thm)],[c_0_1887]) ).
cnf(c_0_2812,plain,
~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,one_one_real),zero_zero_real)),
inference(split_conjunct,[status(thm)],[c_0_1888]) ).
cnf(c_0_2813,plain,
~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),zero_zero_int)),
inference(split_conjunct,[status(thm)],[c_0_1889]) ).
cnf(c_0_2814,plain,
~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),pls)),
inference(split_conjunct,[status(thm)],[c_0_1890]) ).
cnf(c_0_2815,plain,
( hAPP_nat_int(semiri1621563631at_int,number_number_of_nat(X1)) = zero_zero_int
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),number_number_of_int(X1))) ),
inference(split_conjunct,[status(thm)],[c_0_1818]) ).
cnf(c_0_2816,plain,
( hAPP_nat_real(semiri132038758t_real,number_number_of_nat(X1)) = zero_zero_real
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),number_number_of_int(X1))) ),
inference(split_conjunct,[status(thm)],[c_0_1819]) ).
cnf(c_0_2817,plain,
hAPP_int_int(plus_plus_int(bit1(X1)),bit1(X2)) = bit0(hAPP_int_int(plus_plus_int(X1),succ(X2))),
inference(split_conjunct,[status(thm)],[c_0_1891]) ).
cnf(c_0_2818,plain,
bit1(X1) = hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),X1)),X1),
inference(split_conjunct,[status(thm)],[c_0_1892]) ).
cnf(c_0_2819,plain,
( X1 = zero_zero_real
| hAPP_nat_real(power_power_real(X1),number_number_of_nat(bit0(bit1(pls)))) != zero_zero_real ),
inference(split_conjunct,[status(thm)],[c_0_1893]) ).
cnf(c_0_2820,plain,
( X1 = zero_zero_int
| hAPP_nat_int(power_power_int(X1),number_number_of_nat(bit0(bit1(pls)))) != zero_zero_int ),
inference(split_conjunct,[status(thm)],[c_0_1894]) ).
cnf(c_0_2821,plain,
hAPP_int_int(plus_plus_int(bit0(X1)),bit1(X2)) = bit1(hAPP_int_int(plus_plus_int(X1),X2)),
inference(split_conjunct,[status(thm)],[c_0_1895]) ).
cnf(c_0_2822,plain,
hAPP_int_int(plus_plus_int(bit1(X1)),bit0(X2)) = bit1(hAPP_int_int(plus_plus_int(X1),X2)),
inference(split_conjunct,[status(thm)],[c_0_1896]) ).
cnf(c_0_2823,plain,
number267125858f_real(hAPP_int_int(plus_plus_int(X1),X2)) = hAPP_real_real(plus_plus_real(number267125858f_real(X1)),number267125858f_real(X2)),
inference(split_conjunct,[status(thm)],[c_0_1897]) ).
cnf(c_0_2824,plain,
number_number_of_int(hAPP_int_int(plus_plus_int(X1),X2)) = hAPP_int_int(plus_plus_int(number_number_of_int(X1)),number_number_of_int(X2)),
inference(split_conjunct,[status(thm)],[c_0_1898]) ).
cnf(c_0_2825,plain,
hAPP_real_real(plus_plus_real(number267125858f_real(X1)),number267125858f_real(X2)) = number267125858f_real(hAPP_int_int(plus_plus_int(X1),X2)),
inference(split_conjunct,[status(thm)],[c_0_1899]) ).
cnf(c_0_2826,plain,
hAPP_int_int(plus_plus_int(number_number_of_int(X1)),number_number_of_int(X2)) = number_number_of_int(hAPP_int_int(plus_plus_int(X1),X2)),
inference(split_conjunct,[status(thm)],[c_0_1900]) ).
cnf(c_0_2827,plain,
hAPP_int_int(plus_plus_int(bit0(X1)),bit0(X2)) = bit0(hAPP_int_int(plus_plus_int(X1),X2)),
inference(split_conjunct,[status(thm)],[c_0_1901]) ).
cnf(c_0_2828,plain,
hAPP_int_int(plus_plus_int(number_number_of_int(X1)),number_number_of_int(X2)) = number_number_of_int(hAPP_int_int(plus_plus_int(X1),X2)),
inference(split_conjunct,[status(thm)],[c_0_1902]) ).
cnf(c_0_2829,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),pls))
| number_number_of_nat(X1) != zero_zero_nat ),
inference(split_conjunct,[status(thm)],[c_0_1855]) ).
cnf(c_0_2830,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),pls))
| zero_zero_nat != number_number_of_nat(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1856]) ).
cnf(c_0_2831,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2))
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[c_0_1903]) ).
cnf(c_0_2832,plain,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X1),X2))
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[c_0_1776]) ).
cnf(c_0_2833,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[c_0_1904]) ).
cnf(c_0_2834,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[c_0_1778]) ).
cnf(c_0_2835,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[c_0_1782]) ).
cnf(c_0_2836,plain,
hAPP_real_real(plus_plus_real(number267125858f_real(X1)),one_one_real) = number267125858f_real(hAPP_int_int(plus_plus_int(X1),bit1(pls))),
inference(split_conjunct,[status(thm)],[c_0_1905]) ).
cnf(c_0_2837,plain,
hAPP_int_int(plus_plus_int(number_number_of_int(X1)),one_one_int) = number_number_of_int(hAPP_int_int(plus_plus_int(X1),bit1(pls))),
inference(split_conjunct,[status(thm)],[c_0_1906]) ).
cnf(c_0_2838,plain,
hAPP_real_real(plus_plus_real(one_one_real),number267125858f_real(X1)) = number267125858f_real(hAPP_int_int(plus_plus_int(bit1(pls)),X1)),
inference(split_conjunct,[status(thm)],[c_0_1907]) ).
cnf(c_0_2839,plain,
hAPP_int_int(plus_plus_int(one_one_int),number_number_of_int(X1)) = number_number_of_int(hAPP_int_int(plus_plus_int(bit1(pls)),X1)),
inference(split_conjunct,[status(thm)],[c_0_1908]) ).
cnf(c_0_2840,plain,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X1)),
inference(split_conjunct,[status(thm)],[c_0_1909]) ).
cnf(c_0_2841,plain,
hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X1)),
inference(split_conjunct,[status(thm)],[c_0_1910]) ).
cnf(c_0_2842,plain,
hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X1),X1)),
inference(split_conjunct,[status(thm)],[c_0_1911]) ).
cnf(c_0_2843,plain,
hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X1),X1)),
inference(split_conjunct,[status(thm)],[c_0_1912]) ).
cnf(c_0_2844,plain,
hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X1)),
inference(split_conjunct,[status(thm)],[c_0_1913]) ).
cnf(c_0_2845,plain,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),number_number_of_int(pls))),
inference(split_conjunct,[status(thm)],[c_0_1914]) ).
cnf(c_0_2846,plain,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X1)),
inference(split_conjunct,[status(thm)],[c_0_1915]) ).
cnf(c_0_2847,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),zero_zero_nat))
| X1 != zero_zero_nat ),
inference(split_conjunct,[status(thm)],[c_0_1869]) ).
cnf(c_0_2848,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1))
| X1 = zero_zero_nat ),
inference(split_conjunct,[status(thm)],[c_0_1881]) ).
cnf(c_0_2849,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1))
| X1 = zero_zero_nat ),
inference(split_conjunct,[status(thm)],[c_0_1916]) ).
cnf(c_0_2850,plain,
hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),X1)),
inference(split_conjunct,[status(thm)],[c_0_1917]) ).
cnf(c_0_2851,plain,
hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),X1)),
inference(split_conjunct,[status(thm)],[c_0_1918]) ).
cnf(c_0_2852,plain,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),one_one_int)),
inference(split_conjunct,[status(thm)],[c_0_1919]) ).
cnf(c_0_2853,plain,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),one_one_int)),
inference(split_conjunct,[status(thm)],[c_0_1920]) ).
cnf(c_0_2854,plain,
hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),one_one_nat)),
inference(split_conjunct,[status(thm)],[c_0_1921]) ).
cnf(c_0_2855,plain,
hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),one_one_real)),
inference(split_conjunct,[status(thm)],[c_0_1922]) ).
cnf(c_0_2856,plain,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),zero_zero_int)),
inference(split_conjunct,[status(thm)],[c_0_1923]) ).
cnf(c_0_2857,plain,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),pls)),
inference(split_conjunct,[status(thm)],[c_0_1924]) ).
cnf(c_0_2858,plain,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),t)),
inference(split_conjunct,[status(thm)],[c_0_1925]) ).
cnf(c_0_2859,plain,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),one_one_int)),
inference(split_conjunct,[status(thm)],[c_0_1926]) ).
cnf(c_0_2860,plain,
hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),one_one_nat)),
inference(split_conjunct,[status(thm)],[c_0_1927]) ).
cnf(c_0_2861,plain,
hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),one_one_real)),
inference(split_conjunct,[status(thm)],[c_0_1928]) ).
cnf(c_0_2862,plain,
hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),tn)),
inference(split_conjunct,[status(thm)],[c_0_1929]) ).
cnf(c_0_2863,plain,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),one_one_int)),
inference(split_conjunct,[status(thm)],[c_0_1930]) ).
cnf(c_0_2864,plain,
hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),n)),
inference(split_conjunct,[status(thm)],[c_0_1931]) ).
cnf(c_0_2865,plain,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),t)),
inference(split_conjunct,[status(thm)],[c_0_1932]) ).
cnf(c_0_2866,plain,
( X1 = X2
| hAPP_int_int(plus_plus_int(X3),X1) != hAPP_int_int(plus_plus_int(X3),X2) ),
inference(split_conjunct,[status(thm)],[c_0_1933]) ).
cnf(c_0_2867,plain,
( X1 = X2
| hAPP_nat_nat(plus_plus_nat(X3),X1) != hAPP_nat_nat(plus_plus_nat(X3),X2) ),
inference(split_conjunct,[status(thm)],[c_0_1934]) ).
cnf(c_0_2868,plain,
( X1 = X2
| hAPP_real_real(plus_plus_real(X3),X1) != hAPP_real_real(plus_plus_real(X3),X2) ),
inference(split_conjunct,[status(thm)],[c_0_1935]) ).
cnf(c_0_2869,plain,
( X1 = X2
| hAPP_int_int(plus_plus_int(X1),X3) != hAPP_int_int(plus_plus_int(X2),X3) ),
inference(split_conjunct,[status(thm)],[c_0_1936]) ).
cnf(c_0_2870,plain,
( X1 = X2
| hAPP_nat_nat(plus_plus_nat(X1),X3) != hAPP_nat_nat(plus_plus_nat(X2),X3) ),
inference(split_conjunct,[status(thm)],[c_0_1937]) ).
cnf(c_0_2871,plain,
( X1 = X2
| hAPP_real_real(plus_plus_real(X1),X3) != hAPP_real_real(plus_plus_real(X2),X3) ),
inference(split_conjunct,[status(thm)],[c_0_1938]) ).
cnf(c_0_2872,plain,
( X1 = X2
| hAPP_int_int(plus_plus_int(X3),X1) != hAPP_int_int(plus_plus_int(X3),X2) ),
inference(split_conjunct,[status(thm)],[c_0_1939]) ).
cnf(c_0_2873,plain,
( X1 = X2
| hAPP_nat_nat(plus_plus_nat(X3),X1) != hAPP_nat_nat(plus_plus_nat(X3),X2) ),
inference(split_conjunct,[status(thm)],[c_0_1940]) ).
cnf(c_0_2874,plain,
( X1 = X2
| hAPP_real_real(plus_plus_real(X3),X1) != hAPP_real_real(plus_plus_real(X3),X2) ),
inference(split_conjunct,[status(thm)],[c_0_1941]) ).
cnf(c_0_2875,plain,
( X1 = X2
| hAPP_int_int(plus_plus_int(X3),X1) != hAPP_int_int(plus_plus_int(X3),X2) ),
inference(split_conjunct,[status(thm)],[c_0_1942]) ).
cnf(c_0_2876,plain,
( X1 = X2
| hAPP_nat_nat(plus_plus_nat(X3),X1) != hAPP_nat_nat(plus_plus_nat(X3),X2) ),
inference(split_conjunct,[status(thm)],[c_0_1943]) ).
cnf(c_0_2877,plain,
( X1 = X2
| hAPP_real_real(plus_plus_real(X3),X1) != hAPP_real_real(plus_plus_real(X3),X2) ),
inference(split_conjunct,[status(thm)],[c_0_1944]) ).
cnf(c_0_2878,plain,
( X1 = X2
| hAPP_int_int(plus_plus_int(X1),X3) != hAPP_int_int(plus_plus_int(X2),X3) ),
inference(split_conjunct,[status(thm)],[c_0_1945]) ).
cnf(c_0_2879,plain,
( X1 = X2
| hAPP_nat_nat(plus_plus_nat(X1),X3) != hAPP_nat_nat(plus_plus_nat(X2),X3) ),
inference(split_conjunct,[status(thm)],[c_0_1946]) ).
cnf(c_0_2880,plain,
( X1 = X2
| hAPP_real_real(plus_plus_real(X1),X3) != hAPP_real_real(plus_plus_real(X2),X3) ),
inference(split_conjunct,[status(thm)],[c_0_1947]) ).
cnf(c_0_2881,plain,
( X1 = X2
| hAPP_nat_nat(plus_plus_nat(X1),X3) != hAPP_nat_nat(plus_plus_nat(X2),X3) ),
inference(split_conjunct,[status(thm)],[c_0_1948]) ).
cnf(c_0_2882,plain,
( X1 = X2
| hAPP_nat_nat(plus_plus_nat(X3),X1) != hAPP_nat_nat(plus_plus_nat(X3),X2) ),
inference(split_conjunct,[status(thm)],[c_0_1949]) ).
cnf(c_0_2883,plain,
number_number_of_int(bit1(bit1(pls))) = hAPP_nat_int(semiri1621563631at_int,number_number_of_nat(bit1(bit1(pls)))),
inference(split_conjunct,[status(thm)],[c_0_1950]) ).
cnf(c_0_2884,plain,
number_number_of_int(bit0(bit1(pls))) = hAPP_nat_int(semiri1621563631at_int,number_number_of_nat(bit0(bit1(pls)))),
inference(split_conjunct,[status(thm)],[c_0_1951]) ).
cnf(c_0_2885,plain,
( hAPP_nat_real(power_power_real(X1),number_number_of_nat(bit0(bit1(pls)))) = zero_zero_real
| X1 != zero_zero_real ),
inference(split_conjunct,[status(thm)],[c_0_1893]) ).
cnf(c_0_2886,plain,
( hAPP_nat_int(power_power_int(X1),number_number_of_nat(bit0(bit1(pls)))) = zero_zero_int
| X1 != zero_zero_int ),
inference(split_conjunct,[status(thm)],[c_0_1894]) ).
cnf(c_0_2887,plain,
( hAPP_nat_real(power_power_real(X1),number_number_of_nat(X2)) != zero_zero_real
| number_number_of_nat(X2) != zero_zero_nat ),
inference(split_conjunct,[status(thm)],[c_0_1952]) ).
cnf(c_0_2888,plain,
( hAPP_nat_nat(power_power_nat(X1),number_number_of_nat(X2)) != zero_zero_nat
| number_number_of_nat(X2) != zero_zero_nat ),
inference(split_conjunct,[status(thm)],[c_0_1953]) ).
cnf(c_0_2889,plain,
( hAPP_nat_int(power_power_int(X1),number_number_of_nat(X2)) != zero_zero_int
| number_number_of_nat(X2) != zero_zero_nat ),
inference(split_conjunct,[status(thm)],[c_0_1954]) ).
cnf(c_0_2890,plain,
hAPP_nat_real(power_power_real(zero_zero_real),number_number_of_nat(bit0(bit1(pls)))) = zero_zero_real,
inference(split_conjunct,[status(thm)],[c_0_1955]) ).
cnf(c_0_2891,plain,
hAPP_nat_nat(power_power_nat(zero_zero_nat),number_number_of_nat(bit0(bit1(pls)))) = zero_zero_nat,
inference(split_conjunct,[status(thm)],[c_0_1956]) ).
cnf(c_0_2892,plain,
hAPP_nat_int(power_power_int(zero_zero_int),number_number_of_nat(bit0(bit1(pls)))) = zero_zero_int,
inference(split_conjunct,[status(thm)],[c_0_1957]) ).
cnf(c_0_2893,plain,
hAPP_nat_real(power_power_real(one_one_real),number_number_of_nat(bit0(bit1(pls)))) = one_one_real,
inference(split_conjunct,[status(thm)],[c_0_1958]) ).
cnf(c_0_2894,plain,
hAPP_nat_nat(power_power_nat(one_one_nat),number_number_of_nat(bit0(bit1(pls)))) = one_one_nat,
inference(split_conjunct,[status(thm)],[c_0_1959]) ).
cnf(c_0_2895,plain,
hAPP_nat_int(power_power_int(one_one_int),number_number_of_nat(bit0(bit1(pls)))) = one_one_int,
inference(split_conjunct,[status(thm)],[c_0_1960]) ).
cnf(c_0_2896,plain,
( hAPP_int_int(plus_plus_int(X1),X2) = hAPP_int_int(plus_plus_int(X1),X3)
| X2 != X3 ),
inference(split_conjunct,[status(thm)],[c_0_1933]) ).
cnf(c_0_2897,plain,
( hAPP_nat_nat(plus_plus_nat(X1),X2) = hAPP_nat_nat(plus_plus_nat(X1),X3)
| X2 != X3 ),
inference(split_conjunct,[status(thm)],[c_0_1934]) ).
cnf(c_0_2898,plain,
( hAPP_real_real(plus_plus_real(X1),X2) = hAPP_real_real(plus_plus_real(X1),X3)
| X2 != X3 ),
inference(split_conjunct,[status(thm)],[c_0_1935]) ).
cnf(c_0_2899,plain,
( hAPP_int_int(plus_plus_int(X1),X2) = hAPP_int_int(plus_plus_int(X3),X2)
| X1 != X3 ),
inference(split_conjunct,[status(thm)],[c_0_1936]) ).
cnf(c_0_2900,plain,
( hAPP_nat_nat(plus_plus_nat(X1),X2) = hAPP_nat_nat(plus_plus_nat(X3),X2)
| X1 != X3 ),
inference(split_conjunct,[status(thm)],[c_0_1937]) ).
cnf(c_0_2901,plain,
( hAPP_real_real(plus_plus_real(X1),X2) = hAPP_real_real(plus_plus_real(X3),X2)
| X1 != X3 ),
inference(split_conjunct,[status(thm)],[c_0_1938]) ).
cnf(c_0_2902,plain,
( hAPP_nat_nat(plus_plus_nat(X1),X2) = hAPP_nat_nat(plus_plus_nat(X3),X2)
| X1 != X3 ),
inference(split_conjunct,[status(thm)],[c_0_1948]) ).
cnf(c_0_2903,plain,
( hAPP_nat_nat(plus_plus_nat(X1),X2) = hAPP_nat_nat(plus_plus_nat(X1),X3)
| X2 != X3 ),
inference(split_conjunct,[status(thm)],[c_0_1949]) ).
cnf(c_0_2904,plain,
( X1 = zero_zero_real
| hAPP_nat_real(power_power_real(X1),number_number_of_nat(X2)) != zero_zero_real ),
inference(split_conjunct,[status(thm)],[c_0_1952]) ).
cnf(c_0_2905,plain,
( X1 = zero_zero_nat
| hAPP_nat_nat(power_power_nat(X1),number_number_of_nat(X2)) != zero_zero_nat ),
inference(split_conjunct,[status(thm)],[c_0_1953]) ).
cnf(c_0_2906,plain,
( X1 = zero_zero_int
| hAPP_nat_int(power_power_int(X1),number_number_of_nat(X2)) != zero_zero_int ),
inference(split_conjunct,[status(thm)],[c_0_1954]) ).
cnf(c_0_2907,plain,
( X1 = X2
| hAPP_nat_int(semiri1621563631at_int,X1) != hAPP_nat_int(semiri1621563631at_int,X2) ),
inference(split_conjunct,[status(thm)],[c_0_1961]) ).
cnf(c_0_2908,plain,
( X1 = X2
| hAPP_nat_int(semiri1621563631at_int,X1) != hAPP_nat_int(semiri1621563631at_int,X2) ),
inference(split_conjunct,[status(thm)],[c_0_1962]) ).
cnf(c_0_2909,plain,
( X1 = X2
| hAPP_nat_nat(semiri984289939at_nat,X1) != hAPP_nat_nat(semiri984289939at_nat,X2) ),
inference(split_conjunct,[status(thm)],[c_0_1963]) ).
cnf(c_0_2910,plain,
( X1 = X2
| hAPP_nat_real(semiri132038758t_real,X1) != hAPP_nat_real(semiri132038758t_real,X2) ),
inference(split_conjunct,[status(thm)],[c_0_1964]) ).
cnf(c_0_2911,plain,
( X1 = X2
| hAPP_nat_int(semiri1621563631at_int,X1) != hAPP_nat_int(semiri1621563631at_int,X2) ),
inference(split_conjunct,[status(thm)],[c_0_1965]) ).
cnf(c_0_2912,plain,
hAPP_int_int(plus_plus_int(X1),X2) = hAPP_int_int(plus_plus_int(X2),X1),
inference(split_conjunct,[status(thm)],[c_0_1966]) ).
cnf(c_0_2913,plain,
hAPP_nat_nat(plus_plus_nat(X1),X2) = hAPP_nat_nat(plus_plus_nat(X2),X1),
inference(split_conjunct,[status(thm)],[c_0_1967]) ).
cnf(c_0_2914,plain,
hAPP_real_real(plus_plus_real(X1),X2) = hAPP_real_real(plus_plus_real(X2),X1),
inference(split_conjunct,[status(thm)],[c_0_1968]) ).
cnf(c_0_2915,plain,
hAPP_nat_nat(plus_plus_nat(X1),X2) = hAPP_nat_nat(plus_plus_nat(X2),X1),
inference(split_conjunct,[status(thm)],[c_0_1969]) ).
cnf(c_0_2916,plain,
hAPP_int_int(plus_plus_int(X1),X2) = hAPP_int_int(plus_plus_int(X2),X1),
inference(split_conjunct,[status(thm)],[c_0_1970]) ).
cnf(c_0_2917,plain,
number267125858f_real(hAPP_nat_int(semiri1621563631at_int,X1)) = hAPP_nat_real(semiri132038758t_real,X1),
inference(split_conjunct,[status(thm)],[c_0_1971]) ).
cnf(c_0_2918,plain,
number_number_of_int(hAPP_nat_int(semiri1621563631at_int,X1)) = hAPP_nat_int(semiri1621563631at_int,X1),
inference(split_conjunct,[status(thm)],[c_0_1972]) ).
cnf(c_0_2919,plain,
number_number_of_nat(hAPP_nat_int(semiri1621563631at_int,X1)) = hAPP_nat_nat(semiri984289939at_nat,X1),
inference(split_conjunct,[status(thm)],[c_0_1973]) ).
cnf(c_0_2920,plain,
hAPP_nat_nat(if_nat(fFalse,X1),X2) = X2,
inference(split_conjunct,[status(thm)],[c_0_1974]) ).
cnf(c_0_2921,plain,
hAPP_nat_nat(if_nat(fTrue,X1),X2) = X1,
inference(split_conjunct,[status(thm)],[c_0_1975]) ).
cnf(c_0_2922,plain,
( X1 = zero_zero_nat
| X2 = one_one_nat
| hAPP_nat_nat(power_power_nat(X2),X1) != one_one_nat ),
inference(split_conjunct,[status(thm)],[c_0_1976]) ).
cnf(c_0_2923,plain,
( X1 = zero_zero_int
| X2 != hAPP_int_int(plus_plus_int(X2),X1) ),
inference(split_conjunct,[status(thm)],[c_0_1977]) ).
cnf(c_0_2924,plain,
( X1 = zero_zero_nat
| X2 != hAPP_nat_nat(plus_plus_nat(X2),X1) ),
inference(split_conjunct,[status(thm)],[c_0_1978]) ).
cnf(c_0_2925,plain,
( X1 = zero_zero_real
| X2 != hAPP_real_real(plus_plus_real(X2),X1) ),
inference(split_conjunct,[status(thm)],[c_0_1979]) ).
cnf(c_0_2926,plain,
( X1 = zero_zero_nat
| hAPP_nat_nat(plus_plus_nat(X2),X1) != X2 ),
inference(split_conjunct,[status(thm)],[c_0_1980]) ).
cnf(c_0_2927,plain,
( hAPP_nat_nat(power_power_nat(X1),X2) != zero_zero_nat
| X2 != zero_zero_nat ),
inference(split_conjunct,[status(thm)],[c_0_1981]) ).
cnf(c_0_2928,plain,
( hAPP_nat_int(power_power_int(X1),X2) != zero_zero_int
| X2 != zero_zero_nat ),
inference(split_conjunct,[status(thm)],[c_0_1982]) ).
cnf(c_0_2929,plain,
( hAPP_nat_nat(power_power_nat(X1),X2) != zero_zero_nat
| X2 != zero_zero_nat ),
inference(split_conjunct,[status(thm)],[c_0_1983]) ).
cnf(c_0_2930,plain,
( hAPP_nat_real(power_power_real(X1),X2) != zero_zero_real
| X2 != zero_zero_nat ),
inference(split_conjunct,[status(thm)],[c_0_1984]) ).
cnf(c_0_2931,plain,
( X1 = zero_zero_nat
| hAPP_nat_nat(power_power_nat(X1),X2) != zero_zero_nat ),
inference(split_conjunct,[status(thm)],[c_0_1981]) ).
cnf(c_0_2932,plain,
( X1 = zero_zero_int
| zero_zero_int != hAPP_int_int(plus_plus_int(X1),X1) ),
inference(split_conjunct,[status(thm)],[c_0_1985]) ).
cnf(c_0_2933,plain,
( X1 = zero_zero_real
| zero_zero_real != hAPP_real_real(plus_plus_real(X1),X1) ),
inference(split_conjunct,[status(thm)],[c_0_1986]) ).
cnf(c_0_2934,plain,
( X1 = zero_zero_int
| hAPP_nat_int(power_power_int(X1),X2) != zero_zero_int ),
inference(split_conjunct,[status(thm)],[c_0_1982]) ).
cnf(c_0_2935,plain,
( X1 = zero_zero_nat
| hAPP_nat_nat(power_power_nat(X1),X2) != zero_zero_nat ),
inference(split_conjunct,[status(thm)],[c_0_1983]) ).
cnf(c_0_2936,plain,
( X1 = zero_zero_real
| hAPP_nat_real(power_power_real(X1),X2) != zero_zero_real ),
inference(split_conjunct,[status(thm)],[c_0_1984]) ).
cnf(c_0_2937,plain,
( X1 = zero_zero_int
| hAPP_nat_int(power_power_int(X1),X2) != zero_zero_int ),
inference(split_conjunct,[status(thm)],[c_0_1987]) ).
cnf(c_0_2938,plain,
( X1 = zero_zero_real
| hAPP_nat_real(power_power_real(X1),X2) != zero_zero_real ),
inference(split_conjunct,[status(thm)],[c_0_1988]) ).
cnf(c_0_2939,plain,
( X1 = zero_zero_nat
| hAPP_nat_nat(plus_plus_nat(X1),X2) != zero_zero_nat ),
inference(split_conjunct,[status(thm)],[c_0_1989]) ).
cnf(c_0_2940,plain,
( X2 = zero_zero_nat
| hAPP_nat_nat(plus_plus_nat(X1),X2) != zero_zero_nat ),
inference(split_conjunct,[status(thm)],[c_0_1989]) ).
cnf(c_0_2941,plain,
( X1 = zero_zero_real
| hAPP_real_real(plus_plus_real(X1),X1) != zero_zero_real ),
inference(split_conjunct,[status(thm)],[c_0_1990]) ).
cnf(c_0_2942,plain,
( X1 = zero_zero_int
| hAPP_int_int(plus_plus_int(X1),X1) != zero_zero_int ),
inference(split_conjunct,[status(thm)],[c_0_1991]) ).
cnf(c_0_2943,plain,
( hAPP_nat_real(power_power_real(X1),number_number_of_nat(X2)) = zero_zero_real
| number_number_of_nat(X2) = zero_zero_nat
| X1 != zero_zero_real ),
inference(split_conjunct,[status(thm)],[c_0_1952]) ).
cnf(c_0_2944,plain,
( hAPP_nat_nat(power_power_nat(X1),number_number_of_nat(X2)) = zero_zero_nat
| number_number_of_nat(X2) = zero_zero_nat
| X1 != zero_zero_nat ),
inference(split_conjunct,[status(thm)],[c_0_1953]) ).
cnf(c_0_2945,plain,
( hAPP_nat_int(power_power_int(X1),number_number_of_nat(X2)) = zero_zero_int
| number_number_of_nat(X2) = zero_zero_nat
| X1 != zero_zero_int ),
inference(split_conjunct,[status(thm)],[c_0_1954]) ).
cnf(c_0_2946,plain,
number_number_of_int(succ(X1)) = hAPP_int_int(plus_plus_int(one_one_int),number_number_of_int(X1)),
inference(split_conjunct,[status(thm)],[c_0_1992]) ).
cnf(c_0_2947,plain,
number267125858f_real(succ(X1)) = hAPP_real_real(plus_plus_real(one_one_real),number267125858f_real(X1)),
inference(split_conjunct,[status(thm)],[c_0_1993]) ).
cnf(c_0_2948,plain,
hAPP_nat_nat(plus_plus_nat(one_one_nat),one_one_nat) = number_number_of_nat(bit0(bit1(pls))),
inference(split_conjunct,[status(thm)],[c_0_1994]) ).
cnf(c_0_2949,plain,
hAPP_real_real(plus_plus_real(one_one_real),one_one_real) = number267125858f_real(bit0(bit1(pls))),
inference(split_conjunct,[status(thm)],[c_0_1995]) ).
cnf(c_0_2950,plain,
hAPP_nat_nat(plus_plus_nat(one_one_nat),one_one_nat) = number_number_of_nat(bit0(bit1(pls))),
inference(split_conjunct,[status(thm)],[c_0_1996]) ).
cnf(c_0_2951,plain,
hAPP_int_int(plus_plus_int(one_one_int),one_one_int) = number_number_of_int(bit0(bit1(pls))),
inference(split_conjunct,[status(thm)],[c_0_1997]) ).
cnf(c_0_2952,plain,
hAPP_real_real(plus_plus_real(one_one_real),one_one_real) = number267125858f_real(bit0(bit1(pls))),
inference(split_conjunct,[status(thm)],[c_0_1998]) ).
cnf(c_0_2953,plain,
hAPP_int_int(plus_plus_int(one_one_int),one_one_int) = number_number_of_int(bit0(bit1(pls))),
inference(split_conjunct,[status(thm)],[c_0_1999]) ).
cnf(c_0_2954,plain,
( hAPP_nat_real(power_power_real(zero_zero_real),number_number_of_nat(X1)) = one_one_real
| number_number_of_nat(X1) != zero_zero_nat ),
inference(split_conjunct,[status(thm)],[c_0_2000]) ).
cnf(c_0_2955,plain,
( hAPP_nat_nat(power_power_nat(zero_zero_nat),number_number_of_nat(X1)) = one_one_nat
| number_number_of_nat(X1) != zero_zero_nat ),
inference(split_conjunct,[status(thm)],[c_0_2001]) ).
cnf(c_0_2956,plain,
( hAPP_nat_int(power_power_int(zero_zero_int),number_number_of_nat(X1)) = one_one_int
| number_number_of_nat(X1) != zero_zero_nat ),
inference(split_conjunct,[status(thm)],[c_0_2002]) ).
cnf(c_0_2957,plain,
is_bool(hAPP_real_bool(X1,X2)),
inference(split_conjunct,[status(thm)],[c_0_2003]) ).
cnf(c_0_2958,plain,
is_bool(hAPP_nat_bool(X1,X2)),
inference(split_conjunct,[status(thm)],[c_0_2004]) ).
cnf(c_0_2959,plain,
is_bool(hAPP_int_bool(X1,X2)),
inference(split_conjunct,[status(thm)],[c_0_2005]) ).
cnf(c_0_2960,plain,
( hAPP_nat_int(semiri1621563631at_int,X1) = hAPP_nat_int(semiri1621563631at_int,X2)
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[c_0_1961]) ).
cnf(c_0_2961,plain,
( hAPP_nat_int(semiri1621563631at_int,X1) = hAPP_nat_int(semiri1621563631at_int,X2)
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[c_0_1962]) ).
cnf(c_0_2962,plain,
( hAPP_nat_nat(semiri984289939at_nat,X1) = hAPP_nat_nat(semiri984289939at_nat,X2)
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[c_0_1963]) ).
cnf(c_0_2963,plain,
( hAPP_nat_real(semiri132038758t_real,X1) = hAPP_nat_real(semiri132038758t_real,X2)
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[c_0_1964]) ).
cnf(c_0_2964,plain,
( hAPP_nat_int(semiri1621563631at_int,X1) = hAPP_nat_int(semiri1621563631at_int,X2)
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[c_0_1965]) ).
cnf(c_0_2965,plain,
( hAPP_nat_real(power_power_real(zero_zero_real),number_number_of_nat(X1)) = zero_zero_real
| number_number_of_nat(X1) = zero_zero_nat ),
inference(split_conjunct,[status(thm)],[c_0_2000]) ).
cnf(c_0_2966,plain,
( hAPP_nat_nat(power_power_nat(zero_zero_nat),number_number_of_nat(X1)) = zero_zero_nat
| number_number_of_nat(X1) = zero_zero_nat ),
inference(split_conjunct,[status(thm)],[c_0_2001]) ).
cnf(c_0_2967,plain,
( hAPP_nat_int(power_power_int(zero_zero_int),number_number_of_nat(X1)) = zero_zero_int
| number_number_of_nat(X1) = zero_zero_nat ),
inference(split_conjunct,[status(thm)],[c_0_2002]) ).
cnf(c_0_2968,plain,
hAPP_real_real(plus_plus_real(number267125858f_real(pls)),X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_2006]) ).
cnf(c_0_2969,plain,
hAPP_int_int(plus_plus_int(number_number_of_int(pls)),X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_2007]) ).
cnf(c_0_2970,plain,
( hAPP_nat_nat(plus_plus_nat(X1),X2) = zero_zero_nat
| X2 != zero_zero_nat
| X1 != zero_zero_nat ),
inference(split_conjunct,[status(thm)],[c_0_1989]) ).
cnf(c_0_2971,plain,
( hAPP_nat_nat(power_power_nat(X1),X2) = zero_zero_nat
| X2 = zero_zero_nat
| X1 != zero_zero_nat ),
inference(split_conjunct,[status(thm)],[c_0_1981]) ).
cnf(c_0_2972,plain,
( hAPP_nat_int(power_power_int(X1),X2) = zero_zero_int
| X2 = zero_zero_nat
| X1 != zero_zero_int ),
inference(split_conjunct,[status(thm)],[c_0_1982]) ).
cnf(c_0_2973,plain,
( hAPP_nat_nat(power_power_nat(X1),X2) = zero_zero_nat
| X2 = zero_zero_nat
| X1 != zero_zero_nat ),
inference(split_conjunct,[status(thm)],[c_0_1983]) ).
cnf(c_0_2974,plain,
( hAPP_nat_real(power_power_real(X1),X2) = zero_zero_real
| X2 = zero_zero_nat
| X1 != zero_zero_real ),
inference(split_conjunct,[status(thm)],[c_0_1984]) ).
cnf(c_0_2975,plain,
hAPP_real_real(plus_plus_real(X1),number267125858f_real(pls)) = X1,
inference(split_conjunct,[status(thm)],[c_0_2008]) ).
cnf(c_0_2976,plain,
hAPP_int_int(plus_plus_int(X1),number_number_of_int(pls)) = X1,
inference(split_conjunct,[status(thm)],[c_0_2009]) ).
cnf(c_0_2977,plain,
bit0(X1) = hAPP_int_int(plus_plus_int(X1),X1),
inference(split_conjunct,[status(thm)],[c_0_2010]) ).
cnf(c_0_2978,plain,
( X1 = hAPP_int_int(plus_plus_int(X1),X2)
| X2 != zero_zero_int ),
inference(split_conjunct,[status(thm)],[c_0_1977]) ).
cnf(c_0_2979,plain,
( X1 = hAPP_nat_nat(plus_plus_nat(X1),X2)
| X2 != zero_zero_nat ),
inference(split_conjunct,[status(thm)],[c_0_1978]) ).
cnf(c_0_2980,plain,
( X1 = hAPP_real_real(plus_plus_real(X1),X2)
| X2 != zero_zero_real ),
inference(split_conjunct,[status(thm)],[c_0_1979]) ).
cnf(c_0_2981,plain,
( zero_zero_int = hAPP_int_int(plus_plus_int(X1),X1)
| X1 != zero_zero_int ),
inference(split_conjunct,[status(thm)],[c_0_1985]) ).
cnf(c_0_2982,plain,
( zero_zero_real = hAPP_real_real(plus_plus_real(X1),X1)
| X1 != zero_zero_real ),
inference(split_conjunct,[status(thm)],[c_0_1986]) ).
cnf(c_0_2983,plain,
( hAPP_nat_nat(power_power_nat(X1),X2) = one_one_nat
| X1 != one_one_nat ),
inference(split_conjunct,[status(thm)],[c_0_1976]) ).
cnf(c_0_2984,plain,
( hAPP_nat_nat(power_power_nat(X1),X2) = one_one_nat
| X2 != zero_zero_nat ),
inference(split_conjunct,[status(thm)],[c_0_1976]) ).
cnf(c_0_2985,plain,
( hAPP_real_real(plus_plus_real(X1),X1) = zero_zero_real
| X1 != zero_zero_real ),
inference(split_conjunct,[status(thm)],[c_0_1990]) ).
cnf(c_0_2986,plain,
( hAPP_int_int(plus_plus_int(X1),X1) = zero_zero_int
| X1 != zero_zero_int ),
inference(split_conjunct,[status(thm)],[c_0_1991]) ).
cnf(c_0_2987,plain,
succ(X1) = hAPP_int_int(plus_plus_int(X1),one_one_int),
inference(split_conjunct,[status(thm)],[c_0_2011]) ).
cnf(c_0_2988,plain,
( X1 = zero_zero_nat
| hAPP_nat_int(semiri1621563631at_int,X1) != zero_zero_int ),
inference(split_conjunct,[status(thm)],[c_0_2012]) ).
cnf(c_0_2989,plain,
succ(bit1(X1)) = bit0(succ(X1)),
inference(split_conjunct,[status(thm)],[c_0_2013]) ).
cnf(c_0_2990,plain,
( hAPP_nat_real(power_power_real(zero_zero_real),X1) = one_one_real
| X1 != zero_zero_nat ),
inference(split_conjunct,[status(thm)],[c_0_2014]) ).
cnf(c_0_2991,plain,
( hAPP_nat_nat(power_power_nat(zero_zero_nat),X1) = one_one_nat
| X1 != zero_zero_nat ),
inference(split_conjunct,[status(thm)],[c_0_2015]) ).
cnf(c_0_2992,plain,
( hAPP_nat_int(power_power_int(zero_zero_int),X1) = one_one_int
| X1 != zero_zero_nat ),
inference(split_conjunct,[status(thm)],[c_0_2016]) ).
cnf(c_0_2993,plain,
hAPP_nat_int(power_power_int(X1),one_one_nat) = X1,
inference(split_conjunct,[status(thm)],[c_0_2017]) ).
cnf(c_0_2994,plain,
hAPP_nat_nat(power_power_nat(X1),one_one_nat) = X1,
inference(split_conjunct,[status(thm)],[c_0_2018]) ).
cnf(c_0_2995,plain,
hAPP_nat_real(power_power_real(X1),one_one_nat) = X1,
inference(split_conjunct,[status(thm)],[c_0_2019]) ).
cnf(c_0_2996,plain,
hAPP_int_int(plus_plus_int(X1),zero_zero_int) = X1,
inference(split_conjunct,[status(thm)],[c_0_2020]) ).
cnf(c_0_2997,plain,
hAPP_nat_nat(plus_plus_nat(X1),zero_zero_nat) = X1,
inference(split_conjunct,[status(thm)],[c_0_2021]) ).
cnf(c_0_2998,plain,
hAPP_real_real(plus_plus_real(X1),zero_zero_real) = X1,
inference(split_conjunct,[status(thm)],[c_0_2022]) ).
cnf(c_0_2999,plain,
hAPP_int_int(plus_plus_int(X1),zero_zero_int) = X1,
inference(split_conjunct,[status(thm)],[c_0_2023]) ).
cnf(c_0_3000,plain,
hAPP_nat_nat(plus_plus_nat(X1),zero_zero_nat) = X1,
inference(split_conjunct,[status(thm)],[c_0_2024]) ).
cnf(c_0_3001,plain,
hAPP_real_real(plus_plus_real(X1),zero_zero_real) = X1,
inference(split_conjunct,[status(thm)],[c_0_2025]) ).
cnf(c_0_3002,plain,
hAPP_int_int(plus_plus_int(X1),zero_zero_int) = X1,
inference(split_conjunct,[status(thm)],[c_0_2026]) ).
cnf(c_0_3003,plain,
hAPP_nat_nat(plus_plus_nat(X1),zero_zero_nat) = X1,
inference(split_conjunct,[status(thm)],[c_0_2027]) ).
cnf(c_0_3004,plain,
hAPP_real_real(plus_plus_real(X1),zero_zero_real) = X1,
inference(split_conjunct,[status(thm)],[c_0_2028]) ).
cnf(c_0_3005,plain,
hAPP_nat_int(power_power_int(X1),one_one_nat) = X1,
inference(split_conjunct,[status(thm)],[c_0_2029]) ).
cnf(c_0_3006,plain,
hAPP_nat_nat(power_power_nat(X1),one_one_nat) = X1,
inference(split_conjunct,[status(thm)],[c_0_2030]) ).
cnf(c_0_3007,plain,
hAPP_nat_real(power_power_real(X1),one_one_nat) = X1,
inference(split_conjunct,[status(thm)],[c_0_2031]) ).
cnf(c_0_3008,plain,
hAPP_nat_nat(plus_plus_nat(X1),zero_zero_nat) = X1,
inference(split_conjunct,[status(thm)],[c_0_2032]) ).
cnf(c_0_3009,plain,
hAPP_int_int(plus_plus_int(X1),zero_zero_int) = X1,
inference(split_conjunct,[status(thm)],[c_0_2033]) ).
cnf(c_0_3010,plain,
hAPP_int_int(plus_plus_int(X1),pls) = X1,
inference(split_conjunct,[status(thm)],[c_0_2034]) ).
cnf(c_0_3011,plain,
hAPP_nat_int(power_power_int(X1),zero_zero_nat) = one_one_int,
inference(split_conjunct,[status(thm)],[c_0_2035]) ).
cnf(c_0_3012,plain,
hAPP_nat_nat(power_power_nat(X1),zero_zero_nat) = one_one_nat,
inference(split_conjunct,[status(thm)],[c_0_2036]) ).
cnf(c_0_3013,plain,
hAPP_nat_real(power_power_real(X1),zero_zero_nat) = one_one_real,
inference(split_conjunct,[status(thm)],[c_0_2037]) ).
cnf(c_0_3014,plain,
hAPP_nat_int(power_power_int(X1),zero_zero_nat) = one_one_int,
inference(split_conjunct,[status(thm)],[c_0_2038]) ).
cnf(c_0_3015,plain,
hAPP_nat_nat(power_power_nat(X1),zero_zero_nat) = one_one_nat,
inference(split_conjunct,[status(thm)],[c_0_2039]) ).
cnf(c_0_3016,plain,
hAPP_nat_real(power_power_real(X1),zero_zero_nat) = one_one_real,
inference(split_conjunct,[status(thm)],[c_0_2040]) ).
cnf(c_0_3017,plain,
( hAPP_nat_real(power_power_real(zero_zero_real),X1) = zero_zero_real
| X1 = zero_zero_nat ),
inference(split_conjunct,[status(thm)],[c_0_2014]) ).
cnf(c_0_3018,plain,
( hAPP_nat_nat(power_power_nat(zero_zero_nat),X1) = zero_zero_nat
| X1 = zero_zero_nat ),
inference(split_conjunct,[status(thm)],[c_0_2015]) ).
cnf(c_0_3019,plain,
( hAPP_nat_int(power_power_int(zero_zero_int),X1) = zero_zero_int
| X1 = zero_zero_nat ),
inference(split_conjunct,[status(thm)],[c_0_2016]) ).
cnf(c_0_3020,plain,
hAPP_int_int(plus_plus_int(zero_zero_int),X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_2041]) ).
cnf(c_0_3021,plain,
hAPP_nat_nat(plus_plus_nat(zero_zero_nat),X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_2042]) ).
cnf(c_0_3022,plain,
hAPP_real_real(plus_plus_real(zero_zero_real),X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_2043]) ).
cnf(c_0_3023,plain,
hAPP_int_int(plus_plus_int(zero_zero_int),X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_2044]) ).
cnf(c_0_3024,plain,
hAPP_nat_nat(plus_plus_nat(zero_zero_nat),X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_2045]) ).
cnf(c_0_3025,plain,
hAPP_real_real(plus_plus_real(zero_zero_real),X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_2046]) ).
cnf(c_0_3026,plain,
hAPP_int_int(plus_plus_int(zero_zero_int),X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_2047]) ).
cnf(c_0_3027,plain,
hAPP_nat_nat(plus_plus_nat(zero_zero_nat),X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_2048]) ).
cnf(c_0_3028,plain,
hAPP_real_real(plus_plus_real(zero_zero_real),X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_2049]) ).
cnf(c_0_3029,plain,
hAPP_nat_nat(plus_plus_nat(zero_zero_nat),X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_2050]) ).
cnf(c_0_3030,plain,
hAPP_int_int(plus_plus_int(zero_zero_int),X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_2051]) ).
cnf(c_0_3031,plain,
hAPP_int_int(plus_plus_int(pls),X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_2052]) ).
cnf(c_0_3032,plain,
hAPP_nat_int(power_power_int(one_one_int),X1) = one_one_int,
inference(split_conjunct,[status(thm)],[c_0_2053]) ).
cnf(c_0_3033,plain,
hAPP_nat_nat(power_power_nat(one_one_nat),X1) = one_one_nat,
inference(split_conjunct,[status(thm)],[c_0_2054]) ).
cnf(c_0_3034,plain,
hAPP_nat_real(power_power_real(one_one_real),X1) = one_one_real,
inference(split_conjunct,[status(thm)],[c_0_2055]) ).
cnf(c_0_3035,plain,
( X1 = X2
| bit0(X1) != bit0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_2056]) ).
cnf(c_0_3036,plain,
( X1 = X2
| bit1(X1) != bit1(X2) ),
inference(split_conjunct,[status(thm)],[c_0_2057]) ).
cnf(c_0_3037,plain,
( X1 = X2
| number267125858f_real(X1) != number267125858f_real(X2) ),
inference(split_conjunct,[status(thm)],[c_0_2058]) ).
cnf(c_0_3038,plain,
( X1 = X2
| number_number_of_int(X1) != number_number_of_int(X2) ),
inference(split_conjunct,[status(thm)],[c_0_2059]) ).
cnf(c_0_3039,plain,
( hAPP_nat_int(semiri1621563631at_int,X1) = zero_zero_int
| X1 != zero_zero_nat ),
inference(split_conjunct,[status(thm)],[c_0_2012]) ).
cnf(c_0_3040,plain,
succ(bit0(X1)) = bit1(X1),
inference(split_conjunct,[status(thm)],[c_0_2060]) ).
cnf(c_0_3041,plain,
( X1 = number267125858f_real(X2)
| number267125858f_real(X2) != X1 ),
inference(split_conjunct,[status(thm)],[c_0_2061]) ).
cnf(c_0_3042,plain,
( number267125858f_real(X1) = X2
| X2 != number267125858f_real(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2061]) ).
cnf(c_0_3043,plain,
( X1 = number_number_of_int(X2)
| number_number_of_int(X2) != X1 ),
inference(split_conjunct,[status(thm)],[c_0_2062]) ).
cnf(c_0_3044,plain,
( number_number_of_int(X1) = X2
| X2 != number_number_of_int(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2062]) ).
cnf(c_0_3045,plain,
( X1 = number_number_of_nat(X2)
| number_number_of_nat(X2) != X1 ),
inference(split_conjunct,[status(thm)],[c_0_2063]) ).
cnf(c_0_3046,plain,
( number_number_of_nat(X1) = X2
| X2 != number_number_of_nat(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2063]) ).
cnf(c_0_3047,plain,
bit0(X1) != bit1(X2),
inference(split_conjunct,[status(thm)],[c_0_2064]) ).
cnf(c_0_3048,plain,
bit1(X1) != bit0(X2),
inference(split_conjunct,[status(thm)],[c_0_2065]) ).
cnf(c_0_3049,plain,
( bit0(X1) = bit0(X2)
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[c_0_2056]) ).
cnf(c_0_3050,plain,
( bit1(X1) = bit1(X2)
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[c_0_2057]) ).
cnf(c_0_3051,plain,
( number267125858f_real(X1) = number267125858f_real(X2)
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[c_0_2058]) ).
cnf(c_0_3052,plain,
( number_number_of_int(X1) = number_number_of_int(X2)
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[c_0_2059]) ).
cnf(c_0_3053,plain,
zero_zero_int = hAPP_nat_int(semiri1621563631at_int,zero_zero_nat),
inference(split_conjunct,[status(thm)],[c_0_2066]) ).
cnf(c_0_3054,plain,
hAPP_nat_int(semiri1621563631at_int,zero_zero_nat) = zero_zero_int,
inference(split_conjunct,[status(thm)],[c_0_2067]) ).
cnf(c_0_3055,plain,
hAPP_nat_nat(semiri984289939at_nat,zero_zero_nat) = zero_zero_nat,
inference(split_conjunct,[status(thm)],[c_0_2068]) ).
cnf(c_0_3056,plain,
hAPP_nat_real(semiri132038758t_real,zero_zero_nat) = zero_zero_real,
inference(split_conjunct,[status(thm)],[c_0_2069]) ).
cnf(c_0_3057,plain,
one_one_int = hAPP_nat_int(semiri1621563631at_int,one_one_nat),
inference(split_conjunct,[status(thm)],[c_0_2070]) ).
cnf(c_0_3058,plain,
hAPP_nat_int(semiri1621563631at_int,one_one_nat) = one_one_int,
inference(split_conjunct,[status(thm)],[c_0_2071]) ).
cnf(c_0_3059,plain,
hAPP_nat_nat(semiri984289939at_nat,one_one_nat) = one_one_nat,
inference(split_conjunct,[status(thm)],[c_0_2072]) ).
cnf(c_0_3060,plain,
hAPP_nat_real(semiri132038758t_real,one_one_nat) = one_one_real,
inference(split_conjunct,[status(thm)],[c_0_2073]) ).
cnf(c_0_3061,plain,
hAPP_nat_int(semiri1621563631at_int,zero_zero_nat) = zero_zero_int,
inference(split_conjunct,[status(thm)],[c_0_2074]) ).
cnf(c_0_3062,plain,
hAPP_nat_int(semiri1621563631at_int,one_one_nat) = one_one_int,
inference(split_conjunct,[status(thm)],[c_0_2075]) ).
cnf(c_0_3063,plain,
( X1 = fFalse
| X1 = fTrue
| ~ is_bool(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2076]) ).
cnf(c_0_3064,plain,
( pls = X1
| pls != bit0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2077]) ).
cnf(c_0_3065,plain,
( X1 = pls
| bit0(X1) != pls ),
inference(split_conjunct,[status(thm)],[c_0_2078]) ).
cnf(c_0_3066,plain,
number267125858f_real(bit1(pls)) = one_one_real,
inference(split_conjunct,[status(thm)],[c_0_2079]) ).
cnf(c_0_3067,plain,
number_number_of_nat(bit1(pls)) = one_one_nat,
inference(split_conjunct,[status(thm)],[c_0_2080]) ).
cnf(c_0_3068,plain,
number_number_of_int(bit1(pls)) = one_one_int,
inference(split_conjunct,[status(thm)],[c_0_2081]) ).
cnf(c_0_3069,plain,
one_one_nat = number_number_of_nat(bit1(pls)),
inference(split_conjunct,[status(thm)],[c_0_2082]) ).
cnf(c_0_3070,plain,
number_number_of_nat(bit1(pls)) = one_one_nat,
inference(split_conjunct,[status(thm)],[c_0_2083]) ).
cnf(c_0_3071,plain,
one_one_int = number_number_of_int(bit1(pls)),
inference(split_conjunct,[status(thm)],[c_0_2084]) ).
cnf(c_0_3072,plain,
number267125858f_real(bit1(pls)) = one_one_real,
inference(split_conjunct,[status(thm)],[c_0_2085]) ).
cnf(c_0_3073,plain,
number_number_of_int(bit1(pls)) = one_one_int,
inference(split_conjunct,[status(thm)],[c_0_2086]) ).
cnf(c_0_3074,plain,
one_one_real = number267125858f_real(bit1(pls)),
inference(split_conjunct,[status(thm)],[c_0_2087]) ).
cnf(c_0_3075,plain,
one_one_int = number_number_of_int(bit1(pls)),
inference(split_conjunct,[status(thm)],[c_0_2088]) ).
cnf(c_0_3076,plain,
pls != bit1(X1),
inference(split_conjunct,[status(thm)],[c_0_2089]) ).
cnf(c_0_3077,plain,
bit1(X1) != pls,
inference(split_conjunct,[status(thm)],[c_0_2090]) ).
cnf(c_0_3078,plain,
( pls = bit0(X1)
| pls != X1 ),
inference(split_conjunct,[status(thm)],[c_0_2077]) ).
cnf(c_0_3079,plain,
( bit0(X1) = pls
| X1 != pls ),
inference(split_conjunct,[status(thm)],[c_0_2078]) ).
cnf(c_0_3080,plain,
succ(pls) = bit1(pls),
inference(split_conjunct,[status(thm)],[c_0_2091]) ).
cnf(c_0_3081,plain,
number_number_of_int(X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_2092]) ).
cnf(c_0_3082,plain,
( X1 = one_one_int
| one_one_int != X1 ),
inference(split_conjunct,[status(thm)],[c_0_2093]) ).
cnf(c_0_3083,plain,
( one_one_int = X1
| X1 != one_one_int ),
inference(split_conjunct,[status(thm)],[c_0_2093]) ).
cnf(c_0_3084,plain,
( X1 = one_one_nat
| one_one_nat != X1 ),
inference(split_conjunct,[status(thm)],[c_0_2094]) ).
cnf(c_0_3085,plain,
( one_one_nat = X1
| X1 != one_one_nat ),
inference(split_conjunct,[status(thm)],[c_0_2094]) ).
cnf(c_0_3086,plain,
( X1 = one_one_real
| one_one_real != X1 ),
inference(split_conjunct,[status(thm)],[c_0_2095]) ).
cnf(c_0_3087,plain,
( one_one_real = X1
| X1 != one_one_real ),
inference(split_conjunct,[status(thm)],[c_0_2095]) ).
cnf(c_0_3088,plain,
( X1 = zero_zero_int
| zero_zero_int != X1 ),
inference(split_conjunct,[status(thm)],[c_0_2096]) ).
cnf(c_0_3089,plain,
( zero_zero_int = X1
| X1 != zero_zero_int ),
inference(split_conjunct,[status(thm)],[c_0_2096]) ).
cnf(c_0_3090,plain,
( X1 = zero_zero_nat
| zero_zero_nat != X1 ),
inference(split_conjunct,[status(thm)],[c_0_2097]) ).
cnf(c_0_3091,plain,
( zero_zero_nat = X1
| X1 != zero_zero_nat ),
inference(split_conjunct,[status(thm)],[c_0_2097]) ).
cnf(c_0_3092,plain,
( X1 = zero_zero_real
| zero_zero_real != X1 ),
inference(split_conjunct,[status(thm)],[c_0_2098]) ).
cnf(c_0_3093,plain,
( zero_zero_real = X1
| X1 != zero_zero_real ),
inference(split_conjunct,[status(thm)],[c_0_2098]) ).
cnf(c_0_3094,plain,
zero_zero_real = number267125858f_real(pls),
inference(split_conjunct,[status(thm)],[c_0_2099]) ).
cnf(c_0_3095,plain,
zero_zero_int = number_number_of_int(pls),
inference(split_conjunct,[status(thm)],[c_0_2100]) ).
cnf(c_0_3096,plain,
number267125858f_real(pls) = zero_zero_real,
inference(split_conjunct,[status(thm)],[c_0_2101]) ).
cnf(c_0_3097,plain,
number_number_of_int(pls) = zero_zero_int,
inference(split_conjunct,[status(thm)],[c_0_2102]) ).
cnf(c_0_3098,plain,
number267125858f_real(pls) = zero_zero_real,
inference(split_conjunct,[status(thm)],[c_0_2103]) ).
cnf(c_0_3099,plain,
number_number_of_nat(pls) = zero_zero_nat,
inference(split_conjunct,[status(thm)],[c_0_2104]) ).
cnf(c_0_3100,plain,
number_number_of_int(pls) = zero_zero_int,
inference(split_conjunct,[status(thm)],[c_0_2105]) ).
cnf(c_0_3101,plain,
bit0(pls) = pls,
inference(split_conjunct,[status(thm)],[c_0_2106]) ).
cnf(c_0_3102,plain,
zero_zero_nat = number_number_of_nat(pls),
inference(split_conjunct,[status(thm)],[c_0_2107]) ).
cnf(c_0_3103,plain,
number_number_of_nat(pls) = zero_zero_nat,
inference(split_conjunct,[status(thm)],[c_0_2108]) ).
cnf(c_0_3104,plain,
zero_zero_int = number_number_of_int(pls),
inference(split_conjunct,[status(thm)],[c_0_2109]) ).
cnf(c_0_3105,plain,
is_bool(fTrue),
inference(split_conjunct,[status(thm)],[c_0_2110]) ).
cnf(c_0_3106,plain,
is_bool(fFalse),
inference(split_conjunct,[status(thm)],[c_0_2111]) ).
cnf(c_0_3107,plain,
zero_zero_int != one_one_int,
inference(split_conjunct,[status(thm)],[c_0_2112]) ).
cnf(c_0_3108,plain,
zero_zero_nat != one_one_nat,
inference(split_conjunct,[status(thm)],[c_0_2113]) ).
cnf(c_0_3109,plain,
zero_zero_real != one_one_real,
inference(split_conjunct,[status(thm)],[c_0_2114]) ).
cnf(c_0_3110,plain,
one_one_int != zero_zero_int,
inference(split_conjunct,[status(thm)],[c_0_2115]) ).
cnf(c_0_3111,plain,
one_one_nat != zero_zero_nat,
inference(split_conjunct,[status(thm)],[c_0_2116]) ).
cnf(c_0_3112,plain,
one_one_real != zero_zero_real,
inference(split_conjunct,[status(thm)],[c_0_2117]) ).
cnf(c_0_3113,plain,
zero_zero_real != one_one_real,
inference(split_conjunct,[status(thm)],[c_0_2118]) ).
cnf(c_0_3114,plain,
zero_zero_int != one_one_int,
inference(split_conjunct,[status(thm)],[c_0_2119]) ).
cnf(c_0_3115,plain,
pls = zero_zero_int,
inference(split_conjunct,[status(thm)],[c_0_2120]) ).
cnf(c_0_3116,plain,
( X1 = zero_zero_int
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(X1),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_int(power_power_int(X2),number_number_of_nat(bit0(bit1(pls)))))),zero_zero_int)) ),
c_0_2121,
[final] ).
cnf(c_0_3117,plain,
( X2 = zero_zero_int
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(X1),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_int(power_power_int(X2),number_number_of_nat(bit0(bit1(pls)))))),zero_zero_int)) ),
c_0_2122,
[final] ).
cnf(c_0_3118,plain,
( X1 = zero_zero_real
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(plus_plus_real(hAPP_nat_real(power_power_real(X1),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_real(power_power_real(X2),number_number_of_nat(bit0(bit1(pls)))))),zero_zero_real)) ),
c_0_2123,
[final] ).
cnf(c_0_3119,plain,
( X2 = zero_zero_real
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(plus_plus_real(hAPP_nat_real(power_power_real(X1),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_real(power_power_real(X2),number_number_of_nat(bit0(bit1(pls)))))),zero_zero_real)) ),
c_0_2124,
[final] ).
cnf(c_0_3120,plain,
~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(plus_plus_real(hAPP_nat_real(power_power_real(X1),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_real(power_power_real(X2),number_number_of_nat(bit0(bit1(pls)))))),zero_zero_real)),
c_0_2125,
[final] ).
cnf(c_0_3121,plain,
~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(X1),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_int(power_power_int(X2),number_number_of_nat(bit0(bit1(pls)))))),zero_zero_int)),
c_0_2126,
[final] ).
cnf(c_0_3122,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(X1,X2)),X3)),hAPP_nat_nat(X1,hAPP_nat_nat(plus_plus_nat(X2),X3))))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(X1,esk16_3(X2,X3,X1))),hAPP_nat_nat(X1,esk17_3(X2,X3,X1)))) ),
c_0_2127,
[final] ).
cnf(c_0_3123,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(X1,X2)),hAPP_nat_nat(X1,X3)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X3))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(X1,esk20_3(X2,X3,X1))),hAPP_nat_nat(X1,esk21_3(X2,X3,X1)))) ),
c_0_2128,
[final] ).
cnf(c_0_3124,plain,
hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),sqrt(hAPP_real_real(plus_plus_real(hAPP_nat_real(power_power_real(X1),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_real(power_power_real(X2),number_number_of_nat(bit0(bit1(pls)))))))),
c_0_2129,
[final] ).
cnf(c_0_3125,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(X1),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_int(power_power_int(X2),number_number_of_nat(bit0(bit1(pls)))))),zero_zero_int))
| X2 != zero_zero_int
| X1 != zero_zero_int ),
c_0_2130,
[final] ).
cnf(c_0_3126,plain,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(plus_plus_real(hAPP_nat_real(power_power_real(X1),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_real(power_power_real(X2),number_number_of_nat(bit0(bit1(pls)))))),zero_zero_real))
| X2 != zero_zero_real
| X1 != zero_zero_real ),
c_0_2131,
[final] ).
cnf(c_0_3127,plain,
( X1 != zero_zero_real
| X2 != zero_zero_real
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),hAPP_real_real(plus_plus_real(hAPP_nat_real(power_power_real(X2),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_real(power_power_real(X1),number_number_of_nat(bit0(bit1(pls))))))) ),
c_0_2132,
[final] ).
cnf(c_0_3128,plain,
( X1 != zero_zero_int
| X2 != zero_zero_int
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(X2),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_int(power_power_int(X1),number_number_of_nat(bit0(bit1(pls))))))) ),
c_0_2133,
[final] ).
cnf(c_0_3129,plain,
hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(X1),number_number_of_nat(bit0(bit1(pls))))),times_times_int(times_times_int(number_number_of_int(bit0(bit1(pls))),X1),X2))),hAPP_nat_int(power_power_int(X2),number_number_of_nat(bit0(bit1(pls))))) = hAPP_nat_int(power_power_int(hAPP_int_int(plus_plus_int(X1),X2)),number_number_of_nat(bit0(bit1(pls)))),
c_0_2134,
[final] ).
cnf(c_0_3130,plain,
( hBOOL(hAPP_int_bool(X3,X2))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X2))
| ~ hBOOL(hAPP_int_bool(X3,hAPP_int_int(plus_plus_int(X1),one_one_int)))
| ~ hBOOL(hAPP_int_bool(X3,hAPP_int_int(plus_plus_int(esk1_3(X3,X1,X2)),one_one_int))) ),
c_0_2135,
[final] ).
cnf(c_0_3131,plain,
( hBOOL(hAPP_int_bool(X3,X2))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2))
| ~ hBOOL(hAPP_int_bool(X3,X1))
| ~ hBOOL(hAPP_int_bool(X3,hAPP_int_int(plus_plus_int(esk18_3(X3,X1,X2)),one_one_int))) ),
c_0_2136,
[final] ).
cnf(c_0_3132,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(X1,X2)),X3)),hAPP_nat_nat(X1,hAPP_nat_nat(plus_plus_nat(X2),X3))))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,esk16_3(X2,X3,X1)),esk17_3(X2,X3,X1))) ),
c_0_2137,
[final] ).
cnf(c_0_3133,plain,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),hAPP_real_real(plus_plus_real(hAPP_nat_real(power_power_real(X1),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_real(power_power_real(X2),number_number_of_nat(bit0(bit1(pls)))))))
| X1 = zero_zero_real ),
c_0_2138,
[final] ).
cnf(c_0_3134,plain,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),hAPP_real_real(plus_plus_real(hAPP_nat_real(power_power_real(X1),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_real(power_power_real(X2),number_number_of_nat(bit0(bit1(pls)))))))
| X2 = zero_zero_real ),
c_0_2139,
[final] ).
cnf(c_0_3135,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(X1),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_int(power_power_int(X2),number_number_of_nat(bit0(bit1(pls)))))))
| X1 = zero_zero_int ),
c_0_2140,
[final] ).
cnf(c_0_3136,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(X1),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_int(power_power_int(X2),number_number_of_nat(bit0(bit1(pls)))))))
| X2 = zero_zero_int ),
c_0_2141,
[final] ).
cnf(c_0_3137,plain,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(X1),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_int(power_power_int(X2),number_number_of_nat(bit0(bit1(pls))))))),
c_0_2142,
[final] ).
cnf(c_0_3138,plain,
hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),hAPP_real_real(plus_plus_real(hAPP_nat_real(power_power_real(X1),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_real(power_power_real(X2),number_number_of_nat(bit0(bit1(pls))))))),
c_0_2143,
[final] ).
cnf(c_0_3139,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X2))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X2))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_nat_int(power_power_int(X1),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_int(power_power_int(X2),number_number_of_nat(bit0(bit1(pls)))))) ),
c_0_2144,
[final] ).
cnf(c_0_3140,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(power_power_nat(X1),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_nat(power_power_nat(X2),number_number_of_nat(bit0(bit1(pls)))))) ),
c_0_2145,
[final] ).
cnf(c_0_3141,plain,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X1),X2))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X2))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_nat_real(power_power_real(X1),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_real(power_power_real(X2),number_number_of_nat(bit0(bit1(pls)))))) ),
c_0_2146,
[final] ).
cnf(c_0_3142,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X2))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_nat_int(power_power_int(X1),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_int(power_power_int(X2),number_number_of_nat(bit0(bit1(pls)))))) ),
c_0_2147,
[final] ).
cnf(c_0_3143,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(power_power_nat(X1),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_nat(power_power_nat(X2),number_number_of_nat(bit0(bit1(pls)))))) ),
c_0_2148,
[final] ).
cnf(c_0_3144,plain,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X1),X2))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X2))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_nat_real(power_power_real(X1),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_real(power_power_real(X2),number_number_of_nat(bit0(bit1(pls)))))) ),
c_0_2149,
[final] ).
cnf(c_0_3145,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),zero_zero_int))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),X1)),X1)),zero_zero_int)) ),
c_0_2150,
[final] ).
cnf(c_0_3146,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(X1,X2)),hAPP_nat_nat(X1,X3)))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,esk20_3(X2,X3,X1)),esk21_3(X2,X3,X1)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X3)) ),
c_0_2151,
[final] ).
cnf(c_0_3147,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),X1)),X1)),zero_zero_int))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),zero_zero_int)) ),
c_0_2152,
[final] ).
cnf(c_0_3148,plain,
~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_nat_real(power_power_real(X1),number_number_of_nat(bit0(bit1(pls))))),zero_zero_real)),
c_0_2153,
[final] ).
cnf(c_0_3149,plain,
~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_nat_int(power_power_int(X1),number_number_of_nat(bit0(bit1(pls))))),zero_zero_int)),
c_0_2154,
[final] ).
cnf(c_0_3150,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X2))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X2))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_nat_int(power_power_int(X1),X3)),hAPP_nat_int(power_power_int(X2),X3))) ),
c_0_2155,
[final] ).
cnf(c_0_3151,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(power_power_nat(X1),X3)),hAPP_nat_nat(power_power_nat(X2),X3))) ),
c_0_2156,
[final] ).
cnf(c_0_3152,plain,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X1),X2))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X2))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_nat_real(power_power_real(X1),X3)),hAPP_nat_real(power_power_real(X2),X3))) ),
c_0_2157,
[final] ).
cnf(c_0_3153,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_nat_int(power_power_int(X3),X1)),hAPP_nat_int(power_power_int(X3),X2)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),X3)) ),
c_0_2158,
[final] ).
cnf(c_0_3154,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(power_power_nat(X3),X1)),hAPP_nat_nat(power_power_nat(X3),X2)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,one_one_nat),X3)) ),
c_0_2159,
[final] ).
cnf(c_0_3155,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_nat_real(power_power_real(X3),X1)),hAPP_nat_real(power_power_real(X3),X2)))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,one_one_real),X3)) ),
c_0_2160,
[final] ).
cnf(c_0_3156,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X3))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),X1))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_nat_int(power_power_int(X1),X2)),hAPP_nat_int(power_power_int(X1),X3))) ),
c_0_2161,
[final] ).
cnf(c_0_3157,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X3))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,one_one_nat),X1))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(power_power_nat(X1),X2)),hAPP_nat_nat(power_power_nat(X1),X3))) ),
c_0_2162,
[final] ).
cnf(c_0_3158,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X3))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,one_one_real),X1))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_nat_real(power_power_real(X1),X2)),hAPP_nat_real(power_power_real(X1),X3))) ),
c_0_2163,
[final] ).
cnf(c_0_3159,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_nat_int(power_power_int(X3),X1)),hAPP_nat_int(power_power_int(X3),X2)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),X3)) ),
c_0_2164,
[final] ).
cnf(c_0_3160,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(power_power_nat(X3),X1)),hAPP_nat_nat(power_power_nat(X3),X2)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,one_one_nat),X3)) ),
c_0_2165,
[final] ).
cnf(c_0_3161,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_nat_real(power_power_real(X3),X1)),hAPP_nat_real(power_power_real(X3),X2)))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,one_one_real),X3)) ),
c_0_2166,
[final] ).
cnf(c_0_3162,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X2),X3))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),X1))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_nat_int(power_power_int(X1),X2)),hAPP_nat_int(power_power_int(X1),X3))) ),
c_0_2167,
[final] ).
cnf(c_0_3163,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X2),X3))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,one_one_nat),X1))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(power_power_nat(X1),X2)),hAPP_nat_nat(power_power_nat(X1),X3))) ),
c_0_2168,
[final] ).
cnf(c_0_3164,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X2),X3))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,one_one_real),X1))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_nat_real(power_power_real(X1),X2)),hAPP_nat_real(power_power_real(X1),X3))) ),
c_0_2169,
[final] ).
cnf(c_0_3165,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(power_power_nat(X3),X1)),hAPP_nat_nat(power_power_nat(X3),X2)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X3)) ),
c_0_2170,
[final] ).
cnf(c_0_3166,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_nat_int(power_power_int(X1),X2)),hAPP_nat_int(power_power_int(X1),X3)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),one_one_int))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X3),X2)) ),
c_0_2171,
[final] ).
cnf(c_0_3167,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(power_power_nat(X1),X2)),hAPP_nat_nat(power_power_nat(X1),X3)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),one_one_nat))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),X1))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X3),X2)) ),
c_0_2172,
[final] ).
cnf(c_0_3168,plain,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_nat_real(power_power_real(X1),X2)),hAPP_nat_real(power_power_real(X1),X3)))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X1),one_one_real))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X1))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X3),X2)) ),
c_0_2173,
[final] ).
cnf(c_0_3169,plain,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_nat_real(power_power_real(X1),X2)),hAPP_nat_real(power_power_real(X1),X3)))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X1),one_one_real))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X1))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X3),X2)) ),
c_0_2174,
[final] ).
cnf(c_0_3170,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(power_power_nat(X1),X2)),hAPP_nat_nat(power_power_nat(X1),X3)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),one_one_nat))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X3),X2)) ),
c_0_2175,
[final] ).
cnf(c_0_3171,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_nat_int(power_power_int(X1),X2)),hAPP_nat_int(power_power_int(X1),X3)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),one_one_int))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X1))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X3),X2)) ),
c_0_2176,
[final] ).
cnf(c_0_3172,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_nat_int(power_power_int(X1),X2)),hAPP_nat_int(power_power_int(X3),X2)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X2))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X3)) ),
c_0_2177,
[final] ).
cnf(c_0_3173,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(power_power_nat(X1),X2)),hAPP_nat_nat(power_power_nat(X3),X2)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),X1))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X3)) ),
c_0_2178,
[final] ).
cnf(c_0_3174,plain,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_nat_real(power_power_real(X1),X2)),hAPP_nat_real(power_power_real(X3),X2)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X2))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X1))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X1),X3)) ),
c_0_2179,
[final] ).
cnf(c_0_3175,plain,
( hBOOL(hAPP_int_bool(X3,X2))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),esk1_3(X3,X1,X2)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X2))
| ~ hBOOL(hAPP_int_bool(X3,hAPP_int_int(plus_plus_int(X1),one_one_int))) ),
c_0_2180,
[final] ).
cnf(c_0_3176,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(X3),X1)),hAPP_nat_nat(plus_plus_nat(X3),X2))) ),
c_0_2181,
[final] ).
cnf(c_0_3177,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(plus_plus_int(X3),X1)),hAPP_int_int(plus_plus_int(X3),X2))) ),
c_0_2182,
[final] ).
cnf(c_0_3178,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(X3),X1)),hAPP_nat_nat(plus_plus_nat(X3),X2))) ),
c_0_2183,
[final] ).
cnf(c_0_3179,plain,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X1),X2))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(plus_plus_real(X3),X1)),hAPP_real_real(plus_plus_real(X3),X2))) ),
c_0_2184,
[final] ).
cnf(c_0_3180,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(plus_plus_int(X1),X3)),hAPP_int_int(plus_plus_int(X2),X3))) ),
c_0_2185,
[final] ).
cnf(c_0_3181,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(X1),X3)),hAPP_nat_nat(plus_plus_nat(X2),X3))) ),
c_0_2186,
[final] ).
cnf(c_0_3182,plain,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X1),X2))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(plus_plus_real(X1),X3)),hAPP_real_real(plus_plus_real(X2),X3))) ),
c_0_2187,
[final] ).
cnf(c_0_3183,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(plus_plus_int(X3),X1)),hAPP_int_int(plus_plus_int(X3),X2))) ),
c_0_2188,
[final] ).
cnf(c_0_3184,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(X3),X1)),hAPP_nat_nat(plus_plus_nat(X3),X2))) ),
c_0_2189,
[final] ).
cnf(c_0_3185,plain,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X1),X2))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(plus_plus_real(X3),X1)),hAPP_real_real(plus_plus_real(X3),X2))) ),
c_0_2190,
[final] ).
cnf(c_0_3186,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(plus_plus_int(X1),X3)),hAPP_int_int(plus_plus_int(X2),X3))) ),
c_0_2191,
[final] ).
cnf(c_0_3187,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(X1),X3)),hAPP_nat_nat(plus_plus_nat(X2),X3))) ),
c_0_2192,
[final] ).
cnf(c_0_3188,plain,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X1),X2))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(plus_plus_real(X1),X3)),hAPP_real_real(plus_plus_real(X2),X3))) ),
c_0_2193,
[final] ).
cnf(c_0_3189,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X2))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(X1),X3)),hAPP_int_int(plus_plus_int(X2),X3))) ),
c_0_2194,
[final] ).
cnf(c_0_3190,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(X1),X3)),hAPP_nat_nat(plus_plus_nat(X2),X3))) ),
c_0_2195,
[final] ).
cnf(c_0_3191,plain,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X1),X2))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(plus_plus_real(X1),X3)),hAPP_real_real(plus_plus_real(X2),X3))) ),
c_0_2196,
[final] ).
cnf(c_0_3192,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X2))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(X3),X1)),hAPP_int_int(plus_plus_int(X3),X2))) ),
c_0_2197,
[final] ).
cnf(c_0_3193,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(X3),X1)),hAPP_nat_nat(plus_plus_nat(X3),X2))) ),
c_0_2198,
[final] ).
cnf(c_0_3194,plain,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X1),X2))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(plus_plus_real(X3),X1)),hAPP_real_real(plus_plus_real(X3),X2))) ),
c_0_2199,
[final] ).
cnf(c_0_3195,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X2))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(X1),X3)),hAPP_int_int(plus_plus_int(X2),X3))) ),
c_0_2200,
[final] ).
cnf(c_0_3196,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(X1),X3)),hAPP_nat_nat(plus_plus_nat(X2),X3))) ),
c_0_2201,
[final] ).
cnf(c_0_3197,plain,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X1),X2))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(plus_plus_real(X1),X3)),hAPP_real_real(plus_plus_real(X2),X3))) ),
c_0_2202,
[final] ).
cnf(c_0_3198,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X2))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(X3),X1)),hAPP_int_int(plus_plus_int(X3),X2))) ),
c_0_2203,
[final] ).
cnf(c_0_3199,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(X3),X1)),hAPP_nat_nat(plus_plus_nat(X3),X2))) ),
c_0_2204,
[final] ).
cnf(c_0_3200,plain,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X1),X2))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(plus_plus_real(X3),X1)),hAPP_real_real(plus_plus_real(X3),X2))) ),
c_0_2205,
[final] ).
cnf(c_0_3201,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(X3),X1)),hAPP_nat_nat(plus_plus_nat(X3),X2))) ),
c_0_2206,
[final] ).
cnf(c_0_3202,plain,
( hBOOL(hAPP_int_bool(X3,X2))
| hBOOL(hAPP_int_bool(X3,esk1_3(X3,X1,X2)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X2))
| ~ hBOOL(hAPP_int_bool(X3,hAPP_int_int(plus_plus_int(X1),one_one_int))) ),
c_0_2207,
[final] ).
cnf(c_0_3203,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(X1),X2)),hAPP_nat_nat(plus_plus_nat(X3),X4)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X4))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X3)) ),
c_0_2208,
[final] ).
cnf(c_0_3204,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(X1),X2)),hAPP_int_int(plus_plus_int(X3),X4)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X2),X4))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X3)) ),
c_0_2209,
[final] ).
cnf(c_0_3205,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(X1),X2)),hAPP_int_int(plus_plus_int(X3),X4)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X2),X4))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X3)) ),
c_0_2210,
[final] ).
cnf(c_0_3206,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(X1),X2)),hAPP_nat_nat(plus_plus_nat(X3),X4)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X2),X4))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X3)) ),
c_0_2211,
[final] ).
cnf(c_0_3207,plain,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(plus_plus_real(X1),X2)),hAPP_real_real(plus_plus_real(X3),X4)))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X2),X4))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X1),X3)) ),
c_0_2212,
[final] ).
cnf(c_0_3208,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(X1),X2)),hAPP_int_int(plus_plus_int(X3),X4)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X2),X4))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X3)) ),
c_0_2213,
[final] ).
cnf(c_0_3209,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(X1),X2)),hAPP_nat_nat(plus_plus_nat(X3),X4)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X4))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X3)) ),
c_0_2214,
[final] ).
cnf(c_0_3210,plain,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(plus_plus_real(X1),X2)),hAPP_real_real(plus_plus_real(X3),X4)))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X2),X4))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X1),X3)) ),
c_0_2215,
[final] ).
cnf(c_0_3211,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(plus_plus_int(X1),X2)),hAPP_int_int(plus_plus_int(X3),X4)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X2),X4))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X3)) ),
c_0_2216,
[final] ).
cnf(c_0_3212,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(X1),X2)),hAPP_nat_nat(plus_plus_nat(X3),X4)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X4))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X3)) ),
c_0_2217,
[final] ).
cnf(c_0_3213,plain,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(plus_plus_real(X1),X2)),hAPP_real_real(plus_plus_real(X3),X4)))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X2),X4))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X1),X3)) ),
c_0_2218,
[final] ).
cnf(c_0_3214,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(X1),X2)),hAPP_int_int(plus_plus_int(X3),X4)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X2),X4))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X3)) ),
c_0_2219,
[final] ).
cnf(c_0_3215,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(X1),X2)),hAPP_nat_nat(plus_plus_nat(X3),X4)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X2),X4))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X3)) ),
c_0_2220,
[final] ).
cnf(c_0_3216,plain,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(plus_plus_real(X1),X2)),hAPP_real_real(plus_plus_real(X3),X4)))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X2),X4))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X1),X3)) ),
c_0_2221,
[final] ).
cnf(c_0_3217,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(X1),X2)),hAPP_nat_nat(plus_plus_nat(X3),X4)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X2),X4))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X3)) ),
c_0_2222,
[final] ).
cnf(c_0_3218,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_nat_int(power_power_int(X1),X2)),hAPP_nat_int(power_power_int(X3),X2)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X3)) ),
c_0_2223,
[final] ).
cnf(c_0_3219,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(power_power_nat(X1),X2)),hAPP_nat_nat(power_power_nat(X3),X2)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),X1))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X3)) ),
c_0_2224,
[final] ).
cnf(c_0_3220,plain,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_nat_real(power_power_real(X1),X2)),hAPP_nat_real(power_power_real(X3),X2)))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X1))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X1),X3)) ),
c_0_2225,
[final] ).
cnf(c_0_3221,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_nat_int(power_power_int(X1),X2)),hAPP_nat_int(power_power_int(X1),X3)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),X1))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X3)) ),
c_0_2226,
[final] ).
cnf(c_0_3222,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(power_power_nat(X1),X2)),hAPP_nat_nat(power_power_nat(X1),X3)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,one_one_nat),X1))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X3)) ),
c_0_2227,
[final] ).
cnf(c_0_3223,plain,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_nat_real(power_power_real(X1),X2)),hAPP_nat_real(power_power_real(X1),X3)))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,one_one_real),X1))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X3)) ),
c_0_2228,
[final] ).
cnf(c_0_3224,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_nat_int(power_power_int(X1),X2)),hAPP_nat_int(power_power_int(X1),X3)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),X1))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X3)) ),
c_0_2229,
[final] ).
cnf(c_0_3225,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(power_power_nat(X1),X2)),hAPP_nat_nat(power_power_nat(X1),X3)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,one_one_nat),X1))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X3)) ),
c_0_2230,
[final] ).
cnf(c_0_3226,plain,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_nat_real(power_power_real(X1),X2)),hAPP_nat_real(power_power_real(X1),X3)))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,one_one_real),X1))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X3)) ),
c_0_2231,
[final] ).
cnf(c_0_3227,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_nat_int(power_power_int(X1),X2)),hAPP_nat_int(power_power_int(X1),X3)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),X1))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X2),X3)) ),
c_0_2232,
[final] ).
cnf(c_0_3228,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(power_power_nat(X1),X2)),hAPP_nat_nat(power_power_nat(X1),X3)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,one_one_nat),X1))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X2),X3)) ),
c_0_2233,
[final] ).
cnf(c_0_3229,plain,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_nat_real(power_power_real(X1),X2)),hAPP_nat_real(power_power_real(X1),X3)))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,one_one_real),X1))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X2),X3)) ),
c_0_2234,
[final] ).
cnf(c_0_3230,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_nat_int(power_power_int(X1),X2)),hAPP_nat_int(power_power_int(X1),X3)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),X1))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X2),X3)) ),
c_0_2235,
[final] ).
cnf(c_0_3231,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(power_power_nat(X1),X2)),hAPP_nat_nat(power_power_nat(X1),X3)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,one_one_nat),X1))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X2),X3)) ),
c_0_2236,
[final] ).
cnf(c_0_3232,plain,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_nat_real(power_power_real(X1),X2)),hAPP_nat_real(power_power_real(X1),X3)))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,one_one_real),X1))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X2),X3)) ),
c_0_2237,
[final] ).
cnf(c_0_3233,plain,
( X1 = zero_zero_real
| hAPP_real_real(plus_plus_real(hAPP_nat_real(power_power_real(X1),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_real(power_power_real(X2),number_number_of_nat(bit0(bit1(pls))))) != zero_zero_real ),
c_0_2238,
[final] ).
cnf(c_0_3234,plain,
( X2 = zero_zero_real
| hAPP_real_real(plus_plus_real(hAPP_nat_real(power_power_real(X1),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_real(power_power_real(X2),number_number_of_nat(bit0(bit1(pls))))) != zero_zero_real ),
c_0_2239,
[final] ).
cnf(c_0_3235,plain,
( X1 = zero_zero_real
| hAPP_real_real(plus_plus_real(hAPP_nat_real(power_power_real(X1),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_real(power_power_real(X2),number_number_of_nat(bit0(bit1(pls))))) != zero_zero_real ),
c_0_2240,
[final] ).
cnf(c_0_3236,plain,
( X2 = zero_zero_real
| hAPP_real_real(plus_plus_real(hAPP_nat_real(power_power_real(X1),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_real(power_power_real(X2),number_number_of_nat(bit0(bit1(pls))))) != zero_zero_real ),
c_0_2241,
[final] ).
cnf(c_0_3237,plain,
( X1 = zero_zero_int
| hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(X1),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_int(power_power_int(X2),number_number_of_nat(bit0(bit1(pls))))) != zero_zero_int ),
c_0_2242,
[final] ).
cnf(c_0_3238,plain,
( X2 = zero_zero_int
| hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(X1),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_int(power_power_int(X2),number_number_of_nat(bit0(bit1(pls))))) != zero_zero_int ),
c_0_2243,
[final] ).
cnf(c_0_3239,plain,
( hBOOL(hAPP_int_bool(X3,X2))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),esk18_3(X3,X1,X2)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2))
| ~ hBOOL(hAPP_int_bool(X3,X1)) ),
c_0_2244,
[final] ).
cnf(c_0_3240,plain,
hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_nat_real(semiri132038758t_real,X1)),hAPP_nat_real(power_power_real(number267125858f_real(bit0(bit1(pls)))),X1))),
c_0_2245,
[final] ).
cnf(c_0_3241,plain,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_nat_int(semiri1621563631at_int,X1)),hAPP_nat_int(power_power_int(number_number_of_int(bit0(bit1(pls)))),X1))),
c_0_2246,
[final] ).
cnf(c_0_3242,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(X1,X2),X3))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(X1,X2),X3))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(X1,X2),X3))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(X1,X2),X3)) ),
c_0_2247,
[final] ).
cnf(c_0_3243,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(X1),X2)),zero_zero_int))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X2),zero_zero_int))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),zero_zero_int)) ),
c_0_2248,
[final] ).
cnf(c_0_3244,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(X1),X2)),zero_zero_nat))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X2),zero_zero_nat))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),zero_zero_nat)) ),
c_0_2249,
[final] ).
cnf(c_0_3245,plain,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(plus_plus_real(X1),X2)),zero_zero_real))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X2),zero_zero_real))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X1),zero_zero_real)) ),
c_0_2250,
[final] ).
cnf(c_0_3246,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(X1),X2)),zero_zero_int))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X2),zero_zero_int))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),zero_zero_int)) ),
c_0_2251,
[final] ).
cnf(c_0_3247,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(X1),X2)),zero_zero_nat))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),zero_zero_nat))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),zero_zero_nat)) ),
c_0_2252,
[final] ).
cnf(c_0_3248,plain,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(plus_plus_real(X1),X2)),zero_zero_real))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X2),zero_zero_real))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X1),zero_zero_real)) ),
c_0_2253,
[final] ).
cnf(c_0_3249,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(plus_plus_int(X1),X2)),zero_zero_int))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X2),zero_zero_int))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),zero_zero_int)) ),
c_0_2254,
[final] ).
cnf(c_0_3250,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(X1),X2)),zero_zero_nat))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),zero_zero_nat))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),zero_zero_nat)) ),
c_0_2255,
[final] ).
cnf(c_0_3251,plain,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(plus_plus_real(X1),X2)),zero_zero_real))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X2),zero_zero_real))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X1),zero_zero_real)) ),
c_0_2256,
[final] ).
cnf(c_0_3252,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(X1),X2)),zero_zero_int))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X2),zero_zero_int))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),zero_zero_int)) ),
c_0_2257,
[final] ).
cnf(c_0_3253,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(X1),X2)),zero_zero_nat))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X2),zero_zero_nat))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),zero_zero_nat)) ),
c_0_2258,
[final] ).
cnf(c_0_3254,plain,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(plus_plus_real(X1),X2)),zero_zero_real))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X2),zero_zero_real))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X1),zero_zero_real)) ),
c_0_2259,
[final] ).
cnf(c_0_3255,plain,
( hBOOL(hAPP_int_bool(X3,X2))
| hBOOL(hAPP_int_bool(X3,esk18_3(X3,X1,X2)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2))
| ~ hBOOL(hAPP_int_bool(X3,X1)) ),
c_0_2260,
[final] ).
cnf(c_0_3256,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X3))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(X1),X2)),X3)) ),
c_0_2261,
[final] ).
cnf(c_0_3257,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X3))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(X1),X2)),X3)) ),
c_0_2262,
[final] ).
cnf(c_0_3258,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(X1),X3)),X2)) ),
c_0_2263,
[final] ).
cnf(c_0_3259,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(X3),X1)),X2)) ),
c_0_2264,
[final] ).
cnf(c_0_3260,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(X1),X3)),X2)) ),
c_0_2265,
[final] ).
cnf(c_0_3261,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),zero_zero_int))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(plus_plus_int(X1),X1)),zero_zero_int)) ),
c_0_2266,
[final] ).
cnf(c_0_3262,plain,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X1),zero_zero_real))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(plus_plus_real(X1),X1)),zero_zero_real)) ),
c_0_2267,
[final] ).
cnf(c_0_3263,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),zero_zero_int))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(X1),X1)),zero_zero_int)) ),
c_0_2268,
[final] ).
cnf(c_0_3264,plain,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X1),zero_zero_real))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(plus_plus_real(X1),X1)),zero_zero_real)) ),
c_0_2269,
[final] ).
cnf(c_0_3265,plain,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X1),zero_zero_real))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(plus_plus_real(X1),X1)),zero_zero_real)) ),
c_0_2270,
[final] ).
cnf(c_0_3266,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),zero_zero_int))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(X1),X1)),zero_zero_int)) ),
c_0_2271,
[final] ).
cnf(c_0_3267,plain,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(plus_plus_real(X1),X2)),hAPP_real_real(plus_plus_real(X1),X3)))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X2),X3)) ),
c_0_2272,
[final] ).
cnf(c_0_3268,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(X1),X2)),hAPP_nat_nat(plus_plus_nat(X3),X2)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X3)) ),
c_0_2273,
[final] ).
cnf(c_0_3269,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(X1),X2)),hAPP_nat_nat(plus_plus_nat(X1),X3)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X3)) ),
c_0_2274,
[final] ).
cnf(c_0_3270,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(plus_plus_int(X1),X2)),hAPP_int_int(plus_plus_int(X1),X3)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X2),X3)) ),
c_0_2275,
[final] ).
cnf(c_0_3271,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(plus_plus_int(X1),X2)),hAPP_int_int(plus_plus_int(X1),X3)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X2),X3)) ),
c_0_2276,
[final] ).
cnf(c_0_3272,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(X1),X2)),hAPP_nat_nat(plus_plus_nat(X1),X3)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X3)) ),
c_0_2277,
[final] ).
cnf(c_0_3273,plain,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(plus_plus_real(X1),X2)),hAPP_real_real(plus_plus_real(X1),X3)))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X2),X3)) ),
c_0_2278,
[final] ).
cnf(c_0_3274,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(plus_plus_int(X1),X2)),hAPP_int_int(plus_plus_int(X3),X2)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X3)) ),
c_0_2279,
[final] ).
cnf(c_0_3275,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(X1),X2)),hAPP_nat_nat(plus_plus_nat(X3),X2)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X3)) ),
c_0_2280,
[final] ).
cnf(c_0_3276,plain,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(plus_plus_real(X1),X2)),hAPP_real_real(plus_plus_real(X3),X2)))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X1),X3)) ),
c_0_2281,
[final] ).
cnf(c_0_3277,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(plus_plus_int(X1),X2)),hAPP_int_int(plus_plus_int(X1),X3)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X2),X3)) ),
c_0_2282,
[final] ).
cnf(c_0_3278,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(X1),X2)),hAPP_nat_nat(plus_plus_nat(X1),X3)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X3)) ),
c_0_2283,
[final] ).
cnf(c_0_3279,plain,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(plus_plus_real(X1),X2)),hAPP_real_real(plus_plus_real(X1),X3)))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X2),X3)) ),
c_0_2284,
[final] ).
cnf(c_0_3280,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(plus_plus_int(X1),X2)),hAPP_int_int(plus_plus_int(X3),X2)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X3)) ),
c_0_2285,
[final] ).
cnf(c_0_3281,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(X1),X2)),hAPP_nat_nat(plus_plus_nat(X3),X2)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X3)) ),
c_0_2286,
[final] ).
cnf(c_0_3282,plain,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(plus_plus_real(X1),X2)),hAPP_real_real(plus_plus_real(X3),X2)))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X1),X3)) ),
c_0_2287,
[final] ).
cnf(c_0_3283,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(X1),X2)),hAPP_int_int(plus_plus_int(X3),X2)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X3)) ),
c_0_2288,
[final] ).
cnf(c_0_3284,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(X1),X2)),hAPP_nat_nat(plus_plus_nat(X3),X2)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X3)) ),
c_0_2289,
[final] ).
cnf(c_0_3285,plain,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(plus_plus_real(X1),X2)),hAPP_real_real(plus_plus_real(X3),X2)))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X1),X3)) ),
c_0_2290,
[final] ).
cnf(c_0_3286,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(X1),X2)),hAPP_int_int(plus_plus_int(X1),X3)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X2),X3)) ),
c_0_2291,
[final] ).
cnf(c_0_3287,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(X1),X2)),hAPP_nat_nat(plus_plus_nat(X1),X3)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X2),X3)) ),
c_0_2292,
[final] ).
cnf(c_0_3288,plain,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(plus_plus_real(X1),X2)),hAPP_real_real(plus_plus_real(X1),X3)))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X2),X3)) ),
c_0_2293,
[final] ).
cnf(c_0_3289,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(X1),X2)),hAPP_int_int(plus_plus_int(X3),X2)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X3)) ),
c_0_2294,
[final] ).
cnf(c_0_3290,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(X1),X2)),hAPP_nat_nat(plus_plus_nat(X3),X2)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X3)) ),
c_0_2295,
[final] ).
cnf(c_0_3291,plain,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(plus_plus_real(X1),X2)),hAPP_real_real(plus_plus_real(X3),X2)))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X1),X3)) ),
c_0_2296,
[final] ).
cnf(c_0_3292,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(X1),X2)),hAPP_int_int(plus_plus_int(X1),X3)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X2),X3)) ),
c_0_2297,
[final] ).
cnf(c_0_3293,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(X1),X2)),hAPP_nat_nat(plus_plus_nat(X1),X3)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X2),X3)) ),
c_0_2298,
[final] ).
cnf(c_0_3294,plain,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(plus_plus_real(X1),X2)),hAPP_real_real(plus_plus_real(X1),X3)))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X2),X3)) ),
c_0_2299,
[final] ).
cnf(c_0_3295,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(X1),X2)),hAPP_nat_nat(plus_plus_nat(X3),X2)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X3)) ),
c_0_2300,
[final] ).
cnf(c_0_3296,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(X1),X2)),hAPP_nat_nat(plus_plus_nat(X1),X3)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X2),X3)) ),
c_0_2301,
[final] ).
cnf(c_0_3297,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(X1),X2)),hAPP_int_int(plus_plus_int(X3),X2)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X3)) ),
c_0_2302,
[final] ).
cnf(c_0_3298,plain,
( X1 != zero_zero_real
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),hAPP_nat_real(power_power_real(X1),number_number_of_nat(bit0(bit1(pls)))))) ),
c_0_2303,
[final] ).
cnf(c_0_3299,plain,
( X1 != zero_zero_int
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_nat_int(power_power_int(X1),number_number_of_nat(bit0(bit1(pls)))))) ),
c_0_2304,
[final] ).
cnf(c_0_3300,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(X3,X2),X1))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(X3,X2),X1))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(X3,X2),X1)) ),
c_0_2305,
[final] ).
cnf(c_0_3301,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(X1,X2),X3))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X2),X3))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(X1,X2),X3))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(X1,X2),X3)) ),
c_0_2306,
[final] ).
cnf(c_0_3302,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X2))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(plus_plus_int(X1),one_one_int)),X2)) ),
c_0_2307,
[final] ).
cnf(c_0_3303,plain,
hAPP_int_int(plus_plus_int(hAPP_nat_int(semiri1621563631at_int,X1)),hAPP_int_int(plus_plus_int(hAPP_nat_int(semiri1621563631at_int,X2)),X3)) = hAPP_int_int(plus_plus_int(hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(plus_plus_nat(X1),X2))),X3),
c_0_2308,
[final] ).
cnf(c_0_3304,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_nat_int(semiri1621563631at_int,X1)),hAPP_nat_int(semiri1621563631at_int,X2))) ),
c_0_2309,
[final] ).
cnf(c_0_3305,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_nat_int(semiri1621563631at_int,X1)),hAPP_nat_int(semiri1621563631at_int,X2))) ),
c_0_2310,
[final] ).
cnf(c_0_3306,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_nat_int(semiri1621563631at_int,X1)),hAPP_nat_int(semiri1621563631at_int,X2))) ),
c_0_2311,
[final] ).
cnf(c_0_3307,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(semiri984289939at_nat,X1)),hAPP_nat_nat(semiri984289939at_nat,X2))) ),
c_0_2312,
[final] ).
cnf(c_0_3308,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_nat_real(semiri132038758t_real,X1)),hAPP_nat_real(semiri132038758t_real,X2))) ),
c_0_2313,
[final] ).
cnf(c_0_3309,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_nat_int(semiri1621563631at_int,X1)),hAPP_nat_int(semiri1621563631at_int,X2))) ),
c_0_2314,
[final] ).
cnf(c_0_3310,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(semiri984289939at_nat,X1)),hAPP_nat_nat(semiri984289939at_nat,X2))) ),
c_0_2315,
[final] ).
cnf(c_0_3311,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_nat_real(semiri132038758t_real,X1)),hAPP_nat_real(semiri132038758t_real,X2))) ),
c_0_2316,
[final] ).
cnf(c_0_3312,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_nat_int(semiri1621563631at_int,X1)),hAPP_nat_int(semiri1621563631at_int,X2))) ),
c_0_2317,
[final] ).
cnf(c_0_3313,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(semiri984289939at_nat,X1)),hAPP_nat_nat(semiri984289939at_nat,X2))) ),
c_0_2318,
[final] ).
cnf(c_0_3314,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_nat_real(semiri132038758t_real,X1)),hAPP_nat_real(semiri132038758t_real,X2))) ),
c_0_2319,
[final] ).
cnf(c_0_3315,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_nat_int(semiri1621563631at_int,X1)),hAPP_nat_int(semiri1621563631at_int,X2))) ),
c_0_2320,
[final] ).
cnf(c_0_3316,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_nat_int(semiri1621563631at_int,X1)),hAPP_nat_int(semiri1621563631at_int,X2))) ),
c_0_2321,
[final] ).
cnf(c_0_3317,plain,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,esk22_2(X2,X1)),X1))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X1))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X2)) ),
c_0_2322,
[final] ).
cnf(c_0_3318,plain,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,esk22_2(X2,X1)),X2))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X1))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X2)) ),
c_0_2323,
[final] ).
cnf(c_0_3319,plain,
( X1 = X2
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X3))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X2))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1))
| hAPP_nat_int(power_power_int(X1),X3) != hAPP_nat_int(power_power_int(X2),X3) ),
c_0_2324,
[final] ).
cnf(c_0_3320,plain,
( X1 = X2
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X3))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),X1))
| hAPP_nat_nat(power_power_nat(X1),X3) != hAPP_nat_nat(power_power_nat(X2),X3) ),
c_0_2325,
[final] ).
cnf(c_0_3321,plain,
( X1 = X2
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X3))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X2))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X1))
| hAPP_nat_real(power_power_real(X1),X3) != hAPP_nat_real(power_power_real(X2),X3) ),
c_0_2326,
[final] ).
cnf(c_0_3322,plain,
hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,one_one_real),hAPP_nat_real(power_power_real(number267125858f_real(bit0(bit1(pls)))),X1))),
c_0_2327,
[final] ).
cnf(c_0_3323,plain,
( hBOOL(hAPP_nat_bool(X1,zero_zero_nat))
| hBOOL(hAPP_nat_bool(X1,hAPP_nat_nat(plus_plus_nat(esk14_2(X2,X1)),one_one_nat)))
| ~ hBOOL(hAPP_nat_bool(X1,X2)) ),
c_0_2328,
[final] ).
cnf(c_0_3324,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),hAPP_int_int(plus_plus_int(X2),X3)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X3))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X2)) ),
c_0_2329,
[final] ).
cnf(c_0_3325,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),hAPP_nat_nat(plus_plus_nat(X2),X3)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X3))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),X2)) ),
c_0_2330,
[final] ).
cnf(c_0_3326,plain,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X1),hAPP_real_real(plus_plus_real(X2),X3)))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X1),X3))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X2)) ),
c_0_2331,
[final] ).
cnf(c_0_3327,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),hAPP_int_int(plus_plus_int(X2),X3)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X3))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X2)) ),
c_0_2332,
[final] ).
cnf(c_0_3328,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),hAPP_nat_nat(plus_plus_nat(X2),X3)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X3))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X2)) ),
c_0_2333,
[final] ).
cnf(c_0_3329,plain,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X1),hAPP_real_real(plus_plus_real(X2),X3)))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X1),X3))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X2)) ),
c_0_2334,
[final] ).
cnf(c_0_3330,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),hAPP_int_int(plus_plus_int(X2),X3)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X3)) ),
c_0_2335,
[final] ).
cnf(c_0_3331,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),hAPP_nat_nat(plus_plus_nat(X2),X3)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),X3)) ),
c_0_2336,
[final] ).
cnf(c_0_3332,plain,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X1),hAPP_real_real(plus_plus_real(X2),X3)))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X1),X2))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X3)) ),
c_0_2337,
[final] ).
cnf(c_0_3333,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),hAPP_int_int(plus_plus_int(X2),X3)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X3))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X2)) ),
c_0_2338,
[final] ).
cnf(c_0_3334,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),hAPP_nat_nat(plus_plus_nat(X2),X3)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X3))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),X2)) ),
c_0_2339,
[final] ).
cnf(c_0_3335,plain,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X1),hAPP_real_real(plus_plus_real(X2),X3)))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X1),X3))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X2)) ),
c_0_2340,
[final] ).
cnf(c_0_3336,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),hAPP_int_int(plus_plus_int(X2),X3)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X3))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X2)) ),
c_0_2341,
[final] ).
cnf(c_0_3337,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),hAPP_nat_nat(plus_plus_nat(X2),X3)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X3))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X2)) ),
c_0_2342,
[final] ).
cnf(c_0_3338,plain,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X1),hAPP_real_real(plus_plus_real(X2),X3)))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X1),X3))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X2)) ),
c_0_2343,
[final] ).
cnf(c_0_3339,plain,
( X1 = X2
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X2))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1))
| hAPP_nat_int(power_power_int(X1),number_number_of_nat(bit0(bit1(pls)))) != hAPP_nat_int(power_power_int(X2),number_number_of_nat(bit0(bit1(pls)))) ),
c_0_2344,
[final] ).
cnf(c_0_3340,plain,
( X1 = X2
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),X1))
| hAPP_nat_nat(power_power_nat(X1),number_number_of_nat(bit0(bit1(pls)))) != hAPP_nat_nat(power_power_nat(X2),number_number_of_nat(bit0(bit1(pls)))) ),
c_0_2345,
[final] ).
cnf(c_0_3341,plain,
( X1 = X2
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X2))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X1))
| hAPP_nat_real(power_power_real(X1),number_number_of_nat(bit0(bit1(pls)))) != hAPP_nat_real(power_power_real(X2),number_number_of_nat(bit0(bit1(pls)))) ),
c_0_2346,
[final] ).
cnf(c_0_3342,plain,
( X3 = esk4_2(X2,X1)
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X2))
| hAPP_nat_real(power_power_real(X3),X1) != X2
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X3)) ),
c_0_2347,
[final] ).
cnf(c_0_3343,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(plus_plus_nat(X2),X1))) ),
c_0_2348,
[final] ).
cnf(c_0_3344,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,number_number_of_nat(X1)),number_number_of_nat(X2)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X2)) ),
c_0_2349,
[final] ).
cnf(c_0_3345,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_int_int(plus_plus_int(X1),X2)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X2))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1)) ),
c_0_2350,
[final] ).
cnf(c_0_3346,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(plus_plus_nat(X1),X2)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),X1)) ),
c_0_2351,
[final] ).
cnf(c_0_3347,plain,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),hAPP_real_real(plus_plus_real(X1),X2)))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X2))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X1)) ),
c_0_2352,
[final] ).
cnf(c_0_3348,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_int_int(plus_plus_int(X1),X2)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X2))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X1)) ),
c_0_2353,
[final] ).
cnf(c_0_3349,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(plus_plus_nat(X1),X2)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1)) ),
c_0_2354,
[final] ).
cnf(c_0_3350,plain,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),hAPP_real_real(plus_plus_real(X1),X2)))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X2))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X1)) ),
c_0_2355,
[final] ).
cnf(c_0_3351,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_int_int(plus_plus_int(X1),X2)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X2))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1)) ),
c_0_2356,
[final] ).
cnf(c_0_3352,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_int_int(plus_plus_int(X1),X2)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X2))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1)) ),
c_0_2357,
[final] ).
cnf(c_0_3353,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),hAPP_nat_nat(plus_plus_nat(X1),X2)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),X1)) ),
c_0_2358,
[final] ).
cnf(c_0_3354,plain,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),hAPP_real_real(plus_plus_real(X1),X2)))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X2))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X1)) ),
c_0_2359,
[final] ).
cnf(c_0_3355,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_int_int(plus_plus_int(X1),X2)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X2))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X1)) ),
c_0_2360,
[final] ).
cnf(c_0_3356,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(plus_plus_nat(X1),X2)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1)) ),
c_0_2361,
[final] ).
cnf(c_0_3357,plain,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),hAPP_real_real(plus_plus_real(X1),X2)))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X2))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X1)) ),
c_0_2362,
[final] ).
cnf(c_0_3358,plain,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,one_one_real),hAPP_nat_real(power_power_real(X1),X2)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X2))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,one_one_real),X1)) ),
c_0_2363,
[final] ).
cnf(c_0_3359,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,one_one_nat),hAPP_nat_nat(power_power_nat(X1),X2)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,one_one_nat),X1)) ),
c_0_2364,
[final] ).
cnf(c_0_3360,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),hAPP_nat_int(power_power_int(X1),X2)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X2))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),X1)) ),
c_0_2365,
[final] ).
cnf(c_0_3361,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(X3,X2),X1))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X2),X1))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(X3,X2),X1)) ),
c_0_2366,
[final] ).
cnf(c_0_3362,plain,
~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(X1),X2)),X2)),
c_0_2367,
[final] ).
cnf(c_0_3363,plain,
~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(X1),X2)),X1)),
c_0_2368,
[final] ).
cnf(c_0_3364,plain,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(X1)),number_number_of_int(X2)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,number_number_of_int(X2)),number_number_of_int(X1))) ),
c_0_2369,
[final] ).
cnf(c_0_3365,plain,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,number_number_of_nat(X1)),number_number_of_nat(X2)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,number_number_of_nat(X2)),number_number_of_nat(X1))) ),
c_0_2370,
[final] ).
cnf(c_0_3366,plain,
( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,number267125858f_real(X1)),number267125858f_real(X2)))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,number267125858f_real(X2)),number267125858f_real(X1))) ),
c_0_2371,
[final] ).
cnf(c_0_3367,plain,
( X3 = X2
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(X1,X2),X3))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(X1,X2),X3))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(X1,X2),X3)) ),
c_0_2372,
[final] ).
cnf(c_0_3368,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1))
| number_number_of_nat(X2) = zero_zero_nat
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(power_power_nat(X1),number_number_of_nat(X2)))) ),
c_0_2373,
[final] ).
cnf(c_0_3369,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,number_number_of_nat(X1)),number_number_of_nat(X2)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X2))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),X2)) ),
c_0_2374,
[final] ).
cnf(c_0_3370,plain,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),esk22_2(X2,X1)))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X1))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X2)) ),
c_0_2375,
[final] ).
cnf(c_0_3371,plain,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),esk5_2(X2,X1)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X2)) ),
c_0_2376,
[final] ).
cnf(c_0_3372,plain,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),esk4_2(X2,X1)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X2)) ),
c_0_2377,
[final] ).
cnf(c_0_3373,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(plus_plus_int(X1),X1)),zero_zero_int))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),zero_zero_int)) ),
c_0_2378,
[final] ).
cnf(c_0_3374,plain,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(plus_plus_real(X1),X1)),zero_zero_real))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X1),zero_zero_real)) ),
c_0_2379,
[final] ).
cnf(c_0_3375,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(X1),X1)),zero_zero_int))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),zero_zero_int)) ),
c_0_2380,
[final] ).
cnf(c_0_3376,plain,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(plus_plus_real(X1),X1)),zero_zero_real))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X1),zero_zero_real)) ),
c_0_2381,
[final] ).
cnf(c_0_3377,plain,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(plus_plus_real(X1),X1)),zero_zero_real))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X1),zero_zero_real)) ),
c_0_2382,
[final] ).
cnf(c_0_3378,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(X1),X1)),zero_zero_int))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),zero_zero_int)) ),
c_0_2383,
[final] ).
cnf(c_0_3379,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(plus_plus_int(X1),one_one_int)),X2))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X2)) ),
c_0_2384,
[final] ).
cnf(c_0_3380,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(plus_plus_int(X1),one_one_int)),X2))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X2)) ),
c_0_2385,
[final] ).
cnf(c_0_3381,plain,
hAPP_nat_int(power_power_int(hAPP_nat_int(power_power_int(X1),number_number_of_nat(bit0(bit1(pls))))),number_number_of_nat(bit0(bit1(pls)))) = hAPP_nat_int(power_power_int(X1),number_number_of_nat(bit0(bit0(bit1(pls))))),
c_0_2386,
[final] ).
cnf(c_0_3382,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_nat_int(semiri1621563631at_int,X1)),hAPP_nat_int(semiri1621563631at_int,X2)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2)) ),
c_0_2387,
[final] ).
cnf(c_0_3383,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_nat_int(semiri1621563631at_int,X1)),hAPP_nat_int(semiri1621563631at_int,X2)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2)) ),
c_0_2388,
[final] ).
cnf(c_0_3384,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_nat_int(semiri1621563631at_int,X1)),hAPP_nat_int(semiri1621563631at_int,X2)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2)) ),
c_0_2389,
[final] ).
cnf(c_0_3385,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(semiri984289939at_nat,X1)),hAPP_nat_nat(semiri984289939at_nat,X2)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2)) ),
c_0_2390,
[final] ).
cnf(c_0_3386,plain,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_nat_real(semiri132038758t_real,X1)),hAPP_nat_real(semiri132038758t_real,X2)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2)) ),
c_0_2391,
[final] ).
cnf(c_0_3387,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_nat_int(semiri1621563631at_int,X1)),hAPP_nat_int(semiri1621563631at_int,X2)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2)) ),
c_0_2392,
[final] ).
cnf(c_0_3388,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(semiri984289939at_nat,X1)),hAPP_nat_nat(semiri984289939at_nat,X2)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2)) ),
c_0_2393,
[final] ).
cnf(c_0_3389,plain,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_nat_real(semiri132038758t_real,X1)),hAPP_nat_real(semiri132038758t_real,X2)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2)) ),
c_0_2394,
[final] ).
cnf(c_0_3390,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_nat_int(semiri1621563631at_int,X1)),hAPP_nat_int(semiri1621563631at_int,X2)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2)) ),
c_0_2395,
[final] ).
cnf(c_0_3391,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(semiri984289939at_nat,X1)),hAPP_nat_nat(semiri984289939at_nat,X2)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2)) ),
c_0_2396,
[final] ).
cnf(c_0_3392,plain,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_nat_real(semiri132038758t_real,X1)),hAPP_nat_real(semiri132038758t_real,X2)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2)) ),
c_0_2397,
[final] ).
cnf(c_0_3393,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_nat_int(semiri1621563631at_int,X1)),hAPP_nat_int(semiri1621563631at_int,X2)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2)) ),
c_0_2398,
[final] ).
cnf(c_0_3394,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_nat_int(semiri1621563631at_int,X1)),hAPP_nat_int(semiri1621563631at_int,X2)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2)) ),
c_0_2399,
[final] ).
cnf(c_0_3395,plain,
( X1 = one_one_int
| X1 = zero_zero_int
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),number_number_of_int(bit0(bit1(pls)))))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1)) ),
c_0_2400,
[final] ).
cnf(c_0_3396,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),pls))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,number_number_of_nat(X1)),number_number_of_nat(X2))) ),
c_0_2401,
[final] ).
cnf(c_0_3397,plain,
( hBOOL(hAPP_nat_bool(X1,zero_zero_nat))
| ~ hBOOL(hAPP_nat_bool(X1,X2))
| ~ hBOOL(hAPP_nat_bool(X1,X3))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X3),esk19_2(X2,X1))) ),
c_0_2402,
[final] ).
cnf(c_0_3398,plain,
( hBOOL(hAPP_nat_bool(X1,zero_zero_nat))
| ~ hBOOL(hAPP_nat_bool(X1,X2))
| ~ hBOOL(hAPP_nat_bool(X1,X3))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X3),esk14_2(X2,X1))) ),
c_0_2403,
[final] ).
cnf(c_0_3399,plain,
( hAPP_real_real(plus_plus_real(hAPP_nat_real(power_power_real(X1),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_real(power_power_real(X2),number_number_of_nat(bit0(bit1(pls))))) = zero_zero_real
| X2 != zero_zero_real
| X1 != zero_zero_real ),
c_0_2404,
[final] ).
cnf(c_0_3400,plain,
( hAPP_real_real(plus_plus_real(hAPP_nat_real(power_power_real(X1),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_real(power_power_real(X2),number_number_of_nat(bit0(bit1(pls))))) = zero_zero_real
| X2 != zero_zero_real
| X1 != zero_zero_real ),
c_0_2405,
[final] ).
cnf(c_0_3401,plain,
( hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(X1),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_int(power_power_int(X2),number_number_of_nat(bit0(bit1(pls))))) = zero_zero_int
| X2 != zero_zero_int
| X1 != zero_zero_int ),
c_0_2406,
[final] ).
cnf(c_0_3402,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X3),X2))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X3)) ),
c_0_2407,
[final] ).
cnf(c_0_3403,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X3),X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X3)) ),
c_0_2408,
[final] ).
cnf(c_0_3404,plain,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X1),X2))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X3),X2))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X1),X3)) ),
c_0_2409,
[final] ).
cnf(c_0_3405,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X3))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X3),X2)) ),
c_0_2410,
[final] ).
cnf(c_0_3406,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X3))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X3),X2)) ),
c_0_2411,
[final] ).
cnf(c_0_3407,plain,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X1),X2))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X1),X3))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X3),X2)) ),
c_0_2412,
[final] ).
cnf(c_0_3408,plain,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X1),X2))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X3),X2))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X1),X3)) ),
c_0_2413,
[final] ).
cnf(c_0_3409,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X3),X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X3)) ),
c_0_2414,
[final] ).
cnf(c_0_3410,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X3),X2))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X3)) ),
c_0_2415,
[final] ).
cnf(c_0_3411,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,number_number_of_nat(X1)),number_number_of_nat(X2)))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X2))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X2)) ),
c_0_2416,
[final] ).
cnf(c_0_3412,plain,
( X1 = X2
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X2))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),hAPP_int_int(plus_plus_int(X2),one_one_int))) ),
c_0_2417,
[final] ).
cnf(c_0_3413,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),hAPP_int_int(plus_plus_int(X2),one_one_int))) ),
c_0_2418,
[final] ).
cnf(c_0_3414,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1))
| X2 = zero_zero_nat
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(power_power_nat(X1),X2))) ),
c_0_2419,
[final] ).
cnf(c_0_3415,plain,
( X1 = zero_zero_nat
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(power_power_nat(X2),X1))) ),
c_0_2420,
[final] ).
cnf(c_0_3416,plain,
( hAPP_int_int(plus_plus_int(number_number_of_int(X1)),number_number_of_int(X2)) = number_number_of_int(hAPP_int_int(plus_plus_int(X1),X2))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X2))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X1)) ),
c_0_2421,
[final] ).
cnf(c_0_3417,plain,
( hAPP_nat_nat(plus_plus_nat(number_number_of_nat(X1)),number_number_of_nat(X2)) = number_number_of_nat(hAPP_int_int(plus_plus_int(X1),X2))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X2))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X1)) ),
c_0_2422,
[final] ).
cnf(c_0_3418,plain,
( hAPP_real_real(plus_plus_real(number267125858f_real(X1)),number267125858f_real(X2)) = number267125858f_real(hAPP_int_int(plus_plus_int(X1),X2))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X2))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X1)) ),
c_0_2423,
[final] ).
cnf(c_0_3419,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_int_int(plus_plus_int(X1),X1))) ),
c_0_2424,
[final] ).
cnf(c_0_3420,plain,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X1))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),hAPP_real_real(plus_plus_real(X1),X1))) ),
c_0_2425,
[final] ).
cnf(c_0_3421,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X1))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_int_int(plus_plus_int(X1),X1))) ),
c_0_2426,
[final] ).
cnf(c_0_3422,plain,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X1))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),hAPP_real_real(plus_plus_real(X1),X1))) ),
c_0_2427,
[final] ).
cnf(c_0_3423,plain,
( hBOOL(hAPP_int_bool(X1,X2))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X2))
| ~ hBOOL(hAPP_int_bool(X1,hAPP_nat_int(semiri1621563631at_int,esk9_1(X1)))) ),
c_0_2428,
[final] ).
cnf(c_0_3424,plain,
( hAPP_nat_real(power_power_real(esk5_2(X2,X1)),X1) = X2
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X2)) ),
c_0_2429,
[final] ).
cnf(c_0_3425,plain,
( hAPP_nat_real(power_power_real(esk4_2(X2,X1)),X1) = X2
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X2)) ),
c_0_2430,
[final] ).
cnf(c_0_3426,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
| X1 = X2
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(X3,X2),X1))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(X3,X2),X1)) ),
c_0_2431,
[final] ).
cnf(c_0_3427,plain,
( X3 = X2
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(X1,X2),X3))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X2),X3))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(X1,X2),X3)) ),
c_0_2432,
[final] ).
cnf(c_0_3428,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(power_power_nat(X1),number_number_of_nat(X2))))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1)) ),
c_0_2433,
[final] ).
cnf(c_0_3429,plain,
hAPP_real_real(plus_plus_real(number267125858f_real(X1)),hAPP_real_real(plus_plus_real(number267125858f_real(X2)),X3)) = hAPP_real_real(plus_plus_real(number267125858f_real(hAPP_int_int(plus_plus_int(X1),X2))),X3),
c_0_2434,
[final] ).
cnf(c_0_3430,plain,
hAPP_int_int(plus_plus_int(number_number_of_int(X1)),hAPP_int_int(plus_plus_int(number_number_of_int(X2)),X3)) = hAPP_int_int(plus_plus_int(number_number_of_int(hAPP_int_int(plus_plus_int(X1),X2))),X3),
c_0_2435,
[final] ).
cnf(c_0_3431,plain,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),hAPP_nat_int(power_power_int(X1),number_number_of_nat(bit0(bit1(pls)))))),
c_0_2436,
[final] ).
cnf(c_0_3432,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),hAPP_nat_nat(plus_plus_nat(X2),X3)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X3)) ),
c_0_2437,
[final] ).
cnf(c_0_3433,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),hAPP_nat_nat(plus_plus_nat(X2),X3)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2)) ),
c_0_2438,
[final] ).
cnf(c_0_3434,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),hAPP_nat_nat(plus_plus_nat(X2),X3)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X3)) ),
c_0_2439,
[final] ).
cnf(c_0_3435,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),hAPP_nat_nat(plus_plus_nat(X2),X3)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2)) ),
c_0_2440,
[final] ).
cnf(c_0_3436,plain,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),hAPP_nat_real(power_power_real(X1),number_number_of_nat(bit0(bit1(pls))))))
| X1 = zero_zero_real ),
c_0_2441,
[final] ).
cnf(c_0_3437,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_nat_int(power_power_int(X1),number_number_of_nat(bit0(bit1(pls))))))
| X1 = zero_zero_int ),
c_0_2442,
[final] ).
cnf(c_0_3438,plain,
hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(X1),X2)),hAPP_int_int(plus_plus_int(X3),X4)) = hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(X1),X3)),hAPP_int_int(plus_plus_int(X2),X4)),
c_0_2443,
[final] ).
cnf(c_0_3439,plain,
hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(plus_plus_nat(X1),X2)),hAPP_nat_nat(plus_plus_nat(X3),X4)) = hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(plus_plus_nat(X1),X3)),hAPP_nat_nat(plus_plus_nat(X2),X4)),
c_0_2444,
[final] ).
cnf(c_0_3440,plain,
hAPP_real_real(plus_plus_real(hAPP_real_real(plus_plus_real(X1),X2)),hAPP_real_real(plus_plus_real(X3),X4)) = hAPP_real_real(plus_plus_real(hAPP_real_real(plus_plus_real(X1),X3)),hAPP_real_real(plus_plus_real(X2),X4)),
c_0_2445,
[final] ).
cnf(c_0_3441,plain,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_nat_int(power_power_int(X1),number_number_of_nat(bit0(bit1(pls)))))),
c_0_2446,
[final] ).
cnf(c_0_3442,plain,
hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),hAPP_nat_real(power_power_real(X1),number_number_of_nat(bit0(bit1(pls)))))),
c_0_2447,
[final] ).
cnf(c_0_3443,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),hAPP_int_int(plus_plus_int(X2),one_one_int)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2)) ),
c_0_2448,
[final] ).
cnf(c_0_3444,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),hAPP_int_int(plus_plus_int(X2),one_one_int)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X2)) ),
c_0_2449,
[final] ).
cnf(c_0_3445,plain,
( X1 = zero_zero_nat
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_nat_int(semiri1621563631at_int,X1)),zero_zero_int)) ),
c_0_2450,
[final] ).
cnf(c_0_3446,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
| hAPP_nat_nat(plus_plus_nat(X1),X3) != hAPP_nat_nat(plus_plus_nat(X4),X2)
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X4),X3)) ),
c_0_2451,
[final] ).
cnf(c_0_3447,plain,
( hBOOL(hAPP_int_bool(X1,hAPP_nat_int(semiri1621563631at_int,esk6_1(X1))))
| ~ hBOOL(hAPP_int_bool(X1,X2))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X2)) ),
c_0_2452,
[final] ).
cnf(c_0_3448,plain,
~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_nat_int(semiri1621563631at_int,X1)),zero_zero_int)),
c_0_2453,
[final] ).
cnf(c_0_3449,plain,
~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(semiri984289939at_nat,X1)),zero_zero_nat)),
c_0_2454,
[final] ).
cnf(c_0_3450,plain,
~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_nat_real(semiri132038758t_real,X1)),zero_zero_real)),
c_0_2455,
[final] ).
cnf(c_0_3451,plain,
~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_nat_int(semiri1621563631at_int,X1)),zero_zero_int)),
c_0_2456,
[final] ).
cnf(c_0_3452,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1))
| ~ hBOOL(X2)
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1)) ),
c_0_2457,
[final] ).
cnf(c_0_3453,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1))
| ~ hBOOL(X2)
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1)) ),
c_0_2458,
[final] ).
cnf(c_0_3454,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_nat_int(power_power_int(X1),X2)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1)) ),
c_0_2459,
[final] ).
cnf(c_0_3455,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),hAPP_nat_int(power_power_int(X1),X2)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),X1)) ),
c_0_2460,
[final] ).
cnf(c_0_3456,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,one_one_nat),hAPP_nat_nat(power_power_nat(X1),X2)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,one_one_nat),X1)) ),
c_0_2461,
[final] ).
cnf(c_0_3457,plain,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,one_one_real),hAPP_nat_real(power_power_real(X1),X2)))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,one_one_real),X1)) ),
c_0_2462,
[final] ).
cnf(c_0_3458,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_nat_int(power_power_int(X1),X2)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1)) ),
c_0_2463,
[final] ).
cnf(c_0_3459,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),hAPP_nat_nat(power_power_nat(X1),X2)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),X1)) ),
c_0_2464,
[final] ).
cnf(c_0_3460,plain,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),hAPP_nat_real(power_power_real(X1),X2)))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X1)) ),
c_0_2465,
[final] ).
cnf(c_0_3461,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_int_int(plus_plus_int(X1),X1)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1)) ),
c_0_2466,
[final] ).
cnf(c_0_3462,plain,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),hAPP_real_real(plus_plus_real(X1),X1)))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X1)) ),
c_0_2467,
[final] ).
cnf(c_0_3463,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_int_int(plus_plus_int(X1),X1)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X1)) ),
c_0_2468,
[final] ).
cnf(c_0_3464,plain,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),hAPP_real_real(plus_plus_real(X1),X1)))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X1)) ),
c_0_2469,
[final] ).
cnf(c_0_3465,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_nat_int(power_power_int(X1),X2)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X1)) ),
c_0_2470,
[final] ).
cnf(c_0_3466,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(power_power_nat(X1),X2)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1)) ),
c_0_2471,
[final] ).
cnf(c_0_3467,plain,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),hAPP_nat_real(power_power_real(X1),X2)))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X1)) ),
c_0_2472,
[final] ).
cnf(c_0_3468,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(power_power_nat(X1),X2)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1)) ),
c_0_2473,
[final] ).
cnf(c_0_3469,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(plus_plus_nat(X1),X2)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1)) ),
c_0_2474,
[final] ).
cnf(c_0_3470,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(plus_plus_nat(X1),X2)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X2)) ),
c_0_2475,
[final] ).
cnf(c_0_3471,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(power_power_nat(X1),X2)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1)) ),
c_0_2476,
[final] ).
cnf(c_0_3472,plain,
( hBOOL(hAPP_nat_bool(X1,zero_zero_nat))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,esk19_2(X2,X1)),X2))
| ~ hBOOL(hAPP_nat_bool(X1,X2)) ),
c_0_2477,
[final] ).
cnf(c_0_3473,plain,
( hBOOL(hAPP_nat_bool(X1,zero_zero_nat))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,esk14_2(X2,X1)),X2))
| ~ hBOOL(hAPP_nat_bool(X1,X2)) ),
c_0_2478,
[final] ).
cnf(c_0_3474,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1))
| hBOOL(X2)
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1)) ),
c_0_2479,
[final] ).
cnf(c_0_3475,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1))
| hBOOL(X2)
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1)) ),
c_0_2480,
[final] ).
cnf(c_0_3476,plain,
( X1 = zero_zero_int
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X2))
| hAPP_int_int(plus_plus_int(X1),X2) != zero_zero_int ),
c_0_2481,
[final] ).
cnf(c_0_3477,plain,
( X2 = zero_zero_int
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X2))
| hAPP_int_int(plus_plus_int(X1),X2) != zero_zero_int ),
c_0_2482,
[final] ).
cnf(c_0_3478,plain,
( X1 = zero_zero_nat
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),X1))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),X2))
| hAPP_nat_nat(plus_plus_nat(X1),X2) != zero_zero_nat ),
c_0_2483,
[final] ).
cnf(c_0_3479,plain,
( X2 = zero_zero_nat
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),X1))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),X2))
| hAPP_nat_nat(plus_plus_nat(X1),X2) != zero_zero_nat ),
c_0_2484,
[final] ).
cnf(c_0_3480,plain,
( X1 = zero_zero_real
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X1))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X2))
| hAPP_real_real(plus_plus_real(X1),X2) != zero_zero_real ),
c_0_2485,
[final] ).
cnf(c_0_3481,plain,
( X2 = zero_zero_real
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X1))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X2))
| hAPP_real_real(plus_plus_real(X1),X2) != zero_zero_real ),
c_0_2486,
[final] ).
cnf(c_0_3482,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X2))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,bit1(X1)),bit0(X2))) ),
c_0_2487,
[final] ).
cnf(c_0_3483,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X2))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,bit1(X1)),bit0(X2))) ),
c_0_2488,
[final] ).
cnf(c_0_3484,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit0(X1)),bit1(X2))) ),
c_0_2489,
[final] ).
cnf(c_0_3485,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit0(X1)),bit1(X2))) ),
c_0_2490,
[final] ).
cnf(c_0_3486,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,bit0(X1)),bit1(X2))) ),
c_0_2491,
[final] ).
cnf(c_0_3487,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,bit0(X1)),bit1(X2))) ),
c_0_2492,
[final] ).
cnf(c_0_3488,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,number_number_of_int(X1)),number_number_of_int(X2))) ),
c_0_2493,
[final] ).
cnf(c_0_3489,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,number_number_of_int(X1)),number_number_of_int(X2))) ),
c_0_2494,
[final] ).
cnf(c_0_3490,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,number267125858f_real(X1)),number267125858f_real(X2))) ),
c_0_2495,
[final] ).
cnf(c_0_3491,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,bit0(X1)),bit0(X2))) ),
c_0_2496,
[final] ).
cnf(c_0_3492,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,bit0(X1)),bit0(X2))) ),
c_0_2497,
[final] ).
cnf(c_0_3493,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,bit1(X1)),bit1(X2))) ),
c_0_2498,
[final] ).
cnf(c_0_3494,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,bit1(X1)),bit1(X2))) ),
c_0_2499,
[final] ).
cnf(c_0_3495,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,number_number_of_nat(X1)),number_number_of_nat(X2))) ),
c_0_2500,
[final] ).
cnf(c_0_3496,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X2))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit1(X1)),bit0(X2))) ),
c_0_2501,
[final] ).
cnf(c_0_3497,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X2))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit1(X1)),bit0(X2))) ),
c_0_2502,
[final] ).
cnf(c_0_3498,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X2))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit0(X1)),bit0(X2))) ),
c_0_2503,
[final] ).
cnf(c_0_3499,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X2))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit0(X1)),bit0(X2))) ),
c_0_2504,
[final] ).
cnf(c_0_3500,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X2))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit1(X1)),bit1(X2))) ),
c_0_2505,
[final] ).
cnf(c_0_3501,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X2))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit1(X1)),bit1(X2))) ),
c_0_2506,
[final] ).
cnf(c_0_3502,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X2))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,number267125858f_real(X1)),number267125858f_real(X2))) ),
c_0_2507,
[final] ).
cnf(c_0_3503,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X2))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(X1)),number_number_of_int(X2))) ),
c_0_2508,
[final] ).
cnf(c_0_3504,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X2))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(X1)),number_number_of_int(X2))) ),
c_0_2509,
[final] ).
cnf(c_0_3505,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_nat_int(semiri1621563631at_int,X1))) ),
c_0_2510,
[final] ).
cnf(c_0_3506,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),hAPP_nat_real(semiri132038758t_real,X1))) ),
c_0_2511,
[final] ).
cnf(c_0_3507,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(semiri984289939at_nat,X1))) ),
c_0_2512,
[final] ).
cnf(c_0_3508,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_nat_int(semiri1621563631at_int,X1))) ),
c_0_2513,
[final] ).
cnf(c_0_3509,plain,
( hAPP_int_int(plus_plus_int(X1),X2) = zero_zero_int
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X2))
| X2 != zero_zero_int
| X1 != zero_zero_int ),
c_0_2514,
[final] ).
cnf(c_0_3510,plain,
( hAPP_nat_nat(plus_plus_nat(X1),X2) = zero_zero_nat
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),X1))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),X2))
| X2 != zero_zero_nat
| X1 != zero_zero_nat ),
c_0_2515,
[final] ).
cnf(c_0_3511,plain,
( hAPP_real_real(plus_plus_real(X1),X2) = zero_zero_real
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X1))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X2))
| X2 != zero_zero_real
| X1 != zero_zero_real ),
c_0_2516,
[final] ).
cnf(c_0_3512,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_int_int(plus_plus_int(one_one_int),X1)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1)) ),
c_0_2517,
[final] ).
cnf(c_0_3513,plain,
( X2 = X1
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X2),X1)) ),
c_0_2518,
[final] ).
cnf(c_0_3514,plain,
( X2 = X1
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X1)) ),
c_0_2519,
[final] ).
cnf(c_0_3515,plain,
( X2 = X1
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X1),X2))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X2),X1)) ),
c_0_2520,
[final] ).
cnf(c_0_3516,plain,
( X1 = X2
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X2),X1))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2)) ),
c_0_2521,
[final] ).
cnf(c_0_3517,plain,
( X1 = X2
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X1))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2)) ),
c_0_2522,
[final] ).
cnf(c_0_3518,plain,
( X1 = X2
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X2),X1))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X1),X2)) ),
c_0_2523,
[final] ).
cnf(c_0_3519,plain,
( X1 = X2
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X2),X1)) ),
c_0_2524,
[final] ).
cnf(c_0_3520,plain,
( X1 = X2
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X1)) ),
c_0_2525,
[final] ).
cnf(c_0_3521,plain,
( X1 = X2
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X1),X2))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X2),X1)) ),
c_0_2526,
[final] ).
cnf(c_0_3522,plain,
( X1 = X2
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X2),X1))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X1),X2)) ),
c_0_2527,
[final] ).
cnf(c_0_3523,plain,
( X1 = X2
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X1))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2)) ),
c_0_2528,
[final] ).
cnf(c_0_3524,plain,
( X1 = X2
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X2),X1))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2)) ),
c_0_2529,
[final] ).
cnf(c_0_3525,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),esk3_2(X1,X2)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2)) ),
c_0_2530,
[final] ).
cnf(c_0_3526,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
| X1 = X2
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(X3,X2),X1))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X2),X1)) ),
c_0_2531,
[final] ).
cnf(c_0_3527,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),number_number_of_int(bit0(X1))))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),number_number_of_int(X1))) ),
c_0_2532,
[final] ).
cnf(c_0_3528,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),number_number_of_int(bit1(X1))))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),number_number_of_int(X1))) ),
c_0_2533,
[final] ).
cnf(c_0_3529,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),bit1(pls)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,number_number_of_int(X1)),one_one_int)) ),
c_0_2534,
[final] ).
cnf(c_0_3530,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),bit1(pls)))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,number267125858f_real(X1)),one_one_real)) ),
c_0_2535,
[final] ).
cnf(c_0_3531,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),bit1(pls)))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,number267125858f_real(X1)),one_one_real)) ),
c_0_2536,
[final] ).
cnf(c_0_3532,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),bit1(pls)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(X1)),one_one_int)) ),
c_0_2537,
[final] ).
cnf(c_0_3533,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,number_number_of_nat(X1)),number_number_of_nat(X2)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2)) ),
c_0_2538,
[final] ).
cnf(c_0_3534,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,bit1(X1)),bit0(X2)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X2)) ),
c_0_2539,
[final] ).
cnf(c_0_3535,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,bit1(X1)),bit0(X2)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X2)) ),
c_0_2540,
[final] ).
cnf(c_0_3536,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit0(X1)),bit1(X2)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2)) ),
c_0_2541,
[final] ).
cnf(c_0_3537,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit0(X1)),bit1(X2)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2)) ),
c_0_2542,
[final] ).
cnf(c_0_3538,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,bit0(X1)),bit1(X2)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2)) ),
c_0_2543,
[final] ).
cnf(c_0_3539,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,bit0(X1)),bit1(X2)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2)) ),
c_0_2544,
[final] ).
cnf(c_0_3540,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,number_number_of_int(X1)),number_number_of_int(X2)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2)) ),
c_0_2545,
[final] ).
cnf(c_0_3541,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,number_number_of_int(X1)),number_number_of_int(X2)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2)) ),
c_0_2546,
[final] ).
cnf(c_0_3542,plain,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,number267125858f_real(X1)),number267125858f_real(X2)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2)) ),
c_0_2547,
[final] ).
cnf(c_0_3543,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,bit0(X1)),bit0(X2)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2)) ),
c_0_2548,
[final] ).
cnf(c_0_3544,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,bit0(X1)),bit0(X2)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2)) ),
c_0_2549,
[final] ).
cnf(c_0_3545,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,bit1(X1)),bit1(X2)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2)) ),
c_0_2550,
[final] ).
cnf(c_0_3546,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,bit1(X1)),bit1(X2)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2)) ),
c_0_2551,
[final] ).
cnf(c_0_3547,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit1(X1)),bit0(X2)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X2)) ),
c_0_2552,
[final] ).
cnf(c_0_3548,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit1(X1)),bit0(X2)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X2)) ),
c_0_2553,
[final] ).
cnf(c_0_3549,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit0(X1)),bit0(X2)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X2)) ),
c_0_2554,
[final] ).
cnf(c_0_3550,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit0(X1)),bit0(X2)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X2)) ),
c_0_2555,
[final] ).
cnf(c_0_3551,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit1(X1)),bit1(X2)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X2)) ),
c_0_2556,
[final] ).
cnf(c_0_3552,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit1(X1)),bit1(X2)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X2)) ),
c_0_2557,
[final] ).
cnf(c_0_3553,plain,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,number267125858f_real(X1)),number267125858f_real(X2)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X2)) ),
c_0_2558,
[final] ).
cnf(c_0_3554,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(X1)),number_number_of_int(X2)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X2)) ),
c_0_2559,
[final] ).
cnf(c_0_3555,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(X1)),number_number_of_int(X2)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X2)) ),
c_0_2560,
[final] ).
cnf(c_0_3556,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),pls))
| hAPP_nat_nat(plus_plus_nat(number_number_of_nat(X1)),number_number_of_nat(X2)) = number_number_of_nat(X1)
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X2),pls)) ),
c_0_2561,
[final] ).
cnf(c_0_3557,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,number_number_of_nat(X1)),number_number_of_nat(X2)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),pls)) ),
c_0_2562,
[final] ).
cnf(c_0_3558,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),pls))
| hAPP_nat_nat(plus_plus_nat(number_number_of_nat(X1)),number_number_of_nat(X2)) = number_number_of_nat(hAPP_int_int(plus_plus_int(X1),X2))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X2),pls)) ),
c_0_2563,
[final] ).
cnf(c_0_3559,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,number_number_of_int(X1)),one_one_int))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),bit1(pls))) ),
c_0_2564,
[final] ).
cnf(c_0_3560,plain,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,number267125858f_real(X1)),one_one_real))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),bit1(pls))) ),
c_0_2565,
[final] ).
cnf(c_0_3561,plain,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,number267125858f_real(X1)),one_one_real))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),bit1(pls))) ),
c_0_2566,
[final] ).
cnf(c_0_3562,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(X1)),one_one_int))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),bit1(pls))) ),
c_0_2567,
[final] ).
cnf(c_0_3563,plain,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X1),one_one_real))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,sqrt(X1)),one_one_real)) ),
c_0_2568,
[final] ).
cnf(c_0_3564,plain,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X1),zero_zero_real))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,sqrt(X1)),zero_zero_real)) ),
c_0_2569,
[final] ).
cnf(c_0_3565,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),pls))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,bit1(X1)),pls)) ),
c_0_2570,
[final] ).
cnf(c_0_3566,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),pls))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,bit0(X1)),pls)) ),
c_0_2571,
[final] ).
cnf(c_0_3567,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),pls))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,number_number_of_int(X1)),zero_zero_int)) ),
c_0_2572,
[final] ).
cnf(c_0_3568,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),pls))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,number267125858f_real(X1)),zero_zero_real)) ),
c_0_2573,
[final] ).
cnf(c_0_3569,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),zero_zero_int))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit0(X1)),zero_zero_int)) ),
c_0_2574,
[final] ).
cnf(c_0_3570,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),zero_zero_int))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit1(X1)),zero_zero_int)) ),
c_0_2575,
[final] ).
cnf(c_0_3571,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),pls))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit0(X1)),pls)) ),
c_0_2576,
[final] ).
cnf(c_0_3572,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),pls))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit1(X1)),pls)) ),
c_0_2577,
[final] ).
cnf(c_0_3573,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),pls))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,number267125858f_real(X1)),zero_zero_real)) ),
c_0_2578,
[final] ).
cnf(c_0_3574,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),pls))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(X1)),zero_zero_int)) ),
c_0_2579,
[final] ).
cnf(c_0_3575,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_nat_int(semiri1621563631at_int,X1)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1)) ),
c_0_2580,
[final] ).
cnf(c_0_3576,plain,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),hAPP_nat_real(semiri132038758t_real,X1)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1)) ),
c_0_2581,
[final] ).
cnf(c_0_3577,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(semiri984289939at_nat,X1)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1)) ),
c_0_2582,
[final] ).
cnf(c_0_3578,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_nat_int(semiri1621563631at_int,X1)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1)) ),
c_0_2583,
[final] ).
cnf(c_0_3579,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,number_number_of_int(X1)),number_number_of_int(X2)))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(X2)),number_number_of_int(X1))) ),
c_0_2584,
[final] ).
cnf(c_0_3580,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,number_number_of_nat(X1)),number_number_of_nat(X2)))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,number_number_of_nat(X2)),number_number_of_nat(X1))) ),
c_0_2585,
[final] ).
cnf(c_0_3581,plain,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,number267125858f_real(X1)),number267125858f_real(X2)))
| hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,number267125858f_real(X2)),number267125858f_real(X1))) ),
c_0_2586,
[final] ).
cnf(c_0_3582,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),number_number_of_int(X1)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,bit1(pls)),X1)) ),
c_0_2587,
[final] ).
cnf(c_0_3583,plain,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,one_one_real),number267125858f_real(X1)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,bit1(pls)),X1)) ),
c_0_2588,
[final] ).
cnf(c_0_3584,plain,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,one_one_real),number267125858f_real(X1)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit1(pls)),X1)) ),
c_0_2589,
[final] ).
cnf(c_0_3585,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),number_number_of_int(X1)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit1(pls)),X1)) ),
c_0_2590,
[final] ).
cnf(c_0_3586,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,bit1(pls)),X1))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),number_number_of_int(X1))) ),
c_0_2591,
[final] ).
cnf(c_0_3587,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,bit1(pls)),X1))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,one_one_real),number267125858f_real(X1))) ),
c_0_2592,
[final] ).
cnf(c_0_3588,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit1(pls)),X1))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,one_one_real),number267125858f_real(X1))) ),
c_0_2593,
[final] ).
cnf(c_0_3589,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit1(pls)),X1))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),number_number_of_int(X1))) ),
c_0_2594,
[final] ).
cnf(c_0_3590,plain,
( hAPP_int_int(plus_plus_int(X2),hAPP_nat_int(semiri1621563631at_int,esk10_2(X2,X1))) = X1
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X2),X1)) ),
c_0_2595,
[final] ).
cnf(c_0_3591,plain,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,m1),hAPP_int_int(plus_plus_int(one_one_int),hAPP_nat_int(semiri1621563631at_int,n)))),
c_0_2596,
[final] ).
cnf(c_0_3592,plain,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_int_int(plus_plus_int(one_one_int),hAPP_nat_int(semiri1621563631at_int,n)))),
c_0_2597,
[final] ).
cnf(c_0_3593,plain,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,sqrt(X1)),one_one_real))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X1),one_one_real)) ),
c_0_2598,
[final] ).
cnf(c_0_3594,plain,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,sqrt(X1)),zero_zero_real))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X1),zero_zero_real)) ),
c_0_2599,
[final] ).
cnf(c_0_3595,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,bit1(X1)),pls))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),pls)) ),
c_0_2600,
[final] ).
cnf(c_0_3596,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,bit0(X1)),pls))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),pls)) ),
c_0_2601,
[final] ).
cnf(c_0_3597,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,number_number_of_int(X1)),zero_zero_int))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),pls)) ),
c_0_2602,
[final] ).
cnf(c_0_3598,plain,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,number267125858f_real(X1)),zero_zero_real))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),pls)) ),
c_0_2603,
[final] ).
cnf(c_0_3599,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit0(X1)),zero_zero_int))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),zero_zero_int)) ),
c_0_2604,
[final] ).
cnf(c_0_3600,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit1(X1)),zero_zero_int))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),zero_zero_int)) ),
c_0_2605,
[final] ).
cnf(c_0_3601,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit0(X1)),pls))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),pls)) ),
c_0_2606,
[final] ).
cnf(c_0_3602,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit1(X1)),pls))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),pls)) ),
c_0_2607,
[final] ).
cnf(c_0_3603,plain,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,number267125858f_real(X1)),zero_zero_real))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),pls)) ),
c_0_2608,
[final] ).
cnf(c_0_3604,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(X1)),zero_zero_int))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),pls)) ),
c_0_2609,
[final] ).
cnf(c_0_3605,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),esk7_1(X1)))
| ~ hBOOL(hAPP_int_bool(X1,hAPP_nat_int(semiri1621563631at_int,X2))) ),
c_0_2610,
[final] ).
cnf(c_0_3606,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X3))
| ~ hBOOL(X1)
| ~ hBOOL(X2)
| ~ hBOOL(X2)
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X3)) ),
c_0_2611,
[final] ).
cnf(c_0_3607,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X3))
| ~ hBOOL(X1)
| ~ hBOOL(X2)
| ~ hBOOL(X1)
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X3)) ),
c_0_2612,
[final] ).
cnf(c_0_3608,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X2),X1))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2))
| X2 != X1 ),
c_0_2613,
[final] ).
cnf(c_0_3609,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X1))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
| X2 != X1 ),
c_0_2614,
[final] ).
cnf(c_0_3610,plain,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X2),X1))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X1),X2))
| X2 != X1 ),
c_0_2615,
[final] ).
cnf(c_0_3611,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X3),X2))
| X1 != X3 ),
c_0_2616,
[final] ).
cnf(c_0_3612,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X3),X2))
| X1 != X3 ),
c_0_2617,
[final] ).
cnf(c_0_3613,plain,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X1),X2))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X3),X2))
| X1 != X3 ),
c_0_2618,
[final] ).
cnf(c_0_3614,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X3))
| X2 != X3 ),
c_0_2619,
[final] ).
cnf(c_0_3615,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X3))
| X2 != X3 ),
c_0_2620,
[final] ).
cnf(c_0_3616,plain,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X1),X2))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X1),X3))
| X2 != X3 ),
c_0_2621,
[final] ).
cnf(c_0_3617,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2))
| X3 != X2
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X3)) ),
c_0_2622,
[final] ).
cnf(c_0_3618,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
| X3 != X2
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X3)) ),
c_0_2623,
[final] ).
cnf(c_0_3619,plain,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X1),X2))
| X3 != X2
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X1),X3)) ),
c_0_2624,
[final] ).
cnf(c_0_3620,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2))
| X3 != X1
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X3),X2)) ),
c_0_2625,
[final] ).
cnf(c_0_3621,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
| X3 != X1
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X3),X2)) ),
c_0_2626,
[final] ).
cnf(c_0_3622,plain,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X1),X2))
| X3 != X1
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X3),X2)) ),
c_0_2627,
[final] ).
cnf(c_0_3623,plain,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,one_one_real),X1))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,one_one_real),sqrt(X1))) ),
c_0_2628,
[final] ).
cnf(c_0_3624,plain,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X1))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),sqrt(X1))) ),
c_0_2629,
[final] ).
cnf(c_0_3625,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X1))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),bit1(X1))) ),
c_0_2630,
[final] ).
cnf(c_0_3626,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X1))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),bit0(X1))) ),
c_0_2631,
[final] ).
cnf(c_0_3627,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X1))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),bit1(X1))) ),
c_0_2632,
[final] ).
cnf(c_0_3628,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X1))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),number_number_of_int(X1))) ),
c_0_2633,
[final] ).
cnf(c_0_3629,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X1))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),number267125858f_real(X1))) ),
c_0_2634,
[final] ).
cnf(c_0_3630,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),X1))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),number_number_of_nat(X1))) ),
c_0_2635,
[final] ).
cnf(c_0_3631,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),X1))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),bit0(X1))) ),
c_0_2636,
[final] ).
cnf(c_0_3632,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),X1))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),number267125858f_real(X1))) ),
c_0_2637,
[final] ).
cnf(c_0_3633,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),X1))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),number_number_of_int(X1))) ),
c_0_2638,
[final] ).
cnf(c_0_3634,plain,
( hBOOL(X1)
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X3))
| ~ hBOOL(X1)
| ~ hBOOL(X2)
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X3)) ),
c_0_2639,
[final] ).
cnf(c_0_3635,plain,
( hBOOL(X2)
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X3))
| ~ hBOOL(X1)
| ~ hBOOL(X2)
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X3)) ),
c_0_2640,
[final] ).
cnf(c_0_3636,plain,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X1),X2))
| X1 = X2
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X1),X2)) ),
c_0_2641,
[final] ).
cnf(c_0_3637,plain,
( X1 = X2
| hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X1),X2))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X1),X2)) ),
c_0_2642,
[final] ).
cnf(c_0_3638,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
| X1 = X2
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2)) ),
c_0_2643,
[final] ).
cnf(c_0_3639,plain,
( X1 = X2
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2)) ),
c_0_2644,
[final] ).
cnf(c_0_3640,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
| X1 = X2
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2)) ),
c_0_2645,
[final] ).
cnf(c_0_3641,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X2))
| X1 = X2
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2)) ),
c_0_2646,
[final] ).
cnf(c_0_3642,plain,
( hBOOL(X1)
| hBOOL(X2)
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X3))
| ~ hBOOL(X2)
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X3)) ),
c_0_2647,
[final] ).
cnf(c_0_3643,plain,
( hBOOL(X1)
| hBOOL(X2)
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X3))
| ~ hBOOL(X1)
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X3)) ),
c_0_2648,
[final] ).
cnf(c_0_3644,plain,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X1),X2))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X1),X2)) ),
c_0_2649,
[final] ).
cnf(c_0_3645,plain,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X1),X2))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X1),X2)) ),
c_0_2650,
[final] ).
cnf(c_0_3646,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2)) ),
c_0_2651,
[final] ).
cnf(c_0_3647,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2)) ),
c_0_2652,
[final] ).
cnf(c_0_3648,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2)) ),
c_0_2653,
[final] ).
cnf(c_0_3649,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2)) ),
c_0_2654,
[final] ).
cnf(c_0_3650,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X2)) ),
c_0_2655,
[final] ).
cnf(c_0_3651,plain,
( hBOOL(X1)
| hBOOL(X2)
| hBOOL(X1)
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X3))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X3)) ),
c_0_2656,
[final] ).
cnf(c_0_3652,plain,
( hBOOL(X1)
| hBOOL(X2)
| hBOOL(X2)
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X3))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X3)) ),
c_0_2657,
[final] ).
cnf(c_0_3653,plain,
hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(X1),X2)),X3) = hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(X1),X3)),X2),
c_0_2658,
[final] ).
cnf(c_0_3654,plain,
hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(plus_plus_nat(X1),X2)),X3) = hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(plus_plus_nat(X1),X3)),X2),
c_0_2659,
[final] ).
cnf(c_0_3655,plain,
hAPP_real_real(plus_plus_real(hAPP_real_real(plus_plus_real(X1),X2)),X3) = hAPP_real_real(plus_plus_real(hAPP_real_real(plus_plus_real(X1),X3)),X2),
c_0_2660,
[final] ).
cnf(c_0_3656,plain,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,one_one_real),sqrt(X1)))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,one_one_real),X1)) ),
c_0_2661,
[final] ).
cnf(c_0_3657,plain,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),sqrt(X1)))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X1)) ),
c_0_2662,
[final] ).
cnf(c_0_3658,plain,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),sqrt(X1)))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X1)) ),
c_0_2663,
[final] ).
cnf(c_0_3659,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),bit1(X1)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X1)) ),
c_0_2664,
[final] ).
cnf(c_0_3660,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),bit0(X1)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X1)) ),
c_0_2665,
[final] ).
cnf(c_0_3661,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),bit1(X1)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X1)) ),
c_0_2666,
[final] ).
cnf(c_0_3662,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),number_number_of_int(X1)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X1)) ),
c_0_2667,
[final] ).
cnf(c_0_3663,plain,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),number267125858f_real(X1)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X1)) ),
c_0_2668,
[final] ).
cnf(c_0_3664,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),esk2_1(X1)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X1)) ),
c_0_2669,
[final] ).
cnf(c_0_3665,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),number_number_of_nat(X1)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),X1)) ),
c_0_2670,
[final] ).
cnf(c_0_3666,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),bit0(X1)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),X1)) ),
c_0_2671,
[final] ).
cnf(c_0_3667,plain,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),number267125858f_real(X1)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),X1)) ),
c_0_2672,
[final] ).
cnf(c_0_3668,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),number_number_of_int(X1)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),X1)) ),
c_0_2673,
[final] ).
cnf(c_0_3669,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1))
| hBOOL(X2)
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1))
| ~ hBOOL(X3) ),
c_0_2674,
[final] ).
cnf(c_0_3670,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1))
| hBOOL(X2)
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1))
| ~ hBOOL(X3) ),
c_0_2675,
[final] ).
cnf(c_0_3671,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1))
| hBOOL(X3)
| ~ hBOOL(X2)
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1)) ),
c_0_2676,
[final] ).
cnf(c_0_3672,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1))
| hBOOL(X3)
| ~ hBOOL(X2)
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1)) ),
c_0_2677,
[final] ).
cnf(c_0_3673,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X1))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),X1)) ),
c_0_2678,
[final] ).
cnf(c_0_3674,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),X1))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X1)) ),
c_0_2679,
[final] ).
cnf(c_0_3675,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(power_power_nat(X1),number_number_of_nat(X2))))
| number_number_of_nat(X2) != zero_zero_nat ),
c_0_2680,
[final] ).
cnf(c_0_3676,plain,
( X2 = X3
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),X1))
| hAPP_nat_int(power_power_int(X1),X2) != hAPP_nat_int(power_power_int(X1),X3) ),
c_0_2681,
[final] ).
cnf(c_0_3677,plain,
( X2 = X3
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,one_one_nat),X1))
| hAPP_nat_nat(power_power_nat(X1),X2) != hAPP_nat_nat(power_power_nat(X1),X3) ),
c_0_2682,
[final] ).
cnf(c_0_3678,plain,
( X2 = X3
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,one_one_real),X1))
| hAPP_nat_real(power_power_real(X1),X2) != hAPP_nat_real(power_power_real(X1),X3) ),
c_0_2683,
[final] ).
cnf(c_0_3679,plain,
( hAPP_nat_nat(plus_plus_nat(X2),esk13_2(X2,X1)) = X1
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X1)) ),
c_0_2684,
[final] ).
cnf(c_0_3680,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_nat_int(semiri1621563631at_int,X1)),zero_zero_int))
| X1 != zero_zero_nat ),
c_0_2685,
[final] ).
cnf(c_0_3681,plain,
( hAPP_nat_nat(plus_plus_nat(X1),esk3_2(X1,X2)) = X2
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2)) ),
c_0_2686,
[final] ).
cnf(c_0_3682,plain,
( hBOOL(hAPP_int_bool(X1,esk7_1(X1)))
| ~ hBOOL(hAPP_int_bool(X1,hAPP_nat_int(semiri1621563631at_int,X2))) ),
c_0_2687,
[final] ).
cnf(c_0_3683,plain,
( hBOOL(hAPP_int_bool(X1,hAPP_nat_int(semiri1621563631at_int,X2)))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),esk8_1(X1))) ),
c_0_2688,
[final] ).
cnf(c_0_3684,plain,
( hBOOL(hAPP_nat_bool(X1,zero_zero_nat))
| hBOOL(hAPP_nat_bool(X1,esk19_2(X2,X1)))
| ~ hBOOL(hAPP_nat_bool(X1,X2)) ),
c_0_2689,
[final] ).
cnf(c_0_3685,plain,
( hAPP_nat_nat(plus_plus_nat(number_number_of_nat(X1)),number_number_of_nat(X2)) = number_number_of_nat(X2)
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),pls)) ),
c_0_2690,
[final] ).
cnf(c_0_3686,plain,
hAPP_int_int(plus_plus_int(bit0(times_times_int(X1,X2))),X2) = times_times_int(bit1(X1),X2),
c_0_2691,
[final] ).
cnf(c_0_3687,plain,
hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(X1),X2)),X3) = hAPP_int_int(plus_plus_int(X1),hAPP_int_int(plus_plus_int(X2),X3)),
c_0_2692,
[final] ).
cnf(c_0_3688,plain,
hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(plus_plus_nat(X1),X2)),X3) = hAPP_nat_nat(plus_plus_nat(X1),hAPP_nat_nat(plus_plus_nat(X2),X3)),
c_0_2693,
[final] ).
cnf(c_0_3689,plain,
hAPP_real_real(plus_plus_real(hAPP_real_real(plus_plus_real(X1),X2)),X3) = hAPP_real_real(plus_plus_real(X1),hAPP_real_real(plus_plus_real(X2),X3)),
c_0_2694,
[final] ).
cnf(c_0_3690,plain,
hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(X1),X2)),X3) = hAPP_int_int(plus_plus_int(X1),hAPP_int_int(plus_plus_int(X2),X3)),
c_0_2695,
[final] ).
cnf(c_0_3691,plain,
hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(plus_plus_nat(X1),X2)),X3) = hAPP_nat_nat(plus_plus_nat(X1),hAPP_nat_nat(plus_plus_nat(X2),X3)),
c_0_2696,
[final] ).
cnf(c_0_3692,plain,
hAPP_real_real(plus_plus_real(hAPP_real_real(plus_plus_real(X1),X2)),X3) = hAPP_real_real(plus_plus_real(X1),hAPP_real_real(plus_plus_real(X2),X3)),
c_0_2697,
[final] ).
cnf(c_0_3693,plain,
hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(X1),X2)),X3) = hAPP_int_int(plus_plus_int(X1),hAPP_int_int(plus_plus_int(X2),X3)),
c_0_2698,
[final] ).
cnf(c_0_3694,plain,
hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(plus_plus_nat(X1),X2)),X3) = hAPP_nat_nat(plus_plus_nat(X1),hAPP_nat_nat(plus_plus_nat(X2),X3)),
c_0_2699,
[final] ).
cnf(c_0_3695,plain,
hAPP_real_real(plus_plus_real(hAPP_real_real(plus_plus_real(X1),X2)),X3) = hAPP_real_real(plus_plus_real(X1),hAPP_real_real(plus_plus_real(X2),X3)),
c_0_2700,
[final] ).
cnf(c_0_3696,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X2))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X2),X1))
| X2 = X1 ),
c_0_2701,
[final] ).
cnf(c_0_3697,plain,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X1),X2))
| hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X2),X1))
| X2 = X1 ),
c_0_2702,
[final] ).
cnf(c_0_3698,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X2),X1))
| X2 = X1 ),
c_0_2703,
[final] ).
cnf(c_0_3699,plain,
hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(plus_plus_nat(X1),X2)),X3) = hAPP_nat_nat(plus_plus_nat(X1),hAPP_nat_nat(plus_plus_nat(X2),X3)),
c_0_2704,
[final] ).
cnf(c_0_3700,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X2),X1))
| X2 = X1 ),
c_0_2705,
[final] ).
cnf(c_0_3701,plain,
hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(X1),X2)),X3) = hAPP_int_int(plus_plus_int(X1),hAPP_int_int(plus_plus_int(X2),X3)),
c_0_2706,
[final] ).
cnf(c_0_3702,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X2))
| X2 = X1
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X2),X1)) ),
c_0_2707,
[final] ).
cnf(c_0_3703,plain,
( hAPP_nat_int(power_power_int(X1),X2) = hAPP_nat_int(power_power_int(X1),X3)
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),X1))
| X2 != X3 ),
c_0_2708,
[final] ).
cnf(c_0_3704,plain,
( hAPP_nat_nat(power_power_nat(X1),X2) = hAPP_nat_nat(power_power_nat(X1),X3)
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,one_one_nat),X1))
| X2 != X3 ),
c_0_2709,
[final] ).
cnf(c_0_3705,plain,
( hAPP_nat_real(power_power_real(X1),X2) = hAPP_nat_real(power_power_real(X1),X3)
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,one_one_real),X1))
| X2 != X3 ),
c_0_2710,
[final] ).
cnf(c_0_3706,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X2),X1)) ),
c_0_2711,
[final] ).
cnf(c_0_3707,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X1)) ),
c_0_2712,
[final] ).
cnf(c_0_3708,plain,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X1),X2))
| hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X2),X1)) ),
c_0_2713,
[final] ).
cnf(c_0_3709,plain,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X1),X2))
| hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X2),X1)) ),
c_0_2714,
[final] ).
cnf(c_0_3710,plain,
hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),hAPP_nat_nat(plus_plus_nat(X1),X2))),
c_0_2715,
[final] ).
cnf(c_0_3711,plain,
hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),hAPP_nat_nat(plus_plus_nat(X2),X1))),
c_0_2716,
[final] ).
cnf(c_0_3712,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X1)) ),
c_0_2717,
[final] ).
cnf(c_0_3713,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X2),X1)) ),
c_0_2718,
[final] ).
cnf(c_0_3714,plain,
( hAPP_nat_int(semiri1621563631at_int,number_number_of_nat(X1)) = number_number_of_int(X1)
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),number_number_of_int(X1))) ),
c_0_2719,
[final] ).
cnf(c_0_3715,plain,
( hAPP_nat_real(semiri132038758t_real,number_number_of_nat(X1)) = number267125858f_real(X1)
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),number_number_of_int(X1))) ),
c_0_2720,
[final] ).
cnf(c_0_3716,plain,
( hAPP_int_int(plus_plus_int(number_number_of_int(X1)),one_one_int) = number_number_of_int(succ(X1))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X1)) ),
c_0_2721,
[final] ).
cnf(c_0_3717,plain,
( hAPP_nat_nat(plus_plus_nat(number_number_of_nat(X1)),one_one_nat) = number_number_of_nat(succ(X1))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X1)) ),
c_0_2722,
[final] ).
cnf(c_0_3718,plain,
( hAPP_real_real(plus_plus_real(number267125858f_real(X1)),one_one_real) = number267125858f_real(succ(X1))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X1)) ),
c_0_2723,
[final] ).
cnf(c_0_3719,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),hAPP_int_int(plus_plus_int(X2),one_one_int)))
| X1 != X2 ),
c_0_2724,
[final] ).
cnf(c_0_3720,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(power_power_nat(X1),X2)))
| X2 != zero_zero_nat ),
c_0_2725,
[final] ).
cnf(c_0_3721,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(power_power_nat(X1),X2)))
| X2 != zero_zero_nat ),
c_0_2726,
[final] ).
cnf(c_0_3722,plain,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),hAPP_int_int(plus_plus_int(X1),one_one_int))),
c_0_2727,
[final] ).
cnf(c_0_3723,plain,
hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),hAPP_nat_nat(plus_plus_nat(X1),one_one_nat))),
c_0_2728,
[final] ).
cnf(c_0_3724,plain,
hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X1),hAPP_real_real(plus_plus_real(X1),one_one_real))),
c_0_2729,
[final] ).
cnf(c_0_3725,plain,
( hAPP_nat_nat(plus_plus_nat(number_number_of_nat(X1)),one_one_nat) = one_one_nat
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),pls)) ),
c_0_2730,
[final] ).
cnf(c_0_3726,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2))
| X2 != hAPP_int_int(plus_plus_int(X1),hAPP_nat_int(semiri1621563631at_int,X3)) ),
c_0_2731,
[final] ).
cnf(c_0_3727,plain,
( hAPP_int_int(plus_plus_int(one_one_int),number_number_of_int(X1)) = number_number_of_int(succ(X1))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X1)) ),
c_0_2732,
[final] ).
cnf(c_0_3728,plain,
( hAPP_nat_nat(plus_plus_nat(one_one_nat),number_number_of_nat(X1)) = number_number_of_nat(succ(X1))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X1)) ),
c_0_2733,
[final] ).
cnf(c_0_3729,plain,
( hAPP_real_real(plus_plus_real(one_one_real),number267125858f_real(X1)) = number267125858f_real(succ(X1))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X1)) ),
c_0_2734,
[final] ).
cnf(c_0_3730,plain,
( hBOOL(hAPP_int_bool(X1,hAPP_nat_int(semiri1621563631at_int,X2)))
| ~ hBOOL(hAPP_int_bool(X1,esk8_1(X1))) ),
c_0_2735,
[final] ).
cnf(c_0_3731,plain,
hAPP_int_int(plus_plus_int(hAPP_nat_int(semiri1621563631at_int,X1)),hAPP_nat_int(semiri1621563631at_int,X2)) = hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(plus_plus_nat(X1),X2)),
c_0_2736,
[final] ).
cnf(c_0_3732,plain,
hAPP_int_int(plus_plus_int(hAPP_nat_int(semiri1621563631at_int,X1)),hAPP_nat_int(semiri1621563631at_int,X2)) = hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(plus_plus_nat(X1),X2)),
c_0_2737,
[final] ).
cnf(c_0_3733,plain,
hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(semiri984289939at_nat,X1)),hAPP_nat_nat(semiri984289939at_nat,X2)) = hAPP_nat_nat(semiri984289939at_nat,hAPP_nat_nat(plus_plus_nat(X1),X2)),
c_0_2738,
[final] ).
cnf(c_0_3734,plain,
hAPP_real_real(plus_plus_real(hAPP_nat_real(semiri132038758t_real,X1)),hAPP_nat_real(semiri132038758t_real,X2)) = hAPP_nat_real(semiri132038758t_real,hAPP_nat_nat(plus_plus_nat(X1),X2)),
c_0_2739,
[final] ).
cnf(c_0_3735,plain,
hAPP_int_int(plus_plus_int(hAPP_nat_int(semiri1621563631at_int,X1)),hAPP_nat_int(semiri1621563631at_int,X2)) = hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(plus_plus_nat(X1),X2)),
c_0_2740,
[final] ).
cnf(c_0_3736,plain,
( hAPP_nat_nat(plus_plus_nat(one_one_nat),number_number_of_nat(X1)) = one_one_nat
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),pls)) ),
c_0_2741,
[final] ).
cnf(c_0_3737,plain,
( hBOOL(X1)
| ~ hBOOL(X1)
| ~ hBOOL(X2)
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X3))
| ~ hBOOL(X2) ),
c_0_2742,
[final] ).
cnf(c_0_3738,plain,
( hBOOL(X2)
| ~ hBOOL(X1)
| ~ hBOOL(X2)
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X3))
| ~ hBOOL(X1) ),
c_0_2743,
[final] ).
cnf(c_0_3739,plain,
( hBOOL(X1)
| ~ hBOOL(X1)
| ~ hBOOL(X2)
| ~ hBOOL(X2)
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X3)) ),
c_0_2744,
[final] ).
cnf(c_0_3740,plain,
( hBOOL(X2)
| ~ hBOOL(X1)
| ~ hBOOL(X2)
| ~ hBOOL(X1)
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X3)) ),
c_0_2745,
[final] ).
cnf(c_0_3741,plain,
hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),X1)),X1) != zero_zero_int,
c_0_2746,
[final] ).
cnf(c_0_3742,plain,
( hBOOL(X1)
| hBOOL(X2)
| hBOOL(X1)
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X3))
| ~ hBOOL(X2) ),
c_0_2747,
[final] ).
cnf(c_0_3743,plain,
( hBOOL(X1)
| hBOOL(X2)
| hBOOL(X2)
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X3))
| ~ hBOOL(X1) ),
c_0_2748,
[final] ).
cnf(c_0_3744,plain,
( hBOOL(X1)
| hBOOL(X2)
| hBOOL(X1)
| ~ hBOOL(X2)
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X3)) ),
c_0_2749,
[final] ).
cnf(c_0_3745,plain,
( hBOOL(X1)
| hBOOL(X2)
| hBOOL(X2)
| ~ hBOOL(X1)
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X3)) ),
c_0_2750,
[final] ).
cnf(c_0_3746,plain,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),number_number_of_int(bit0(bit1(pls))))),
c_0_2751,
[final] ).
cnf(c_0_3747,plain,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),number_number_of_int(bit1(bit1(pls))))),
c_0_2752,
[final] ).
cnf(c_0_3748,plain,
hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),number_number_of_nat(bit0(bit1(pls))))),
c_0_2753,
[final] ).
cnf(c_0_3749,plain,
( hAPP_nat_int(semiri1621563631at_int,esk15_1(X1)) = X1
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1)) ),
c_0_2754,
[final] ).
cnf(c_0_3750,plain,
( hAPP_nat_int(semiri1621563631at_int,esk12_1(X1)) = X1
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1)) ),
c_0_2755,
[final] ).
cnf(c_0_3751,plain,
( hAPP_nat_int(semiri1621563631at_int,esk11_1(X1)) = X1
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1)) ),
c_0_2756,
[final] ).
cnf(c_0_3752,plain,
( hAPP_nat_int(semiri1621563631at_int,esk2_1(X1)) = X1
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X1)) ),
c_0_2757,
[final] ).
cnf(c_0_3753,plain,
hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),hAPP_real_real(plus_plus_real(one_one_real),one_one_real))),
c_0_2758,
[final] ).
cnf(c_0_3754,plain,
hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(plus_plus_nat(one_one_nat),one_one_nat))),
c_0_2759,
[final] ).
cnf(c_0_3755,plain,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_int_int(plus_plus_int(one_one_int),one_one_int))),
c_0_2760,
[final] ).
cnf(c_0_3756,plain,
hAPP_real_real(plus_plus_real(hAPP_real_real(plus_plus_real(one_one_real),number267125858f_real(X1))),number267125858f_real(X1)) = number267125858f_real(bit1(X1)),
c_0_2761,
[final] ).
cnf(c_0_3757,plain,
hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),number_number_of_int(X1))),number_number_of_int(X1)) = number_number_of_int(bit1(X1)),
c_0_2762,
[final] ).
cnf(c_0_3758,plain,
hAPP_real_real(plus_plus_real(hAPP_real_real(plus_plus_real(zero_zero_real),number267125858f_real(X1))),number267125858f_real(X1)) = number267125858f_real(bit0(X1)),
c_0_2763,
[final] ).
cnf(c_0_3759,plain,
hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(zero_zero_int),number_number_of_int(X1))),number_number_of_int(X1)) = number_number_of_int(bit0(X1)),
c_0_2764,
[final] ).
cnf(c_0_3760,plain,
( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X1),X2))
| X1 != X2 ),
c_0_2765,
[final] ).
cnf(c_0_3761,plain,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
| X1 != X2 ),
c_0_2766,
[final] ).
cnf(c_0_3762,plain,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X2))
| X1 != X2 ),
c_0_2767,
[final] ).
cnf(c_0_3763,plain,
( X1 != X2
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2)) ),
c_0_2768,
[final] ).
cnf(c_0_3764,plain,
( X1 != X2
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X2),X1)) ),
c_0_2769,
[final] ).
cnf(c_0_3765,plain,
( X1 != X2
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2)) ),
c_0_2770,
[final] ).
cnf(c_0_3766,plain,
( X1 != X2
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X2),X1)) ),
c_0_2771,
[final] ).
cnf(c_0_3767,plain,
( X1 != zero_zero_nat
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X2),X1)) ),
c_0_2772,
[final] ).
cnf(c_0_3768,plain,
~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X1)),
c_0_2773,
[final] ).
cnf(c_0_3769,plain,
~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X1)),
c_0_2774,
[final] ).
cnf(c_0_3770,plain,
( number_number_of_nat(X1) = zero_zero_nat
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),pls)) ),
c_0_2775,
[final] ).
cnf(c_0_3771,plain,
( number_number_of_nat(X1) = zero_zero_nat
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),pls)) ),
c_0_2776,
[final] ).
cnf(c_0_3772,plain,
( sqrt(X1) != zero_zero_real
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X1)) ),
c_0_2777,
[final] ).
cnf(c_0_3773,plain,
hAPP_int_int(plus_plus_int(X1),hAPP_int_int(plus_plus_int(X2),X3)) = hAPP_int_int(plus_plus_int(X2),hAPP_int_int(plus_plus_int(X1),X3)),
c_0_2778,
[final] ).
cnf(c_0_3774,plain,
hAPP_nat_nat(plus_plus_nat(X1),hAPP_nat_nat(plus_plus_nat(X2),X3)) = hAPP_nat_nat(plus_plus_nat(X2),hAPP_nat_nat(plus_plus_nat(X1),X3)),
c_0_2779,
[final] ).
cnf(c_0_3775,plain,
hAPP_real_real(plus_plus_real(X1),hAPP_real_real(plus_plus_real(X2),X3)) = hAPP_real_real(plus_plus_real(X2),hAPP_real_real(plus_plus_real(X1),X3)),
c_0_2780,
[final] ).
cnf(c_0_3776,plain,
hAPP_nat_int(power_power_int(hAPP_nat_int(semiri1621563631at_int,X1)),X2) = hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(power_power_nat(X1),X2)),
c_0_2781,
[final] ).
cnf(c_0_3777,plain,
hAPP_nat_int(power_power_int(hAPP_nat_int(semiri1621563631at_int,X1)),X2) = hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(power_power_nat(X1),X2)),
c_0_2782,
[final] ).
cnf(c_0_3778,plain,
hAPP_nat_nat(power_power_nat(hAPP_nat_nat(semiri984289939at_nat,X1)),X2) = hAPP_nat_nat(semiri984289939at_nat,hAPP_nat_nat(power_power_nat(X1),X2)),
c_0_2783,
[final] ).
cnf(c_0_3779,plain,
hAPP_nat_real(power_power_real(hAPP_nat_real(semiri132038758t_real,X1)),X2) = hAPP_nat_real(semiri132038758t_real,hAPP_nat_nat(power_power_nat(X1),X2)),
c_0_2784,
[final] ).
cnf(c_0_3780,plain,
hAPP_nat_nat(plus_plus_nat(X1),hAPP_nat_nat(plus_plus_nat(X2),X3)) = hAPP_nat_nat(plus_plus_nat(X2),hAPP_nat_nat(plus_plus_nat(X1),X3)),
c_0_2785,
[final] ).
cnf(c_0_3781,plain,
hAPP_int_int(plus_plus_int(X1),hAPP_int_int(plus_plus_int(X2),X3)) = hAPP_int_int(plus_plus_int(X2),hAPP_int_int(plus_plus_int(X1),X3)),
c_0_2786,
[final] ).
cnf(c_0_3782,plain,
hAPP_nat_int(power_power_int(hAPP_nat_int(semiri1621563631at_int,X1)),X2) = hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(power_power_nat(X1),X2)),
c_0_2787,
[final] ).
cnf(c_0_3783,plain,
hAPP_nat_int(power_power_int(hAPP_nat_int(semiri1621563631at_int,X1)),X2) = hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(power_power_nat(X1),X2)),
c_0_2788,
[final] ).
cnf(c_0_3784,plain,
( X1 = zero_zero_nat
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),zero_zero_nat)) ),
c_0_2789,
[final] ).
cnf(c_0_3785,plain,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_nat_int(semiri1621563631at_int,X1))),
c_0_2790,
[final] ).
cnf(c_0_3786,plain,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_nat_int(semiri1621563631at_int,X1))),
c_0_2791,
[final] ).
cnf(c_0_3787,plain,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_nat_int(semiri1621563631at_int,X1))),
c_0_2792,
[final] ).
cnf(c_0_3788,plain,
hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),hAPP_nat_nat(semiri984289939at_nat,X1))),
c_0_2793,
[final] ).
cnf(c_0_3789,plain,
hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),hAPP_nat_real(semiri132038758t_real,X1))),
c_0_2794,
[final] ).
cnf(c_0_3790,plain,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_nat_int(semiri1621563631at_int,X1))),
c_0_2795,
[final] ).
cnf(c_0_3791,plain,
hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),hAPP_nat_nat(semiri984289939at_nat,X1))),
c_0_2796,
[final] ).
cnf(c_0_3792,plain,
hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),hAPP_nat_real(semiri132038758t_real,X1))),
c_0_2797,
[final] ).
cnf(c_0_3793,plain,
~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),zero_zero_nat)),
c_0_2798,
[final] ).
cnf(c_0_3794,plain,
~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),zero_zero_nat)),
c_0_2799,
[final] ).
cnf(c_0_3795,plain,
~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),zero_zero_nat)),
c_0_2800,
[final] ).
cnf(c_0_3796,plain,
( hAPP_nat_nat(plus_plus_nat(number_number_of_nat(X1)),one_one_nat) = number_number_of_nat(succ(X1))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),pls)) ),
c_0_2801,
[final] ).
cnf(c_0_3797,plain,
( X1 != zero_zero_nat
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1)) ),
c_0_2802,
[final] ).
cnf(c_0_3798,plain,
( hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(if_nat(X2,X1),X3)) = hAPP_nat_int(semiri1621563631at_int,X1)
| ~ hBOOL(X2) ),
c_0_2803,
[final] ).
cnf(c_0_3799,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
| X2 != hAPP_nat_nat(plus_plus_nat(X1),X3) ),
c_0_2804,
[final] ).
cnf(c_0_3800,plain,
( hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(if_nat(X2,X3),X1)) = hAPP_nat_int(semiri1621563631at_int,X1)
| hBOOL(X2) ),
c_0_2805,
[final] ).
cnf(c_0_3801,plain,
( hAPP_nat_nat(plus_plus_nat(one_one_nat),number_number_of_nat(X1)) = number_number_of_nat(succ(X1))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),pls)) ),
c_0_2806,
[final] ).
cnf(c_0_3802,plain,
~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),zero_zero_int)),
c_0_2807,
[final] ).
cnf(c_0_3803,plain,
~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,one_one_nat),zero_zero_nat)),
c_0_2808,
[final] ).
cnf(c_0_3804,plain,
~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,one_one_real),zero_zero_real)),
c_0_2809,
[final] ).
cnf(c_0_3805,plain,
~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),zero_zero_int)),
c_0_2810,
[final] ).
cnf(c_0_3806,plain,
~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,one_one_nat),zero_zero_nat)),
c_0_2811,
[final] ).
cnf(c_0_3807,plain,
~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,one_one_real),zero_zero_real)),
c_0_2812,
[final] ).
cnf(c_0_3808,plain,
~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),zero_zero_int)),
c_0_2813,
[final] ).
cnf(c_0_3809,plain,
~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),pls)),
c_0_2814,
[final] ).
cnf(c_0_3810,plain,
( hAPP_nat_int(semiri1621563631at_int,number_number_of_nat(X1)) = zero_zero_int
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),number_number_of_int(X1))) ),
c_0_2815,
[final] ).
cnf(c_0_3811,plain,
( hAPP_nat_real(semiri132038758t_real,number_number_of_nat(X1)) = zero_zero_real
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),number_number_of_int(X1))) ),
c_0_2816,
[final] ).
cnf(c_0_3812,plain,
bit0(hAPP_int_int(plus_plus_int(X1),succ(X2))) = hAPP_int_int(plus_plus_int(bit1(X1)),bit1(X2)),
c_0_2817,
[final] ).
cnf(c_0_3813,plain,
hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),X1)),X1) = bit1(X1),
c_0_2818,
[final] ).
cnf(c_0_3814,plain,
( X1 = zero_zero_real
| hAPP_nat_real(power_power_real(X1),number_number_of_nat(bit0(bit1(pls)))) != zero_zero_real ),
c_0_2819,
[final] ).
cnf(c_0_3815,plain,
( X1 = zero_zero_int
| hAPP_nat_int(power_power_int(X1),number_number_of_nat(bit0(bit1(pls)))) != zero_zero_int ),
c_0_2820,
[final] ).
cnf(c_0_3816,plain,
hAPP_int_int(plus_plus_int(bit0(X1)),bit1(X2)) = bit1(hAPP_int_int(plus_plus_int(X1),X2)),
c_0_2821,
[final] ).
cnf(c_0_3817,plain,
hAPP_int_int(plus_plus_int(bit1(X1)),bit0(X2)) = bit1(hAPP_int_int(plus_plus_int(X1),X2)),
c_0_2822,
[final] ).
cnf(c_0_3818,plain,
hAPP_real_real(plus_plus_real(number267125858f_real(X1)),number267125858f_real(X2)) = number267125858f_real(hAPP_int_int(plus_plus_int(X1),X2)),
c_0_2823,
[final] ).
cnf(c_0_3819,plain,
hAPP_int_int(plus_plus_int(number_number_of_int(X1)),number_number_of_int(X2)) = number_number_of_int(hAPP_int_int(plus_plus_int(X1),X2)),
c_0_2824,
[final] ).
cnf(c_0_3820,plain,
hAPP_real_real(plus_plus_real(number267125858f_real(X1)),number267125858f_real(X2)) = number267125858f_real(hAPP_int_int(plus_plus_int(X1),X2)),
c_0_2825,
[final] ).
cnf(c_0_3821,plain,
hAPP_int_int(plus_plus_int(number_number_of_int(X1)),number_number_of_int(X2)) = number_number_of_int(hAPP_int_int(plus_plus_int(X1),X2)),
c_0_2826,
[final] ).
cnf(c_0_3822,plain,
hAPP_int_int(plus_plus_int(bit0(X1)),bit0(X2)) = bit0(hAPP_int_int(plus_plus_int(X1),X2)),
c_0_2827,
[final] ).
cnf(c_0_3823,plain,
hAPP_int_int(plus_plus_int(number_number_of_int(X1)),number_number_of_int(X2)) = number_number_of_int(hAPP_int_int(plus_plus_int(X1),X2)),
c_0_2828,
[final] ).
cnf(c_0_3824,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),pls))
| number_number_of_nat(X1) != zero_zero_nat ),
c_0_2829,
[final] ).
cnf(c_0_3825,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),pls))
| number_number_of_nat(X1) != zero_zero_nat ),
c_0_2830,
[final] ).
cnf(c_0_3826,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2))
| X1 != X2 ),
c_0_2831,
[final] ).
cnf(c_0_3827,plain,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X1),X2))
| X1 != X2 ),
c_0_2832,
[final] ).
cnf(c_0_3828,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
| X1 != X2 ),
c_0_2833,
[final] ).
cnf(c_0_3829,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
| X1 != X2 ),
c_0_2834,
[final] ).
cnf(c_0_3830,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
| X1 != X2 ),
c_0_2835,
[final] ).
cnf(c_0_3831,plain,
number267125858f_real(hAPP_int_int(plus_plus_int(X1),bit1(pls))) = hAPP_real_real(plus_plus_real(number267125858f_real(X1)),one_one_real),
c_0_2836,
[final] ).
cnf(c_0_3832,plain,
number_number_of_int(hAPP_int_int(plus_plus_int(X1),bit1(pls))) = hAPP_int_int(plus_plus_int(number_number_of_int(X1)),one_one_int),
c_0_2837,
[final] ).
cnf(c_0_3833,plain,
number267125858f_real(hAPP_int_int(plus_plus_int(bit1(pls)),X1)) = hAPP_real_real(plus_plus_real(one_one_real),number267125858f_real(X1)),
c_0_2838,
[final] ).
cnf(c_0_3834,plain,
number_number_of_int(hAPP_int_int(plus_plus_int(bit1(pls)),X1)) = hAPP_int_int(plus_plus_int(one_one_int),number_number_of_int(X1)),
c_0_2839,
[final] ).
cnf(c_0_3835,plain,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X1)),
c_0_2840,
[final] ).
cnf(c_0_3836,plain,
hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X1)),
c_0_2841,
[final] ).
cnf(c_0_3837,plain,
hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X1),X1)),
c_0_2842,
[final] ).
cnf(c_0_3838,plain,
hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X1),X1)),
c_0_2843,
[final] ).
cnf(c_0_3839,plain,
hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X1)),
c_0_2844,
[final] ).
cnf(c_0_3840,plain,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),number_number_of_int(pls))),
c_0_2845,
[final] ).
cnf(c_0_3841,plain,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X1)),
c_0_2846,
[final] ).
cnf(c_0_3842,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),zero_zero_nat))
| X1 != zero_zero_nat ),
c_0_2847,
[final] ).
cnf(c_0_3843,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1))
| X1 = zero_zero_nat ),
c_0_2848,
[final] ).
cnf(c_0_3844,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1))
| X1 = zero_zero_nat ),
c_0_2849,
[final] ).
cnf(c_0_3845,plain,
hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),X1)),
c_0_2850,
[final] ).
cnf(c_0_3846,plain,
hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),X1)),
c_0_2851,
[final] ).
cnf(c_0_3847,plain,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),one_one_int)),
c_0_2852,
[final] ).
cnf(c_0_3848,plain,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),one_one_int)),
c_0_2853,
[final] ).
cnf(c_0_3849,plain,
hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),one_one_nat)),
c_0_2854,
[final] ).
cnf(c_0_3850,plain,
hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),one_one_real)),
c_0_2855,
[final] ).
cnf(c_0_3851,plain,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),zero_zero_int)),
c_0_2856,
[final] ).
cnf(c_0_3852,plain,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),pls)),
c_0_2857,
[final] ).
cnf(c_0_3853,plain,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),t)),
c_0_2858,
[final] ).
cnf(c_0_3854,plain,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),one_one_int)),
c_0_2859,
[final] ).
cnf(c_0_3855,plain,
hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),one_one_nat)),
c_0_2860,
[final] ).
cnf(c_0_3856,plain,
hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),one_one_real)),
c_0_2861,
[final] ).
cnf(c_0_3857,plain,
hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),tn)),
c_0_2862,
[final] ).
cnf(c_0_3858,plain,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),one_one_int)),
c_0_2863,
[final] ).
cnf(c_0_3859,plain,
hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),n)),
c_0_2864,
[final] ).
cnf(c_0_3860,plain,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),t)),
c_0_2865,
[final] ).
cnf(c_0_3861,plain,
( X1 = X2
| hAPP_int_int(plus_plus_int(X3),X1) != hAPP_int_int(plus_plus_int(X3),X2) ),
c_0_2866,
[final] ).
cnf(c_0_3862,plain,
( X1 = X2
| hAPP_nat_nat(plus_plus_nat(X3),X1) != hAPP_nat_nat(plus_plus_nat(X3),X2) ),
c_0_2867,
[final] ).
cnf(c_0_3863,plain,
( X1 = X2
| hAPP_real_real(plus_plus_real(X3),X1) != hAPP_real_real(plus_plus_real(X3),X2) ),
c_0_2868,
[final] ).
cnf(c_0_3864,plain,
( X1 = X2
| hAPP_int_int(plus_plus_int(X1),X3) != hAPP_int_int(plus_plus_int(X2),X3) ),
c_0_2869,
[final] ).
cnf(c_0_3865,plain,
( X1 = X2
| hAPP_nat_nat(plus_plus_nat(X1),X3) != hAPP_nat_nat(plus_plus_nat(X2),X3) ),
c_0_2870,
[final] ).
cnf(c_0_3866,plain,
( X1 = X2
| hAPP_real_real(plus_plus_real(X1),X3) != hAPP_real_real(plus_plus_real(X2),X3) ),
c_0_2871,
[final] ).
cnf(c_0_3867,plain,
( X1 = X2
| hAPP_int_int(plus_plus_int(X3),X1) != hAPP_int_int(plus_plus_int(X3),X2) ),
c_0_2872,
[final] ).
cnf(c_0_3868,plain,
( X1 = X2
| hAPP_nat_nat(plus_plus_nat(X3),X1) != hAPP_nat_nat(plus_plus_nat(X3),X2) ),
c_0_2873,
[final] ).
cnf(c_0_3869,plain,
( X1 = X2
| hAPP_real_real(plus_plus_real(X3),X1) != hAPP_real_real(plus_plus_real(X3),X2) ),
c_0_2874,
[final] ).
cnf(c_0_3870,plain,
( X1 = X2
| hAPP_int_int(plus_plus_int(X3),X1) != hAPP_int_int(plus_plus_int(X3),X2) ),
c_0_2875,
[final] ).
cnf(c_0_3871,plain,
( X1 = X2
| hAPP_nat_nat(plus_plus_nat(X3),X1) != hAPP_nat_nat(plus_plus_nat(X3),X2) ),
c_0_2876,
[final] ).
cnf(c_0_3872,plain,
( X1 = X2
| hAPP_real_real(plus_plus_real(X3),X1) != hAPP_real_real(plus_plus_real(X3),X2) ),
c_0_2877,
[final] ).
cnf(c_0_3873,plain,
( X1 = X2
| hAPP_int_int(plus_plus_int(X1),X3) != hAPP_int_int(plus_plus_int(X2),X3) ),
c_0_2878,
[final] ).
cnf(c_0_3874,plain,
( X1 = X2
| hAPP_nat_nat(plus_plus_nat(X1),X3) != hAPP_nat_nat(plus_plus_nat(X2),X3) ),
c_0_2879,
[final] ).
cnf(c_0_3875,plain,
( X1 = X2
| hAPP_real_real(plus_plus_real(X1),X3) != hAPP_real_real(plus_plus_real(X2),X3) ),
c_0_2880,
[final] ).
cnf(c_0_3876,plain,
( X1 = X2
| hAPP_nat_nat(plus_plus_nat(X1),X3) != hAPP_nat_nat(plus_plus_nat(X2),X3) ),
c_0_2881,
[final] ).
cnf(c_0_3877,plain,
( X1 = X2
| hAPP_nat_nat(plus_plus_nat(X3),X1) != hAPP_nat_nat(plus_plus_nat(X3),X2) ),
c_0_2882,
[final] ).
cnf(c_0_3878,plain,
hAPP_nat_int(semiri1621563631at_int,number_number_of_nat(bit1(bit1(pls)))) = number_number_of_int(bit1(bit1(pls))),
c_0_2883,
[final] ).
cnf(c_0_3879,plain,
hAPP_nat_int(semiri1621563631at_int,number_number_of_nat(bit0(bit1(pls)))) = number_number_of_int(bit0(bit1(pls))),
c_0_2884,
[final] ).
cnf(c_0_3880,plain,
( hAPP_nat_real(power_power_real(X1),number_number_of_nat(bit0(bit1(pls)))) = zero_zero_real
| X1 != zero_zero_real ),
c_0_2885,
[final] ).
cnf(c_0_3881,plain,
( hAPP_nat_int(power_power_int(X1),number_number_of_nat(bit0(bit1(pls)))) = zero_zero_int
| X1 != zero_zero_int ),
c_0_2886,
[final] ).
cnf(c_0_3882,plain,
( hAPP_nat_real(power_power_real(X1),number_number_of_nat(X2)) != zero_zero_real
| number_number_of_nat(X2) != zero_zero_nat ),
c_0_2887,
[final] ).
cnf(c_0_3883,plain,
( hAPP_nat_nat(power_power_nat(X1),number_number_of_nat(X2)) != zero_zero_nat
| number_number_of_nat(X2) != zero_zero_nat ),
c_0_2888,
[final] ).
cnf(c_0_3884,plain,
( hAPP_nat_int(power_power_int(X1),number_number_of_nat(X2)) != zero_zero_int
| number_number_of_nat(X2) != zero_zero_nat ),
c_0_2889,
[final] ).
cnf(c_0_3885,plain,
hAPP_nat_real(power_power_real(zero_zero_real),number_number_of_nat(bit0(bit1(pls)))) = zero_zero_real,
c_0_2890,
[final] ).
cnf(c_0_3886,plain,
hAPP_nat_nat(power_power_nat(zero_zero_nat),number_number_of_nat(bit0(bit1(pls)))) = zero_zero_nat,
c_0_2891,
[final] ).
cnf(c_0_3887,plain,
hAPP_nat_int(power_power_int(zero_zero_int),number_number_of_nat(bit0(bit1(pls)))) = zero_zero_int,
c_0_2892,
[final] ).
cnf(c_0_3888,plain,
hAPP_nat_real(power_power_real(one_one_real),number_number_of_nat(bit0(bit1(pls)))) = one_one_real,
c_0_2893,
[final] ).
cnf(c_0_3889,plain,
hAPP_nat_nat(power_power_nat(one_one_nat),number_number_of_nat(bit0(bit1(pls)))) = one_one_nat,
c_0_2894,
[final] ).
cnf(c_0_3890,plain,
hAPP_nat_int(power_power_int(one_one_int),number_number_of_nat(bit0(bit1(pls)))) = one_one_int,
c_0_2895,
[final] ).
cnf(c_0_3891,plain,
( hAPP_int_int(plus_plus_int(X1),X2) = hAPP_int_int(plus_plus_int(X1),X3)
| X2 != X3 ),
c_0_2896,
[final] ).
cnf(c_0_3892,plain,
( hAPP_nat_nat(plus_plus_nat(X1),X2) = hAPP_nat_nat(plus_plus_nat(X1),X3)
| X2 != X3 ),
c_0_2897,
[final] ).
cnf(c_0_3893,plain,
( hAPP_real_real(plus_plus_real(X1),X2) = hAPP_real_real(plus_plus_real(X1),X3)
| X2 != X3 ),
c_0_2898,
[final] ).
cnf(c_0_3894,plain,
( hAPP_int_int(plus_plus_int(X1),X2) = hAPP_int_int(plus_plus_int(X3),X2)
| X1 != X3 ),
c_0_2899,
[final] ).
cnf(c_0_3895,plain,
( hAPP_nat_nat(plus_plus_nat(X1),X2) = hAPP_nat_nat(plus_plus_nat(X3),X2)
| X1 != X3 ),
c_0_2900,
[final] ).
cnf(c_0_3896,plain,
( hAPP_real_real(plus_plus_real(X1),X2) = hAPP_real_real(plus_plus_real(X3),X2)
| X1 != X3 ),
c_0_2901,
[final] ).
cnf(c_0_3897,plain,
( hAPP_nat_nat(plus_plus_nat(X1),X2) = hAPP_nat_nat(plus_plus_nat(X3),X2)
| X1 != X3 ),
c_0_2902,
[final] ).
cnf(c_0_3898,plain,
( hAPP_nat_nat(plus_plus_nat(X1),X2) = hAPP_nat_nat(plus_plus_nat(X1),X3)
| X2 != X3 ),
c_0_2903,
[final] ).
cnf(c_0_3899,plain,
( X1 = zero_zero_real
| hAPP_nat_real(power_power_real(X1),number_number_of_nat(X2)) != zero_zero_real ),
c_0_2904,
[final] ).
cnf(c_0_3900,plain,
( X1 = zero_zero_nat
| hAPP_nat_nat(power_power_nat(X1),number_number_of_nat(X2)) != zero_zero_nat ),
c_0_2905,
[final] ).
cnf(c_0_3901,plain,
( X1 = zero_zero_int
| hAPP_nat_int(power_power_int(X1),number_number_of_nat(X2)) != zero_zero_int ),
c_0_2906,
[final] ).
cnf(c_0_3902,plain,
( X1 = X2
| hAPP_nat_int(semiri1621563631at_int,X1) != hAPP_nat_int(semiri1621563631at_int,X2) ),
c_0_2907,
[final] ).
cnf(c_0_3903,plain,
( X1 = X2
| hAPP_nat_int(semiri1621563631at_int,X1) != hAPP_nat_int(semiri1621563631at_int,X2) ),
c_0_2908,
[final] ).
cnf(c_0_3904,plain,
( X1 = X2
| hAPP_nat_nat(semiri984289939at_nat,X1) != hAPP_nat_nat(semiri984289939at_nat,X2) ),
c_0_2909,
[final] ).
cnf(c_0_3905,plain,
( X1 = X2
| hAPP_nat_real(semiri132038758t_real,X1) != hAPP_nat_real(semiri132038758t_real,X2) ),
c_0_2910,
[final] ).
cnf(c_0_3906,plain,
( X1 = X2
| hAPP_nat_int(semiri1621563631at_int,X1) != hAPP_nat_int(semiri1621563631at_int,X2) ),
c_0_2911,
[final] ).
cnf(c_0_3907,plain,
hAPP_int_int(plus_plus_int(X1),X2) = hAPP_int_int(plus_plus_int(X2),X1),
c_0_2912,
[final] ).
cnf(c_0_3908,plain,
hAPP_nat_nat(plus_plus_nat(X1),X2) = hAPP_nat_nat(plus_plus_nat(X2),X1),
c_0_2913,
[final] ).
cnf(c_0_3909,plain,
hAPP_real_real(plus_plus_real(X1),X2) = hAPP_real_real(plus_plus_real(X2),X1),
c_0_2914,
[final] ).
cnf(c_0_3910,plain,
hAPP_nat_nat(plus_plus_nat(X1),X2) = hAPP_nat_nat(plus_plus_nat(X2),X1),
c_0_2915,
[final] ).
cnf(c_0_3911,plain,
hAPP_int_int(plus_plus_int(X1),X2) = hAPP_int_int(plus_plus_int(X2),X1),
c_0_2916,
[final] ).
cnf(c_0_3912,plain,
number267125858f_real(hAPP_nat_int(semiri1621563631at_int,X1)) = hAPP_nat_real(semiri132038758t_real,X1),
c_0_2917,
[final] ).
cnf(c_0_3913,plain,
number_number_of_int(hAPP_nat_int(semiri1621563631at_int,X1)) = hAPP_nat_int(semiri1621563631at_int,X1),
c_0_2918,
[final] ).
cnf(c_0_3914,plain,
number_number_of_nat(hAPP_nat_int(semiri1621563631at_int,X1)) = hAPP_nat_nat(semiri984289939at_nat,X1),
c_0_2919,
[final] ).
cnf(c_0_3915,plain,
hAPP_nat_nat(if_nat(fFalse,X1),X2) = X2,
c_0_2920,
[final] ).
cnf(c_0_3916,plain,
hAPP_nat_nat(if_nat(fTrue,X1),X2) = X1,
c_0_2921,
[final] ).
cnf(c_0_3917,plain,
( X1 = zero_zero_nat
| X2 = one_one_nat
| hAPP_nat_nat(power_power_nat(X2),X1) != one_one_nat ),
c_0_2922,
[final] ).
cnf(c_0_3918,plain,
( X1 = zero_zero_int
| hAPP_int_int(plus_plus_int(X2),X1) != X2 ),
c_0_2923,
[final] ).
cnf(c_0_3919,plain,
( X1 = zero_zero_nat
| hAPP_nat_nat(plus_plus_nat(X2),X1) != X2 ),
c_0_2924,
[final] ).
cnf(c_0_3920,plain,
( X1 = zero_zero_real
| hAPP_real_real(plus_plus_real(X2),X1) != X2 ),
c_0_2925,
[final] ).
cnf(c_0_3921,plain,
( X1 = zero_zero_nat
| hAPP_nat_nat(plus_plus_nat(X2),X1) != X2 ),
c_0_2926,
[final] ).
cnf(c_0_3922,plain,
( hAPP_nat_nat(power_power_nat(X1),X2) != zero_zero_nat
| X2 != zero_zero_nat ),
c_0_2927,
[final] ).
cnf(c_0_3923,plain,
( hAPP_nat_int(power_power_int(X1),X2) != zero_zero_int
| X2 != zero_zero_nat ),
c_0_2928,
[final] ).
cnf(c_0_3924,plain,
( hAPP_nat_nat(power_power_nat(X1),X2) != zero_zero_nat
| X2 != zero_zero_nat ),
c_0_2929,
[final] ).
cnf(c_0_3925,plain,
( hAPP_nat_real(power_power_real(X1),X2) != zero_zero_real
| X2 != zero_zero_nat ),
c_0_2930,
[final] ).
cnf(c_0_3926,plain,
( X1 = zero_zero_nat
| hAPP_nat_nat(power_power_nat(X1),X2) != zero_zero_nat ),
c_0_2931,
[final] ).
cnf(c_0_3927,plain,
( X1 = zero_zero_int
| hAPP_int_int(plus_plus_int(X1),X1) != zero_zero_int ),
c_0_2932,
[final] ).
cnf(c_0_3928,plain,
( X1 = zero_zero_real
| hAPP_real_real(plus_plus_real(X1),X1) != zero_zero_real ),
c_0_2933,
[final] ).
cnf(c_0_3929,plain,
( X1 = zero_zero_int
| hAPP_nat_int(power_power_int(X1),X2) != zero_zero_int ),
c_0_2934,
[final] ).
cnf(c_0_3930,plain,
( X1 = zero_zero_nat
| hAPP_nat_nat(power_power_nat(X1),X2) != zero_zero_nat ),
c_0_2935,
[final] ).
cnf(c_0_3931,plain,
( X1 = zero_zero_real
| hAPP_nat_real(power_power_real(X1),X2) != zero_zero_real ),
c_0_2936,
[final] ).
cnf(c_0_3932,plain,
( X1 = zero_zero_int
| hAPP_nat_int(power_power_int(X1),X2) != zero_zero_int ),
c_0_2937,
[final] ).
cnf(c_0_3933,plain,
( X1 = zero_zero_real
| hAPP_nat_real(power_power_real(X1),X2) != zero_zero_real ),
c_0_2938,
[final] ).
cnf(c_0_3934,plain,
( X1 = zero_zero_nat
| hAPP_nat_nat(plus_plus_nat(X1),X2) != zero_zero_nat ),
c_0_2939,
[final] ).
cnf(c_0_3935,plain,
( X2 = zero_zero_nat
| hAPP_nat_nat(plus_plus_nat(X1),X2) != zero_zero_nat ),
c_0_2940,
[final] ).
cnf(c_0_3936,plain,
( X1 = zero_zero_real
| hAPP_real_real(plus_plus_real(X1),X1) != zero_zero_real ),
c_0_2941,
[final] ).
cnf(c_0_3937,plain,
( X1 = zero_zero_int
| hAPP_int_int(plus_plus_int(X1),X1) != zero_zero_int ),
c_0_2942,
[final] ).
cnf(c_0_3938,plain,
( hAPP_nat_real(power_power_real(X1),number_number_of_nat(X2)) = zero_zero_real
| number_number_of_nat(X2) = zero_zero_nat
| X1 != zero_zero_real ),
c_0_2943,
[final] ).
cnf(c_0_3939,plain,
( hAPP_nat_nat(power_power_nat(X1),number_number_of_nat(X2)) = zero_zero_nat
| number_number_of_nat(X2) = zero_zero_nat
| X1 != zero_zero_nat ),
c_0_2944,
[final] ).
cnf(c_0_3940,plain,
( hAPP_nat_int(power_power_int(X1),number_number_of_nat(X2)) = zero_zero_int
| number_number_of_nat(X2) = zero_zero_nat
| X1 != zero_zero_int ),
c_0_2945,
[final] ).
cnf(c_0_3941,plain,
hAPP_int_int(plus_plus_int(one_one_int),number_number_of_int(X1)) = number_number_of_int(succ(X1)),
c_0_2946,
[final] ).
cnf(c_0_3942,plain,
hAPP_real_real(plus_plus_real(one_one_real),number267125858f_real(X1)) = number267125858f_real(succ(X1)),
c_0_2947,
[final] ).
cnf(c_0_3943,plain,
number_number_of_nat(bit0(bit1(pls))) = hAPP_nat_nat(plus_plus_nat(one_one_nat),one_one_nat),
c_0_2948,
[final] ).
cnf(c_0_3944,plain,
number267125858f_real(bit0(bit1(pls))) = hAPP_real_real(plus_plus_real(one_one_real),one_one_real),
c_0_2949,
[final] ).
cnf(c_0_3945,plain,
number_number_of_nat(bit0(bit1(pls))) = hAPP_nat_nat(plus_plus_nat(one_one_nat),one_one_nat),
c_0_2950,
[final] ).
cnf(c_0_3946,plain,
number_number_of_int(bit0(bit1(pls))) = hAPP_int_int(plus_plus_int(one_one_int),one_one_int),
c_0_2951,
[final] ).
cnf(c_0_3947,plain,
number267125858f_real(bit0(bit1(pls))) = hAPP_real_real(plus_plus_real(one_one_real),one_one_real),
c_0_2952,
[final] ).
cnf(c_0_3948,plain,
number_number_of_int(bit0(bit1(pls))) = hAPP_int_int(plus_plus_int(one_one_int),one_one_int),
c_0_2953,
[final] ).
cnf(c_0_3949,plain,
( hAPP_nat_real(power_power_real(zero_zero_real),number_number_of_nat(X1)) = one_one_real
| number_number_of_nat(X1) != zero_zero_nat ),
c_0_2954,
[final] ).
cnf(c_0_3950,plain,
( hAPP_nat_nat(power_power_nat(zero_zero_nat),number_number_of_nat(X1)) = one_one_nat
| number_number_of_nat(X1) != zero_zero_nat ),
c_0_2955,
[final] ).
cnf(c_0_3951,plain,
( hAPP_nat_int(power_power_int(zero_zero_int),number_number_of_nat(X1)) = one_one_int
| number_number_of_nat(X1) != zero_zero_nat ),
c_0_2956,
[final] ).
cnf(c_0_3952,plain,
is_bool(hAPP_real_bool(X1,X2)),
c_0_2957,
[final] ).
cnf(c_0_3953,plain,
is_bool(hAPP_nat_bool(X1,X2)),
c_0_2958,
[final] ).
cnf(c_0_3954,plain,
is_bool(hAPP_int_bool(X1,X2)),
c_0_2959,
[final] ).
cnf(c_0_3955,plain,
( hAPP_nat_int(semiri1621563631at_int,X1) = hAPP_nat_int(semiri1621563631at_int,X2)
| X1 != X2 ),
c_0_2960,
[final] ).
cnf(c_0_3956,plain,
( hAPP_nat_int(semiri1621563631at_int,X1) = hAPP_nat_int(semiri1621563631at_int,X2)
| X1 != X2 ),
c_0_2961,
[final] ).
cnf(c_0_3957,plain,
( hAPP_nat_nat(semiri984289939at_nat,X1) = hAPP_nat_nat(semiri984289939at_nat,X2)
| X1 != X2 ),
c_0_2962,
[final] ).
cnf(c_0_3958,plain,
( hAPP_nat_real(semiri132038758t_real,X1) = hAPP_nat_real(semiri132038758t_real,X2)
| X1 != X2 ),
c_0_2963,
[final] ).
cnf(c_0_3959,plain,
( hAPP_nat_int(semiri1621563631at_int,X1) = hAPP_nat_int(semiri1621563631at_int,X2)
| X1 != X2 ),
c_0_2964,
[final] ).
cnf(c_0_3960,plain,
( hAPP_nat_real(power_power_real(zero_zero_real),number_number_of_nat(X1)) = zero_zero_real
| number_number_of_nat(X1) = zero_zero_nat ),
c_0_2965,
[final] ).
cnf(c_0_3961,plain,
( hAPP_nat_nat(power_power_nat(zero_zero_nat),number_number_of_nat(X1)) = zero_zero_nat
| number_number_of_nat(X1) = zero_zero_nat ),
c_0_2966,
[final] ).
cnf(c_0_3962,plain,
( hAPP_nat_int(power_power_int(zero_zero_int),number_number_of_nat(X1)) = zero_zero_int
| number_number_of_nat(X1) = zero_zero_nat ),
c_0_2967,
[final] ).
cnf(c_0_3963,plain,
hAPP_real_real(plus_plus_real(number267125858f_real(pls)),X1) = X1,
c_0_2968,
[final] ).
cnf(c_0_3964,plain,
hAPP_int_int(plus_plus_int(number_number_of_int(pls)),X1) = X1,
c_0_2969,
[final] ).
cnf(c_0_3965,plain,
( hAPP_nat_nat(plus_plus_nat(X1),X2) = zero_zero_nat
| X2 != zero_zero_nat
| X1 != zero_zero_nat ),
c_0_2970,
[final] ).
cnf(c_0_3966,plain,
( hAPP_nat_nat(power_power_nat(X1),X2) = zero_zero_nat
| X2 = zero_zero_nat
| X1 != zero_zero_nat ),
c_0_2971,
[final] ).
cnf(c_0_3967,plain,
( hAPP_nat_int(power_power_int(X1),X2) = zero_zero_int
| X2 = zero_zero_nat
| X1 != zero_zero_int ),
c_0_2972,
[final] ).
cnf(c_0_3968,plain,
( hAPP_nat_nat(power_power_nat(X1),X2) = zero_zero_nat
| X2 = zero_zero_nat
| X1 != zero_zero_nat ),
c_0_2973,
[final] ).
cnf(c_0_3969,plain,
( hAPP_nat_real(power_power_real(X1),X2) = zero_zero_real
| X2 = zero_zero_nat
| X1 != zero_zero_real ),
c_0_2974,
[final] ).
cnf(c_0_3970,plain,
hAPP_real_real(plus_plus_real(X1),number267125858f_real(pls)) = X1,
c_0_2975,
[final] ).
cnf(c_0_3971,plain,
hAPP_int_int(plus_plus_int(X1),number_number_of_int(pls)) = X1,
c_0_2976,
[final] ).
cnf(c_0_3972,plain,
hAPP_int_int(plus_plus_int(X1),X1) = bit0(X1),
c_0_2977,
[final] ).
cnf(c_0_3973,plain,
( hAPP_int_int(plus_plus_int(X1),X2) = X1
| X2 != zero_zero_int ),
c_0_2978,
[final] ).
cnf(c_0_3974,plain,
( hAPP_nat_nat(plus_plus_nat(X1),X2) = X1
| X2 != zero_zero_nat ),
c_0_2979,
[final] ).
cnf(c_0_3975,plain,
( hAPP_real_real(plus_plus_real(X1),X2) = X1
| X2 != zero_zero_real ),
c_0_2980,
[final] ).
cnf(c_0_3976,plain,
( hAPP_int_int(plus_plus_int(X1),X1) = zero_zero_int
| X1 != zero_zero_int ),
c_0_2981,
[final] ).
cnf(c_0_3977,plain,
( hAPP_real_real(plus_plus_real(X1),X1) = zero_zero_real
| X1 != zero_zero_real ),
c_0_2982,
[final] ).
cnf(c_0_3978,plain,
( hAPP_nat_nat(power_power_nat(X1),X2) = one_one_nat
| X1 != one_one_nat ),
c_0_2983,
[final] ).
cnf(c_0_3979,plain,
( hAPP_nat_nat(power_power_nat(X1),X2) = one_one_nat
| X2 != zero_zero_nat ),
c_0_2984,
[final] ).
cnf(c_0_3980,plain,
( hAPP_real_real(plus_plus_real(X1),X1) = zero_zero_real
| X1 != zero_zero_real ),
c_0_2985,
[final] ).
cnf(c_0_3981,plain,
( hAPP_int_int(plus_plus_int(X1),X1) = zero_zero_int
| X1 != zero_zero_int ),
c_0_2986,
[final] ).
cnf(c_0_3982,plain,
hAPP_int_int(plus_plus_int(X1),one_one_int) = succ(X1),
c_0_2987,
[final] ).
cnf(c_0_3983,plain,
( X1 = zero_zero_nat
| hAPP_nat_int(semiri1621563631at_int,X1) != zero_zero_int ),
c_0_2988,
[final] ).
cnf(c_0_3984,plain,
succ(bit1(X1)) = bit0(succ(X1)),
c_0_2989,
[final] ).
cnf(c_0_3985,plain,
( hAPP_nat_real(power_power_real(zero_zero_real),X1) = one_one_real
| X1 != zero_zero_nat ),
c_0_2990,
[final] ).
cnf(c_0_3986,plain,
( hAPP_nat_nat(power_power_nat(zero_zero_nat),X1) = one_one_nat
| X1 != zero_zero_nat ),
c_0_2991,
[final] ).
cnf(c_0_3987,plain,
( hAPP_nat_int(power_power_int(zero_zero_int),X1) = one_one_int
| X1 != zero_zero_nat ),
c_0_2992,
[final] ).
cnf(c_0_3988,plain,
hAPP_nat_int(power_power_int(X1),one_one_nat) = X1,
c_0_2993,
[final] ).
cnf(c_0_3989,plain,
hAPP_nat_nat(power_power_nat(X1),one_one_nat) = X1,
c_0_2994,
[final] ).
cnf(c_0_3990,plain,
hAPP_nat_real(power_power_real(X1),one_one_nat) = X1,
c_0_2995,
[final] ).
cnf(c_0_3991,plain,
hAPP_int_int(plus_plus_int(X1),zero_zero_int) = X1,
c_0_2996,
[final] ).
cnf(c_0_3992,plain,
hAPP_nat_nat(plus_plus_nat(X1),zero_zero_nat) = X1,
c_0_2997,
[final] ).
cnf(c_0_3993,plain,
hAPP_real_real(plus_plus_real(X1),zero_zero_real) = X1,
c_0_2998,
[final] ).
cnf(c_0_3994,plain,
hAPP_int_int(plus_plus_int(X1),zero_zero_int) = X1,
c_0_2999,
[final] ).
cnf(c_0_3995,plain,
hAPP_nat_nat(plus_plus_nat(X1),zero_zero_nat) = X1,
c_0_3000,
[final] ).
cnf(c_0_3996,plain,
hAPP_real_real(plus_plus_real(X1),zero_zero_real) = X1,
c_0_3001,
[final] ).
cnf(c_0_3997,plain,
hAPP_int_int(plus_plus_int(X1),zero_zero_int) = X1,
c_0_3002,
[final] ).
cnf(c_0_3998,plain,
hAPP_nat_nat(plus_plus_nat(X1),zero_zero_nat) = X1,
c_0_3003,
[final] ).
cnf(c_0_3999,plain,
hAPP_real_real(plus_plus_real(X1),zero_zero_real) = X1,
c_0_3004,
[final] ).
cnf(c_0_4000,plain,
hAPP_nat_int(power_power_int(X1),one_one_nat) = X1,
c_0_3005,
[final] ).
cnf(c_0_4001,plain,
hAPP_nat_nat(power_power_nat(X1),one_one_nat) = X1,
c_0_3006,
[final] ).
cnf(c_0_4002,plain,
hAPP_nat_real(power_power_real(X1),one_one_nat) = X1,
c_0_3007,
[final] ).
cnf(c_0_4003,plain,
hAPP_nat_nat(plus_plus_nat(X1),zero_zero_nat) = X1,
c_0_3008,
[final] ).
cnf(c_0_4004,plain,
hAPP_int_int(plus_plus_int(X1),zero_zero_int) = X1,
c_0_3009,
[final] ).
cnf(c_0_4005,plain,
hAPP_int_int(plus_plus_int(X1),pls) = X1,
c_0_3010,
[final] ).
cnf(c_0_4006,plain,
hAPP_nat_int(power_power_int(X1),zero_zero_nat) = one_one_int,
c_0_3011,
[final] ).
cnf(c_0_4007,plain,
hAPP_nat_nat(power_power_nat(X1),zero_zero_nat) = one_one_nat,
c_0_3012,
[final] ).
cnf(c_0_4008,plain,
hAPP_nat_real(power_power_real(X1),zero_zero_nat) = one_one_real,
c_0_3013,
[final] ).
cnf(c_0_4009,plain,
hAPP_nat_int(power_power_int(X1),zero_zero_nat) = one_one_int,
c_0_3014,
[final] ).
cnf(c_0_4010,plain,
hAPP_nat_nat(power_power_nat(X1),zero_zero_nat) = one_one_nat,
c_0_3015,
[final] ).
cnf(c_0_4011,plain,
hAPP_nat_real(power_power_real(X1),zero_zero_nat) = one_one_real,
c_0_3016,
[final] ).
cnf(c_0_4012,plain,
( hAPP_nat_real(power_power_real(zero_zero_real),X1) = zero_zero_real
| X1 = zero_zero_nat ),
c_0_3017,
[final] ).
cnf(c_0_4013,plain,
( hAPP_nat_nat(power_power_nat(zero_zero_nat),X1) = zero_zero_nat
| X1 = zero_zero_nat ),
c_0_3018,
[final] ).
cnf(c_0_4014,plain,
( hAPP_nat_int(power_power_int(zero_zero_int),X1) = zero_zero_int
| X1 = zero_zero_nat ),
c_0_3019,
[final] ).
cnf(c_0_4015,plain,
hAPP_int_int(plus_plus_int(zero_zero_int),X1) = X1,
c_0_3020,
[final] ).
cnf(c_0_4016,plain,
hAPP_nat_nat(plus_plus_nat(zero_zero_nat),X1) = X1,
c_0_3021,
[final] ).
cnf(c_0_4017,plain,
hAPP_real_real(plus_plus_real(zero_zero_real),X1) = X1,
c_0_3022,
[final] ).
cnf(c_0_4018,plain,
hAPP_int_int(plus_plus_int(zero_zero_int),X1) = X1,
c_0_3023,
[final] ).
cnf(c_0_4019,plain,
hAPP_nat_nat(plus_plus_nat(zero_zero_nat),X1) = X1,
c_0_3024,
[final] ).
cnf(c_0_4020,plain,
hAPP_real_real(plus_plus_real(zero_zero_real),X1) = X1,
c_0_3025,
[final] ).
cnf(c_0_4021,plain,
hAPP_int_int(plus_plus_int(zero_zero_int),X1) = X1,
c_0_3026,
[final] ).
cnf(c_0_4022,plain,
hAPP_nat_nat(plus_plus_nat(zero_zero_nat),X1) = X1,
c_0_3027,
[final] ).
cnf(c_0_4023,plain,
hAPP_real_real(plus_plus_real(zero_zero_real),X1) = X1,
c_0_3028,
[final] ).
cnf(c_0_4024,plain,
hAPP_nat_nat(plus_plus_nat(zero_zero_nat),X1) = X1,
c_0_3029,
[final] ).
cnf(c_0_4025,plain,
hAPP_int_int(plus_plus_int(zero_zero_int),X1) = X1,
c_0_3030,
[final] ).
cnf(c_0_4026,plain,
hAPP_int_int(plus_plus_int(pls),X1) = X1,
c_0_3031,
[final] ).
cnf(c_0_4027,plain,
hAPP_nat_int(power_power_int(one_one_int),X1) = one_one_int,
c_0_3032,
[final] ).
cnf(c_0_4028,plain,
hAPP_nat_nat(power_power_nat(one_one_nat),X1) = one_one_nat,
c_0_3033,
[final] ).
cnf(c_0_4029,plain,
hAPP_nat_real(power_power_real(one_one_real),X1) = one_one_real,
c_0_3034,
[final] ).
cnf(c_0_4030,plain,
( X1 = X2
| bit0(X1) != bit0(X2) ),
c_0_3035,
[final] ).
cnf(c_0_4031,plain,
( X1 = X2
| bit1(X1) != bit1(X2) ),
c_0_3036,
[final] ).
cnf(c_0_4032,plain,
( X1 = X2
| number267125858f_real(X1) != number267125858f_real(X2) ),
c_0_3037,
[final] ).
cnf(c_0_4033,plain,
( X1 = X2
| number_number_of_int(X1) != number_number_of_int(X2) ),
c_0_3038,
[final] ).
cnf(c_0_4034,plain,
( hAPP_nat_int(semiri1621563631at_int,X1) = zero_zero_int
| X1 != zero_zero_nat ),
c_0_3039,
[final] ).
cnf(c_0_4035,plain,
succ(bit0(X1)) = bit1(X1),
c_0_3040,
[final] ).
cnf(c_0_4036,plain,
( X1 = number267125858f_real(X2)
| number267125858f_real(X2) != X1 ),
c_0_3041,
[final] ).
cnf(c_0_4037,plain,
( number267125858f_real(X1) = X2
| X2 != number267125858f_real(X1) ),
c_0_3042,
[final] ).
cnf(c_0_4038,plain,
( X1 = number_number_of_int(X2)
| number_number_of_int(X2) != X1 ),
c_0_3043,
[final] ).
cnf(c_0_4039,plain,
( number_number_of_int(X1) = X2
| X2 != number_number_of_int(X1) ),
c_0_3044,
[final] ).
cnf(c_0_4040,plain,
( X1 = number_number_of_nat(X2)
| number_number_of_nat(X2) != X1 ),
c_0_3045,
[final] ).
cnf(c_0_4041,plain,
( number_number_of_nat(X1) = X2
| X2 != number_number_of_nat(X1) ),
c_0_3046,
[final] ).
cnf(c_0_4042,plain,
bit0(X1) != bit1(X2),
c_0_3047,
[final] ).
cnf(c_0_4043,plain,
bit1(X1) != bit0(X2),
c_0_3048,
[final] ).
cnf(c_0_4044,plain,
( bit0(X1) = bit0(X2)
| X1 != X2 ),
c_0_3049,
[final] ).
cnf(c_0_4045,plain,
( bit1(X1) = bit1(X2)
| X1 != X2 ),
c_0_3050,
[final] ).
cnf(c_0_4046,plain,
( number267125858f_real(X1) = number267125858f_real(X2)
| X1 != X2 ),
c_0_3051,
[final] ).
cnf(c_0_4047,plain,
( number_number_of_int(X1) = number_number_of_int(X2)
| X1 != X2 ),
c_0_3052,
[final] ).
cnf(c_0_4048,plain,
hAPP_nat_int(semiri1621563631at_int,zero_zero_nat) = zero_zero_int,
c_0_3053,
[final] ).
cnf(c_0_4049,plain,
hAPP_nat_int(semiri1621563631at_int,zero_zero_nat) = zero_zero_int,
c_0_3054,
[final] ).
cnf(c_0_4050,plain,
hAPP_nat_nat(semiri984289939at_nat,zero_zero_nat) = zero_zero_nat,
c_0_3055,
[final] ).
cnf(c_0_4051,plain,
hAPP_nat_real(semiri132038758t_real,zero_zero_nat) = zero_zero_real,
c_0_3056,
[final] ).
cnf(c_0_4052,plain,
hAPP_nat_int(semiri1621563631at_int,one_one_nat) = one_one_int,
c_0_3057,
[final] ).
cnf(c_0_4053,plain,
hAPP_nat_int(semiri1621563631at_int,one_one_nat) = one_one_int,
c_0_3058,
[final] ).
cnf(c_0_4054,plain,
hAPP_nat_nat(semiri984289939at_nat,one_one_nat) = one_one_nat,
c_0_3059,
[final] ).
cnf(c_0_4055,plain,
hAPP_nat_real(semiri132038758t_real,one_one_nat) = one_one_real,
c_0_3060,
[final] ).
cnf(c_0_4056,plain,
hAPP_nat_int(semiri1621563631at_int,zero_zero_nat) = zero_zero_int,
c_0_3061,
[final] ).
cnf(c_0_4057,plain,
hAPP_nat_int(semiri1621563631at_int,one_one_nat) = one_one_int,
c_0_3062,
[final] ).
cnf(c_0_4058,plain,
( X1 = fFalse
| X1 = fTrue
| ~ is_bool(X1) ),
c_0_3063,
[final] ).
cnf(c_0_4059,plain,
( pls = X1
| bit0(X1) != pls ),
c_0_3064,
[final] ).
cnf(c_0_4060,plain,
( X1 = pls
| bit0(X1) != pls ),
c_0_3065,
[final] ).
cnf(c_0_4061,plain,
number267125858f_real(bit1(pls)) = one_one_real,
c_0_3066,
[final] ).
cnf(c_0_4062,plain,
number_number_of_nat(bit1(pls)) = one_one_nat,
c_0_3067,
[final] ).
cnf(c_0_4063,plain,
number_number_of_int(bit1(pls)) = one_one_int,
c_0_3068,
[final] ).
cnf(c_0_4064,plain,
number_number_of_nat(bit1(pls)) = one_one_nat,
c_0_3069,
[final] ).
cnf(c_0_4065,plain,
number_number_of_nat(bit1(pls)) = one_one_nat,
c_0_3070,
[final] ).
cnf(c_0_4066,plain,
number_number_of_int(bit1(pls)) = one_one_int,
c_0_3071,
[final] ).
cnf(c_0_4067,plain,
number267125858f_real(bit1(pls)) = one_one_real,
c_0_3072,
[final] ).
cnf(c_0_4068,plain,
number_number_of_int(bit1(pls)) = one_one_int,
c_0_3073,
[final] ).
cnf(c_0_4069,plain,
number267125858f_real(bit1(pls)) = one_one_real,
c_0_3074,
[final] ).
cnf(c_0_4070,plain,
number_number_of_int(bit1(pls)) = one_one_int,
c_0_3075,
[final] ).
cnf(c_0_4071,plain,
bit1(X1) != pls,
c_0_3076,
[final] ).
cnf(c_0_4072,plain,
bit1(X1) != pls,
c_0_3077,
[final] ).
cnf(c_0_4073,plain,
( bit0(X1) = pls
| pls != X1 ),
c_0_3078,
[final] ).
cnf(c_0_4074,plain,
( bit0(X1) = pls
| X1 != pls ),
c_0_3079,
[final] ).
cnf(c_0_4075,plain,
succ(pls) = bit1(pls),
c_0_3080,
[final] ).
cnf(c_0_4076,plain,
number_number_of_int(X1) = X1,
c_0_3081,
[final] ).
cnf(c_0_4077,plain,
( X1 = one_one_int
| one_one_int != X1 ),
c_0_3082,
[final] ).
cnf(c_0_4078,plain,
( one_one_int = X1
| X1 != one_one_int ),
c_0_3083,
[final] ).
cnf(c_0_4079,plain,
( X1 = one_one_nat
| one_one_nat != X1 ),
c_0_3084,
[final] ).
cnf(c_0_4080,plain,
( one_one_nat = X1
| X1 != one_one_nat ),
c_0_3085,
[final] ).
cnf(c_0_4081,plain,
( X1 = one_one_real
| one_one_real != X1 ),
c_0_3086,
[final] ).
cnf(c_0_4082,plain,
( one_one_real = X1
| X1 != one_one_real ),
c_0_3087,
[final] ).
cnf(c_0_4083,plain,
( X1 = zero_zero_int
| zero_zero_int != X1 ),
c_0_3088,
[final] ).
cnf(c_0_4084,plain,
( zero_zero_int = X1
| X1 != zero_zero_int ),
c_0_3089,
[final] ).
cnf(c_0_4085,plain,
( X1 = zero_zero_nat
| zero_zero_nat != X1 ),
c_0_3090,
[final] ).
cnf(c_0_4086,plain,
( zero_zero_nat = X1
| X1 != zero_zero_nat ),
c_0_3091,
[final] ).
cnf(c_0_4087,plain,
( X1 = zero_zero_real
| zero_zero_real != X1 ),
c_0_3092,
[final] ).
cnf(c_0_4088,plain,
( zero_zero_real = X1
| X1 != zero_zero_real ),
c_0_3093,
[final] ).
cnf(c_0_4089,plain,
number267125858f_real(pls) = zero_zero_real,
c_0_3094,
[final] ).
cnf(c_0_4090,plain,
number_number_of_int(pls) = zero_zero_int,
c_0_3095,
[final] ).
cnf(c_0_4091,plain,
number267125858f_real(pls) = zero_zero_real,
c_0_3096,
[final] ).
cnf(c_0_4092,plain,
number_number_of_int(pls) = zero_zero_int,
c_0_3097,
[final] ).
cnf(c_0_4093,plain,
number267125858f_real(pls) = zero_zero_real,
c_0_3098,
[final] ).
cnf(c_0_4094,plain,
number_number_of_nat(pls) = zero_zero_nat,
c_0_3099,
[final] ).
cnf(c_0_4095,plain,
number_number_of_int(pls) = zero_zero_int,
c_0_3100,
[final] ).
cnf(c_0_4096,plain,
bit0(pls) = pls,
c_0_3101,
[final] ).
cnf(c_0_4097,plain,
number_number_of_nat(pls) = zero_zero_nat,
c_0_3102,
[final] ).
cnf(c_0_4098,plain,
number_number_of_nat(pls) = zero_zero_nat,
c_0_3103,
[final] ).
cnf(c_0_4099,plain,
number_number_of_int(pls) = zero_zero_int,
c_0_3104,
[final] ).
cnf(c_0_4100,plain,
is_bool(fTrue),
c_0_3105,
[final] ).
cnf(c_0_4101,plain,
is_bool(fFalse),
c_0_3106,
[final] ).
cnf(c_0_4102,plain,
one_one_int != zero_zero_int,
c_0_3107,
[final] ).
cnf(c_0_4103,plain,
zero_zero_nat != one_one_nat,
c_0_3108,
[final] ).
cnf(c_0_4104,plain,
one_one_real != zero_zero_real,
c_0_3109,
[final] ).
cnf(c_0_4105,plain,
one_one_int != zero_zero_int,
c_0_3110,
[final] ).
cnf(c_0_4106,plain,
zero_zero_nat != one_one_nat,
c_0_3111,
[final] ).
cnf(c_0_4107,plain,
one_one_real != zero_zero_real,
c_0_3112,
[final] ).
cnf(c_0_4108,plain,
one_one_real != zero_zero_real,
c_0_3113,
[final] ).
cnf(c_0_4109,plain,
one_one_int != zero_zero_int,
c_0_3114,
[final] ).
cnf(c_0_4110,plain,
pls = zero_zero_int,
c_0_3115,
[final] ).
% End CNF derivation
% Generating one_way clauses for all literals in the CNF.
cnf(c_0_3116_0,axiom,
( X1 = zero_zero_int
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(X1),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_int(power_power_int(X2),number_number_of_nat(bit0(bit1(pls)))))),zero_zero_int)) ),
inference(literals_permutation,[status(thm)],[c_0_3116]) ).
cnf(c_0_3116_1,axiom,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(X1),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_int(power_power_int(X2),number_number_of_nat(bit0(bit1(pls)))))),zero_zero_int))
| X1 = zero_zero_int ),
inference(literals_permutation,[status(thm)],[c_0_3116]) ).
cnf(c_0_3117_0,axiom,
( X2 = zero_zero_int
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(X1),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_int(power_power_int(X2),number_number_of_nat(bit0(bit1(pls)))))),zero_zero_int)) ),
inference(literals_permutation,[status(thm)],[c_0_3117]) ).
cnf(c_0_3117_1,axiom,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(X1),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_int(power_power_int(X2),number_number_of_nat(bit0(bit1(pls)))))),zero_zero_int))
| X2 = zero_zero_int ),
inference(literals_permutation,[status(thm)],[c_0_3117]) ).
cnf(c_0_3118_0,axiom,
( X1 = zero_zero_real
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(plus_plus_real(hAPP_nat_real(power_power_real(X1),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_real(power_power_real(X2),number_number_of_nat(bit0(bit1(pls)))))),zero_zero_real)) ),
inference(literals_permutation,[status(thm)],[c_0_3118]) ).
cnf(c_0_3118_1,axiom,
( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(plus_plus_real(hAPP_nat_real(power_power_real(X1),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_real(power_power_real(X2),number_number_of_nat(bit0(bit1(pls)))))),zero_zero_real))
| X1 = zero_zero_real ),
inference(literals_permutation,[status(thm)],[c_0_3118]) ).
cnf(c_0_3119_0,axiom,
( X2 = zero_zero_real
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(plus_plus_real(hAPP_nat_real(power_power_real(X1),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_real(power_power_real(X2),number_number_of_nat(bit0(bit1(pls)))))),zero_zero_real)) ),
inference(literals_permutation,[status(thm)],[c_0_3119]) ).
cnf(c_0_3119_1,axiom,
( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(plus_plus_real(hAPP_nat_real(power_power_real(X1),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_real(power_power_real(X2),number_number_of_nat(bit0(bit1(pls)))))),zero_zero_real))
| X2 = zero_zero_real ),
inference(literals_permutation,[status(thm)],[c_0_3119]) ).
cnf(c_0_3122_0,axiom,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(X1,X2)),X3)),hAPP_nat_nat(X1,hAPP_nat_nat(plus_plus_nat(X2),X3))))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(X1,sk1_esk16_3(X2,X3,X1))),hAPP_nat_nat(X1,sk1_esk17_3(X2,X3,X1)))) ),
inference(literals_permutation,[status(thm)],[c_0_3122]) ).
cnf(c_0_3122_1,axiom,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(X1,sk1_esk16_3(X2,X3,X1))),hAPP_nat_nat(X1,sk1_esk17_3(X2,X3,X1))))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(X1,X2)),X3)),hAPP_nat_nat(X1,hAPP_nat_nat(plus_plus_nat(X2),X3)))) ),
inference(literals_permutation,[status(thm)],[c_0_3122]) ).
cnf(c_0_3123_0,axiom,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(X1,X2)),hAPP_nat_nat(X1,X3)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X3))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(X1,sk1_esk20_3(X2,X3,X1))),hAPP_nat_nat(X1,sk1_esk21_3(X2,X3,X1)))) ),
inference(literals_permutation,[status(thm)],[c_0_3123]) ).
cnf(c_0_3123_1,axiom,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X3))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(X1,X2)),hAPP_nat_nat(X1,X3)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(X1,sk1_esk20_3(X2,X3,X1))),hAPP_nat_nat(X1,sk1_esk21_3(X2,X3,X1)))) ),
inference(literals_permutation,[status(thm)],[c_0_3123]) ).
cnf(c_0_3123_2,axiom,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(X1,sk1_esk20_3(X2,X3,X1))),hAPP_nat_nat(X1,sk1_esk21_3(X2,X3,X1))))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X3))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(X1,X2)),hAPP_nat_nat(X1,X3))) ),
inference(literals_permutation,[status(thm)],[c_0_3123]) ).
cnf(c_0_3125_0,axiom,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(X1),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_int(power_power_int(X2),number_number_of_nat(bit0(bit1(pls)))))),zero_zero_int))
| X2 != zero_zero_int
| X1 != zero_zero_int ),
inference(literals_permutation,[status(thm)],[c_0_3125]) ).
cnf(c_0_3125_1,axiom,
( X2 != zero_zero_int
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(X1),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_int(power_power_int(X2),number_number_of_nat(bit0(bit1(pls)))))),zero_zero_int))
| X1 != zero_zero_int ),
inference(literals_permutation,[status(thm)],[c_0_3125]) ).
cnf(c_0_3125_2,axiom,
( X1 != zero_zero_int
| X2 != zero_zero_int
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(X1),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_int(power_power_int(X2),number_number_of_nat(bit0(bit1(pls)))))),zero_zero_int)) ),
inference(literals_permutation,[status(thm)],[c_0_3125]) ).
cnf(c_0_3126_0,axiom,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(plus_plus_real(hAPP_nat_real(power_power_real(X1),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_real(power_power_real(X2),number_number_of_nat(bit0(bit1(pls)))))),zero_zero_real))
| X2 != zero_zero_real
| X1 != zero_zero_real ),
inference(literals_permutation,[status(thm)],[c_0_3126]) ).
cnf(c_0_3126_1,axiom,
( X2 != zero_zero_real
| hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(plus_plus_real(hAPP_nat_real(power_power_real(X1),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_real(power_power_real(X2),number_number_of_nat(bit0(bit1(pls)))))),zero_zero_real))
| X1 != zero_zero_real ),
inference(literals_permutation,[status(thm)],[c_0_3126]) ).
cnf(c_0_3126_2,axiom,
( X1 != zero_zero_real
| X2 != zero_zero_real
| hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(plus_plus_real(hAPP_nat_real(power_power_real(X1),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_real(power_power_real(X2),number_number_of_nat(bit0(bit1(pls)))))),zero_zero_real)) ),
inference(literals_permutation,[status(thm)],[c_0_3126]) ).
cnf(c_0_3127_0,axiom,
( X1 != zero_zero_real
| X2 != zero_zero_real
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),hAPP_real_real(plus_plus_real(hAPP_nat_real(power_power_real(X2),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_real(power_power_real(X1),number_number_of_nat(bit0(bit1(pls))))))) ),
inference(literals_permutation,[status(thm)],[c_0_3127]) ).
cnf(c_0_3127_1,axiom,
( X2 != zero_zero_real
| X1 != zero_zero_real
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),hAPP_real_real(plus_plus_real(hAPP_nat_real(power_power_real(X2),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_real(power_power_real(X1),number_number_of_nat(bit0(bit1(pls))))))) ),
inference(literals_permutation,[status(thm)],[c_0_3127]) ).
cnf(c_0_3127_2,axiom,
( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),hAPP_real_real(plus_plus_real(hAPP_nat_real(power_power_real(X2),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_real(power_power_real(X1),number_number_of_nat(bit0(bit1(pls)))))))
| X2 != zero_zero_real
| X1 != zero_zero_real ),
inference(literals_permutation,[status(thm)],[c_0_3127]) ).
cnf(c_0_3128_0,axiom,
( X1 != zero_zero_int
| X2 != zero_zero_int
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(X2),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_int(power_power_int(X1),number_number_of_nat(bit0(bit1(pls))))))) ),
inference(literals_permutation,[status(thm)],[c_0_3128]) ).
cnf(c_0_3128_1,axiom,
( X2 != zero_zero_int
| X1 != zero_zero_int
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(X2),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_int(power_power_int(X1),number_number_of_nat(bit0(bit1(pls))))))) ),
inference(literals_permutation,[status(thm)],[c_0_3128]) ).
cnf(c_0_3128_2,axiom,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(X2),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_int(power_power_int(X1),number_number_of_nat(bit0(bit1(pls)))))))
| X2 != zero_zero_int
| X1 != zero_zero_int ),
inference(literals_permutation,[status(thm)],[c_0_3128]) ).
cnf(c_0_3130_0,axiom,
( hBOOL(hAPP_int_bool(X3,X2))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X2))
| ~ hBOOL(hAPP_int_bool(X3,hAPP_int_int(plus_plus_int(X1),one_one_int)))
| ~ hBOOL(hAPP_int_bool(X3,hAPP_int_int(plus_plus_int(sk1_esk1_3(X3,X1,X2)),one_one_int))) ),
inference(literals_permutation,[status(thm)],[c_0_3130]) ).
cnf(c_0_3130_1,axiom,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X2))
| hBOOL(hAPP_int_bool(X3,X2))
| ~ hBOOL(hAPP_int_bool(X3,hAPP_int_int(plus_plus_int(X1),one_one_int)))
| ~ hBOOL(hAPP_int_bool(X3,hAPP_int_int(plus_plus_int(sk1_esk1_3(X3,X1,X2)),one_one_int))) ),
inference(literals_permutation,[status(thm)],[c_0_3130]) ).
cnf(c_0_3130_2,axiom,
( ~ hBOOL(hAPP_int_bool(X3,hAPP_int_int(plus_plus_int(X1),one_one_int)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X2))
| hBOOL(hAPP_int_bool(X3,X2))
| ~ hBOOL(hAPP_int_bool(X3,hAPP_int_int(plus_plus_int(sk1_esk1_3(X3,X1,X2)),one_one_int))) ),
inference(literals_permutation,[status(thm)],[c_0_3130]) ).
cnf(c_0_3130_3,axiom,
( ~ hBOOL(hAPP_int_bool(X3,hAPP_int_int(plus_plus_int(sk1_esk1_3(X3,X1,X2)),one_one_int)))
| ~ hBOOL(hAPP_int_bool(X3,hAPP_int_int(plus_plus_int(X1),one_one_int)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X2))
| hBOOL(hAPP_int_bool(X3,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3130]) ).
cnf(c_0_3131_0,axiom,
( hBOOL(hAPP_int_bool(X3,X2))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2))
| ~ hBOOL(hAPP_int_bool(X3,X1))
| ~ hBOOL(hAPP_int_bool(X3,hAPP_int_int(plus_plus_int(sk1_esk18_3(X3,X1,X2)),one_one_int))) ),
inference(literals_permutation,[status(thm)],[c_0_3131]) ).
cnf(c_0_3131_1,axiom,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2))
| hBOOL(hAPP_int_bool(X3,X2))
| ~ hBOOL(hAPP_int_bool(X3,X1))
| ~ hBOOL(hAPP_int_bool(X3,hAPP_int_int(plus_plus_int(sk1_esk18_3(X3,X1,X2)),one_one_int))) ),
inference(literals_permutation,[status(thm)],[c_0_3131]) ).
cnf(c_0_3131_2,axiom,
( ~ hBOOL(hAPP_int_bool(X3,X1))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2))
| hBOOL(hAPP_int_bool(X3,X2))
| ~ hBOOL(hAPP_int_bool(X3,hAPP_int_int(plus_plus_int(sk1_esk18_3(X3,X1,X2)),one_one_int))) ),
inference(literals_permutation,[status(thm)],[c_0_3131]) ).
cnf(c_0_3131_3,axiom,
( ~ hBOOL(hAPP_int_bool(X3,hAPP_int_int(plus_plus_int(sk1_esk18_3(X3,X1,X2)),one_one_int)))
| ~ hBOOL(hAPP_int_bool(X3,X1))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2))
| hBOOL(hAPP_int_bool(X3,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3131]) ).
cnf(c_0_3132_0,axiom,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(X1,X2)),X3)),hAPP_nat_nat(X1,hAPP_nat_nat(plus_plus_nat(X2),X3))))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,sk1_esk16_3(X2,X3,X1)),sk1_esk17_3(X2,X3,X1))) ),
inference(literals_permutation,[status(thm)],[c_0_3132]) ).
cnf(c_0_3132_1,axiom,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,sk1_esk16_3(X2,X3,X1)),sk1_esk17_3(X2,X3,X1)))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(X1,X2)),X3)),hAPP_nat_nat(X1,hAPP_nat_nat(plus_plus_nat(X2),X3)))) ),
inference(literals_permutation,[status(thm)],[c_0_3132]) ).
cnf(c_0_3133_0,axiom,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),hAPP_real_real(plus_plus_real(hAPP_nat_real(power_power_real(X1),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_real(power_power_real(X2),number_number_of_nat(bit0(bit1(pls)))))))
| X1 = zero_zero_real ),
inference(literals_permutation,[status(thm)],[c_0_3133]) ).
cnf(c_0_3133_1,axiom,
( X1 = zero_zero_real
| hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),hAPP_real_real(plus_plus_real(hAPP_nat_real(power_power_real(X1),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_real(power_power_real(X2),number_number_of_nat(bit0(bit1(pls))))))) ),
inference(literals_permutation,[status(thm)],[c_0_3133]) ).
cnf(c_0_3134_0,axiom,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),hAPP_real_real(plus_plus_real(hAPP_nat_real(power_power_real(X1),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_real(power_power_real(X2),number_number_of_nat(bit0(bit1(pls)))))))
| X2 = zero_zero_real ),
inference(literals_permutation,[status(thm)],[c_0_3134]) ).
cnf(c_0_3134_1,axiom,
( X2 = zero_zero_real
| hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),hAPP_real_real(plus_plus_real(hAPP_nat_real(power_power_real(X1),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_real(power_power_real(X2),number_number_of_nat(bit0(bit1(pls))))))) ),
inference(literals_permutation,[status(thm)],[c_0_3134]) ).
cnf(c_0_3135_0,axiom,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(X1),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_int(power_power_int(X2),number_number_of_nat(bit0(bit1(pls)))))))
| X1 = zero_zero_int ),
inference(literals_permutation,[status(thm)],[c_0_3135]) ).
cnf(c_0_3135_1,axiom,
( X1 = zero_zero_int
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(X1),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_int(power_power_int(X2),number_number_of_nat(bit0(bit1(pls))))))) ),
inference(literals_permutation,[status(thm)],[c_0_3135]) ).
cnf(c_0_3136_0,axiom,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(X1),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_int(power_power_int(X2),number_number_of_nat(bit0(bit1(pls)))))))
| X2 = zero_zero_int ),
inference(literals_permutation,[status(thm)],[c_0_3136]) ).
cnf(c_0_3136_1,axiom,
( X2 = zero_zero_int
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(X1),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_int(power_power_int(X2),number_number_of_nat(bit0(bit1(pls))))))) ),
inference(literals_permutation,[status(thm)],[c_0_3136]) ).
cnf(c_0_3139_0,axiom,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X2))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X2))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_nat_int(power_power_int(X1),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_int(power_power_int(X2),number_number_of_nat(bit0(bit1(pls)))))) ),
inference(literals_permutation,[status(thm)],[c_0_3139]) ).
cnf(c_0_3139_1,axiom,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X2))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X2))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_nat_int(power_power_int(X1),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_int(power_power_int(X2),number_number_of_nat(bit0(bit1(pls)))))) ),
inference(literals_permutation,[status(thm)],[c_0_3139]) ).
cnf(c_0_3139_2,axiom,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_nat_int(power_power_int(X1),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_int(power_power_int(X2),number_number_of_nat(bit0(bit1(pls))))))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X2))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3139]) ).
cnf(c_0_3140_0,axiom,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(power_power_nat(X1),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_nat(power_power_nat(X2),number_number_of_nat(bit0(bit1(pls)))))) ),
inference(literals_permutation,[status(thm)],[c_0_3140]) ).
cnf(c_0_3140_1,axiom,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),X2))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(power_power_nat(X1),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_nat(power_power_nat(X2),number_number_of_nat(bit0(bit1(pls)))))) ),
inference(literals_permutation,[status(thm)],[c_0_3140]) ).
cnf(c_0_3140_2,axiom,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(power_power_nat(X1),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_nat(power_power_nat(X2),number_number_of_nat(bit0(bit1(pls))))))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),X2))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3140]) ).
cnf(c_0_3141_0,axiom,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X1),X2))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X2))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_nat_real(power_power_real(X1),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_real(power_power_real(X2),number_number_of_nat(bit0(bit1(pls)))))) ),
inference(literals_permutation,[status(thm)],[c_0_3141]) ).
cnf(c_0_3141_1,axiom,
( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X2))
| hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X1),X2))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_nat_real(power_power_real(X1),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_real(power_power_real(X2),number_number_of_nat(bit0(bit1(pls)))))) ),
inference(literals_permutation,[status(thm)],[c_0_3141]) ).
cnf(c_0_3141_2,axiom,
( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_nat_real(power_power_real(X1),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_real(power_power_real(X2),number_number_of_nat(bit0(bit1(pls))))))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X2))
| hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3141]) ).
cnf(c_0_3142_0,axiom,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X2))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_nat_int(power_power_int(X1),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_int(power_power_int(X2),number_number_of_nat(bit0(bit1(pls)))))) ),
inference(literals_permutation,[status(thm)],[c_0_3142]) ).
cnf(c_0_3142_1,axiom,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X2))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_nat_int(power_power_int(X1),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_int(power_power_int(X2),number_number_of_nat(bit0(bit1(pls)))))) ),
inference(literals_permutation,[status(thm)],[c_0_3142]) ).
cnf(c_0_3142_2,axiom,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_nat_int(power_power_int(X1),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_int(power_power_int(X2),number_number_of_nat(bit0(bit1(pls))))))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X2))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3142]) ).
cnf(c_0_3143_0,axiom,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(power_power_nat(X1),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_nat(power_power_nat(X2),number_number_of_nat(bit0(bit1(pls)))))) ),
inference(literals_permutation,[status(thm)],[c_0_3143]) ).
cnf(c_0_3143_1,axiom,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),X2))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(power_power_nat(X1),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_nat(power_power_nat(X2),number_number_of_nat(bit0(bit1(pls)))))) ),
inference(literals_permutation,[status(thm)],[c_0_3143]) ).
cnf(c_0_3143_2,axiom,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(power_power_nat(X1),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_nat(power_power_nat(X2),number_number_of_nat(bit0(bit1(pls))))))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),X2))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3143]) ).
cnf(c_0_3144_0,axiom,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X1),X2))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X2))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_nat_real(power_power_real(X1),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_real(power_power_real(X2),number_number_of_nat(bit0(bit1(pls)))))) ),
inference(literals_permutation,[status(thm)],[c_0_3144]) ).
cnf(c_0_3144_1,axiom,
( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X2))
| hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X1),X2))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_nat_real(power_power_real(X1),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_real(power_power_real(X2),number_number_of_nat(bit0(bit1(pls)))))) ),
inference(literals_permutation,[status(thm)],[c_0_3144]) ).
cnf(c_0_3144_2,axiom,
( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_nat_real(power_power_real(X1),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_real(power_power_real(X2),number_number_of_nat(bit0(bit1(pls))))))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X2))
| hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3144]) ).
cnf(c_0_3145_0,axiom,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),zero_zero_int))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),X1)),X1)),zero_zero_int)) ),
inference(literals_permutation,[status(thm)],[c_0_3145]) ).
cnf(c_0_3145_1,axiom,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),X1)),X1)),zero_zero_int))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),zero_zero_int)) ),
inference(literals_permutation,[status(thm)],[c_0_3145]) ).
cnf(c_0_3146_0,axiom,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(X1,X2)),hAPP_nat_nat(X1,X3)))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,sk1_esk20_3(X2,X3,X1)),sk1_esk21_3(X2,X3,X1)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3146]) ).
cnf(c_0_3146_1,axiom,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,sk1_esk20_3(X2,X3,X1)),sk1_esk21_3(X2,X3,X1)))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(X1,X2)),hAPP_nat_nat(X1,X3)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3146]) ).
cnf(c_0_3146_2,axiom,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X3))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,sk1_esk20_3(X2,X3,X1)),sk1_esk21_3(X2,X3,X1)))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(X1,X2)),hAPP_nat_nat(X1,X3))) ),
inference(literals_permutation,[status(thm)],[c_0_3146]) ).
cnf(c_0_3147_0,axiom,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),X1)),X1)),zero_zero_int))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),zero_zero_int)) ),
inference(literals_permutation,[status(thm)],[c_0_3147]) ).
cnf(c_0_3147_1,axiom,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),zero_zero_int))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),X1)),X1)),zero_zero_int)) ),
inference(literals_permutation,[status(thm)],[c_0_3147]) ).
cnf(c_0_3150_0,axiom,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X2))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X2))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_nat_int(power_power_int(X1),X3)),hAPP_nat_int(power_power_int(X2),X3))) ),
inference(literals_permutation,[status(thm)],[c_0_3150]) ).
cnf(c_0_3150_1,axiom,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X2))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X2))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_nat_int(power_power_int(X1),X3)),hAPP_nat_int(power_power_int(X2),X3))) ),
inference(literals_permutation,[status(thm)],[c_0_3150]) ).
cnf(c_0_3150_2,axiom,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_nat_int(power_power_int(X1),X3)),hAPP_nat_int(power_power_int(X2),X3)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X2))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3150]) ).
cnf(c_0_3151_0,axiom,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(power_power_nat(X1),X3)),hAPP_nat_nat(power_power_nat(X2),X3))) ),
inference(literals_permutation,[status(thm)],[c_0_3151]) ).
cnf(c_0_3151_1,axiom,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),X2))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(power_power_nat(X1),X3)),hAPP_nat_nat(power_power_nat(X2),X3))) ),
inference(literals_permutation,[status(thm)],[c_0_3151]) ).
cnf(c_0_3151_2,axiom,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(power_power_nat(X1),X3)),hAPP_nat_nat(power_power_nat(X2),X3)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),X2))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3151]) ).
cnf(c_0_3152_0,axiom,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X1),X2))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X2))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_nat_real(power_power_real(X1),X3)),hAPP_nat_real(power_power_real(X2),X3))) ),
inference(literals_permutation,[status(thm)],[c_0_3152]) ).
cnf(c_0_3152_1,axiom,
( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X2))
| hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X1),X2))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_nat_real(power_power_real(X1),X3)),hAPP_nat_real(power_power_real(X2),X3))) ),
inference(literals_permutation,[status(thm)],[c_0_3152]) ).
cnf(c_0_3152_2,axiom,
( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_nat_real(power_power_real(X1),X3)),hAPP_nat_real(power_power_real(X2),X3)))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X2))
| hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3152]) ).
cnf(c_0_3153_0,axiom,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_nat_int(power_power_int(X3),X1)),hAPP_nat_int(power_power_int(X3),X2)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3153]) ).
cnf(c_0_3153_1,axiom,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_nat_int(power_power_int(X3),X1)),hAPP_nat_int(power_power_int(X3),X2)))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3153]) ).
cnf(c_0_3153_2,axiom,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),X3))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_nat_int(power_power_int(X3),X1)),hAPP_nat_int(power_power_int(X3),X2)))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3153]) ).
cnf(c_0_3154_0,axiom,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(power_power_nat(X3),X1)),hAPP_nat_nat(power_power_nat(X3),X2)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,one_one_nat),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3154]) ).
cnf(c_0_3154_1,axiom,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(power_power_nat(X3),X1)),hAPP_nat_nat(power_power_nat(X3),X2)))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,one_one_nat),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3154]) ).
cnf(c_0_3154_2,axiom,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,one_one_nat),X3))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(power_power_nat(X3),X1)),hAPP_nat_nat(power_power_nat(X3),X2)))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3154]) ).
cnf(c_0_3155_0,axiom,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_nat_real(power_power_real(X3),X1)),hAPP_nat_real(power_power_real(X3),X2)))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,one_one_real),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3155]) ).
cnf(c_0_3155_1,axiom,
( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_nat_real(power_power_real(X3),X1)),hAPP_nat_real(power_power_real(X3),X2)))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,one_one_real),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3155]) ).
cnf(c_0_3155_2,axiom,
( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,one_one_real),X3))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_nat_real(power_power_real(X3),X1)),hAPP_nat_real(power_power_real(X3),X2)))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3155]) ).
cnf(c_0_3156_0,axiom,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X3))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),X1))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_nat_int(power_power_int(X1),X2)),hAPP_nat_int(power_power_int(X1),X3))) ),
inference(literals_permutation,[status(thm)],[c_0_3156]) ).
cnf(c_0_3156_1,axiom,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),X1))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X3))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_nat_int(power_power_int(X1),X2)),hAPP_nat_int(power_power_int(X1),X3))) ),
inference(literals_permutation,[status(thm)],[c_0_3156]) ).
cnf(c_0_3156_2,axiom,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_nat_int(power_power_int(X1),X2)),hAPP_nat_int(power_power_int(X1),X3)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),X1))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3156]) ).
cnf(c_0_3157_0,axiom,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X3))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,one_one_nat),X1))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(power_power_nat(X1),X2)),hAPP_nat_nat(power_power_nat(X1),X3))) ),
inference(literals_permutation,[status(thm)],[c_0_3157]) ).
cnf(c_0_3157_1,axiom,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,one_one_nat),X1))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X3))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(power_power_nat(X1),X2)),hAPP_nat_nat(power_power_nat(X1),X3))) ),
inference(literals_permutation,[status(thm)],[c_0_3157]) ).
cnf(c_0_3157_2,axiom,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(power_power_nat(X1),X2)),hAPP_nat_nat(power_power_nat(X1),X3)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,one_one_nat),X1))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3157]) ).
cnf(c_0_3158_0,axiom,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X3))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,one_one_real),X1))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_nat_real(power_power_real(X1),X2)),hAPP_nat_real(power_power_real(X1),X3))) ),
inference(literals_permutation,[status(thm)],[c_0_3158]) ).
cnf(c_0_3158_1,axiom,
( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,one_one_real),X1))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X3))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_nat_real(power_power_real(X1),X2)),hAPP_nat_real(power_power_real(X1),X3))) ),
inference(literals_permutation,[status(thm)],[c_0_3158]) ).
cnf(c_0_3158_2,axiom,
( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_nat_real(power_power_real(X1),X2)),hAPP_nat_real(power_power_real(X1),X3)))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,one_one_real),X1))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3158]) ).
cnf(c_0_3159_0,axiom,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_nat_int(power_power_int(X3),X1)),hAPP_nat_int(power_power_int(X3),X2)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3159]) ).
cnf(c_0_3159_1,axiom,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_nat_int(power_power_int(X3),X1)),hAPP_nat_int(power_power_int(X3),X2)))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3159]) ).
cnf(c_0_3159_2,axiom,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),X3))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_nat_int(power_power_int(X3),X1)),hAPP_nat_int(power_power_int(X3),X2)))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3159]) ).
cnf(c_0_3160_0,axiom,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(power_power_nat(X3),X1)),hAPP_nat_nat(power_power_nat(X3),X2)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,one_one_nat),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3160]) ).
cnf(c_0_3160_1,axiom,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(power_power_nat(X3),X1)),hAPP_nat_nat(power_power_nat(X3),X2)))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,one_one_nat),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3160]) ).
cnf(c_0_3160_2,axiom,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,one_one_nat),X3))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(power_power_nat(X3),X1)),hAPP_nat_nat(power_power_nat(X3),X2)))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3160]) ).
cnf(c_0_3161_0,axiom,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_nat_real(power_power_real(X3),X1)),hAPP_nat_real(power_power_real(X3),X2)))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,one_one_real),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3161]) ).
cnf(c_0_3161_1,axiom,
( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_nat_real(power_power_real(X3),X1)),hAPP_nat_real(power_power_real(X3),X2)))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,one_one_real),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3161]) ).
cnf(c_0_3161_2,axiom,
( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,one_one_real),X3))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_nat_real(power_power_real(X3),X1)),hAPP_nat_real(power_power_real(X3),X2)))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3161]) ).
cnf(c_0_3162_0,axiom,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X2),X3))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),X1))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_nat_int(power_power_int(X1),X2)),hAPP_nat_int(power_power_int(X1),X3))) ),
inference(literals_permutation,[status(thm)],[c_0_3162]) ).
cnf(c_0_3162_1,axiom,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),X1))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X2),X3))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_nat_int(power_power_int(X1),X2)),hAPP_nat_int(power_power_int(X1),X3))) ),
inference(literals_permutation,[status(thm)],[c_0_3162]) ).
cnf(c_0_3162_2,axiom,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_nat_int(power_power_int(X1),X2)),hAPP_nat_int(power_power_int(X1),X3)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),X1))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3162]) ).
cnf(c_0_3163_0,axiom,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X2),X3))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,one_one_nat),X1))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(power_power_nat(X1),X2)),hAPP_nat_nat(power_power_nat(X1),X3))) ),
inference(literals_permutation,[status(thm)],[c_0_3163]) ).
cnf(c_0_3163_1,axiom,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,one_one_nat),X1))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X2),X3))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(power_power_nat(X1),X2)),hAPP_nat_nat(power_power_nat(X1),X3))) ),
inference(literals_permutation,[status(thm)],[c_0_3163]) ).
cnf(c_0_3163_2,axiom,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(power_power_nat(X1),X2)),hAPP_nat_nat(power_power_nat(X1),X3)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,one_one_nat),X1))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3163]) ).
cnf(c_0_3164_0,axiom,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X2),X3))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,one_one_real),X1))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_nat_real(power_power_real(X1),X2)),hAPP_nat_real(power_power_real(X1),X3))) ),
inference(literals_permutation,[status(thm)],[c_0_3164]) ).
cnf(c_0_3164_1,axiom,
( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,one_one_real),X1))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X2),X3))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_nat_real(power_power_real(X1),X2)),hAPP_nat_real(power_power_real(X1),X3))) ),
inference(literals_permutation,[status(thm)],[c_0_3164]) ).
cnf(c_0_3164_2,axiom,
( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_nat_real(power_power_real(X1),X2)),hAPP_nat_real(power_power_real(X1),X3)))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,one_one_real),X1))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3164]) ).
cnf(c_0_3165_0,axiom,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(power_power_nat(X3),X1)),hAPP_nat_nat(power_power_nat(X3),X2)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3165]) ).
cnf(c_0_3165_1,axiom,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(power_power_nat(X3),X1)),hAPP_nat_nat(power_power_nat(X3),X2)))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3165]) ).
cnf(c_0_3165_2,axiom,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X3))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(power_power_nat(X3),X1)),hAPP_nat_nat(power_power_nat(X3),X2)))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3165]) ).
cnf(c_0_3166_0,axiom,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_nat_int(power_power_int(X1),X2)),hAPP_nat_int(power_power_int(X1),X3)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),one_one_int))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X3),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3166]) ).
cnf(c_0_3166_1,axiom,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),one_one_int))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_nat_int(power_power_int(X1),X2)),hAPP_nat_int(power_power_int(X1),X3)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X3),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3166]) ).
cnf(c_0_3166_2,axiom,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),one_one_int))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_nat_int(power_power_int(X1),X2)),hAPP_nat_int(power_power_int(X1),X3)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X3),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3166]) ).
cnf(c_0_3166_3,axiom,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X3),X2))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),one_one_int))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_nat_int(power_power_int(X1),X2)),hAPP_nat_int(power_power_int(X1),X3))) ),
inference(literals_permutation,[status(thm)],[c_0_3166]) ).
cnf(c_0_3167_0,axiom,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(power_power_nat(X1),X2)),hAPP_nat_nat(power_power_nat(X1),X3)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),one_one_nat))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),X1))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X3),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3167]) ).
cnf(c_0_3167_1,axiom,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),one_one_nat))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(power_power_nat(X1),X2)),hAPP_nat_nat(power_power_nat(X1),X3)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),X1))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X3),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3167]) ).
cnf(c_0_3167_2,axiom,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),X1))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),one_one_nat))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(power_power_nat(X1),X2)),hAPP_nat_nat(power_power_nat(X1),X3)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X3),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3167]) ).
cnf(c_0_3167_3,axiom,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X3),X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),X1))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),one_one_nat))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(power_power_nat(X1),X2)),hAPP_nat_nat(power_power_nat(X1),X3))) ),
inference(literals_permutation,[status(thm)],[c_0_3167]) ).
cnf(c_0_3168_0,axiom,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_nat_real(power_power_real(X1),X2)),hAPP_nat_real(power_power_real(X1),X3)))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X1),one_one_real))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X1))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X3),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3168]) ).
cnf(c_0_3168_1,axiom,
( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X1),one_one_real))
| hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_nat_real(power_power_real(X1),X2)),hAPP_nat_real(power_power_real(X1),X3)))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X1))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X3),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3168]) ).
cnf(c_0_3168_2,axiom,
( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X1))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X1),one_one_real))
| hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_nat_real(power_power_real(X1),X2)),hAPP_nat_real(power_power_real(X1),X3)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X3),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3168]) ).
cnf(c_0_3168_3,axiom,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X3),X2))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X1))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X1),one_one_real))
| hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_nat_real(power_power_real(X1),X2)),hAPP_nat_real(power_power_real(X1),X3))) ),
inference(literals_permutation,[status(thm)],[c_0_3168]) ).
cnf(c_0_3169_0,axiom,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_nat_real(power_power_real(X1),X2)),hAPP_nat_real(power_power_real(X1),X3)))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X1),one_one_real))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X1))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X3),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3169]) ).
cnf(c_0_3169_1,axiom,
( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X1),one_one_real))
| hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_nat_real(power_power_real(X1),X2)),hAPP_nat_real(power_power_real(X1),X3)))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X1))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X3),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3169]) ).
cnf(c_0_3169_2,axiom,
( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X1))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X1),one_one_real))
| hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_nat_real(power_power_real(X1),X2)),hAPP_nat_real(power_power_real(X1),X3)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X3),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3169]) ).
cnf(c_0_3169_3,axiom,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X3),X2))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X1))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X1),one_one_real))
| hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_nat_real(power_power_real(X1),X2)),hAPP_nat_real(power_power_real(X1),X3))) ),
inference(literals_permutation,[status(thm)],[c_0_3169]) ).
cnf(c_0_3170_0,axiom,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(power_power_nat(X1),X2)),hAPP_nat_nat(power_power_nat(X1),X3)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),one_one_nat))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X3),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3170]) ).
cnf(c_0_3170_1,axiom,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),one_one_nat))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(power_power_nat(X1),X2)),hAPP_nat_nat(power_power_nat(X1),X3)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X3),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3170]) ).
cnf(c_0_3170_2,axiom,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),one_one_nat))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(power_power_nat(X1),X2)),hAPP_nat_nat(power_power_nat(X1),X3)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X3),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3170]) ).
cnf(c_0_3170_3,axiom,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X3),X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),one_one_nat))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(power_power_nat(X1),X2)),hAPP_nat_nat(power_power_nat(X1),X3))) ),
inference(literals_permutation,[status(thm)],[c_0_3170]) ).
cnf(c_0_3171_0,axiom,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_nat_int(power_power_int(X1),X2)),hAPP_nat_int(power_power_int(X1),X3)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),one_one_int))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X1))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X3),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3171]) ).
cnf(c_0_3171_1,axiom,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),one_one_int))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_nat_int(power_power_int(X1),X2)),hAPP_nat_int(power_power_int(X1),X3)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X1))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X3),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3171]) ).
cnf(c_0_3171_2,axiom,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X1))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),one_one_int))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_nat_int(power_power_int(X1),X2)),hAPP_nat_int(power_power_int(X1),X3)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X3),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3171]) ).
cnf(c_0_3171_3,axiom,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X3),X2))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X1))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),one_one_int))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_nat_int(power_power_int(X1),X2)),hAPP_nat_int(power_power_int(X1),X3))) ),
inference(literals_permutation,[status(thm)],[c_0_3171]) ).
cnf(c_0_3172_0,axiom,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_nat_int(power_power_int(X1),X2)),hAPP_nat_int(power_power_int(X3),X2)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X2))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3172]) ).
cnf(c_0_3172_1,axiom,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X2))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_nat_int(power_power_int(X1),X2)),hAPP_nat_int(power_power_int(X3),X2)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3172]) ).
cnf(c_0_3172_2,axiom,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X2))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_nat_int(power_power_int(X1),X2)),hAPP_nat_int(power_power_int(X3),X2)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3172]) ).
cnf(c_0_3172_3,axiom,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X3))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X2))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_nat_int(power_power_int(X1),X2)),hAPP_nat_int(power_power_int(X3),X2))) ),
inference(literals_permutation,[status(thm)],[c_0_3172]) ).
cnf(c_0_3173_0,axiom,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(power_power_nat(X1),X2)),hAPP_nat_nat(power_power_nat(X3),X2)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),X1))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3173]) ).
cnf(c_0_3173_1,axiom,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X2))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(power_power_nat(X1),X2)),hAPP_nat_nat(power_power_nat(X3),X2)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),X1))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3173]) ).
cnf(c_0_3173_2,axiom,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),X1))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X2))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(power_power_nat(X1),X2)),hAPP_nat_nat(power_power_nat(X3),X2)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3173]) ).
cnf(c_0_3173_3,axiom,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X3))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),X1))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X2))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(power_power_nat(X1),X2)),hAPP_nat_nat(power_power_nat(X3),X2))) ),
inference(literals_permutation,[status(thm)],[c_0_3173]) ).
cnf(c_0_3174_0,axiom,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_nat_real(power_power_real(X1),X2)),hAPP_nat_real(power_power_real(X3),X2)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X2))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X1))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X1),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3174]) ).
cnf(c_0_3174_1,axiom,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X2))
| hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_nat_real(power_power_real(X1),X2)),hAPP_nat_real(power_power_real(X3),X2)))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X1))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X1),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3174]) ).
cnf(c_0_3174_2,axiom,
( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X1))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X2))
| hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_nat_real(power_power_real(X1),X2)),hAPP_nat_real(power_power_real(X3),X2)))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X1),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3174]) ).
cnf(c_0_3174_3,axiom,
( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X1),X3))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X1))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X2))
| hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_nat_real(power_power_real(X1),X2)),hAPP_nat_real(power_power_real(X3),X2))) ),
inference(literals_permutation,[status(thm)],[c_0_3174]) ).
cnf(c_0_3175_0,axiom,
( hBOOL(hAPP_int_bool(X3,X2))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),sk1_esk1_3(X3,X1,X2)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X2))
| ~ hBOOL(hAPP_int_bool(X3,hAPP_int_int(plus_plus_int(X1),one_one_int))) ),
inference(literals_permutation,[status(thm)],[c_0_3175]) ).
cnf(c_0_3175_1,axiom,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),sk1_esk1_3(X3,X1,X2)))
| hBOOL(hAPP_int_bool(X3,X2))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X2))
| ~ hBOOL(hAPP_int_bool(X3,hAPP_int_int(plus_plus_int(X1),one_one_int))) ),
inference(literals_permutation,[status(thm)],[c_0_3175]) ).
cnf(c_0_3175_2,axiom,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X2))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),sk1_esk1_3(X3,X1,X2)))
| hBOOL(hAPP_int_bool(X3,X2))
| ~ hBOOL(hAPP_int_bool(X3,hAPP_int_int(plus_plus_int(X1),one_one_int))) ),
inference(literals_permutation,[status(thm)],[c_0_3175]) ).
cnf(c_0_3175_3,axiom,
( ~ hBOOL(hAPP_int_bool(X3,hAPP_int_int(plus_plus_int(X1),one_one_int)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X2))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),sk1_esk1_3(X3,X1,X2)))
| hBOOL(hAPP_int_bool(X3,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3175]) ).
cnf(c_0_3176_0,axiom,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(X3),X1)),hAPP_nat_nat(plus_plus_nat(X3),X2))) ),
inference(literals_permutation,[status(thm)],[c_0_3176]) ).
cnf(c_0_3176_1,axiom,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(X3),X1)),hAPP_nat_nat(plus_plus_nat(X3),X2)))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3176]) ).
cnf(c_0_3177_0,axiom,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(plus_plus_int(X3),X1)),hAPP_int_int(plus_plus_int(X3),X2))) ),
inference(literals_permutation,[status(thm)],[c_0_3177]) ).
cnf(c_0_3177_1,axiom,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(plus_plus_int(X3),X1)),hAPP_int_int(plus_plus_int(X3),X2)))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3177]) ).
cnf(c_0_3178_0,axiom,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(X3),X1)),hAPP_nat_nat(plus_plus_nat(X3),X2))) ),
inference(literals_permutation,[status(thm)],[c_0_3178]) ).
cnf(c_0_3178_1,axiom,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(X3),X1)),hAPP_nat_nat(plus_plus_nat(X3),X2)))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3178]) ).
cnf(c_0_3179_0,axiom,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X1),X2))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(plus_plus_real(X3),X1)),hAPP_real_real(plus_plus_real(X3),X2))) ),
inference(literals_permutation,[status(thm)],[c_0_3179]) ).
cnf(c_0_3179_1,axiom,
( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(plus_plus_real(X3),X1)),hAPP_real_real(plus_plus_real(X3),X2)))
| hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3179]) ).
cnf(c_0_3180_0,axiom,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(plus_plus_int(X1),X3)),hAPP_int_int(plus_plus_int(X2),X3))) ),
inference(literals_permutation,[status(thm)],[c_0_3180]) ).
cnf(c_0_3180_1,axiom,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(plus_plus_int(X1),X3)),hAPP_int_int(plus_plus_int(X2),X3)))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3180]) ).
cnf(c_0_3181_0,axiom,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(X1),X3)),hAPP_nat_nat(plus_plus_nat(X2),X3))) ),
inference(literals_permutation,[status(thm)],[c_0_3181]) ).
cnf(c_0_3181_1,axiom,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(X1),X3)),hAPP_nat_nat(plus_plus_nat(X2),X3)))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3181]) ).
cnf(c_0_3182_0,axiom,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X1),X2))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(plus_plus_real(X1),X3)),hAPP_real_real(plus_plus_real(X2),X3))) ),
inference(literals_permutation,[status(thm)],[c_0_3182]) ).
cnf(c_0_3182_1,axiom,
( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(plus_plus_real(X1),X3)),hAPP_real_real(plus_plus_real(X2),X3)))
| hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3182]) ).
cnf(c_0_3183_0,axiom,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(plus_plus_int(X3),X1)),hAPP_int_int(plus_plus_int(X3),X2))) ),
inference(literals_permutation,[status(thm)],[c_0_3183]) ).
cnf(c_0_3183_1,axiom,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(plus_plus_int(X3),X1)),hAPP_int_int(plus_plus_int(X3),X2)))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3183]) ).
cnf(c_0_3184_0,axiom,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(X3),X1)),hAPP_nat_nat(plus_plus_nat(X3),X2))) ),
inference(literals_permutation,[status(thm)],[c_0_3184]) ).
cnf(c_0_3184_1,axiom,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(X3),X1)),hAPP_nat_nat(plus_plus_nat(X3),X2)))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3184]) ).
cnf(c_0_3185_0,axiom,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X1),X2))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(plus_plus_real(X3),X1)),hAPP_real_real(plus_plus_real(X3),X2))) ),
inference(literals_permutation,[status(thm)],[c_0_3185]) ).
cnf(c_0_3185_1,axiom,
( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(plus_plus_real(X3),X1)),hAPP_real_real(plus_plus_real(X3),X2)))
| hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3185]) ).
cnf(c_0_3186_0,axiom,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(plus_plus_int(X1),X3)),hAPP_int_int(plus_plus_int(X2),X3))) ),
inference(literals_permutation,[status(thm)],[c_0_3186]) ).
cnf(c_0_3186_1,axiom,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(plus_plus_int(X1),X3)),hAPP_int_int(plus_plus_int(X2),X3)))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3186]) ).
cnf(c_0_3187_0,axiom,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(X1),X3)),hAPP_nat_nat(plus_plus_nat(X2),X3))) ),
inference(literals_permutation,[status(thm)],[c_0_3187]) ).
cnf(c_0_3187_1,axiom,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(X1),X3)),hAPP_nat_nat(plus_plus_nat(X2),X3)))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3187]) ).
cnf(c_0_3188_0,axiom,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X1),X2))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(plus_plus_real(X1),X3)),hAPP_real_real(plus_plus_real(X2),X3))) ),
inference(literals_permutation,[status(thm)],[c_0_3188]) ).
cnf(c_0_3188_1,axiom,
( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(plus_plus_real(X1),X3)),hAPP_real_real(plus_plus_real(X2),X3)))
| hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3188]) ).
cnf(c_0_3189_0,axiom,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X2))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(X1),X3)),hAPP_int_int(plus_plus_int(X2),X3))) ),
inference(literals_permutation,[status(thm)],[c_0_3189]) ).
cnf(c_0_3189_1,axiom,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(X1),X3)),hAPP_int_int(plus_plus_int(X2),X3)))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3189]) ).
cnf(c_0_3190_0,axiom,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(X1),X3)),hAPP_nat_nat(plus_plus_nat(X2),X3))) ),
inference(literals_permutation,[status(thm)],[c_0_3190]) ).
cnf(c_0_3190_1,axiom,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(X1),X3)),hAPP_nat_nat(plus_plus_nat(X2),X3)))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3190]) ).
cnf(c_0_3191_0,axiom,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X1),X2))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(plus_plus_real(X1),X3)),hAPP_real_real(plus_plus_real(X2),X3))) ),
inference(literals_permutation,[status(thm)],[c_0_3191]) ).
cnf(c_0_3191_1,axiom,
( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(plus_plus_real(X1),X3)),hAPP_real_real(plus_plus_real(X2),X3)))
| hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3191]) ).
cnf(c_0_3192_0,axiom,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X2))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(X3),X1)),hAPP_int_int(plus_plus_int(X3),X2))) ),
inference(literals_permutation,[status(thm)],[c_0_3192]) ).
cnf(c_0_3192_1,axiom,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(X3),X1)),hAPP_int_int(plus_plus_int(X3),X2)))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3192]) ).
cnf(c_0_3193_0,axiom,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(X3),X1)),hAPP_nat_nat(plus_plus_nat(X3),X2))) ),
inference(literals_permutation,[status(thm)],[c_0_3193]) ).
cnf(c_0_3193_1,axiom,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(X3),X1)),hAPP_nat_nat(plus_plus_nat(X3),X2)))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3193]) ).
cnf(c_0_3194_0,axiom,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X1),X2))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(plus_plus_real(X3),X1)),hAPP_real_real(plus_plus_real(X3),X2))) ),
inference(literals_permutation,[status(thm)],[c_0_3194]) ).
cnf(c_0_3194_1,axiom,
( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(plus_plus_real(X3),X1)),hAPP_real_real(plus_plus_real(X3),X2)))
| hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3194]) ).
cnf(c_0_3195_0,axiom,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X2))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(X1),X3)),hAPP_int_int(plus_plus_int(X2),X3))) ),
inference(literals_permutation,[status(thm)],[c_0_3195]) ).
cnf(c_0_3195_1,axiom,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(X1),X3)),hAPP_int_int(plus_plus_int(X2),X3)))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3195]) ).
cnf(c_0_3196_0,axiom,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(X1),X3)),hAPP_nat_nat(plus_plus_nat(X2),X3))) ),
inference(literals_permutation,[status(thm)],[c_0_3196]) ).
cnf(c_0_3196_1,axiom,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(X1),X3)),hAPP_nat_nat(plus_plus_nat(X2),X3)))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3196]) ).
cnf(c_0_3197_0,axiom,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X1),X2))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(plus_plus_real(X1),X3)),hAPP_real_real(plus_plus_real(X2),X3))) ),
inference(literals_permutation,[status(thm)],[c_0_3197]) ).
cnf(c_0_3197_1,axiom,
( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(plus_plus_real(X1),X3)),hAPP_real_real(plus_plus_real(X2),X3)))
| hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3197]) ).
cnf(c_0_3198_0,axiom,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X2))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(X3),X1)),hAPP_int_int(plus_plus_int(X3),X2))) ),
inference(literals_permutation,[status(thm)],[c_0_3198]) ).
cnf(c_0_3198_1,axiom,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(X3),X1)),hAPP_int_int(plus_plus_int(X3),X2)))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3198]) ).
cnf(c_0_3199_0,axiom,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(X3),X1)),hAPP_nat_nat(plus_plus_nat(X3),X2))) ),
inference(literals_permutation,[status(thm)],[c_0_3199]) ).
cnf(c_0_3199_1,axiom,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(X3),X1)),hAPP_nat_nat(plus_plus_nat(X3),X2)))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3199]) ).
cnf(c_0_3200_0,axiom,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X1),X2))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(plus_plus_real(X3),X1)),hAPP_real_real(plus_plus_real(X3),X2))) ),
inference(literals_permutation,[status(thm)],[c_0_3200]) ).
cnf(c_0_3200_1,axiom,
( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(plus_plus_real(X3),X1)),hAPP_real_real(plus_plus_real(X3),X2)))
| hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3200]) ).
cnf(c_0_3201_0,axiom,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(X3),X1)),hAPP_nat_nat(plus_plus_nat(X3),X2))) ),
inference(literals_permutation,[status(thm)],[c_0_3201]) ).
cnf(c_0_3201_1,axiom,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(X3),X1)),hAPP_nat_nat(plus_plus_nat(X3),X2)))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3201]) ).
cnf(c_0_3202_0,axiom,
( hBOOL(hAPP_int_bool(X3,X2))
| hBOOL(hAPP_int_bool(X3,sk1_esk1_3(X3,X1,X2)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X2))
| ~ hBOOL(hAPP_int_bool(X3,hAPP_int_int(plus_plus_int(X1),one_one_int))) ),
inference(literals_permutation,[status(thm)],[c_0_3202]) ).
cnf(c_0_3202_1,axiom,
( hBOOL(hAPP_int_bool(X3,sk1_esk1_3(X3,X1,X2)))
| hBOOL(hAPP_int_bool(X3,X2))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X2))
| ~ hBOOL(hAPP_int_bool(X3,hAPP_int_int(plus_plus_int(X1),one_one_int))) ),
inference(literals_permutation,[status(thm)],[c_0_3202]) ).
cnf(c_0_3202_2,axiom,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X2))
| hBOOL(hAPP_int_bool(X3,sk1_esk1_3(X3,X1,X2)))
| hBOOL(hAPP_int_bool(X3,X2))
| ~ hBOOL(hAPP_int_bool(X3,hAPP_int_int(plus_plus_int(X1),one_one_int))) ),
inference(literals_permutation,[status(thm)],[c_0_3202]) ).
cnf(c_0_3202_3,axiom,
( ~ hBOOL(hAPP_int_bool(X3,hAPP_int_int(plus_plus_int(X1),one_one_int)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X2))
| hBOOL(hAPP_int_bool(X3,sk1_esk1_3(X3,X1,X2)))
| hBOOL(hAPP_int_bool(X3,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3202]) ).
cnf(c_0_3203_0,axiom,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(X1),X2)),hAPP_nat_nat(plus_plus_nat(X3),X4)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X4))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3203]) ).
cnf(c_0_3203_1,axiom,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X4))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(X1),X2)),hAPP_nat_nat(plus_plus_nat(X3),X4)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3203]) ).
cnf(c_0_3203_2,axiom,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X3))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X4))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(X1),X2)),hAPP_nat_nat(plus_plus_nat(X3),X4))) ),
inference(literals_permutation,[status(thm)],[c_0_3203]) ).
cnf(c_0_3204_0,axiom,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(X1),X2)),hAPP_int_int(plus_plus_int(X3),X4)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X2),X4))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3204]) ).
cnf(c_0_3204_1,axiom,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X2),X4))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(X1),X2)),hAPP_int_int(plus_plus_int(X3),X4)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3204]) ).
cnf(c_0_3204_2,axiom,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X3))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X2),X4))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(X1),X2)),hAPP_int_int(plus_plus_int(X3),X4))) ),
inference(literals_permutation,[status(thm)],[c_0_3204]) ).
cnf(c_0_3205_0,axiom,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(X1),X2)),hAPP_int_int(plus_plus_int(X3),X4)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X2),X4))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3205]) ).
cnf(c_0_3205_1,axiom,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X2),X4))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(X1),X2)),hAPP_int_int(plus_plus_int(X3),X4)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3205]) ).
cnf(c_0_3205_2,axiom,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X3))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X2),X4))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(X1),X2)),hAPP_int_int(plus_plus_int(X3),X4))) ),
inference(literals_permutation,[status(thm)],[c_0_3205]) ).
cnf(c_0_3206_0,axiom,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(X1),X2)),hAPP_nat_nat(plus_plus_nat(X3),X4)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X2),X4))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3206]) ).
cnf(c_0_3206_1,axiom,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X2),X4))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(X1),X2)),hAPP_nat_nat(plus_plus_nat(X3),X4)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3206]) ).
cnf(c_0_3206_2,axiom,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X3))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X2),X4))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(X1),X2)),hAPP_nat_nat(plus_plus_nat(X3),X4))) ),
inference(literals_permutation,[status(thm)],[c_0_3206]) ).
cnf(c_0_3207_0,axiom,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(plus_plus_real(X1),X2)),hAPP_real_real(plus_plus_real(X3),X4)))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X2),X4))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X1),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3207]) ).
cnf(c_0_3207_1,axiom,
( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X2),X4))
| hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(plus_plus_real(X1),X2)),hAPP_real_real(plus_plus_real(X3),X4)))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X1),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3207]) ).
cnf(c_0_3207_2,axiom,
( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X1),X3))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X2),X4))
| hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(plus_plus_real(X1),X2)),hAPP_real_real(plus_plus_real(X3),X4))) ),
inference(literals_permutation,[status(thm)],[c_0_3207]) ).
cnf(c_0_3208_0,axiom,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(X1),X2)),hAPP_int_int(plus_plus_int(X3),X4)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X2),X4))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3208]) ).
cnf(c_0_3208_1,axiom,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X2),X4))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(X1),X2)),hAPP_int_int(plus_plus_int(X3),X4)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3208]) ).
cnf(c_0_3208_2,axiom,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X3))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X2),X4))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(X1),X2)),hAPP_int_int(plus_plus_int(X3),X4))) ),
inference(literals_permutation,[status(thm)],[c_0_3208]) ).
cnf(c_0_3209_0,axiom,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(X1),X2)),hAPP_nat_nat(plus_plus_nat(X3),X4)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X4))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3209]) ).
cnf(c_0_3209_1,axiom,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X4))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(X1),X2)),hAPP_nat_nat(plus_plus_nat(X3),X4)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3209]) ).
cnf(c_0_3209_2,axiom,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X3))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X4))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(X1),X2)),hAPP_nat_nat(plus_plus_nat(X3),X4))) ),
inference(literals_permutation,[status(thm)],[c_0_3209]) ).
cnf(c_0_3210_0,axiom,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(plus_plus_real(X1),X2)),hAPP_real_real(plus_plus_real(X3),X4)))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X2),X4))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X1),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3210]) ).
cnf(c_0_3210_1,axiom,
( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X2),X4))
| hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(plus_plus_real(X1),X2)),hAPP_real_real(plus_plus_real(X3),X4)))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X1),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3210]) ).
cnf(c_0_3210_2,axiom,
( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X1),X3))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X2),X4))
| hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(plus_plus_real(X1),X2)),hAPP_real_real(plus_plus_real(X3),X4))) ),
inference(literals_permutation,[status(thm)],[c_0_3210]) ).
cnf(c_0_3211_0,axiom,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(plus_plus_int(X1),X2)),hAPP_int_int(plus_plus_int(X3),X4)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X2),X4))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3211]) ).
cnf(c_0_3211_1,axiom,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X2),X4))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(plus_plus_int(X1),X2)),hAPP_int_int(plus_plus_int(X3),X4)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3211]) ).
cnf(c_0_3211_2,axiom,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X3))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X2),X4))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(plus_plus_int(X1),X2)),hAPP_int_int(plus_plus_int(X3),X4))) ),
inference(literals_permutation,[status(thm)],[c_0_3211]) ).
cnf(c_0_3212_0,axiom,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(X1),X2)),hAPP_nat_nat(plus_plus_nat(X3),X4)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X4))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3212]) ).
cnf(c_0_3212_1,axiom,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X4))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(X1),X2)),hAPP_nat_nat(plus_plus_nat(X3),X4)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3212]) ).
cnf(c_0_3212_2,axiom,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X3))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X4))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(X1),X2)),hAPP_nat_nat(plus_plus_nat(X3),X4))) ),
inference(literals_permutation,[status(thm)],[c_0_3212]) ).
cnf(c_0_3213_0,axiom,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(plus_plus_real(X1),X2)),hAPP_real_real(plus_plus_real(X3),X4)))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X2),X4))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X1),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3213]) ).
cnf(c_0_3213_1,axiom,
( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X2),X4))
| hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(plus_plus_real(X1),X2)),hAPP_real_real(plus_plus_real(X3),X4)))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X1),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3213]) ).
cnf(c_0_3213_2,axiom,
( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X1),X3))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X2),X4))
| hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(plus_plus_real(X1),X2)),hAPP_real_real(plus_plus_real(X3),X4))) ),
inference(literals_permutation,[status(thm)],[c_0_3213]) ).
cnf(c_0_3214_0,axiom,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(X1),X2)),hAPP_int_int(plus_plus_int(X3),X4)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X2),X4))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3214]) ).
cnf(c_0_3214_1,axiom,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X2),X4))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(X1),X2)),hAPP_int_int(plus_plus_int(X3),X4)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3214]) ).
cnf(c_0_3214_2,axiom,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X3))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X2),X4))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(X1),X2)),hAPP_int_int(plus_plus_int(X3),X4))) ),
inference(literals_permutation,[status(thm)],[c_0_3214]) ).
cnf(c_0_3215_0,axiom,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(X1),X2)),hAPP_nat_nat(plus_plus_nat(X3),X4)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X2),X4))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3215]) ).
cnf(c_0_3215_1,axiom,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X2),X4))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(X1),X2)),hAPP_nat_nat(plus_plus_nat(X3),X4)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3215]) ).
cnf(c_0_3215_2,axiom,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X3))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X2),X4))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(X1),X2)),hAPP_nat_nat(plus_plus_nat(X3),X4))) ),
inference(literals_permutation,[status(thm)],[c_0_3215]) ).
cnf(c_0_3216_0,axiom,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(plus_plus_real(X1),X2)),hAPP_real_real(plus_plus_real(X3),X4)))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X2),X4))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X1),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3216]) ).
cnf(c_0_3216_1,axiom,
( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X2),X4))
| hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(plus_plus_real(X1),X2)),hAPP_real_real(plus_plus_real(X3),X4)))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X1),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3216]) ).
cnf(c_0_3216_2,axiom,
( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X1),X3))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X2),X4))
| hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(plus_plus_real(X1),X2)),hAPP_real_real(plus_plus_real(X3),X4))) ),
inference(literals_permutation,[status(thm)],[c_0_3216]) ).
cnf(c_0_3217_0,axiom,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(X1),X2)),hAPP_nat_nat(plus_plus_nat(X3),X4)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X2),X4))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3217]) ).
cnf(c_0_3217_1,axiom,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X2),X4))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(X1),X2)),hAPP_nat_nat(plus_plus_nat(X3),X4)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3217]) ).
cnf(c_0_3217_2,axiom,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X3))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X2),X4))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(X1),X2)),hAPP_nat_nat(plus_plus_nat(X3),X4))) ),
inference(literals_permutation,[status(thm)],[c_0_3217]) ).
cnf(c_0_3218_0,axiom,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_nat_int(power_power_int(X1),X2)),hAPP_nat_int(power_power_int(X3),X2)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3218]) ).
cnf(c_0_3218_1,axiom,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_nat_int(power_power_int(X1),X2)),hAPP_nat_int(power_power_int(X3),X2)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3218]) ).
cnf(c_0_3218_2,axiom,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X3))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_nat_int(power_power_int(X1),X2)),hAPP_nat_int(power_power_int(X3),X2))) ),
inference(literals_permutation,[status(thm)],[c_0_3218]) ).
cnf(c_0_3219_0,axiom,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(power_power_nat(X1),X2)),hAPP_nat_nat(power_power_nat(X3),X2)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),X1))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3219]) ).
cnf(c_0_3219_1,axiom,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),X1))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(power_power_nat(X1),X2)),hAPP_nat_nat(power_power_nat(X3),X2)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3219]) ).
cnf(c_0_3219_2,axiom,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X3))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),X1))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(power_power_nat(X1),X2)),hAPP_nat_nat(power_power_nat(X3),X2))) ),
inference(literals_permutation,[status(thm)],[c_0_3219]) ).
cnf(c_0_3220_0,axiom,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_nat_real(power_power_real(X1),X2)),hAPP_nat_real(power_power_real(X3),X2)))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X1))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X1),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3220]) ).
cnf(c_0_3220_1,axiom,
( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X1))
| hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_nat_real(power_power_real(X1),X2)),hAPP_nat_real(power_power_real(X3),X2)))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X1),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3220]) ).
cnf(c_0_3220_2,axiom,
( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X1),X3))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X1))
| hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_nat_real(power_power_real(X1),X2)),hAPP_nat_real(power_power_real(X3),X2))) ),
inference(literals_permutation,[status(thm)],[c_0_3220]) ).
cnf(c_0_3221_0,axiom,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_nat_int(power_power_int(X1),X2)),hAPP_nat_int(power_power_int(X1),X3)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),X1))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3221]) ).
cnf(c_0_3221_1,axiom,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),X1))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_nat_int(power_power_int(X1),X2)),hAPP_nat_int(power_power_int(X1),X3)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3221]) ).
cnf(c_0_3221_2,axiom,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X3))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),X1))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_nat_int(power_power_int(X1),X2)),hAPP_nat_int(power_power_int(X1),X3))) ),
inference(literals_permutation,[status(thm)],[c_0_3221]) ).
cnf(c_0_3222_0,axiom,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(power_power_nat(X1),X2)),hAPP_nat_nat(power_power_nat(X1),X3)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,one_one_nat),X1))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3222]) ).
cnf(c_0_3222_1,axiom,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,one_one_nat),X1))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(power_power_nat(X1),X2)),hAPP_nat_nat(power_power_nat(X1),X3)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3222]) ).
cnf(c_0_3222_2,axiom,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X3))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,one_one_nat),X1))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(power_power_nat(X1),X2)),hAPP_nat_nat(power_power_nat(X1),X3))) ),
inference(literals_permutation,[status(thm)],[c_0_3222]) ).
cnf(c_0_3223_0,axiom,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_nat_real(power_power_real(X1),X2)),hAPP_nat_real(power_power_real(X1),X3)))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,one_one_real),X1))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3223]) ).
cnf(c_0_3223_1,axiom,
( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,one_one_real),X1))
| hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_nat_real(power_power_real(X1),X2)),hAPP_nat_real(power_power_real(X1),X3)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3223]) ).
cnf(c_0_3223_2,axiom,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X3))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,one_one_real),X1))
| hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_nat_real(power_power_real(X1),X2)),hAPP_nat_real(power_power_real(X1),X3))) ),
inference(literals_permutation,[status(thm)],[c_0_3223]) ).
cnf(c_0_3224_0,axiom,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_nat_int(power_power_int(X1),X2)),hAPP_nat_int(power_power_int(X1),X3)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),X1))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3224]) ).
cnf(c_0_3224_1,axiom,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),X1))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_nat_int(power_power_int(X1),X2)),hAPP_nat_int(power_power_int(X1),X3)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3224]) ).
cnf(c_0_3224_2,axiom,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X3))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),X1))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_nat_int(power_power_int(X1),X2)),hAPP_nat_int(power_power_int(X1),X3))) ),
inference(literals_permutation,[status(thm)],[c_0_3224]) ).
cnf(c_0_3225_0,axiom,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(power_power_nat(X1),X2)),hAPP_nat_nat(power_power_nat(X1),X3)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,one_one_nat),X1))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3225]) ).
cnf(c_0_3225_1,axiom,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,one_one_nat),X1))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(power_power_nat(X1),X2)),hAPP_nat_nat(power_power_nat(X1),X3)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3225]) ).
cnf(c_0_3225_2,axiom,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X3))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,one_one_nat),X1))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(power_power_nat(X1),X2)),hAPP_nat_nat(power_power_nat(X1),X3))) ),
inference(literals_permutation,[status(thm)],[c_0_3225]) ).
cnf(c_0_3226_0,axiom,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_nat_real(power_power_real(X1),X2)),hAPP_nat_real(power_power_real(X1),X3)))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,one_one_real),X1))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3226]) ).
cnf(c_0_3226_1,axiom,
( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,one_one_real),X1))
| hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_nat_real(power_power_real(X1),X2)),hAPP_nat_real(power_power_real(X1),X3)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3226]) ).
cnf(c_0_3226_2,axiom,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X3))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,one_one_real),X1))
| hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_nat_real(power_power_real(X1),X2)),hAPP_nat_real(power_power_real(X1),X3))) ),
inference(literals_permutation,[status(thm)],[c_0_3226]) ).
cnf(c_0_3227_0,axiom,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_nat_int(power_power_int(X1),X2)),hAPP_nat_int(power_power_int(X1),X3)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),X1))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3227]) ).
cnf(c_0_3227_1,axiom,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),X1))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_nat_int(power_power_int(X1),X2)),hAPP_nat_int(power_power_int(X1),X3)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3227]) ).
cnf(c_0_3227_2,axiom,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X2),X3))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),X1))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_nat_int(power_power_int(X1),X2)),hAPP_nat_int(power_power_int(X1),X3))) ),
inference(literals_permutation,[status(thm)],[c_0_3227]) ).
cnf(c_0_3228_0,axiom,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(power_power_nat(X1),X2)),hAPP_nat_nat(power_power_nat(X1),X3)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,one_one_nat),X1))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3228]) ).
cnf(c_0_3228_1,axiom,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,one_one_nat),X1))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(power_power_nat(X1),X2)),hAPP_nat_nat(power_power_nat(X1),X3)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3228]) ).
cnf(c_0_3228_2,axiom,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X2),X3))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,one_one_nat),X1))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(power_power_nat(X1),X2)),hAPP_nat_nat(power_power_nat(X1),X3))) ),
inference(literals_permutation,[status(thm)],[c_0_3228]) ).
cnf(c_0_3229_0,axiom,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_nat_real(power_power_real(X1),X2)),hAPP_nat_real(power_power_real(X1),X3)))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,one_one_real),X1))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3229]) ).
cnf(c_0_3229_1,axiom,
( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,one_one_real),X1))
| hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_nat_real(power_power_real(X1),X2)),hAPP_nat_real(power_power_real(X1),X3)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3229]) ).
cnf(c_0_3229_2,axiom,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X2),X3))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,one_one_real),X1))
| hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_nat_real(power_power_real(X1),X2)),hAPP_nat_real(power_power_real(X1),X3))) ),
inference(literals_permutation,[status(thm)],[c_0_3229]) ).
cnf(c_0_3230_0,axiom,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_nat_int(power_power_int(X1),X2)),hAPP_nat_int(power_power_int(X1),X3)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),X1))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3230]) ).
cnf(c_0_3230_1,axiom,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),X1))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_nat_int(power_power_int(X1),X2)),hAPP_nat_int(power_power_int(X1),X3)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3230]) ).
cnf(c_0_3230_2,axiom,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X2),X3))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),X1))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_nat_int(power_power_int(X1),X2)),hAPP_nat_int(power_power_int(X1),X3))) ),
inference(literals_permutation,[status(thm)],[c_0_3230]) ).
cnf(c_0_3231_0,axiom,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(power_power_nat(X1),X2)),hAPP_nat_nat(power_power_nat(X1),X3)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,one_one_nat),X1))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3231]) ).
cnf(c_0_3231_1,axiom,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,one_one_nat),X1))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(power_power_nat(X1),X2)),hAPP_nat_nat(power_power_nat(X1),X3)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3231]) ).
cnf(c_0_3231_2,axiom,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X2),X3))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,one_one_nat),X1))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(power_power_nat(X1),X2)),hAPP_nat_nat(power_power_nat(X1),X3))) ),
inference(literals_permutation,[status(thm)],[c_0_3231]) ).
cnf(c_0_3232_0,axiom,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_nat_real(power_power_real(X1),X2)),hAPP_nat_real(power_power_real(X1),X3)))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,one_one_real),X1))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3232]) ).
cnf(c_0_3232_1,axiom,
( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,one_one_real),X1))
| hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_nat_real(power_power_real(X1),X2)),hAPP_nat_real(power_power_real(X1),X3)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3232]) ).
cnf(c_0_3232_2,axiom,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X2),X3))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,one_one_real),X1))
| hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_nat_real(power_power_real(X1),X2)),hAPP_nat_real(power_power_real(X1),X3))) ),
inference(literals_permutation,[status(thm)],[c_0_3232]) ).
cnf(c_0_3233_0,axiom,
( X1 = zero_zero_real
| hAPP_real_real(plus_plus_real(hAPP_nat_real(power_power_real(X1),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_real(power_power_real(X2),number_number_of_nat(bit0(bit1(pls))))) != zero_zero_real ),
inference(literals_permutation,[status(thm)],[c_0_3233]) ).
cnf(c_0_3233_1,axiom,
( hAPP_real_real(plus_plus_real(hAPP_nat_real(power_power_real(X1),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_real(power_power_real(X2),number_number_of_nat(bit0(bit1(pls))))) != zero_zero_real
| X1 = zero_zero_real ),
inference(literals_permutation,[status(thm)],[c_0_3233]) ).
cnf(c_0_3234_0,axiom,
( X2 = zero_zero_real
| hAPP_real_real(plus_plus_real(hAPP_nat_real(power_power_real(X1),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_real(power_power_real(X2),number_number_of_nat(bit0(bit1(pls))))) != zero_zero_real ),
inference(literals_permutation,[status(thm)],[c_0_3234]) ).
cnf(c_0_3234_1,axiom,
( hAPP_real_real(plus_plus_real(hAPP_nat_real(power_power_real(X1),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_real(power_power_real(X2),number_number_of_nat(bit0(bit1(pls))))) != zero_zero_real
| X2 = zero_zero_real ),
inference(literals_permutation,[status(thm)],[c_0_3234]) ).
cnf(c_0_3235_0,axiom,
( X1 = zero_zero_real
| hAPP_real_real(plus_plus_real(hAPP_nat_real(power_power_real(X1),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_real(power_power_real(X2),number_number_of_nat(bit0(bit1(pls))))) != zero_zero_real ),
inference(literals_permutation,[status(thm)],[c_0_3235]) ).
cnf(c_0_3235_1,axiom,
( hAPP_real_real(plus_plus_real(hAPP_nat_real(power_power_real(X1),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_real(power_power_real(X2),number_number_of_nat(bit0(bit1(pls))))) != zero_zero_real
| X1 = zero_zero_real ),
inference(literals_permutation,[status(thm)],[c_0_3235]) ).
cnf(c_0_3236_0,axiom,
( X2 = zero_zero_real
| hAPP_real_real(plus_plus_real(hAPP_nat_real(power_power_real(X1),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_real(power_power_real(X2),number_number_of_nat(bit0(bit1(pls))))) != zero_zero_real ),
inference(literals_permutation,[status(thm)],[c_0_3236]) ).
cnf(c_0_3236_1,axiom,
( hAPP_real_real(plus_plus_real(hAPP_nat_real(power_power_real(X1),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_real(power_power_real(X2),number_number_of_nat(bit0(bit1(pls))))) != zero_zero_real
| X2 = zero_zero_real ),
inference(literals_permutation,[status(thm)],[c_0_3236]) ).
cnf(c_0_3237_0,axiom,
( X1 = zero_zero_int
| hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(X1),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_int(power_power_int(X2),number_number_of_nat(bit0(bit1(pls))))) != zero_zero_int ),
inference(literals_permutation,[status(thm)],[c_0_3237]) ).
cnf(c_0_3237_1,axiom,
( hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(X1),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_int(power_power_int(X2),number_number_of_nat(bit0(bit1(pls))))) != zero_zero_int
| X1 = zero_zero_int ),
inference(literals_permutation,[status(thm)],[c_0_3237]) ).
cnf(c_0_3238_0,axiom,
( X2 = zero_zero_int
| hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(X1),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_int(power_power_int(X2),number_number_of_nat(bit0(bit1(pls))))) != zero_zero_int ),
inference(literals_permutation,[status(thm)],[c_0_3238]) ).
cnf(c_0_3238_1,axiom,
( hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(X1),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_int(power_power_int(X2),number_number_of_nat(bit0(bit1(pls))))) != zero_zero_int
| X2 = zero_zero_int ),
inference(literals_permutation,[status(thm)],[c_0_3238]) ).
cnf(c_0_3239_0,axiom,
( hBOOL(hAPP_int_bool(X3,X2))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),sk1_esk18_3(X3,X1,X2)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2))
| ~ hBOOL(hAPP_int_bool(X3,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_3239]) ).
cnf(c_0_3239_1,axiom,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),sk1_esk18_3(X3,X1,X2)))
| hBOOL(hAPP_int_bool(X3,X2))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2))
| ~ hBOOL(hAPP_int_bool(X3,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_3239]) ).
cnf(c_0_3239_2,axiom,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),sk1_esk18_3(X3,X1,X2)))
| hBOOL(hAPP_int_bool(X3,X2))
| ~ hBOOL(hAPP_int_bool(X3,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_3239]) ).
cnf(c_0_3239_3,axiom,
( ~ hBOOL(hAPP_int_bool(X3,X1))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),sk1_esk18_3(X3,X1,X2)))
| hBOOL(hAPP_int_bool(X3,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3239]) ).
cnf(c_0_3242_0,axiom,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(X1,X2),X3))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(X1,X2),X3))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(X1,X2),X3))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(X1,X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3242]) ).
cnf(c_0_3242_1,axiom,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(X1,X2),X3))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(X1,X2),X3))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(X1,X2),X3))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(X1,X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3242]) ).
cnf(c_0_3242_2,axiom,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(X1,X2),X3))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(X1,X2),X3))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(X1,X2),X3))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(X1,X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3242]) ).
cnf(c_0_3242_3,axiom,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(X1,X2),X3))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(X1,X2),X3))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(X1,X2),X3))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(X1,X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3242]) ).
cnf(c_0_3243_0,axiom,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(X1),X2)),zero_zero_int))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X2),zero_zero_int))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),zero_zero_int)) ),
inference(literals_permutation,[status(thm)],[c_0_3243]) ).
cnf(c_0_3243_1,axiom,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X2),zero_zero_int))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(X1),X2)),zero_zero_int))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),zero_zero_int)) ),
inference(literals_permutation,[status(thm)],[c_0_3243]) ).
cnf(c_0_3243_2,axiom,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),zero_zero_int))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X2),zero_zero_int))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(X1),X2)),zero_zero_int)) ),
inference(literals_permutation,[status(thm)],[c_0_3243]) ).
cnf(c_0_3244_0,axiom,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(X1),X2)),zero_zero_nat))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X2),zero_zero_nat))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),zero_zero_nat)) ),
inference(literals_permutation,[status(thm)],[c_0_3244]) ).
cnf(c_0_3244_1,axiom,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X2),zero_zero_nat))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(X1),X2)),zero_zero_nat))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),zero_zero_nat)) ),
inference(literals_permutation,[status(thm)],[c_0_3244]) ).
cnf(c_0_3244_2,axiom,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),zero_zero_nat))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X2),zero_zero_nat))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(X1),X2)),zero_zero_nat)) ),
inference(literals_permutation,[status(thm)],[c_0_3244]) ).
cnf(c_0_3245_0,axiom,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(plus_plus_real(X1),X2)),zero_zero_real))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X2),zero_zero_real))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X1),zero_zero_real)) ),
inference(literals_permutation,[status(thm)],[c_0_3245]) ).
cnf(c_0_3245_1,axiom,
( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X2),zero_zero_real))
| hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(plus_plus_real(X1),X2)),zero_zero_real))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X1),zero_zero_real)) ),
inference(literals_permutation,[status(thm)],[c_0_3245]) ).
cnf(c_0_3245_2,axiom,
( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X1),zero_zero_real))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X2),zero_zero_real))
| hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(plus_plus_real(X1),X2)),zero_zero_real)) ),
inference(literals_permutation,[status(thm)],[c_0_3245]) ).
cnf(c_0_3246_0,axiom,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(X1),X2)),zero_zero_int))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X2),zero_zero_int))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),zero_zero_int)) ),
inference(literals_permutation,[status(thm)],[c_0_3246]) ).
cnf(c_0_3246_1,axiom,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X2),zero_zero_int))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(X1),X2)),zero_zero_int))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),zero_zero_int)) ),
inference(literals_permutation,[status(thm)],[c_0_3246]) ).
cnf(c_0_3246_2,axiom,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),zero_zero_int))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X2),zero_zero_int))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(X1),X2)),zero_zero_int)) ),
inference(literals_permutation,[status(thm)],[c_0_3246]) ).
cnf(c_0_3247_0,axiom,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(X1),X2)),zero_zero_nat))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),zero_zero_nat))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),zero_zero_nat)) ),
inference(literals_permutation,[status(thm)],[c_0_3247]) ).
cnf(c_0_3247_1,axiom,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),zero_zero_nat))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(X1),X2)),zero_zero_nat))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),zero_zero_nat)) ),
inference(literals_permutation,[status(thm)],[c_0_3247]) ).
cnf(c_0_3247_2,axiom,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),zero_zero_nat))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),zero_zero_nat))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(X1),X2)),zero_zero_nat)) ),
inference(literals_permutation,[status(thm)],[c_0_3247]) ).
cnf(c_0_3248_0,axiom,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(plus_plus_real(X1),X2)),zero_zero_real))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X2),zero_zero_real))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X1),zero_zero_real)) ),
inference(literals_permutation,[status(thm)],[c_0_3248]) ).
cnf(c_0_3248_1,axiom,
( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X2),zero_zero_real))
| hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(plus_plus_real(X1),X2)),zero_zero_real))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X1),zero_zero_real)) ),
inference(literals_permutation,[status(thm)],[c_0_3248]) ).
cnf(c_0_3248_2,axiom,
( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X1),zero_zero_real))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X2),zero_zero_real))
| hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(plus_plus_real(X1),X2)),zero_zero_real)) ),
inference(literals_permutation,[status(thm)],[c_0_3248]) ).
cnf(c_0_3249_0,axiom,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(plus_plus_int(X1),X2)),zero_zero_int))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X2),zero_zero_int))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),zero_zero_int)) ),
inference(literals_permutation,[status(thm)],[c_0_3249]) ).
cnf(c_0_3249_1,axiom,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X2),zero_zero_int))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(plus_plus_int(X1),X2)),zero_zero_int))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),zero_zero_int)) ),
inference(literals_permutation,[status(thm)],[c_0_3249]) ).
cnf(c_0_3249_2,axiom,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),zero_zero_int))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X2),zero_zero_int))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(plus_plus_int(X1),X2)),zero_zero_int)) ),
inference(literals_permutation,[status(thm)],[c_0_3249]) ).
cnf(c_0_3250_0,axiom,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(X1),X2)),zero_zero_nat))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),zero_zero_nat))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),zero_zero_nat)) ),
inference(literals_permutation,[status(thm)],[c_0_3250]) ).
cnf(c_0_3250_1,axiom,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),zero_zero_nat))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(X1),X2)),zero_zero_nat))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),zero_zero_nat)) ),
inference(literals_permutation,[status(thm)],[c_0_3250]) ).
cnf(c_0_3250_2,axiom,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),zero_zero_nat))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),zero_zero_nat))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(X1),X2)),zero_zero_nat)) ),
inference(literals_permutation,[status(thm)],[c_0_3250]) ).
cnf(c_0_3251_0,axiom,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(plus_plus_real(X1),X2)),zero_zero_real))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X2),zero_zero_real))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X1),zero_zero_real)) ),
inference(literals_permutation,[status(thm)],[c_0_3251]) ).
cnf(c_0_3251_1,axiom,
( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X2),zero_zero_real))
| hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(plus_plus_real(X1),X2)),zero_zero_real))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X1),zero_zero_real)) ),
inference(literals_permutation,[status(thm)],[c_0_3251]) ).
cnf(c_0_3251_2,axiom,
( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X1),zero_zero_real))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X2),zero_zero_real))
| hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(plus_plus_real(X1),X2)),zero_zero_real)) ),
inference(literals_permutation,[status(thm)],[c_0_3251]) ).
cnf(c_0_3252_0,axiom,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(X1),X2)),zero_zero_int))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X2),zero_zero_int))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),zero_zero_int)) ),
inference(literals_permutation,[status(thm)],[c_0_3252]) ).
cnf(c_0_3252_1,axiom,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X2),zero_zero_int))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(X1),X2)),zero_zero_int))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),zero_zero_int)) ),
inference(literals_permutation,[status(thm)],[c_0_3252]) ).
cnf(c_0_3252_2,axiom,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),zero_zero_int))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X2),zero_zero_int))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(X1),X2)),zero_zero_int)) ),
inference(literals_permutation,[status(thm)],[c_0_3252]) ).
cnf(c_0_3253_0,axiom,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(X1),X2)),zero_zero_nat))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X2),zero_zero_nat))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),zero_zero_nat)) ),
inference(literals_permutation,[status(thm)],[c_0_3253]) ).
cnf(c_0_3253_1,axiom,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X2),zero_zero_nat))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(X1),X2)),zero_zero_nat))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),zero_zero_nat)) ),
inference(literals_permutation,[status(thm)],[c_0_3253]) ).
cnf(c_0_3253_2,axiom,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),zero_zero_nat))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X2),zero_zero_nat))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(X1),X2)),zero_zero_nat)) ),
inference(literals_permutation,[status(thm)],[c_0_3253]) ).
cnf(c_0_3254_0,axiom,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(plus_plus_real(X1),X2)),zero_zero_real))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X2),zero_zero_real))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X1),zero_zero_real)) ),
inference(literals_permutation,[status(thm)],[c_0_3254]) ).
cnf(c_0_3254_1,axiom,
( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X2),zero_zero_real))
| hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(plus_plus_real(X1),X2)),zero_zero_real))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X1),zero_zero_real)) ),
inference(literals_permutation,[status(thm)],[c_0_3254]) ).
cnf(c_0_3254_2,axiom,
( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X1),zero_zero_real))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X2),zero_zero_real))
| hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(plus_plus_real(X1),X2)),zero_zero_real)) ),
inference(literals_permutation,[status(thm)],[c_0_3254]) ).
cnf(c_0_3255_0,axiom,
( hBOOL(hAPP_int_bool(X3,X2))
| hBOOL(hAPP_int_bool(X3,sk1_esk18_3(X3,X1,X2)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2))
| ~ hBOOL(hAPP_int_bool(X3,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_3255]) ).
cnf(c_0_3255_1,axiom,
( hBOOL(hAPP_int_bool(X3,sk1_esk18_3(X3,X1,X2)))
| hBOOL(hAPP_int_bool(X3,X2))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2))
| ~ hBOOL(hAPP_int_bool(X3,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_3255]) ).
cnf(c_0_3255_2,axiom,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2))
| hBOOL(hAPP_int_bool(X3,sk1_esk18_3(X3,X1,X2)))
| hBOOL(hAPP_int_bool(X3,X2))
| ~ hBOOL(hAPP_int_bool(X3,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_3255]) ).
cnf(c_0_3255_3,axiom,
( ~ hBOOL(hAPP_int_bool(X3,X1))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2))
| hBOOL(hAPP_int_bool(X3,sk1_esk18_3(X3,X1,X2)))
| hBOOL(hAPP_int_bool(X3,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3255]) ).
cnf(c_0_3256_0,axiom,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X3))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(X1),X2)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3256]) ).
cnf(c_0_3256_1,axiom,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(X1),X2)),X3))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3256]) ).
cnf(c_0_3257_0,axiom,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X3))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(X1),X2)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3257]) ).
cnf(c_0_3257_1,axiom,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(X1),X2)),X3))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3257]) ).
cnf(c_0_3258_0,axiom,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(X1),X3)),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3258]) ).
cnf(c_0_3258_1,axiom,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(X1),X3)),X2))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3258]) ).
cnf(c_0_3259_0,axiom,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(X3),X1)),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3259]) ).
cnf(c_0_3259_1,axiom,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(X3),X1)),X2))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3259]) ).
cnf(c_0_3260_0,axiom,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(X1),X3)),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3260]) ).
cnf(c_0_3260_1,axiom,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(X1),X3)),X2))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3260]) ).
cnf(c_0_3261_0,axiom,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),zero_zero_int))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(plus_plus_int(X1),X1)),zero_zero_int)) ),
inference(literals_permutation,[status(thm)],[c_0_3261]) ).
cnf(c_0_3261_1,axiom,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(plus_plus_int(X1),X1)),zero_zero_int))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),zero_zero_int)) ),
inference(literals_permutation,[status(thm)],[c_0_3261]) ).
cnf(c_0_3262_0,axiom,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X1),zero_zero_real))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(plus_plus_real(X1),X1)),zero_zero_real)) ),
inference(literals_permutation,[status(thm)],[c_0_3262]) ).
cnf(c_0_3262_1,axiom,
( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(plus_plus_real(X1),X1)),zero_zero_real))
| hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X1),zero_zero_real)) ),
inference(literals_permutation,[status(thm)],[c_0_3262]) ).
cnf(c_0_3263_0,axiom,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),zero_zero_int))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(X1),X1)),zero_zero_int)) ),
inference(literals_permutation,[status(thm)],[c_0_3263]) ).
cnf(c_0_3263_1,axiom,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(X1),X1)),zero_zero_int))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),zero_zero_int)) ),
inference(literals_permutation,[status(thm)],[c_0_3263]) ).
cnf(c_0_3264_0,axiom,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X1),zero_zero_real))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(plus_plus_real(X1),X1)),zero_zero_real)) ),
inference(literals_permutation,[status(thm)],[c_0_3264]) ).
cnf(c_0_3264_1,axiom,
( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(plus_plus_real(X1),X1)),zero_zero_real))
| hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X1),zero_zero_real)) ),
inference(literals_permutation,[status(thm)],[c_0_3264]) ).
cnf(c_0_3265_0,axiom,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X1),zero_zero_real))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(plus_plus_real(X1),X1)),zero_zero_real)) ),
inference(literals_permutation,[status(thm)],[c_0_3265]) ).
cnf(c_0_3265_1,axiom,
( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(plus_plus_real(X1),X1)),zero_zero_real))
| hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X1),zero_zero_real)) ),
inference(literals_permutation,[status(thm)],[c_0_3265]) ).
cnf(c_0_3266_0,axiom,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),zero_zero_int))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(X1),X1)),zero_zero_int)) ),
inference(literals_permutation,[status(thm)],[c_0_3266]) ).
cnf(c_0_3266_1,axiom,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(X1),X1)),zero_zero_int))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),zero_zero_int)) ),
inference(literals_permutation,[status(thm)],[c_0_3266]) ).
cnf(c_0_3267_0,axiom,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(plus_plus_real(X1),X2)),hAPP_real_real(plus_plus_real(X1),X3)))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3267]) ).
cnf(c_0_3267_1,axiom,
( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X2),X3))
| hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(plus_plus_real(X1),X2)),hAPP_real_real(plus_plus_real(X1),X3))) ),
inference(literals_permutation,[status(thm)],[c_0_3267]) ).
cnf(c_0_3268_0,axiom,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(X1),X2)),hAPP_nat_nat(plus_plus_nat(X3),X2)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3268]) ).
cnf(c_0_3268_1,axiom,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X3))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(X1),X2)),hAPP_nat_nat(plus_plus_nat(X3),X2))) ),
inference(literals_permutation,[status(thm)],[c_0_3268]) ).
cnf(c_0_3269_0,axiom,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(X1),X2)),hAPP_nat_nat(plus_plus_nat(X1),X3)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3269]) ).
cnf(c_0_3269_1,axiom,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X3))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(X1),X2)),hAPP_nat_nat(plus_plus_nat(X1),X3))) ),
inference(literals_permutation,[status(thm)],[c_0_3269]) ).
cnf(c_0_3270_0,axiom,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(plus_plus_int(X1),X2)),hAPP_int_int(plus_plus_int(X1),X3)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3270]) ).
cnf(c_0_3270_1,axiom,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X2),X3))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(plus_plus_int(X1),X2)),hAPP_int_int(plus_plus_int(X1),X3))) ),
inference(literals_permutation,[status(thm)],[c_0_3270]) ).
cnf(c_0_3271_0,axiom,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(plus_plus_int(X1),X2)),hAPP_int_int(plus_plus_int(X1),X3)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3271]) ).
cnf(c_0_3271_1,axiom,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X2),X3))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(plus_plus_int(X1),X2)),hAPP_int_int(plus_plus_int(X1),X3))) ),
inference(literals_permutation,[status(thm)],[c_0_3271]) ).
cnf(c_0_3272_0,axiom,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(X1),X2)),hAPP_nat_nat(plus_plus_nat(X1),X3)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3272]) ).
cnf(c_0_3272_1,axiom,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X3))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(X1),X2)),hAPP_nat_nat(plus_plus_nat(X1),X3))) ),
inference(literals_permutation,[status(thm)],[c_0_3272]) ).
cnf(c_0_3273_0,axiom,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(plus_plus_real(X1),X2)),hAPP_real_real(plus_plus_real(X1),X3)))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3273]) ).
cnf(c_0_3273_1,axiom,
( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X2),X3))
| hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(plus_plus_real(X1),X2)),hAPP_real_real(plus_plus_real(X1),X3))) ),
inference(literals_permutation,[status(thm)],[c_0_3273]) ).
cnf(c_0_3274_0,axiom,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(plus_plus_int(X1),X2)),hAPP_int_int(plus_plus_int(X3),X2)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3274]) ).
cnf(c_0_3274_1,axiom,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X3))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(plus_plus_int(X1),X2)),hAPP_int_int(plus_plus_int(X3),X2))) ),
inference(literals_permutation,[status(thm)],[c_0_3274]) ).
cnf(c_0_3275_0,axiom,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(X1),X2)),hAPP_nat_nat(plus_plus_nat(X3),X2)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3275]) ).
cnf(c_0_3275_1,axiom,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X3))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(X1),X2)),hAPP_nat_nat(plus_plus_nat(X3),X2))) ),
inference(literals_permutation,[status(thm)],[c_0_3275]) ).
cnf(c_0_3276_0,axiom,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(plus_plus_real(X1),X2)),hAPP_real_real(plus_plus_real(X3),X2)))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X1),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3276]) ).
cnf(c_0_3276_1,axiom,
( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X1),X3))
| hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(plus_plus_real(X1),X2)),hAPP_real_real(plus_plus_real(X3),X2))) ),
inference(literals_permutation,[status(thm)],[c_0_3276]) ).
cnf(c_0_3277_0,axiom,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(plus_plus_int(X1),X2)),hAPP_int_int(plus_plus_int(X1),X3)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3277]) ).
cnf(c_0_3277_1,axiom,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X2),X3))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(plus_plus_int(X1),X2)),hAPP_int_int(plus_plus_int(X1),X3))) ),
inference(literals_permutation,[status(thm)],[c_0_3277]) ).
cnf(c_0_3278_0,axiom,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(X1),X2)),hAPP_nat_nat(plus_plus_nat(X1),X3)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3278]) ).
cnf(c_0_3278_1,axiom,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X3))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(X1),X2)),hAPP_nat_nat(plus_plus_nat(X1),X3))) ),
inference(literals_permutation,[status(thm)],[c_0_3278]) ).
cnf(c_0_3279_0,axiom,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(plus_plus_real(X1),X2)),hAPP_real_real(plus_plus_real(X1),X3)))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3279]) ).
cnf(c_0_3279_1,axiom,
( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X2),X3))
| hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(plus_plus_real(X1),X2)),hAPP_real_real(plus_plus_real(X1),X3))) ),
inference(literals_permutation,[status(thm)],[c_0_3279]) ).
cnf(c_0_3280_0,axiom,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(plus_plus_int(X1),X2)),hAPP_int_int(plus_plus_int(X3),X2)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3280]) ).
cnf(c_0_3280_1,axiom,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X3))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(plus_plus_int(X1),X2)),hAPP_int_int(plus_plus_int(X3),X2))) ),
inference(literals_permutation,[status(thm)],[c_0_3280]) ).
cnf(c_0_3281_0,axiom,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(X1),X2)),hAPP_nat_nat(plus_plus_nat(X3),X2)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3281]) ).
cnf(c_0_3281_1,axiom,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X3))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(X1),X2)),hAPP_nat_nat(plus_plus_nat(X3),X2))) ),
inference(literals_permutation,[status(thm)],[c_0_3281]) ).
cnf(c_0_3282_0,axiom,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(plus_plus_real(X1),X2)),hAPP_real_real(plus_plus_real(X3),X2)))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X1),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3282]) ).
cnf(c_0_3282_1,axiom,
( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X1),X3))
| hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(plus_plus_real(X1),X2)),hAPP_real_real(plus_plus_real(X3),X2))) ),
inference(literals_permutation,[status(thm)],[c_0_3282]) ).
cnf(c_0_3283_0,axiom,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(X1),X2)),hAPP_int_int(plus_plus_int(X3),X2)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3283]) ).
cnf(c_0_3283_1,axiom,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X3))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(X1),X2)),hAPP_int_int(plus_plus_int(X3),X2))) ),
inference(literals_permutation,[status(thm)],[c_0_3283]) ).
cnf(c_0_3284_0,axiom,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(X1),X2)),hAPP_nat_nat(plus_plus_nat(X3),X2)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3284]) ).
cnf(c_0_3284_1,axiom,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X3))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(X1),X2)),hAPP_nat_nat(plus_plus_nat(X3),X2))) ),
inference(literals_permutation,[status(thm)],[c_0_3284]) ).
cnf(c_0_3285_0,axiom,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(plus_plus_real(X1),X2)),hAPP_real_real(plus_plus_real(X3),X2)))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X1),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3285]) ).
cnf(c_0_3285_1,axiom,
( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X1),X3))
| hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(plus_plus_real(X1),X2)),hAPP_real_real(plus_plus_real(X3),X2))) ),
inference(literals_permutation,[status(thm)],[c_0_3285]) ).
cnf(c_0_3286_0,axiom,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(X1),X2)),hAPP_int_int(plus_plus_int(X1),X3)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3286]) ).
cnf(c_0_3286_1,axiom,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X2),X3))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(X1),X2)),hAPP_int_int(plus_plus_int(X1),X3))) ),
inference(literals_permutation,[status(thm)],[c_0_3286]) ).
cnf(c_0_3287_0,axiom,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(X1),X2)),hAPP_nat_nat(plus_plus_nat(X1),X3)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3287]) ).
cnf(c_0_3287_1,axiom,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X2),X3))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(X1),X2)),hAPP_nat_nat(plus_plus_nat(X1),X3))) ),
inference(literals_permutation,[status(thm)],[c_0_3287]) ).
cnf(c_0_3288_0,axiom,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(plus_plus_real(X1),X2)),hAPP_real_real(plus_plus_real(X1),X3)))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3288]) ).
cnf(c_0_3288_1,axiom,
( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X2),X3))
| hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(plus_plus_real(X1),X2)),hAPP_real_real(plus_plus_real(X1),X3))) ),
inference(literals_permutation,[status(thm)],[c_0_3288]) ).
cnf(c_0_3289_0,axiom,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(X1),X2)),hAPP_int_int(plus_plus_int(X3),X2)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3289]) ).
cnf(c_0_3289_1,axiom,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X3))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(X1),X2)),hAPP_int_int(plus_plus_int(X3),X2))) ),
inference(literals_permutation,[status(thm)],[c_0_3289]) ).
cnf(c_0_3290_0,axiom,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(X1),X2)),hAPP_nat_nat(plus_plus_nat(X3),X2)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3290]) ).
cnf(c_0_3290_1,axiom,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X3))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(X1),X2)),hAPP_nat_nat(plus_plus_nat(X3),X2))) ),
inference(literals_permutation,[status(thm)],[c_0_3290]) ).
cnf(c_0_3291_0,axiom,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(plus_plus_real(X1),X2)),hAPP_real_real(plus_plus_real(X3),X2)))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X1),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3291]) ).
cnf(c_0_3291_1,axiom,
( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X1),X3))
| hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(plus_plus_real(X1),X2)),hAPP_real_real(plus_plus_real(X3),X2))) ),
inference(literals_permutation,[status(thm)],[c_0_3291]) ).
cnf(c_0_3292_0,axiom,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(X1),X2)),hAPP_int_int(plus_plus_int(X1),X3)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3292]) ).
cnf(c_0_3292_1,axiom,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X2),X3))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(X1),X2)),hAPP_int_int(plus_plus_int(X1),X3))) ),
inference(literals_permutation,[status(thm)],[c_0_3292]) ).
cnf(c_0_3293_0,axiom,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(X1),X2)),hAPP_nat_nat(plus_plus_nat(X1),X3)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3293]) ).
cnf(c_0_3293_1,axiom,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X2),X3))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(X1),X2)),hAPP_nat_nat(plus_plus_nat(X1),X3))) ),
inference(literals_permutation,[status(thm)],[c_0_3293]) ).
cnf(c_0_3294_0,axiom,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(plus_plus_real(X1),X2)),hAPP_real_real(plus_plus_real(X1),X3)))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3294]) ).
cnf(c_0_3294_1,axiom,
( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X2),X3))
| hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(plus_plus_real(X1),X2)),hAPP_real_real(plus_plus_real(X1),X3))) ),
inference(literals_permutation,[status(thm)],[c_0_3294]) ).
cnf(c_0_3295_0,axiom,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(X1),X2)),hAPP_nat_nat(plus_plus_nat(X3),X2)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3295]) ).
cnf(c_0_3295_1,axiom,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X3))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(X1),X2)),hAPP_nat_nat(plus_plus_nat(X3),X2))) ),
inference(literals_permutation,[status(thm)],[c_0_3295]) ).
cnf(c_0_3296_0,axiom,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(X1),X2)),hAPP_nat_nat(plus_plus_nat(X1),X3)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3296]) ).
cnf(c_0_3296_1,axiom,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X2),X3))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(X1),X2)),hAPP_nat_nat(plus_plus_nat(X1),X3))) ),
inference(literals_permutation,[status(thm)],[c_0_3296]) ).
cnf(c_0_3297_0,axiom,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(X1),X2)),hAPP_int_int(plus_plus_int(X3),X2)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3297]) ).
cnf(c_0_3297_1,axiom,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X3))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(X1),X2)),hAPP_int_int(plus_plus_int(X3),X2))) ),
inference(literals_permutation,[status(thm)],[c_0_3297]) ).
cnf(c_0_3298_0,axiom,
( X1 != zero_zero_real
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),hAPP_nat_real(power_power_real(X1),number_number_of_nat(bit0(bit1(pls)))))) ),
inference(literals_permutation,[status(thm)],[c_0_3298]) ).
cnf(c_0_3298_1,axiom,
( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),hAPP_nat_real(power_power_real(X1),number_number_of_nat(bit0(bit1(pls))))))
| X1 != zero_zero_real ),
inference(literals_permutation,[status(thm)],[c_0_3298]) ).
cnf(c_0_3299_0,axiom,
( X1 != zero_zero_int
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_nat_int(power_power_int(X1),number_number_of_nat(bit0(bit1(pls)))))) ),
inference(literals_permutation,[status(thm)],[c_0_3299]) ).
cnf(c_0_3299_1,axiom,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_nat_int(power_power_int(X1),number_number_of_nat(bit0(bit1(pls))))))
| X1 != zero_zero_int ),
inference(literals_permutation,[status(thm)],[c_0_3299]) ).
cnf(c_0_3300_0,axiom,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(X3,X2),X1))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(X3,X2),X1))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(X3,X2),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_3300]) ).
cnf(c_0_3300_1,axiom,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(X3,X2),X1))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(X3,X2),X1))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(X3,X2),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_3300]) ).
cnf(c_0_3300_2,axiom,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(X3,X2),X1))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(X3,X2),X1))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(X3,X2),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_3300]) ).
cnf(c_0_3300_3,axiom,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(X3,X2),X1))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(X3,X2),X1))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(X3,X2),X1))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3300]) ).
cnf(c_0_3301_0,axiom,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(X1,X2),X3))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X2),X3))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(X1,X2),X3))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(X1,X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3301]) ).
cnf(c_0_3301_1,axiom,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X2),X3))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(X1,X2),X3))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(X1,X2),X3))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(X1,X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3301]) ).
cnf(c_0_3301_2,axiom,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(X1,X2),X3))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X2),X3))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(X1,X2),X3))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(X1,X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3301]) ).
cnf(c_0_3301_3,axiom,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(X1,X2),X3))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(X1,X2),X3))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X2),X3))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(X1,X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3301]) ).
cnf(c_0_3302_0,axiom,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X2))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(plus_plus_int(X1),one_one_int)),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3302]) ).
cnf(c_0_3302_1,axiom,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(plus_plus_int(X1),one_one_int)),X2))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3302]) ).
cnf(c_0_3304_0,axiom,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_nat_int(semiri1621563631at_int,X1)),hAPP_nat_int(semiri1621563631at_int,X2))) ),
inference(literals_permutation,[status(thm)],[c_0_3304]) ).
cnf(c_0_3304_1,axiom,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_nat_int(semiri1621563631at_int,X1)),hAPP_nat_int(semiri1621563631at_int,X2)))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3304]) ).
cnf(c_0_3305_0,axiom,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_nat_int(semiri1621563631at_int,X1)),hAPP_nat_int(semiri1621563631at_int,X2))) ),
inference(literals_permutation,[status(thm)],[c_0_3305]) ).
cnf(c_0_3305_1,axiom,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_nat_int(semiri1621563631at_int,X1)),hAPP_nat_int(semiri1621563631at_int,X2)))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3305]) ).
cnf(c_0_3306_0,axiom,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_nat_int(semiri1621563631at_int,X1)),hAPP_nat_int(semiri1621563631at_int,X2))) ),
inference(literals_permutation,[status(thm)],[c_0_3306]) ).
cnf(c_0_3306_1,axiom,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_nat_int(semiri1621563631at_int,X1)),hAPP_nat_int(semiri1621563631at_int,X2)))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3306]) ).
cnf(c_0_3307_0,axiom,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(semiri984289939at_nat,X1)),hAPP_nat_nat(semiri984289939at_nat,X2))) ),
inference(literals_permutation,[status(thm)],[c_0_3307]) ).
cnf(c_0_3307_1,axiom,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(semiri984289939at_nat,X1)),hAPP_nat_nat(semiri984289939at_nat,X2)))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3307]) ).
cnf(c_0_3308_0,axiom,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_nat_real(semiri132038758t_real,X1)),hAPP_nat_real(semiri132038758t_real,X2))) ),
inference(literals_permutation,[status(thm)],[c_0_3308]) ).
cnf(c_0_3308_1,axiom,
( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_nat_real(semiri132038758t_real,X1)),hAPP_nat_real(semiri132038758t_real,X2)))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3308]) ).
cnf(c_0_3309_0,axiom,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_nat_int(semiri1621563631at_int,X1)),hAPP_nat_int(semiri1621563631at_int,X2))) ),
inference(literals_permutation,[status(thm)],[c_0_3309]) ).
cnf(c_0_3309_1,axiom,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_nat_int(semiri1621563631at_int,X1)),hAPP_nat_int(semiri1621563631at_int,X2)))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3309]) ).
cnf(c_0_3310_0,axiom,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(semiri984289939at_nat,X1)),hAPP_nat_nat(semiri984289939at_nat,X2))) ),
inference(literals_permutation,[status(thm)],[c_0_3310]) ).
cnf(c_0_3310_1,axiom,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(semiri984289939at_nat,X1)),hAPP_nat_nat(semiri984289939at_nat,X2)))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3310]) ).
cnf(c_0_3311_0,axiom,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_nat_real(semiri132038758t_real,X1)),hAPP_nat_real(semiri132038758t_real,X2))) ),
inference(literals_permutation,[status(thm)],[c_0_3311]) ).
cnf(c_0_3311_1,axiom,
( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_nat_real(semiri132038758t_real,X1)),hAPP_nat_real(semiri132038758t_real,X2)))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3311]) ).
cnf(c_0_3312_0,axiom,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_nat_int(semiri1621563631at_int,X1)),hAPP_nat_int(semiri1621563631at_int,X2))) ),
inference(literals_permutation,[status(thm)],[c_0_3312]) ).
cnf(c_0_3312_1,axiom,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_nat_int(semiri1621563631at_int,X1)),hAPP_nat_int(semiri1621563631at_int,X2)))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3312]) ).
cnf(c_0_3313_0,axiom,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(semiri984289939at_nat,X1)),hAPP_nat_nat(semiri984289939at_nat,X2))) ),
inference(literals_permutation,[status(thm)],[c_0_3313]) ).
cnf(c_0_3313_1,axiom,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(semiri984289939at_nat,X1)),hAPP_nat_nat(semiri984289939at_nat,X2)))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3313]) ).
cnf(c_0_3314_0,axiom,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_nat_real(semiri132038758t_real,X1)),hAPP_nat_real(semiri132038758t_real,X2))) ),
inference(literals_permutation,[status(thm)],[c_0_3314]) ).
cnf(c_0_3314_1,axiom,
( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_nat_real(semiri132038758t_real,X1)),hAPP_nat_real(semiri132038758t_real,X2)))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3314]) ).
cnf(c_0_3315_0,axiom,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_nat_int(semiri1621563631at_int,X1)),hAPP_nat_int(semiri1621563631at_int,X2))) ),
inference(literals_permutation,[status(thm)],[c_0_3315]) ).
cnf(c_0_3315_1,axiom,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_nat_int(semiri1621563631at_int,X1)),hAPP_nat_int(semiri1621563631at_int,X2)))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3315]) ).
cnf(c_0_3316_0,axiom,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_nat_int(semiri1621563631at_int,X1)),hAPP_nat_int(semiri1621563631at_int,X2))) ),
inference(literals_permutation,[status(thm)],[c_0_3316]) ).
cnf(c_0_3316_1,axiom,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_nat_int(semiri1621563631at_int,X1)),hAPP_nat_int(semiri1621563631at_int,X2)))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3316]) ).
cnf(c_0_3317_0,axiom,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,sk1_esk22_2(X2,X1)),X1))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X1))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3317]) ).
cnf(c_0_3317_1,axiom,
( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X1))
| hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,sk1_esk22_2(X2,X1)),X1))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3317]) ).
cnf(c_0_3317_2,axiom,
( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X2))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X1))
| hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,sk1_esk22_2(X2,X1)),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_3317]) ).
cnf(c_0_3318_0,axiom,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,sk1_esk22_2(X2,X1)),X2))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X1))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3318]) ).
cnf(c_0_3318_1,axiom,
( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X1))
| hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,sk1_esk22_2(X2,X1)),X2))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3318]) ).
cnf(c_0_3318_2,axiom,
( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X2))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X1))
| hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,sk1_esk22_2(X2,X1)),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3318]) ).
cnf(c_0_3319_0,axiom,
( X1 = X2
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X3))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X2))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1))
| hAPP_nat_int(power_power_int(X1),X3) != hAPP_nat_int(power_power_int(X2),X3) ),
inference(literals_permutation,[status(thm)],[c_0_3319]) ).
cnf(c_0_3319_1,axiom,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X3))
| X1 = X2
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X2))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1))
| hAPP_nat_int(power_power_int(X1),X3) != hAPP_nat_int(power_power_int(X2),X3) ),
inference(literals_permutation,[status(thm)],[c_0_3319]) ).
cnf(c_0_3319_2,axiom,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X3))
| X1 = X2
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1))
| hAPP_nat_int(power_power_int(X1),X3) != hAPP_nat_int(power_power_int(X2),X3) ),
inference(literals_permutation,[status(thm)],[c_0_3319]) ).
cnf(c_0_3319_3,axiom,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X3))
| X1 = X2
| hAPP_nat_int(power_power_int(X1),X3) != hAPP_nat_int(power_power_int(X2),X3) ),
inference(literals_permutation,[status(thm)],[c_0_3319]) ).
cnf(c_0_3319_4,axiom,
( hAPP_nat_int(power_power_int(X1),X3) != hAPP_nat_int(power_power_int(X2),X3)
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X3))
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_3319]) ).
cnf(c_0_3320_0,axiom,
( X1 = X2
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X3))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),X1))
| hAPP_nat_nat(power_power_nat(X1),X3) != hAPP_nat_nat(power_power_nat(X2),X3) ),
inference(literals_permutation,[status(thm)],[c_0_3320]) ).
cnf(c_0_3320_1,axiom,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X3))
| X1 = X2
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),X1))
| hAPP_nat_nat(power_power_nat(X1),X3) != hAPP_nat_nat(power_power_nat(X2),X3) ),
inference(literals_permutation,[status(thm)],[c_0_3320]) ).
cnf(c_0_3320_2,axiom,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X3))
| X1 = X2
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),X1))
| hAPP_nat_nat(power_power_nat(X1),X3) != hAPP_nat_nat(power_power_nat(X2),X3) ),
inference(literals_permutation,[status(thm)],[c_0_3320]) ).
cnf(c_0_3320_3,axiom,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),X1))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X3))
| X1 = X2
| hAPP_nat_nat(power_power_nat(X1),X3) != hAPP_nat_nat(power_power_nat(X2),X3) ),
inference(literals_permutation,[status(thm)],[c_0_3320]) ).
cnf(c_0_3320_4,axiom,
( hAPP_nat_nat(power_power_nat(X1),X3) != hAPP_nat_nat(power_power_nat(X2),X3)
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),X1))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X3))
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_3320]) ).
cnf(c_0_3321_0,axiom,
( X1 = X2
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X3))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X2))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X1))
| hAPP_nat_real(power_power_real(X1),X3) != hAPP_nat_real(power_power_real(X2),X3) ),
inference(literals_permutation,[status(thm)],[c_0_3321]) ).
cnf(c_0_3321_1,axiom,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X3))
| X1 = X2
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X2))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X1))
| hAPP_nat_real(power_power_real(X1),X3) != hAPP_nat_real(power_power_real(X2),X3) ),
inference(literals_permutation,[status(thm)],[c_0_3321]) ).
cnf(c_0_3321_2,axiom,
( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X3))
| X1 = X2
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X1))
| hAPP_nat_real(power_power_real(X1),X3) != hAPP_nat_real(power_power_real(X2),X3) ),
inference(literals_permutation,[status(thm)],[c_0_3321]) ).
cnf(c_0_3321_3,axiom,
( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X1))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X3))
| X1 = X2
| hAPP_nat_real(power_power_real(X1),X3) != hAPP_nat_real(power_power_real(X2),X3) ),
inference(literals_permutation,[status(thm)],[c_0_3321]) ).
cnf(c_0_3321_4,axiom,
( hAPP_nat_real(power_power_real(X1),X3) != hAPP_nat_real(power_power_real(X2),X3)
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X1))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X3))
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_3321]) ).
cnf(c_0_3323_0,axiom,
( hBOOL(hAPP_nat_bool(X1,zero_zero_nat))
| hBOOL(hAPP_nat_bool(X1,hAPP_nat_nat(plus_plus_nat(sk1_esk14_2(X2,X1)),one_one_nat)))
| ~ hBOOL(hAPP_nat_bool(X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3323]) ).
cnf(c_0_3323_1,axiom,
( hBOOL(hAPP_nat_bool(X1,hAPP_nat_nat(plus_plus_nat(sk1_esk14_2(X2,X1)),one_one_nat)))
| hBOOL(hAPP_nat_bool(X1,zero_zero_nat))
| ~ hBOOL(hAPP_nat_bool(X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3323]) ).
cnf(c_0_3323_2,axiom,
( ~ hBOOL(hAPP_nat_bool(X1,X2))
| hBOOL(hAPP_nat_bool(X1,hAPP_nat_nat(plus_plus_nat(sk1_esk14_2(X2,X1)),one_one_nat)))
| hBOOL(hAPP_nat_bool(X1,zero_zero_nat)) ),
inference(literals_permutation,[status(thm)],[c_0_3323]) ).
cnf(c_0_3324_0,axiom,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),hAPP_int_int(plus_plus_int(X2),X3)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X3))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3324]) ).
cnf(c_0_3324_1,axiom,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X3))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),hAPP_int_int(plus_plus_int(X2),X3)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3324]) ).
cnf(c_0_3324_2,axiom,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X2))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X3))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),hAPP_int_int(plus_plus_int(X2),X3))) ),
inference(literals_permutation,[status(thm)],[c_0_3324]) ).
cnf(c_0_3325_0,axiom,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),hAPP_nat_nat(plus_plus_nat(X2),X3)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X3))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3325]) ).
cnf(c_0_3325_1,axiom,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X3))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),hAPP_nat_nat(plus_plus_nat(X2),X3)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3325]) ).
cnf(c_0_3325_2,axiom,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X3))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),hAPP_nat_nat(plus_plus_nat(X2),X3))) ),
inference(literals_permutation,[status(thm)],[c_0_3325]) ).
cnf(c_0_3326_0,axiom,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X1),hAPP_real_real(plus_plus_real(X2),X3)))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X1),X3))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3326]) ).
cnf(c_0_3326_1,axiom,
( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X1),X3))
| hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X1),hAPP_real_real(plus_plus_real(X2),X3)))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3326]) ).
cnf(c_0_3326_2,axiom,
( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X2))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X1),X3))
| hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X1),hAPP_real_real(plus_plus_real(X2),X3))) ),
inference(literals_permutation,[status(thm)],[c_0_3326]) ).
cnf(c_0_3327_0,axiom,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),hAPP_int_int(plus_plus_int(X2),X3)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X3))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3327]) ).
cnf(c_0_3327_1,axiom,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X3))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),hAPP_int_int(plus_plus_int(X2),X3)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3327]) ).
cnf(c_0_3327_2,axiom,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X2))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X3))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),hAPP_int_int(plus_plus_int(X2),X3))) ),
inference(literals_permutation,[status(thm)],[c_0_3327]) ).
cnf(c_0_3328_0,axiom,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),hAPP_nat_nat(plus_plus_nat(X2),X3)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X3))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3328]) ).
cnf(c_0_3328_1,axiom,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X3))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),hAPP_nat_nat(plus_plus_nat(X2),X3)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3328]) ).
cnf(c_0_3328_2,axiom,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X3))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),hAPP_nat_nat(plus_plus_nat(X2),X3))) ),
inference(literals_permutation,[status(thm)],[c_0_3328]) ).
cnf(c_0_3329_0,axiom,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X1),hAPP_real_real(plus_plus_real(X2),X3)))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X1),X3))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3329]) ).
cnf(c_0_3329_1,axiom,
( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X1),X3))
| hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X1),hAPP_real_real(plus_plus_real(X2),X3)))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3329]) ).
cnf(c_0_3329_2,axiom,
( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X2))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X1),X3))
| hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X1),hAPP_real_real(plus_plus_real(X2),X3))) ),
inference(literals_permutation,[status(thm)],[c_0_3329]) ).
cnf(c_0_3330_0,axiom,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),hAPP_int_int(plus_plus_int(X2),X3)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3330]) ).
cnf(c_0_3330_1,axiom,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),hAPP_int_int(plus_plus_int(X2),X3)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3330]) ).
cnf(c_0_3330_2,axiom,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X3))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),hAPP_int_int(plus_plus_int(X2),X3))) ),
inference(literals_permutation,[status(thm)],[c_0_3330]) ).
cnf(c_0_3331_0,axiom,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),hAPP_nat_nat(plus_plus_nat(X2),X3)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3331]) ).
cnf(c_0_3331_1,axiom,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),hAPP_nat_nat(plus_plus_nat(X2),X3)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3331]) ).
cnf(c_0_3331_2,axiom,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),X3))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),hAPP_nat_nat(plus_plus_nat(X2),X3))) ),
inference(literals_permutation,[status(thm)],[c_0_3331]) ).
cnf(c_0_3332_0,axiom,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X1),hAPP_real_real(plus_plus_real(X2),X3)))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X1),X2))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3332]) ).
cnf(c_0_3332_1,axiom,
( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X1),X2))
| hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X1),hAPP_real_real(plus_plus_real(X2),X3)))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3332]) ).
cnf(c_0_3332_2,axiom,
( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X3))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X1),X2))
| hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X1),hAPP_real_real(plus_plus_real(X2),X3))) ),
inference(literals_permutation,[status(thm)],[c_0_3332]) ).
cnf(c_0_3333_0,axiom,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),hAPP_int_int(plus_plus_int(X2),X3)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X3))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3333]) ).
cnf(c_0_3333_1,axiom,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X3))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),hAPP_int_int(plus_plus_int(X2),X3)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3333]) ).
cnf(c_0_3333_2,axiom,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X2))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X3))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),hAPP_int_int(plus_plus_int(X2),X3))) ),
inference(literals_permutation,[status(thm)],[c_0_3333]) ).
cnf(c_0_3334_0,axiom,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),hAPP_nat_nat(plus_plus_nat(X2),X3)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X3))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3334]) ).
cnf(c_0_3334_1,axiom,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X3))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),hAPP_nat_nat(plus_plus_nat(X2),X3)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3334]) ).
cnf(c_0_3334_2,axiom,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X3))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),hAPP_nat_nat(plus_plus_nat(X2),X3))) ),
inference(literals_permutation,[status(thm)],[c_0_3334]) ).
cnf(c_0_3335_0,axiom,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X1),hAPP_real_real(plus_plus_real(X2),X3)))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X1),X3))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3335]) ).
cnf(c_0_3335_1,axiom,
( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X1),X3))
| hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X1),hAPP_real_real(plus_plus_real(X2),X3)))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3335]) ).
cnf(c_0_3335_2,axiom,
( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X2))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X1),X3))
| hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X1),hAPP_real_real(plus_plus_real(X2),X3))) ),
inference(literals_permutation,[status(thm)],[c_0_3335]) ).
cnf(c_0_3336_0,axiom,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),hAPP_int_int(plus_plus_int(X2),X3)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X3))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3336]) ).
cnf(c_0_3336_1,axiom,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X3))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),hAPP_int_int(plus_plus_int(X2),X3)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3336]) ).
cnf(c_0_3336_2,axiom,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X2))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X3))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),hAPP_int_int(plus_plus_int(X2),X3))) ),
inference(literals_permutation,[status(thm)],[c_0_3336]) ).
cnf(c_0_3337_0,axiom,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),hAPP_nat_nat(plus_plus_nat(X2),X3)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X3))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3337]) ).
cnf(c_0_3337_1,axiom,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X3))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),hAPP_nat_nat(plus_plus_nat(X2),X3)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3337]) ).
cnf(c_0_3337_2,axiom,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X3))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),hAPP_nat_nat(plus_plus_nat(X2),X3))) ),
inference(literals_permutation,[status(thm)],[c_0_3337]) ).
cnf(c_0_3338_0,axiom,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X1),hAPP_real_real(plus_plus_real(X2),X3)))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X1),X3))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3338]) ).
cnf(c_0_3338_1,axiom,
( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X1),X3))
| hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X1),hAPP_real_real(plus_plus_real(X2),X3)))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3338]) ).
cnf(c_0_3338_2,axiom,
( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X2))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X1),X3))
| hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X1),hAPP_real_real(plus_plus_real(X2),X3))) ),
inference(literals_permutation,[status(thm)],[c_0_3338]) ).
cnf(c_0_3339_0,axiom,
( X1 = X2
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X2))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1))
| hAPP_nat_int(power_power_int(X1),number_number_of_nat(bit0(bit1(pls)))) != hAPP_nat_int(power_power_int(X2),number_number_of_nat(bit0(bit1(pls)))) ),
inference(literals_permutation,[status(thm)],[c_0_3339]) ).
cnf(c_0_3339_1,axiom,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X2))
| X1 = X2
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1))
| hAPP_nat_int(power_power_int(X1),number_number_of_nat(bit0(bit1(pls)))) != hAPP_nat_int(power_power_int(X2),number_number_of_nat(bit0(bit1(pls)))) ),
inference(literals_permutation,[status(thm)],[c_0_3339]) ).
cnf(c_0_3339_2,axiom,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X2))
| X1 = X2
| hAPP_nat_int(power_power_int(X1),number_number_of_nat(bit0(bit1(pls)))) != hAPP_nat_int(power_power_int(X2),number_number_of_nat(bit0(bit1(pls)))) ),
inference(literals_permutation,[status(thm)],[c_0_3339]) ).
cnf(c_0_3339_3,axiom,
( hAPP_nat_int(power_power_int(X1),number_number_of_nat(bit0(bit1(pls)))) != hAPP_nat_int(power_power_int(X2),number_number_of_nat(bit0(bit1(pls))))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X2))
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_3339]) ).
cnf(c_0_3340_0,axiom,
( X1 = X2
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),X1))
| hAPP_nat_nat(power_power_nat(X1),number_number_of_nat(bit0(bit1(pls)))) != hAPP_nat_nat(power_power_nat(X2),number_number_of_nat(bit0(bit1(pls)))) ),
inference(literals_permutation,[status(thm)],[c_0_3340]) ).
cnf(c_0_3340_1,axiom,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),X2))
| X1 = X2
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),X1))
| hAPP_nat_nat(power_power_nat(X1),number_number_of_nat(bit0(bit1(pls)))) != hAPP_nat_nat(power_power_nat(X2),number_number_of_nat(bit0(bit1(pls)))) ),
inference(literals_permutation,[status(thm)],[c_0_3340]) ).
cnf(c_0_3340_2,axiom,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),X1))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),X2))
| X1 = X2
| hAPP_nat_nat(power_power_nat(X1),number_number_of_nat(bit0(bit1(pls)))) != hAPP_nat_nat(power_power_nat(X2),number_number_of_nat(bit0(bit1(pls)))) ),
inference(literals_permutation,[status(thm)],[c_0_3340]) ).
cnf(c_0_3340_3,axiom,
( hAPP_nat_nat(power_power_nat(X1),number_number_of_nat(bit0(bit1(pls)))) != hAPP_nat_nat(power_power_nat(X2),number_number_of_nat(bit0(bit1(pls))))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),X1))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),X2))
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_3340]) ).
cnf(c_0_3341_0,axiom,
( X1 = X2
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X2))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X1))
| hAPP_nat_real(power_power_real(X1),number_number_of_nat(bit0(bit1(pls)))) != hAPP_nat_real(power_power_real(X2),number_number_of_nat(bit0(bit1(pls)))) ),
inference(literals_permutation,[status(thm)],[c_0_3341]) ).
cnf(c_0_3341_1,axiom,
( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X2))
| X1 = X2
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X1))
| hAPP_nat_real(power_power_real(X1),number_number_of_nat(bit0(bit1(pls)))) != hAPP_nat_real(power_power_real(X2),number_number_of_nat(bit0(bit1(pls)))) ),
inference(literals_permutation,[status(thm)],[c_0_3341]) ).
cnf(c_0_3341_2,axiom,
( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X1))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X2))
| X1 = X2
| hAPP_nat_real(power_power_real(X1),number_number_of_nat(bit0(bit1(pls)))) != hAPP_nat_real(power_power_real(X2),number_number_of_nat(bit0(bit1(pls)))) ),
inference(literals_permutation,[status(thm)],[c_0_3341]) ).
cnf(c_0_3341_3,axiom,
( hAPP_nat_real(power_power_real(X1),number_number_of_nat(bit0(bit1(pls)))) != hAPP_nat_real(power_power_real(X2),number_number_of_nat(bit0(bit1(pls))))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X1))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X2))
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_3341]) ).
cnf(c_0_3342_0,axiom,
( X3 = sk1_esk4_2(X2,X1)
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X2))
| hAPP_nat_real(power_power_real(X3),X1) != X2
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3342]) ).
cnf(c_0_3342_1,axiom,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1))
| X3 = sk1_esk4_2(X2,X1)
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X2))
| hAPP_nat_real(power_power_real(X3),X1) != X2
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3342]) ).
cnf(c_0_3342_2,axiom,
( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1))
| X3 = sk1_esk4_2(X2,X1)
| hAPP_nat_real(power_power_real(X3),X1) != X2
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3342]) ).
cnf(c_0_3342_3,axiom,
( hAPP_nat_real(power_power_real(X3),X1) != X2
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1))
| X3 = sk1_esk4_2(X2,X1)
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3342]) ).
cnf(c_0_3342_4,axiom,
( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X3))
| hAPP_nat_real(power_power_real(X3),X1) != X2
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1))
| X3 = sk1_esk4_2(X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_3342]) ).
cnf(c_0_3343_0,axiom,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(plus_plus_nat(X2),X1))) ),
inference(literals_permutation,[status(thm)],[c_0_3343]) ).
cnf(c_0_3343_1,axiom,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X2))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(plus_plus_nat(X2),X1))) ),
inference(literals_permutation,[status(thm)],[c_0_3343]) ).
cnf(c_0_3343_2,axiom,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(plus_plus_nat(X2),X1)))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X2))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_3343]) ).
cnf(c_0_3344_0,axiom,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,number_number_of_nat(X1)),number_number_of_nat(X2)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3344]) ).
cnf(c_0_3344_1,axiom,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,number_number_of_nat(X1)),number_number_of_nat(X2)))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),X2))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3344]) ).
cnf(c_0_3344_2,axiom,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,number_number_of_nat(X1)),number_number_of_nat(X2)))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3344]) ).
cnf(c_0_3345_0,axiom,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_int_int(plus_plus_int(X1),X2)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X2))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_3345]) ).
cnf(c_0_3345_1,axiom,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X2))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_int_int(plus_plus_int(X1),X2)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_3345]) ).
cnf(c_0_3345_2,axiom,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X2))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_int_int(plus_plus_int(X1),X2))) ),
inference(literals_permutation,[status(thm)],[c_0_3345]) ).
cnf(c_0_3346_0,axiom,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(plus_plus_nat(X1),X2)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_3346]) ).
cnf(c_0_3346_1,axiom,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X2))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(plus_plus_nat(X1),X2)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_3346]) ).
cnf(c_0_3346_2,axiom,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),X1))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X2))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(plus_plus_nat(X1),X2))) ),
inference(literals_permutation,[status(thm)],[c_0_3346]) ).
cnf(c_0_3347_0,axiom,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),hAPP_real_real(plus_plus_real(X1),X2)))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X2))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_3347]) ).
cnf(c_0_3347_1,axiom,
( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X2))
| hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),hAPP_real_real(plus_plus_real(X1),X2)))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_3347]) ).
cnf(c_0_3347_2,axiom,
( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X1))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X2))
| hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),hAPP_real_real(plus_plus_real(X1),X2))) ),
inference(literals_permutation,[status(thm)],[c_0_3347]) ).
cnf(c_0_3348_0,axiom,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_int_int(plus_plus_int(X1),X2)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X2))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_3348]) ).
cnf(c_0_3348_1,axiom,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X2))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_int_int(plus_plus_int(X1),X2)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_3348]) ).
cnf(c_0_3348_2,axiom,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X1))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X2))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_int_int(plus_plus_int(X1),X2))) ),
inference(literals_permutation,[status(thm)],[c_0_3348]) ).
cnf(c_0_3349_0,axiom,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(plus_plus_nat(X1),X2)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_3349]) ).
cnf(c_0_3349_1,axiom,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),X2))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(plus_plus_nat(X1),X2)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_3349]) ).
cnf(c_0_3349_2,axiom,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),X2))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(plus_plus_nat(X1),X2))) ),
inference(literals_permutation,[status(thm)],[c_0_3349]) ).
cnf(c_0_3350_0,axiom,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),hAPP_real_real(plus_plus_real(X1),X2)))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X2))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_3350]) ).
cnf(c_0_3350_1,axiom,
( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X2))
| hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),hAPP_real_real(plus_plus_real(X1),X2)))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_3350]) ).
cnf(c_0_3350_2,axiom,
( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X1))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X2))
| hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),hAPP_real_real(plus_plus_real(X1),X2))) ),
inference(literals_permutation,[status(thm)],[c_0_3350]) ).
cnf(c_0_3351_0,axiom,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_int_int(plus_plus_int(X1),X2)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X2))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_3351]) ).
cnf(c_0_3351_1,axiom,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X2))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_int_int(plus_plus_int(X1),X2)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_3351]) ).
cnf(c_0_3351_2,axiom,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X2))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_int_int(plus_plus_int(X1),X2))) ),
inference(literals_permutation,[status(thm)],[c_0_3351]) ).
cnf(c_0_3352_0,axiom,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_int_int(plus_plus_int(X1),X2)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X2))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_3352]) ).
cnf(c_0_3352_1,axiom,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X2))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_int_int(plus_plus_int(X1),X2)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_3352]) ).
cnf(c_0_3352_2,axiom,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X2))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_int_int(plus_plus_int(X1),X2))) ),
inference(literals_permutation,[status(thm)],[c_0_3352]) ).
cnf(c_0_3353_0,axiom,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),hAPP_nat_nat(plus_plus_nat(X1),X2)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_3353]) ).
cnf(c_0_3353_1,axiom,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),X2))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),hAPP_nat_nat(plus_plus_nat(X1),X2)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_3353]) ).
cnf(c_0_3353_2,axiom,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),X1))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),X2))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),hAPP_nat_nat(plus_plus_nat(X1),X2))) ),
inference(literals_permutation,[status(thm)],[c_0_3353]) ).
cnf(c_0_3354_0,axiom,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),hAPP_real_real(plus_plus_real(X1),X2)))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X2))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_3354]) ).
cnf(c_0_3354_1,axiom,
( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X2))
| hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),hAPP_real_real(plus_plus_real(X1),X2)))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_3354]) ).
cnf(c_0_3354_2,axiom,
( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X1))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X2))
| hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),hAPP_real_real(plus_plus_real(X1),X2))) ),
inference(literals_permutation,[status(thm)],[c_0_3354]) ).
cnf(c_0_3355_0,axiom,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_int_int(plus_plus_int(X1),X2)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X2))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_3355]) ).
cnf(c_0_3355_1,axiom,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X2))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_int_int(plus_plus_int(X1),X2)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_3355]) ).
cnf(c_0_3355_2,axiom,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X1))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X2))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_int_int(plus_plus_int(X1),X2))) ),
inference(literals_permutation,[status(thm)],[c_0_3355]) ).
cnf(c_0_3356_0,axiom,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(plus_plus_nat(X1),X2)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_3356]) ).
cnf(c_0_3356_1,axiom,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X2))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(plus_plus_nat(X1),X2)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_3356]) ).
cnf(c_0_3356_2,axiom,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X2))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(plus_plus_nat(X1),X2))) ),
inference(literals_permutation,[status(thm)],[c_0_3356]) ).
cnf(c_0_3357_0,axiom,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),hAPP_real_real(plus_plus_real(X1),X2)))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X2))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_3357]) ).
cnf(c_0_3357_1,axiom,
( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X2))
| hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),hAPP_real_real(plus_plus_real(X1),X2)))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_3357]) ).
cnf(c_0_3357_2,axiom,
( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X1))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X2))
| hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),hAPP_real_real(plus_plus_real(X1),X2))) ),
inference(literals_permutation,[status(thm)],[c_0_3357]) ).
cnf(c_0_3358_0,axiom,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,one_one_real),hAPP_nat_real(power_power_real(X1),X2)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X2))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,one_one_real),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_3358]) ).
cnf(c_0_3358_1,axiom,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X2))
| hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,one_one_real),hAPP_nat_real(power_power_real(X1),X2)))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,one_one_real),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_3358]) ).
cnf(c_0_3358_2,axiom,
( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,one_one_real),X1))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X2))
| hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,one_one_real),hAPP_nat_real(power_power_real(X1),X2))) ),
inference(literals_permutation,[status(thm)],[c_0_3358]) ).
cnf(c_0_3359_0,axiom,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,one_one_nat),hAPP_nat_nat(power_power_nat(X1),X2)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,one_one_nat),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_3359]) ).
cnf(c_0_3359_1,axiom,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X2))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,one_one_nat),hAPP_nat_nat(power_power_nat(X1),X2)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,one_one_nat),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_3359]) ).
cnf(c_0_3359_2,axiom,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,one_one_nat),X1))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X2))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,one_one_nat),hAPP_nat_nat(power_power_nat(X1),X2))) ),
inference(literals_permutation,[status(thm)],[c_0_3359]) ).
cnf(c_0_3360_0,axiom,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),hAPP_nat_int(power_power_int(X1),X2)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X2))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_3360]) ).
cnf(c_0_3360_1,axiom,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X2))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),hAPP_nat_int(power_power_int(X1),X2)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_3360]) ).
cnf(c_0_3360_2,axiom,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),X1))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X2))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),hAPP_nat_int(power_power_int(X1),X2))) ),
inference(literals_permutation,[status(thm)],[c_0_3360]) ).
cnf(c_0_3361_0,axiom,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(X3,X2),X1))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X2),X1))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(X3,X2),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_3361]) ).
cnf(c_0_3361_1,axiom,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(X3,X2),X1))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X2),X1))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(X3,X2),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_3361]) ).
cnf(c_0_3361_2,axiom,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X2),X1))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(X3,X2),X1))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(X3,X2),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_3361]) ).
cnf(c_0_3361_3,axiom,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(X3,X2),X1))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X2),X1))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(X3,X2),X1))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3361]) ).
cnf(c_0_3364_0,axiom,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(X1)),number_number_of_int(X2)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,number_number_of_int(X2)),number_number_of_int(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_3364]) ).
cnf(c_0_3364_1,axiom,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,number_number_of_int(X2)),number_number_of_int(X1)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(X1)),number_number_of_int(X2))) ),
inference(literals_permutation,[status(thm)],[c_0_3364]) ).
cnf(c_0_3365_0,axiom,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,number_number_of_nat(X1)),number_number_of_nat(X2)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,number_number_of_nat(X2)),number_number_of_nat(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_3365]) ).
cnf(c_0_3365_1,axiom,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,number_number_of_nat(X2)),number_number_of_nat(X1)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,number_number_of_nat(X1)),number_number_of_nat(X2))) ),
inference(literals_permutation,[status(thm)],[c_0_3365]) ).
cnf(c_0_3366_0,axiom,
( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,number267125858f_real(X1)),number267125858f_real(X2)))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,number267125858f_real(X2)),number267125858f_real(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_3366]) ).
cnf(c_0_3366_1,axiom,
( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,number267125858f_real(X2)),number267125858f_real(X1)))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,number267125858f_real(X1)),number267125858f_real(X2))) ),
inference(literals_permutation,[status(thm)],[c_0_3366]) ).
cnf(c_0_3367_0,axiom,
( X3 = X2
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(X1,X2),X3))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(X1,X2),X3))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(X1,X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3367]) ).
cnf(c_0_3367_1,axiom,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(X1,X2),X3))
| X3 = X2
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(X1,X2),X3))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(X1,X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3367]) ).
cnf(c_0_3367_2,axiom,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(X1,X2),X3))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(X1,X2),X3))
| X3 = X2
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(X1,X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3367]) ).
cnf(c_0_3367_3,axiom,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(X1,X2),X3))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(X1,X2),X3))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(X1,X2),X3))
| X3 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_3367]) ).
cnf(c_0_3368_0,axiom,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1))
| number_number_of_nat(X2) = zero_zero_nat
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(power_power_nat(X1),number_number_of_nat(X2)))) ),
inference(literals_permutation,[status(thm)],[c_0_3368]) ).
cnf(c_0_3368_1,axiom,
( number_number_of_nat(X2) = zero_zero_nat
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(power_power_nat(X1),number_number_of_nat(X2)))) ),
inference(literals_permutation,[status(thm)],[c_0_3368]) ).
cnf(c_0_3368_2,axiom,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(power_power_nat(X1),number_number_of_nat(X2))))
| number_number_of_nat(X2) = zero_zero_nat
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_3368]) ).
cnf(c_0_3369_0,axiom,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,number_number_of_nat(X1)),number_number_of_nat(X2)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X2))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3369]) ).
cnf(c_0_3369_1,axiom,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X2))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,number_number_of_nat(X1)),number_number_of_nat(X2)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3369]) ).
cnf(c_0_3369_2,axiom,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),X2))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X2))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,number_number_of_nat(X1)),number_number_of_nat(X2))) ),
inference(literals_permutation,[status(thm)],[c_0_3369]) ).
cnf(c_0_3370_0,axiom,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),sk1_esk22_2(X2,X1)))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X1))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3370]) ).
cnf(c_0_3370_1,axiom,
( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X1))
| hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),sk1_esk22_2(X2,X1)))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3370]) ).
cnf(c_0_3370_2,axiom,
( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X2))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X1))
| hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),sk1_esk22_2(X2,X1))) ),
inference(literals_permutation,[status(thm)],[c_0_3370]) ).
cnf(c_0_3371_0,axiom,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),sk1_esk5_2(X2,X1)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3371]) ).
cnf(c_0_3371_1,axiom,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1))
| hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),sk1_esk5_2(X2,X1)))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3371]) ).
cnf(c_0_3371_2,axiom,
( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1))
| hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),sk1_esk5_2(X2,X1))) ),
inference(literals_permutation,[status(thm)],[c_0_3371]) ).
cnf(c_0_3372_0,axiom,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),sk1_esk4_2(X2,X1)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3372]) ).
cnf(c_0_3372_1,axiom,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1))
| hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),sk1_esk4_2(X2,X1)))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3372]) ).
cnf(c_0_3372_2,axiom,
( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1))
| hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),sk1_esk4_2(X2,X1))) ),
inference(literals_permutation,[status(thm)],[c_0_3372]) ).
cnf(c_0_3373_0,axiom,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(plus_plus_int(X1),X1)),zero_zero_int))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),zero_zero_int)) ),
inference(literals_permutation,[status(thm)],[c_0_3373]) ).
cnf(c_0_3373_1,axiom,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),zero_zero_int))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(plus_plus_int(X1),X1)),zero_zero_int)) ),
inference(literals_permutation,[status(thm)],[c_0_3373]) ).
cnf(c_0_3374_0,axiom,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(plus_plus_real(X1),X1)),zero_zero_real))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X1),zero_zero_real)) ),
inference(literals_permutation,[status(thm)],[c_0_3374]) ).
cnf(c_0_3374_1,axiom,
( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X1),zero_zero_real))
| hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(plus_plus_real(X1),X1)),zero_zero_real)) ),
inference(literals_permutation,[status(thm)],[c_0_3374]) ).
cnf(c_0_3375_0,axiom,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(X1),X1)),zero_zero_int))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),zero_zero_int)) ),
inference(literals_permutation,[status(thm)],[c_0_3375]) ).
cnf(c_0_3375_1,axiom,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),zero_zero_int))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(X1),X1)),zero_zero_int)) ),
inference(literals_permutation,[status(thm)],[c_0_3375]) ).
cnf(c_0_3376_0,axiom,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(plus_plus_real(X1),X1)),zero_zero_real))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X1),zero_zero_real)) ),
inference(literals_permutation,[status(thm)],[c_0_3376]) ).
cnf(c_0_3376_1,axiom,
( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X1),zero_zero_real))
| hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(plus_plus_real(X1),X1)),zero_zero_real)) ),
inference(literals_permutation,[status(thm)],[c_0_3376]) ).
cnf(c_0_3377_0,axiom,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(plus_plus_real(X1),X1)),zero_zero_real))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X1),zero_zero_real)) ),
inference(literals_permutation,[status(thm)],[c_0_3377]) ).
cnf(c_0_3377_1,axiom,
( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X1),zero_zero_real))
| hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(plus_plus_real(X1),X1)),zero_zero_real)) ),
inference(literals_permutation,[status(thm)],[c_0_3377]) ).
cnf(c_0_3378_0,axiom,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(X1),X1)),zero_zero_int))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),zero_zero_int)) ),
inference(literals_permutation,[status(thm)],[c_0_3378]) ).
cnf(c_0_3378_1,axiom,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),zero_zero_int))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(X1),X1)),zero_zero_int)) ),
inference(literals_permutation,[status(thm)],[c_0_3378]) ).
cnf(c_0_3379_0,axiom,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(plus_plus_int(X1),one_one_int)),X2))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3379]) ).
cnf(c_0_3379_1,axiom,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X2))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(plus_plus_int(X1),one_one_int)),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3379]) ).
cnf(c_0_3380_0,axiom,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(plus_plus_int(X1),one_one_int)),X2))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3380]) ).
cnf(c_0_3380_1,axiom,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X2))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(plus_plus_int(X1),one_one_int)),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3380]) ).
cnf(c_0_3382_0,axiom,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_nat_int(semiri1621563631at_int,X1)),hAPP_nat_int(semiri1621563631at_int,X2)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3382]) ).
cnf(c_0_3382_1,axiom,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_nat_int(semiri1621563631at_int,X1)),hAPP_nat_int(semiri1621563631at_int,X2))) ),
inference(literals_permutation,[status(thm)],[c_0_3382]) ).
cnf(c_0_3383_0,axiom,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_nat_int(semiri1621563631at_int,X1)),hAPP_nat_int(semiri1621563631at_int,X2)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3383]) ).
cnf(c_0_3383_1,axiom,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_nat_int(semiri1621563631at_int,X1)),hAPP_nat_int(semiri1621563631at_int,X2))) ),
inference(literals_permutation,[status(thm)],[c_0_3383]) ).
cnf(c_0_3384_0,axiom,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_nat_int(semiri1621563631at_int,X1)),hAPP_nat_int(semiri1621563631at_int,X2)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3384]) ).
cnf(c_0_3384_1,axiom,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_nat_int(semiri1621563631at_int,X1)),hAPP_nat_int(semiri1621563631at_int,X2))) ),
inference(literals_permutation,[status(thm)],[c_0_3384]) ).
cnf(c_0_3385_0,axiom,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(semiri984289939at_nat,X1)),hAPP_nat_nat(semiri984289939at_nat,X2)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3385]) ).
cnf(c_0_3385_1,axiom,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(semiri984289939at_nat,X1)),hAPP_nat_nat(semiri984289939at_nat,X2))) ),
inference(literals_permutation,[status(thm)],[c_0_3385]) ).
cnf(c_0_3386_0,axiom,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_nat_real(semiri132038758t_real,X1)),hAPP_nat_real(semiri132038758t_real,X2)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3386]) ).
cnf(c_0_3386_1,axiom,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
| hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_nat_real(semiri132038758t_real,X1)),hAPP_nat_real(semiri132038758t_real,X2))) ),
inference(literals_permutation,[status(thm)],[c_0_3386]) ).
cnf(c_0_3387_0,axiom,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_nat_int(semiri1621563631at_int,X1)),hAPP_nat_int(semiri1621563631at_int,X2)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3387]) ).
cnf(c_0_3387_1,axiom,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_nat_int(semiri1621563631at_int,X1)),hAPP_nat_int(semiri1621563631at_int,X2))) ),
inference(literals_permutation,[status(thm)],[c_0_3387]) ).
cnf(c_0_3388_0,axiom,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(semiri984289939at_nat,X1)),hAPP_nat_nat(semiri984289939at_nat,X2)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3388]) ).
cnf(c_0_3388_1,axiom,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(semiri984289939at_nat,X1)),hAPP_nat_nat(semiri984289939at_nat,X2))) ),
inference(literals_permutation,[status(thm)],[c_0_3388]) ).
cnf(c_0_3389_0,axiom,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_nat_real(semiri132038758t_real,X1)),hAPP_nat_real(semiri132038758t_real,X2)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3389]) ).
cnf(c_0_3389_1,axiom,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
| hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_nat_real(semiri132038758t_real,X1)),hAPP_nat_real(semiri132038758t_real,X2))) ),
inference(literals_permutation,[status(thm)],[c_0_3389]) ).
cnf(c_0_3390_0,axiom,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_nat_int(semiri1621563631at_int,X1)),hAPP_nat_int(semiri1621563631at_int,X2)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3390]) ).
cnf(c_0_3390_1,axiom,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_nat_int(semiri1621563631at_int,X1)),hAPP_nat_int(semiri1621563631at_int,X2))) ),
inference(literals_permutation,[status(thm)],[c_0_3390]) ).
cnf(c_0_3391_0,axiom,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(semiri984289939at_nat,X1)),hAPP_nat_nat(semiri984289939at_nat,X2)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3391]) ).
cnf(c_0_3391_1,axiom,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(semiri984289939at_nat,X1)),hAPP_nat_nat(semiri984289939at_nat,X2))) ),
inference(literals_permutation,[status(thm)],[c_0_3391]) ).
cnf(c_0_3392_0,axiom,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_nat_real(semiri132038758t_real,X1)),hAPP_nat_real(semiri132038758t_real,X2)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3392]) ).
cnf(c_0_3392_1,axiom,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
| hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_nat_real(semiri132038758t_real,X1)),hAPP_nat_real(semiri132038758t_real,X2))) ),
inference(literals_permutation,[status(thm)],[c_0_3392]) ).
cnf(c_0_3393_0,axiom,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_nat_int(semiri1621563631at_int,X1)),hAPP_nat_int(semiri1621563631at_int,X2)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3393]) ).
cnf(c_0_3393_1,axiom,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_nat_int(semiri1621563631at_int,X1)),hAPP_nat_int(semiri1621563631at_int,X2))) ),
inference(literals_permutation,[status(thm)],[c_0_3393]) ).
cnf(c_0_3394_0,axiom,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_nat_int(semiri1621563631at_int,X1)),hAPP_nat_int(semiri1621563631at_int,X2)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3394]) ).
cnf(c_0_3394_1,axiom,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_nat_int(semiri1621563631at_int,X1)),hAPP_nat_int(semiri1621563631at_int,X2))) ),
inference(literals_permutation,[status(thm)],[c_0_3394]) ).
cnf(c_0_3395_0,axiom,
( X1 = one_one_int
| X1 = zero_zero_int
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),number_number_of_int(bit0(bit1(pls)))))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_3395]) ).
cnf(c_0_3395_1,axiom,
( X1 = zero_zero_int
| X1 = one_one_int
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),number_number_of_int(bit0(bit1(pls)))))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_3395]) ).
cnf(c_0_3395_2,axiom,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),number_number_of_int(bit0(bit1(pls)))))
| X1 = zero_zero_int
| X1 = one_one_int
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_3395]) ).
cnf(c_0_3395_3,axiom,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),number_number_of_int(bit0(bit1(pls)))))
| X1 = zero_zero_int
| X1 = one_one_int ),
inference(literals_permutation,[status(thm)],[c_0_3395]) ).
cnf(c_0_3396_0,axiom,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),pls))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,number_number_of_nat(X1)),number_number_of_nat(X2))) ),
inference(literals_permutation,[status(thm)],[c_0_3396]) ).
cnf(c_0_3396_1,axiom,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),pls))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,number_number_of_nat(X1)),number_number_of_nat(X2))) ),
inference(literals_permutation,[status(thm)],[c_0_3396]) ).
cnf(c_0_3396_2,axiom,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,number_number_of_nat(X1)),number_number_of_nat(X2)))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),pls)) ),
inference(literals_permutation,[status(thm)],[c_0_3396]) ).
cnf(c_0_3397_0,axiom,
( hBOOL(hAPP_nat_bool(X1,zero_zero_nat))
| ~ hBOOL(hAPP_nat_bool(X1,X2))
| ~ hBOOL(hAPP_nat_bool(X1,X3))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X3),sk1_esk19_2(X2,X1))) ),
inference(literals_permutation,[status(thm)],[c_0_3397]) ).
cnf(c_0_3397_1,axiom,
( ~ hBOOL(hAPP_nat_bool(X1,X2))
| hBOOL(hAPP_nat_bool(X1,zero_zero_nat))
| ~ hBOOL(hAPP_nat_bool(X1,X3))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X3),sk1_esk19_2(X2,X1))) ),
inference(literals_permutation,[status(thm)],[c_0_3397]) ).
cnf(c_0_3397_2,axiom,
( ~ hBOOL(hAPP_nat_bool(X1,X3))
| ~ hBOOL(hAPP_nat_bool(X1,X2))
| hBOOL(hAPP_nat_bool(X1,zero_zero_nat))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X3),sk1_esk19_2(X2,X1))) ),
inference(literals_permutation,[status(thm)],[c_0_3397]) ).
cnf(c_0_3397_3,axiom,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X3),sk1_esk19_2(X2,X1)))
| ~ hBOOL(hAPP_nat_bool(X1,X3))
| ~ hBOOL(hAPP_nat_bool(X1,X2))
| hBOOL(hAPP_nat_bool(X1,zero_zero_nat)) ),
inference(literals_permutation,[status(thm)],[c_0_3397]) ).
cnf(c_0_3398_0,axiom,
( hBOOL(hAPP_nat_bool(X1,zero_zero_nat))
| ~ hBOOL(hAPP_nat_bool(X1,X2))
| ~ hBOOL(hAPP_nat_bool(X1,X3))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X3),sk1_esk14_2(X2,X1))) ),
inference(literals_permutation,[status(thm)],[c_0_3398]) ).
cnf(c_0_3398_1,axiom,
( ~ hBOOL(hAPP_nat_bool(X1,X2))
| hBOOL(hAPP_nat_bool(X1,zero_zero_nat))
| ~ hBOOL(hAPP_nat_bool(X1,X3))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X3),sk1_esk14_2(X2,X1))) ),
inference(literals_permutation,[status(thm)],[c_0_3398]) ).
cnf(c_0_3398_2,axiom,
( ~ hBOOL(hAPP_nat_bool(X1,X3))
| ~ hBOOL(hAPP_nat_bool(X1,X2))
| hBOOL(hAPP_nat_bool(X1,zero_zero_nat))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X3),sk1_esk14_2(X2,X1))) ),
inference(literals_permutation,[status(thm)],[c_0_3398]) ).
cnf(c_0_3398_3,axiom,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X3),sk1_esk14_2(X2,X1)))
| ~ hBOOL(hAPP_nat_bool(X1,X3))
| ~ hBOOL(hAPP_nat_bool(X1,X2))
| hBOOL(hAPP_nat_bool(X1,zero_zero_nat)) ),
inference(literals_permutation,[status(thm)],[c_0_3398]) ).
cnf(c_0_3399_0,axiom,
( hAPP_real_real(plus_plus_real(hAPP_nat_real(power_power_real(X1),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_real(power_power_real(X2),number_number_of_nat(bit0(bit1(pls))))) = zero_zero_real
| X2 != zero_zero_real
| X1 != zero_zero_real ),
inference(literals_permutation,[status(thm)],[c_0_3399]) ).
cnf(c_0_3399_1,axiom,
( X2 != zero_zero_real
| hAPP_real_real(plus_plus_real(hAPP_nat_real(power_power_real(X1),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_real(power_power_real(X2),number_number_of_nat(bit0(bit1(pls))))) = zero_zero_real
| X1 != zero_zero_real ),
inference(literals_permutation,[status(thm)],[c_0_3399]) ).
cnf(c_0_3399_2,axiom,
( X1 != zero_zero_real
| X2 != zero_zero_real
| hAPP_real_real(plus_plus_real(hAPP_nat_real(power_power_real(X1),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_real(power_power_real(X2),number_number_of_nat(bit0(bit1(pls))))) = zero_zero_real ),
inference(literals_permutation,[status(thm)],[c_0_3399]) ).
cnf(c_0_3400_0,axiom,
( hAPP_real_real(plus_plus_real(hAPP_nat_real(power_power_real(X1),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_real(power_power_real(X2),number_number_of_nat(bit0(bit1(pls))))) = zero_zero_real
| X2 != zero_zero_real
| X1 != zero_zero_real ),
inference(literals_permutation,[status(thm)],[c_0_3400]) ).
cnf(c_0_3400_1,axiom,
( X2 != zero_zero_real
| hAPP_real_real(plus_plus_real(hAPP_nat_real(power_power_real(X1),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_real(power_power_real(X2),number_number_of_nat(bit0(bit1(pls))))) = zero_zero_real
| X1 != zero_zero_real ),
inference(literals_permutation,[status(thm)],[c_0_3400]) ).
cnf(c_0_3400_2,axiom,
( X1 != zero_zero_real
| X2 != zero_zero_real
| hAPP_real_real(plus_plus_real(hAPP_nat_real(power_power_real(X1),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_real(power_power_real(X2),number_number_of_nat(bit0(bit1(pls))))) = zero_zero_real ),
inference(literals_permutation,[status(thm)],[c_0_3400]) ).
cnf(c_0_3401_0,axiom,
( hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(X1),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_int(power_power_int(X2),number_number_of_nat(bit0(bit1(pls))))) = zero_zero_int
| X2 != zero_zero_int
| X1 != zero_zero_int ),
inference(literals_permutation,[status(thm)],[c_0_3401]) ).
cnf(c_0_3401_1,axiom,
( X2 != zero_zero_int
| hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(X1),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_int(power_power_int(X2),number_number_of_nat(bit0(bit1(pls))))) = zero_zero_int
| X1 != zero_zero_int ),
inference(literals_permutation,[status(thm)],[c_0_3401]) ).
cnf(c_0_3401_2,axiom,
( X1 != zero_zero_int
| X2 != zero_zero_int
| hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(X1),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_int(power_power_int(X2),number_number_of_nat(bit0(bit1(pls))))) = zero_zero_int ),
inference(literals_permutation,[status(thm)],[c_0_3401]) ).
cnf(c_0_3402_0,axiom,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X3),X2))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3402]) ).
cnf(c_0_3402_1,axiom,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X3),X2))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3402]) ).
cnf(c_0_3402_2,axiom,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X3))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X3),X2))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3402]) ).
cnf(c_0_3403_0,axiom,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X3),X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3403]) ).
cnf(c_0_3403_1,axiom,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X3),X2))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3403]) ).
cnf(c_0_3403_2,axiom,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X3))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X3),X2))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3403]) ).
cnf(c_0_3404_0,axiom,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X1),X2))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X3),X2))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X1),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3404]) ).
cnf(c_0_3404_1,axiom,
( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X3),X2))
| hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X1),X2))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X1),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3404]) ).
cnf(c_0_3404_2,axiom,
( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X1),X3))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X3),X2))
| hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3404]) ).
cnf(c_0_3405_0,axiom,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X3))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X3),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3405]) ).
cnf(c_0_3405_1,axiom,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X3))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X3),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3405]) ).
cnf(c_0_3405_2,axiom,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X3),X2))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X3))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3405]) ).
cnf(c_0_3406_0,axiom,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X3))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X3),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3406]) ).
cnf(c_0_3406_1,axiom,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X3))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X3),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3406]) ).
cnf(c_0_3406_2,axiom,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X3),X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X3))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3406]) ).
cnf(c_0_3407_0,axiom,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X1),X2))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X1),X3))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X3),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3407]) ).
cnf(c_0_3407_1,axiom,
( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X1),X3))
| hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X1),X2))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X3),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3407]) ).
cnf(c_0_3407_2,axiom,
( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X3),X2))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X1),X3))
| hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3407]) ).
cnf(c_0_3408_0,axiom,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X1),X2))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X3),X2))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X1),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3408]) ).
cnf(c_0_3408_1,axiom,
( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X3),X2))
| hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X1),X2))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X1),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3408]) ).
cnf(c_0_3408_2,axiom,
( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X1),X3))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X3),X2))
| hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3408]) ).
cnf(c_0_3409_0,axiom,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X3),X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3409]) ).
cnf(c_0_3409_1,axiom,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X3),X2))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3409]) ).
cnf(c_0_3409_2,axiom,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X3))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X3),X2))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3409]) ).
cnf(c_0_3410_0,axiom,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X3),X2))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3410]) ).
cnf(c_0_3410_1,axiom,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X3),X2))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3410]) ).
cnf(c_0_3410_2,axiom,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X3))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X3),X2))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3410]) ).
cnf(c_0_3411_0,axiom,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,number_number_of_nat(X1)),number_number_of_nat(X2)))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X2))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3411]) ).
cnf(c_0_3411_1,axiom,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X2))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,number_number_of_nat(X1)),number_number_of_nat(X2)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3411]) ).
cnf(c_0_3411_2,axiom,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X2))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X2))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,number_number_of_nat(X1)),number_number_of_nat(X2))) ),
inference(literals_permutation,[status(thm)],[c_0_3411]) ).
cnf(c_0_3412_0,axiom,
( X1 = X2
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X2))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),hAPP_int_int(plus_plus_int(X2),one_one_int))) ),
inference(literals_permutation,[status(thm)],[c_0_3412]) ).
cnf(c_0_3412_1,axiom,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X2))
| X1 = X2
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),hAPP_int_int(plus_plus_int(X2),one_one_int))) ),
inference(literals_permutation,[status(thm)],[c_0_3412]) ).
cnf(c_0_3412_2,axiom,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),hAPP_int_int(plus_plus_int(X2),one_one_int)))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X2))
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_3412]) ).
cnf(c_0_3413_0,axiom,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),hAPP_int_int(plus_plus_int(X2),one_one_int))) ),
inference(literals_permutation,[status(thm)],[c_0_3413]) ).
cnf(c_0_3413_1,axiom,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),hAPP_int_int(plus_plus_int(X2),one_one_int)))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3413]) ).
cnf(c_0_3414_0,axiom,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1))
| X2 = zero_zero_nat
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(power_power_nat(X1),X2))) ),
inference(literals_permutation,[status(thm)],[c_0_3414]) ).
cnf(c_0_3414_1,axiom,
( X2 = zero_zero_nat
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(power_power_nat(X1),X2))) ),
inference(literals_permutation,[status(thm)],[c_0_3414]) ).
cnf(c_0_3414_2,axiom,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(power_power_nat(X1),X2)))
| X2 = zero_zero_nat
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_3414]) ).
cnf(c_0_3415_0,axiom,
( X1 = zero_zero_nat
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(power_power_nat(X2),X1))) ),
inference(literals_permutation,[status(thm)],[c_0_3415]) ).
cnf(c_0_3415_1,axiom,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X2))
| X1 = zero_zero_nat
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(power_power_nat(X2),X1))) ),
inference(literals_permutation,[status(thm)],[c_0_3415]) ).
cnf(c_0_3415_2,axiom,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(power_power_nat(X2),X1)))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X2))
| X1 = zero_zero_nat ),
inference(literals_permutation,[status(thm)],[c_0_3415]) ).
cnf(c_0_3416_0,axiom,
( hAPP_int_int(plus_plus_int(number_number_of_int(X1)),number_number_of_int(X2)) = number_number_of_int(hAPP_int_int(plus_plus_int(X1),X2))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X2))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_3416]) ).
cnf(c_0_3416_1,axiom,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X2))
| hAPP_int_int(plus_plus_int(number_number_of_int(X1)),number_number_of_int(X2)) = number_number_of_int(hAPP_int_int(plus_plus_int(X1),X2))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_3416]) ).
cnf(c_0_3416_2,axiom,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X1))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X2))
| hAPP_int_int(plus_plus_int(number_number_of_int(X1)),number_number_of_int(X2)) = number_number_of_int(hAPP_int_int(plus_plus_int(X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3416]) ).
cnf(c_0_3417_0,axiom,
( hAPP_nat_nat(plus_plus_nat(number_number_of_nat(X1)),number_number_of_nat(X2)) = number_number_of_nat(hAPP_int_int(plus_plus_int(X1),X2))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X2))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_3417]) ).
cnf(c_0_3417_1,axiom,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X2))
| hAPP_nat_nat(plus_plus_nat(number_number_of_nat(X1)),number_number_of_nat(X2)) = number_number_of_nat(hAPP_int_int(plus_plus_int(X1),X2))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_3417]) ).
cnf(c_0_3417_2,axiom,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X1))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X2))
| hAPP_nat_nat(plus_plus_nat(number_number_of_nat(X1)),number_number_of_nat(X2)) = number_number_of_nat(hAPP_int_int(plus_plus_int(X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3417]) ).
cnf(c_0_3418_0,axiom,
( hAPP_real_real(plus_plus_real(number267125858f_real(X1)),number267125858f_real(X2)) = number267125858f_real(hAPP_int_int(plus_plus_int(X1),X2))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X2))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_3418]) ).
cnf(c_0_3418_1,axiom,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X2))
| hAPP_real_real(plus_plus_real(number267125858f_real(X1)),number267125858f_real(X2)) = number267125858f_real(hAPP_int_int(plus_plus_int(X1),X2))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_3418]) ).
cnf(c_0_3418_2,axiom,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X1))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X2))
| hAPP_real_real(plus_plus_real(number267125858f_real(X1)),number267125858f_real(X2)) = number267125858f_real(hAPP_int_int(plus_plus_int(X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3418]) ).
cnf(c_0_3419_0,axiom,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_int_int(plus_plus_int(X1),X1))) ),
inference(literals_permutation,[status(thm)],[c_0_3419]) ).
cnf(c_0_3419_1,axiom,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_int_int(plus_plus_int(X1),X1)))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_3419]) ).
cnf(c_0_3420_0,axiom,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X1))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),hAPP_real_real(plus_plus_real(X1),X1))) ),
inference(literals_permutation,[status(thm)],[c_0_3420]) ).
cnf(c_0_3420_1,axiom,
( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),hAPP_real_real(plus_plus_real(X1),X1)))
| hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_3420]) ).
cnf(c_0_3421_0,axiom,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X1))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_int_int(plus_plus_int(X1),X1))) ),
inference(literals_permutation,[status(thm)],[c_0_3421]) ).
cnf(c_0_3421_1,axiom,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_int_int(plus_plus_int(X1),X1)))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_3421]) ).
cnf(c_0_3422_0,axiom,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X1))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),hAPP_real_real(plus_plus_real(X1),X1))) ),
inference(literals_permutation,[status(thm)],[c_0_3422]) ).
cnf(c_0_3422_1,axiom,
( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),hAPP_real_real(plus_plus_real(X1),X1)))
| hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_3422]) ).
cnf(c_0_3423_0,axiom,
( hBOOL(hAPP_int_bool(X1,X2))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X2))
| ~ hBOOL(hAPP_int_bool(X1,hAPP_nat_int(semiri1621563631at_int,sk1_esk9_1(X1)))) ),
inference(literals_permutation,[status(thm)],[c_0_3423]) ).
cnf(c_0_3423_1,axiom,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X2))
| hBOOL(hAPP_int_bool(X1,X2))
| ~ hBOOL(hAPP_int_bool(X1,hAPP_nat_int(semiri1621563631at_int,sk1_esk9_1(X1)))) ),
inference(literals_permutation,[status(thm)],[c_0_3423]) ).
cnf(c_0_3423_2,axiom,
( ~ hBOOL(hAPP_int_bool(X1,hAPP_nat_int(semiri1621563631at_int,sk1_esk9_1(X1))))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X2))
| hBOOL(hAPP_int_bool(X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3423]) ).
cnf(c_0_3424_0,axiom,
( hAPP_nat_real(power_power_real(sk1_esk5_2(X2,X1)),X1) = X2
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3424]) ).
cnf(c_0_3424_1,axiom,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1))
| hAPP_nat_real(power_power_real(sk1_esk5_2(X2,X1)),X1) = X2
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3424]) ).
cnf(c_0_3424_2,axiom,
( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1))
| hAPP_nat_real(power_power_real(sk1_esk5_2(X2,X1)),X1) = X2 ),
inference(literals_permutation,[status(thm)],[c_0_3424]) ).
cnf(c_0_3425_0,axiom,
( hAPP_nat_real(power_power_real(sk1_esk4_2(X2,X1)),X1) = X2
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3425]) ).
cnf(c_0_3425_1,axiom,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1))
| hAPP_nat_real(power_power_real(sk1_esk4_2(X2,X1)),X1) = X2
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3425]) ).
cnf(c_0_3425_2,axiom,
( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1))
| hAPP_nat_real(power_power_real(sk1_esk4_2(X2,X1)),X1) = X2 ),
inference(literals_permutation,[status(thm)],[c_0_3425]) ).
cnf(c_0_3426_0,axiom,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
| X1 = X2
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(X3,X2),X1))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(X3,X2),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_3426]) ).
cnf(c_0_3426_1,axiom,
( X1 = X2
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(X3,X2),X1))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(X3,X2),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_3426]) ).
cnf(c_0_3426_2,axiom,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(X3,X2),X1))
| X1 = X2
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(X3,X2),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_3426]) ).
cnf(c_0_3426_3,axiom,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(X3,X2),X1))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(X3,X2),X1))
| X1 = X2
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3426]) ).
cnf(c_0_3427_0,axiom,
( X3 = X2
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(X1,X2),X3))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X2),X3))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(X1,X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3427]) ).
cnf(c_0_3427_1,axiom,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(X1,X2),X3))
| X3 = X2
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X2),X3))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(X1,X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3427]) ).
cnf(c_0_3427_2,axiom,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X2),X3))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(X1,X2),X3))
| X3 = X2
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(X1,X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3427]) ).
cnf(c_0_3427_3,axiom,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(X1,X2),X3))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X2),X3))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(X1,X2),X3))
| X3 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_3427]) ).
cnf(c_0_3428_0,axiom,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(power_power_nat(X1),number_number_of_nat(X2))))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_3428]) ).
cnf(c_0_3428_1,axiom,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(power_power_nat(X1),number_number_of_nat(X2)))) ),
inference(literals_permutation,[status(thm)],[c_0_3428]) ).
cnf(c_0_3432_0,axiom,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),hAPP_nat_nat(plus_plus_nat(X2),X3)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3432]) ).
cnf(c_0_3432_1,axiom,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X3))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),hAPP_nat_nat(plus_plus_nat(X2),X3))) ),
inference(literals_permutation,[status(thm)],[c_0_3432]) ).
cnf(c_0_3433_0,axiom,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),hAPP_nat_nat(plus_plus_nat(X2),X3)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3433]) ).
cnf(c_0_3433_1,axiom,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),hAPP_nat_nat(plus_plus_nat(X2),X3))) ),
inference(literals_permutation,[status(thm)],[c_0_3433]) ).
cnf(c_0_3434_0,axiom,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),hAPP_nat_nat(plus_plus_nat(X2),X3)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3434]) ).
cnf(c_0_3434_1,axiom,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X3))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),hAPP_nat_nat(plus_plus_nat(X2),X3))) ),
inference(literals_permutation,[status(thm)],[c_0_3434]) ).
cnf(c_0_3435_0,axiom,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),hAPP_nat_nat(plus_plus_nat(X2),X3)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3435]) ).
cnf(c_0_3435_1,axiom,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),hAPP_nat_nat(plus_plus_nat(X2),X3))) ),
inference(literals_permutation,[status(thm)],[c_0_3435]) ).
cnf(c_0_3436_0,axiom,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),hAPP_nat_real(power_power_real(X1),number_number_of_nat(bit0(bit1(pls))))))
| X1 = zero_zero_real ),
inference(literals_permutation,[status(thm)],[c_0_3436]) ).
cnf(c_0_3436_1,axiom,
( X1 = zero_zero_real
| hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),hAPP_nat_real(power_power_real(X1),number_number_of_nat(bit0(bit1(pls)))))) ),
inference(literals_permutation,[status(thm)],[c_0_3436]) ).
cnf(c_0_3437_0,axiom,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_nat_int(power_power_int(X1),number_number_of_nat(bit0(bit1(pls))))))
| X1 = zero_zero_int ),
inference(literals_permutation,[status(thm)],[c_0_3437]) ).
cnf(c_0_3437_1,axiom,
( X1 = zero_zero_int
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_nat_int(power_power_int(X1),number_number_of_nat(bit0(bit1(pls)))))) ),
inference(literals_permutation,[status(thm)],[c_0_3437]) ).
cnf(c_0_3443_0,axiom,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),hAPP_int_int(plus_plus_int(X2),one_one_int)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3443]) ).
cnf(c_0_3443_1,axiom,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),hAPP_int_int(plus_plus_int(X2),one_one_int))) ),
inference(literals_permutation,[status(thm)],[c_0_3443]) ).
cnf(c_0_3444_0,axiom,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),hAPP_int_int(plus_plus_int(X2),one_one_int)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3444]) ).
cnf(c_0_3444_1,axiom,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X2))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),hAPP_int_int(plus_plus_int(X2),one_one_int))) ),
inference(literals_permutation,[status(thm)],[c_0_3444]) ).
cnf(c_0_3445_0,axiom,
( X1 = zero_zero_nat
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_nat_int(semiri1621563631at_int,X1)),zero_zero_int)) ),
inference(literals_permutation,[status(thm)],[c_0_3445]) ).
cnf(c_0_3445_1,axiom,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_nat_int(semiri1621563631at_int,X1)),zero_zero_int))
| X1 = zero_zero_nat ),
inference(literals_permutation,[status(thm)],[c_0_3445]) ).
cnf(c_0_3446_0,axiom,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
| hAPP_nat_nat(plus_plus_nat(X1),X3) != hAPP_nat_nat(plus_plus_nat(X4),X2)
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X4),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3446]) ).
cnf(c_0_3446_1,axiom,
( hAPP_nat_nat(plus_plus_nat(X1),X3) != hAPP_nat_nat(plus_plus_nat(X4),X2)
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X4),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3446]) ).
cnf(c_0_3446_2,axiom,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X4),X3))
| hAPP_nat_nat(plus_plus_nat(X1),X3) != hAPP_nat_nat(plus_plus_nat(X4),X2)
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3446]) ).
cnf(c_0_3447_0,axiom,
( hBOOL(hAPP_int_bool(X1,hAPP_nat_int(semiri1621563631at_int,sk1_esk6_1(X1))))
| ~ hBOOL(hAPP_int_bool(X1,X2))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3447]) ).
cnf(c_0_3447_1,axiom,
( ~ hBOOL(hAPP_int_bool(X1,X2))
| hBOOL(hAPP_int_bool(X1,hAPP_nat_int(semiri1621563631at_int,sk1_esk6_1(X1))))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3447]) ).
cnf(c_0_3447_2,axiom,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X2))
| ~ hBOOL(hAPP_int_bool(X1,X2))
| hBOOL(hAPP_int_bool(X1,hAPP_nat_int(semiri1621563631at_int,sk1_esk6_1(X1)))) ),
inference(literals_permutation,[status(thm)],[c_0_3447]) ).
cnf(c_0_3452_0,axiom,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1))
| ~ hBOOL(X2)
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_3452]) ).
cnf(c_0_3452_1,axiom,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1))
| ~ hBOOL(X2)
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_3452]) ).
cnf(c_0_3452_2,axiom,
( ~ hBOOL(X2)
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_3452]) ).
cnf(c_0_3452_3,axiom,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1))
| ~ hBOOL(X2)
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_3452]) ).
cnf(c_0_3453_0,axiom,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1))
| ~ hBOOL(X2)
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_3453]) ).
cnf(c_0_3453_1,axiom,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1))
| ~ hBOOL(X2)
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_3453]) ).
cnf(c_0_3453_2,axiom,
( ~ hBOOL(X2)
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_3453]) ).
cnf(c_0_3453_3,axiom,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1))
| ~ hBOOL(X2)
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_3453]) ).
cnf(c_0_3454_0,axiom,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_nat_int(power_power_int(X1),X2)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_3454]) ).
cnf(c_0_3454_1,axiom,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_nat_int(power_power_int(X1),X2))) ),
inference(literals_permutation,[status(thm)],[c_0_3454]) ).
cnf(c_0_3455_0,axiom,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),hAPP_nat_int(power_power_int(X1),X2)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_3455]) ).
cnf(c_0_3455_1,axiom,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),X1))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),hAPP_nat_int(power_power_int(X1),X2))) ),
inference(literals_permutation,[status(thm)],[c_0_3455]) ).
cnf(c_0_3456_0,axiom,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,one_one_nat),hAPP_nat_nat(power_power_nat(X1),X2)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,one_one_nat),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_3456]) ).
cnf(c_0_3456_1,axiom,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,one_one_nat),X1))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,one_one_nat),hAPP_nat_nat(power_power_nat(X1),X2))) ),
inference(literals_permutation,[status(thm)],[c_0_3456]) ).
cnf(c_0_3457_0,axiom,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,one_one_real),hAPP_nat_real(power_power_real(X1),X2)))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,one_one_real),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_3457]) ).
cnf(c_0_3457_1,axiom,
( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,one_one_real),X1))
| hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,one_one_real),hAPP_nat_real(power_power_real(X1),X2))) ),
inference(literals_permutation,[status(thm)],[c_0_3457]) ).
cnf(c_0_3458_0,axiom,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_nat_int(power_power_int(X1),X2)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_3458]) ).
cnf(c_0_3458_1,axiom,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_nat_int(power_power_int(X1),X2))) ),
inference(literals_permutation,[status(thm)],[c_0_3458]) ).
cnf(c_0_3459_0,axiom,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),hAPP_nat_nat(power_power_nat(X1),X2)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_3459]) ).
cnf(c_0_3459_1,axiom,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),X1))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),hAPP_nat_nat(power_power_nat(X1),X2))) ),
inference(literals_permutation,[status(thm)],[c_0_3459]) ).
cnf(c_0_3460_0,axiom,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),hAPP_nat_real(power_power_real(X1),X2)))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_3460]) ).
cnf(c_0_3460_1,axiom,
( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X1))
| hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),hAPP_nat_real(power_power_real(X1),X2))) ),
inference(literals_permutation,[status(thm)],[c_0_3460]) ).
cnf(c_0_3461_0,axiom,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_int_int(plus_plus_int(X1),X1)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_3461]) ).
cnf(c_0_3461_1,axiom,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_int_int(plus_plus_int(X1),X1))) ),
inference(literals_permutation,[status(thm)],[c_0_3461]) ).
cnf(c_0_3462_0,axiom,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),hAPP_real_real(plus_plus_real(X1),X1)))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_3462]) ).
cnf(c_0_3462_1,axiom,
( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X1))
| hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),hAPP_real_real(plus_plus_real(X1),X1))) ),
inference(literals_permutation,[status(thm)],[c_0_3462]) ).
cnf(c_0_3463_0,axiom,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_int_int(plus_plus_int(X1),X1)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_3463]) ).
cnf(c_0_3463_1,axiom,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X1))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_int_int(plus_plus_int(X1),X1))) ),
inference(literals_permutation,[status(thm)],[c_0_3463]) ).
cnf(c_0_3464_0,axiom,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),hAPP_real_real(plus_plus_real(X1),X1)))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_3464]) ).
cnf(c_0_3464_1,axiom,
( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X1))
| hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),hAPP_real_real(plus_plus_real(X1),X1))) ),
inference(literals_permutation,[status(thm)],[c_0_3464]) ).
cnf(c_0_3465_0,axiom,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_nat_int(power_power_int(X1),X2)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_3465]) ).
cnf(c_0_3465_1,axiom,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X1))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_nat_int(power_power_int(X1),X2))) ),
inference(literals_permutation,[status(thm)],[c_0_3465]) ).
cnf(c_0_3466_0,axiom,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(power_power_nat(X1),X2)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_3466]) ).
cnf(c_0_3466_1,axiom,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(power_power_nat(X1),X2))) ),
inference(literals_permutation,[status(thm)],[c_0_3466]) ).
cnf(c_0_3467_0,axiom,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),hAPP_nat_real(power_power_real(X1),X2)))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_3467]) ).
cnf(c_0_3467_1,axiom,
( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X1))
| hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),hAPP_nat_real(power_power_real(X1),X2))) ),
inference(literals_permutation,[status(thm)],[c_0_3467]) ).
cnf(c_0_3468_0,axiom,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(power_power_nat(X1),X2)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_3468]) ).
cnf(c_0_3468_1,axiom,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(power_power_nat(X1),X2))) ),
inference(literals_permutation,[status(thm)],[c_0_3468]) ).
cnf(c_0_3469_0,axiom,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(plus_plus_nat(X1),X2)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_3469]) ).
cnf(c_0_3469_1,axiom,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(plus_plus_nat(X1),X2))) ),
inference(literals_permutation,[status(thm)],[c_0_3469]) ).
cnf(c_0_3470_0,axiom,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(plus_plus_nat(X1),X2)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3470]) ).
cnf(c_0_3470_1,axiom,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X2))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(plus_plus_nat(X1),X2))) ),
inference(literals_permutation,[status(thm)],[c_0_3470]) ).
cnf(c_0_3471_0,axiom,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(power_power_nat(X1),X2)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_3471]) ).
cnf(c_0_3471_1,axiom,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(power_power_nat(X1),X2))) ),
inference(literals_permutation,[status(thm)],[c_0_3471]) ).
cnf(c_0_3472_0,axiom,
( hBOOL(hAPP_nat_bool(X1,zero_zero_nat))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,sk1_esk19_2(X2,X1)),X2))
| ~ hBOOL(hAPP_nat_bool(X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3472]) ).
cnf(c_0_3472_1,axiom,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,sk1_esk19_2(X2,X1)),X2))
| hBOOL(hAPP_nat_bool(X1,zero_zero_nat))
| ~ hBOOL(hAPP_nat_bool(X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3472]) ).
cnf(c_0_3472_2,axiom,
( ~ hBOOL(hAPP_nat_bool(X1,X2))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,sk1_esk19_2(X2,X1)),X2))
| hBOOL(hAPP_nat_bool(X1,zero_zero_nat)) ),
inference(literals_permutation,[status(thm)],[c_0_3472]) ).
cnf(c_0_3473_0,axiom,
( hBOOL(hAPP_nat_bool(X1,zero_zero_nat))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,sk1_esk14_2(X2,X1)),X2))
| ~ hBOOL(hAPP_nat_bool(X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3473]) ).
cnf(c_0_3473_1,axiom,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,sk1_esk14_2(X2,X1)),X2))
| hBOOL(hAPP_nat_bool(X1,zero_zero_nat))
| ~ hBOOL(hAPP_nat_bool(X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3473]) ).
cnf(c_0_3473_2,axiom,
( ~ hBOOL(hAPP_nat_bool(X1,X2))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,sk1_esk14_2(X2,X1)),X2))
| hBOOL(hAPP_nat_bool(X1,zero_zero_nat)) ),
inference(literals_permutation,[status(thm)],[c_0_3473]) ).
cnf(c_0_3474_0,axiom,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1))
| hBOOL(X2)
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_3474]) ).
cnf(c_0_3474_1,axiom,
( hBOOL(X2)
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_3474]) ).
cnf(c_0_3474_2,axiom,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1))
| hBOOL(X2)
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_3474]) ).
cnf(c_0_3474_3,axiom,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1))
| hBOOL(X2)
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_3474]) ).
cnf(c_0_3475_0,axiom,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1))
| hBOOL(X2)
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_3475]) ).
cnf(c_0_3475_1,axiom,
( hBOOL(X2)
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_3475]) ).
cnf(c_0_3475_2,axiom,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1))
| hBOOL(X2)
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_3475]) ).
cnf(c_0_3475_3,axiom,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1))
| hBOOL(X2)
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_3475]) ).
cnf(c_0_3476_0,axiom,
( X1 = zero_zero_int
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X2))
| hAPP_int_int(plus_plus_int(X1),X2) != zero_zero_int ),
inference(literals_permutation,[status(thm)],[c_0_3476]) ).
cnf(c_0_3476_1,axiom,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1))
| X1 = zero_zero_int
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X2))
| hAPP_int_int(plus_plus_int(X1),X2) != zero_zero_int ),
inference(literals_permutation,[status(thm)],[c_0_3476]) ).
cnf(c_0_3476_2,axiom,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X2))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1))
| X1 = zero_zero_int
| hAPP_int_int(plus_plus_int(X1),X2) != zero_zero_int ),
inference(literals_permutation,[status(thm)],[c_0_3476]) ).
cnf(c_0_3476_3,axiom,
( hAPP_int_int(plus_plus_int(X1),X2) != zero_zero_int
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X2))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1))
| X1 = zero_zero_int ),
inference(literals_permutation,[status(thm)],[c_0_3476]) ).
cnf(c_0_3477_0,axiom,
( X2 = zero_zero_int
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X2))
| hAPP_int_int(plus_plus_int(X1),X2) != zero_zero_int ),
inference(literals_permutation,[status(thm)],[c_0_3477]) ).
cnf(c_0_3477_1,axiom,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1))
| X2 = zero_zero_int
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X2))
| hAPP_int_int(plus_plus_int(X1),X2) != zero_zero_int ),
inference(literals_permutation,[status(thm)],[c_0_3477]) ).
cnf(c_0_3477_2,axiom,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X2))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1))
| X2 = zero_zero_int
| hAPP_int_int(plus_plus_int(X1),X2) != zero_zero_int ),
inference(literals_permutation,[status(thm)],[c_0_3477]) ).
cnf(c_0_3477_3,axiom,
( hAPP_int_int(plus_plus_int(X1),X2) != zero_zero_int
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X2))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1))
| X2 = zero_zero_int ),
inference(literals_permutation,[status(thm)],[c_0_3477]) ).
cnf(c_0_3478_0,axiom,
( X1 = zero_zero_nat
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),X1))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),X2))
| hAPP_nat_nat(plus_plus_nat(X1),X2) != zero_zero_nat ),
inference(literals_permutation,[status(thm)],[c_0_3478]) ).
cnf(c_0_3478_1,axiom,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),X1))
| X1 = zero_zero_nat
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),X2))
| hAPP_nat_nat(plus_plus_nat(X1),X2) != zero_zero_nat ),
inference(literals_permutation,[status(thm)],[c_0_3478]) ).
cnf(c_0_3478_2,axiom,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),X1))
| X1 = zero_zero_nat
| hAPP_nat_nat(plus_plus_nat(X1),X2) != zero_zero_nat ),
inference(literals_permutation,[status(thm)],[c_0_3478]) ).
cnf(c_0_3478_3,axiom,
( hAPP_nat_nat(plus_plus_nat(X1),X2) != zero_zero_nat
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),X1))
| X1 = zero_zero_nat ),
inference(literals_permutation,[status(thm)],[c_0_3478]) ).
cnf(c_0_3479_0,axiom,
( X2 = zero_zero_nat
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),X1))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),X2))
| hAPP_nat_nat(plus_plus_nat(X1),X2) != zero_zero_nat ),
inference(literals_permutation,[status(thm)],[c_0_3479]) ).
cnf(c_0_3479_1,axiom,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),X1))
| X2 = zero_zero_nat
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),X2))
| hAPP_nat_nat(plus_plus_nat(X1),X2) != zero_zero_nat ),
inference(literals_permutation,[status(thm)],[c_0_3479]) ).
cnf(c_0_3479_2,axiom,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),X1))
| X2 = zero_zero_nat
| hAPP_nat_nat(plus_plus_nat(X1),X2) != zero_zero_nat ),
inference(literals_permutation,[status(thm)],[c_0_3479]) ).
cnf(c_0_3479_3,axiom,
( hAPP_nat_nat(plus_plus_nat(X1),X2) != zero_zero_nat
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),X1))
| X2 = zero_zero_nat ),
inference(literals_permutation,[status(thm)],[c_0_3479]) ).
cnf(c_0_3480_0,axiom,
( X1 = zero_zero_real
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X1))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X2))
| hAPP_real_real(plus_plus_real(X1),X2) != zero_zero_real ),
inference(literals_permutation,[status(thm)],[c_0_3480]) ).
cnf(c_0_3480_1,axiom,
( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X1))
| X1 = zero_zero_real
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X2))
| hAPP_real_real(plus_plus_real(X1),X2) != zero_zero_real ),
inference(literals_permutation,[status(thm)],[c_0_3480]) ).
cnf(c_0_3480_2,axiom,
( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X2))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X1))
| X1 = zero_zero_real
| hAPP_real_real(plus_plus_real(X1),X2) != zero_zero_real ),
inference(literals_permutation,[status(thm)],[c_0_3480]) ).
cnf(c_0_3480_3,axiom,
( hAPP_real_real(plus_plus_real(X1),X2) != zero_zero_real
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X2))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X1))
| X1 = zero_zero_real ),
inference(literals_permutation,[status(thm)],[c_0_3480]) ).
cnf(c_0_3481_0,axiom,
( X2 = zero_zero_real
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X1))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X2))
| hAPP_real_real(plus_plus_real(X1),X2) != zero_zero_real ),
inference(literals_permutation,[status(thm)],[c_0_3481]) ).
cnf(c_0_3481_1,axiom,
( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X1))
| X2 = zero_zero_real
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X2))
| hAPP_real_real(plus_plus_real(X1),X2) != zero_zero_real ),
inference(literals_permutation,[status(thm)],[c_0_3481]) ).
cnf(c_0_3481_2,axiom,
( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X2))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X1))
| X2 = zero_zero_real
| hAPP_real_real(plus_plus_real(X1),X2) != zero_zero_real ),
inference(literals_permutation,[status(thm)],[c_0_3481]) ).
cnf(c_0_3481_3,axiom,
( hAPP_real_real(plus_plus_real(X1),X2) != zero_zero_real
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X2))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X1))
| X2 = zero_zero_real ),
inference(literals_permutation,[status(thm)],[c_0_3481]) ).
cnf(c_0_3482_0,axiom,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X2))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,bit1(X1)),bit0(X2))) ),
inference(literals_permutation,[status(thm)],[c_0_3482]) ).
cnf(c_0_3482_1,axiom,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,bit1(X1)),bit0(X2)))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3482]) ).
cnf(c_0_3483_0,axiom,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X2))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,bit1(X1)),bit0(X2))) ),
inference(literals_permutation,[status(thm)],[c_0_3483]) ).
cnf(c_0_3483_1,axiom,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,bit1(X1)),bit0(X2)))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3483]) ).
cnf(c_0_3484_0,axiom,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit0(X1)),bit1(X2))) ),
inference(literals_permutation,[status(thm)],[c_0_3484]) ).
cnf(c_0_3484_1,axiom,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit0(X1)),bit1(X2)))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3484]) ).
cnf(c_0_3485_0,axiom,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit0(X1)),bit1(X2))) ),
inference(literals_permutation,[status(thm)],[c_0_3485]) ).
cnf(c_0_3485_1,axiom,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit0(X1)),bit1(X2)))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3485]) ).
cnf(c_0_3486_0,axiom,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,bit0(X1)),bit1(X2))) ),
inference(literals_permutation,[status(thm)],[c_0_3486]) ).
cnf(c_0_3486_1,axiom,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,bit0(X1)),bit1(X2)))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3486]) ).
cnf(c_0_3487_0,axiom,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,bit0(X1)),bit1(X2))) ),
inference(literals_permutation,[status(thm)],[c_0_3487]) ).
cnf(c_0_3487_1,axiom,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,bit0(X1)),bit1(X2)))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3487]) ).
cnf(c_0_3488_0,axiom,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,number_number_of_int(X1)),number_number_of_int(X2))) ),
inference(literals_permutation,[status(thm)],[c_0_3488]) ).
cnf(c_0_3488_1,axiom,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,number_number_of_int(X1)),number_number_of_int(X2)))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3488]) ).
cnf(c_0_3489_0,axiom,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,number_number_of_int(X1)),number_number_of_int(X2))) ),
inference(literals_permutation,[status(thm)],[c_0_3489]) ).
cnf(c_0_3489_1,axiom,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,number_number_of_int(X1)),number_number_of_int(X2)))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3489]) ).
cnf(c_0_3490_0,axiom,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,number267125858f_real(X1)),number267125858f_real(X2))) ),
inference(literals_permutation,[status(thm)],[c_0_3490]) ).
cnf(c_0_3490_1,axiom,
( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,number267125858f_real(X1)),number267125858f_real(X2)))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3490]) ).
cnf(c_0_3491_0,axiom,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,bit0(X1)),bit0(X2))) ),
inference(literals_permutation,[status(thm)],[c_0_3491]) ).
cnf(c_0_3491_1,axiom,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,bit0(X1)),bit0(X2)))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3491]) ).
cnf(c_0_3492_0,axiom,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,bit0(X1)),bit0(X2))) ),
inference(literals_permutation,[status(thm)],[c_0_3492]) ).
cnf(c_0_3492_1,axiom,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,bit0(X1)),bit0(X2)))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3492]) ).
cnf(c_0_3493_0,axiom,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,bit1(X1)),bit1(X2))) ),
inference(literals_permutation,[status(thm)],[c_0_3493]) ).
cnf(c_0_3493_1,axiom,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,bit1(X1)),bit1(X2)))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3493]) ).
cnf(c_0_3494_0,axiom,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,bit1(X1)),bit1(X2))) ),
inference(literals_permutation,[status(thm)],[c_0_3494]) ).
cnf(c_0_3494_1,axiom,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,bit1(X1)),bit1(X2)))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3494]) ).
cnf(c_0_3495_0,axiom,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,number_number_of_nat(X1)),number_number_of_nat(X2))) ),
inference(literals_permutation,[status(thm)],[c_0_3495]) ).
cnf(c_0_3495_1,axiom,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,number_number_of_nat(X1)),number_number_of_nat(X2)))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3495]) ).
cnf(c_0_3496_0,axiom,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X2))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit1(X1)),bit0(X2))) ),
inference(literals_permutation,[status(thm)],[c_0_3496]) ).
cnf(c_0_3496_1,axiom,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit1(X1)),bit0(X2)))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3496]) ).
cnf(c_0_3497_0,axiom,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X2))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit1(X1)),bit0(X2))) ),
inference(literals_permutation,[status(thm)],[c_0_3497]) ).
cnf(c_0_3497_1,axiom,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit1(X1)),bit0(X2)))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3497]) ).
cnf(c_0_3498_0,axiom,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X2))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit0(X1)),bit0(X2))) ),
inference(literals_permutation,[status(thm)],[c_0_3498]) ).
cnf(c_0_3498_1,axiom,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit0(X1)),bit0(X2)))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3498]) ).
cnf(c_0_3499_0,axiom,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X2))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit0(X1)),bit0(X2))) ),
inference(literals_permutation,[status(thm)],[c_0_3499]) ).
cnf(c_0_3499_1,axiom,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit0(X1)),bit0(X2)))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3499]) ).
cnf(c_0_3500_0,axiom,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X2))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit1(X1)),bit1(X2))) ),
inference(literals_permutation,[status(thm)],[c_0_3500]) ).
cnf(c_0_3500_1,axiom,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit1(X1)),bit1(X2)))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3500]) ).
cnf(c_0_3501_0,axiom,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X2))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit1(X1)),bit1(X2))) ),
inference(literals_permutation,[status(thm)],[c_0_3501]) ).
cnf(c_0_3501_1,axiom,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit1(X1)),bit1(X2)))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3501]) ).
cnf(c_0_3502_0,axiom,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X2))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,number267125858f_real(X1)),number267125858f_real(X2))) ),
inference(literals_permutation,[status(thm)],[c_0_3502]) ).
cnf(c_0_3502_1,axiom,
( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,number267125858f_real(X1)),number267125858f_real(X2)))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3502]) ).
cnf(c_0_3503_0,axiom,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X2))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(X1)),number_number_of_int(X2))) ),
inference(literals_permutation,[status(thm)],[c_0_3503]) ).
cnf(c_0_3503_1,axiom,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(X1)),number_number_of_int(X2)))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3503]) ).
cnf(c_0_3504_0,axiom,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X2))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(X1)),number_number_of_int(X2))) ),
inference(literals_permutation,[status(thm)],[c_0_3504]) ).
cnf(c_0_3504_1,axiom,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(X1)),number_number_of_int(X2)))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3504]) ).
cnf(c_0_3505_0,axiom,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_nat_int(semiri1621563631at_int,X1))) ),
inference(literals_permutation,[status(thm)],[c_0_3505]) ).
cnf(c_0_3505_1,axiom,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_nat_int(semiri1621563631at_int,X1)))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_3505]) ).
cnf(c_0_3506_0,axiom,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),hAPP_nat_real(semiri132038758t_real,X1))) ),
inference(literals_permutation,[status(thm)],[c_0_3506]) ).
cnf(c_0_3506_1,axiom,
( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),hAPP_nat_real(semiri132038758t_real,X1)))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_3506]) ).
cnf(c_0_3507_0,axiom,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(semiri984289939at_nat,X1))) ),
inference(literals_permutation,[status(thm)],[c_0_3507]) ).
cnf(c_0_3507_1,axiom,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(semiri984289939at_nat,X1)))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_3507]) ).
cnf(c_0_3508_0,axiom,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_nat_int(semiri1621563631at_int,X1))) ),
inference(literals_permutation,[status(thm)],[c_0_3508]) ).
cnf(c_0_3508_1,axiom,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_nat_int(semiri1621563631at_int,X1)))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_3508]) ).
cnf(c_0_3509_0,axiom,
( hAPP_int_int(plus_plus_int(X1),X2) = zero_zero_int
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X2))
| X2 != zero_zero_int
| X1 != zero_zero_int ),
inference(literals_permutation,[status(thm)],[c_0_3509]) ).
cnf(c_0_3509_1,axiom,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1))
| hAPP_int_int(plus_plus_int(X1),X2) = zero_zero_int
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X2))
| X2 != zero_zero_int
| X1 != zero_zero_int ),
inference(literals_permutation,[status(thm)],[c_0_3509]) ).
cnf(c_0_3509_2,axiom,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X2))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1))
| hAPP_int_int(plus_plus_int(X1),X2) = zero_zero_int
| X2 != zero_zero_int
| X1 != zero_zero_int ),
inference(literals_permutation,[status(thm)],[c_0_3509]) ).
cnf(c_0_3509_3,axiom,
( X2 != zero_zero_int
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X2))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1))
| hAPP_int_int(plus_plus_int(X1),X2) = zero_zero_int
| X1 != zero_zero_int ),
inference(literals_permutation,[status(thm)],[c_0_3509]) ).
cnf(c_0_3509_4,axiom,
( X1 != zero_zero_int
| X2 != zero_zero_int
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X2))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1))
| hAPP_int_int(plus_plus_int(X1),X2) = zero_zero_int ),
inference(literals_permutation,[status(thm)],[c_0_3509]) ).
cnf(c_0_3510_0,axiom,
( hAPP_nat_nat(plus_plus_nat(X1),X2) = zero_zero_nat
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),X1))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),X2))
| X2 != zero_zero_nat
| X1 != zero_zero_nat ),
inference(literals_permutation,[status(thm)],[c_0_3510]) ).
cnf(c_0_3510_1,axiom,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),X1))
| hAPP_nat_nat(plus_plus_nat(X1),X2) = zero_zero_nat
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),X2))
| X2 != zero_zero_nat
| X1 != zero_zero_nat ),
inference(literals_permutation,[status(thm)],[c_0_3510]) ).
cnf(c_0_3510_2,axiom,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),X1))
| hAPP_nat_nat(plus_plus_nat(X1),X2) = zero_zero_nat
| X2 != zero_zero_nat
| X1 != zero_zero_nat ),
inference(literals_permutation,[status(thm)],[c_0_3510]) ).
cnf(c_0_3510_3,axiom,
( X2 != zero_zero_nat
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),X1))
| hAPP_nat_nat(plus_plus_nat(X1),X2) = zero_zero_nat
| X1 != zero_zero_nat ),
inference(literals_permutation,[status(thm)],[c_0_3510]) ).
cnf(c_0_3510_4,axiom,
( X1 != zero_zero_nat
| X2 != zero_zero_nat
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),X1))
| hAPP_nat_nat(plus_plus_nat(X1),X2) = zero_zero_nat ),
inference(literals_permutation,[status(thm)],[c_0_3510]) ).
cnf(c_0_3511_0,axiom,
( hAPP_real_real(plus_plus_real(X1),X2) = zero_zero_real
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X1))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X2))
| X2 != zero_zero_real
| X1 != zero_zero_real ),
inference(literals_permutation,[status(thm)],[c_0_3511]) ).
cnf(c_0_3511_1,axiom,
( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X1))
| hAPP_real_real(plus_plus_real(X1),X2) = zero_zero_real
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X2))
| X2 != zero_zero_real
| X1 != zero_zero_real ),
inference(literals_permutation,[status(thm)],[c_0_3511]) ).
cnf(c_0_3511_2,axiom,
( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X2))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X1))
| hAPP_real_real(plus_plus_real(X1),X2) = zero_zero_real
| X2 != zero_zero_real
| X1 != zero_zero_real ),
inference(literals_permutation,[status(thm)],[c_0_3511]) ).
cnf(c_0_3511_3,axiom,
( X2 != zero_zero_real
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X2))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X1))
| hAPP_real_real(plus_plus_real(X1),X2) = zero_zero_real
| X1 != zero_zero_real ),
inference(literals_permutation,[status(thm)],[c_0_3511]) ).
cnf(c_0_3511_4,axiom,
( X1 != zero_zero_real
| X2 != zero_zero_real
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X2))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X1))
| hAPP_real_real(plus_plus_real(X1),X2) = zero_zero_real ),
inference(literals_permutation,[status(thm)],[c_0_3511]) ).
cnf(c_0_3512_0,axiom,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_int_int(plus_plus_int(one_one_int),X1)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_3512]) ).
cnf(c_0_3512_1,axiom,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_int_int(plus_plus_int(one_one_int),X1))) ),
inference(literals_permutation,[status(thm)],[c_0_3512]) ).
cnf(c_0_3513_0,axiom,
( X2 = X1
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X2),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_3513]) ).
cnf(c_0_3513_1,axiom,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2))
| X2 = X1
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X2),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_3513]) ).
cnf(c_0_3513_2,axiom,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X2),X1))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2))
| X2 = X1 ),
inference(literals_permutation,[status(thm)],[c_0_3513]) ).
cnf(c_0_3514_0,axiom,
( X2 = X1
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_3514]) ).
cnf(c_0_3514_1,axiom,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
| X2 = X1
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_3514]) ).
cnf(c_0_3514_2,axiom,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X1))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
| X2 = X1 ),
inference(literals_permutation,[status(thm)],[c_0_3514]) ).
cnf(c_0_3515_0,axiom,
( X2 = X1
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X1),X2))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X2),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_3515]) ).
cnf(c_0_3515_1,axiom,
( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X1),X2))
| X2 = X1
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X2),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_3515]) ).
cnf(c_0_3515_2,axiom,
( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X2),X1))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X1),X2))
| X2 = X1 ),
inference(literals_permutation,[status(thm)],[c_0_3515]) ).
cnf(c_0_3516_0,axiom,
( X1 = X2
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X2),X1))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3516]) ).
cnf(c_0_3516_1,axiom,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X2),X1))
| X1 = X2
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3516]) ).
cnf(c_0_3516_2,axiom,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X2),X1))
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_3516]) ).
cnf(c_0_3517_0,axiom,
( X1 = X2
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X1))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3517]) ).
cnf(c_0_3517_1,axiom,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X1))
| X1 = X2
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3517]) ).
cnf(c_0_3517_2,axiom,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X1))
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_3517]) ).
cnf(c_0_3518_0,axiom,
( X1 = X2
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X2),X1))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3518]) ).
cnf(c_0_3518_1,axiom,
( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X2),X1))
| X1 = X2
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3518]) ).
cnf(c_0_3518_2,axiom,
( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X1),X2))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X2),X1))
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_3518]) ).
cnf(c_0_3519_0,axiom,
( X1 = X2
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X2),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_3519]) ).
cnf(c_0_3519_1,axiom,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2))
| X1 = X2
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X2),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_3519]) ).
cnf(c_0_3519_2,axiom,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X2),X1))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2))
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_3519]) ).
cnf(c_0_3520_0,axiom,
( X1 = X2
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_3520]) ).
cnf(c_0_3520_1,axiom,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
| X1 = X2
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_3520]) ).
cnf(c_0_3520_2,axiom,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X1))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_3520]) ).
cnf(c_0_3521_0,axiom,
( X1 = X2
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X1),X2))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X2),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_3521]) ).
cnf(c_0_3521_1,axiom,
( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X1),X2))
| X1 = X2
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X2),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_3521]) ).
cnf(c_0_3521_2,axiom,
( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X2),X1))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X1),X2))
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_3521]) ).
cnf(c_0_3522_0,axiom,
( X1 = X2
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X2),X1))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3522]) ).
cnf(c_0_3522_1,axiom,
( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X2),X1))
| X1 = X2
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3522]) ).
cnf(c_0_3522_2,axiom,
( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X1),X2))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X2),X1))
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_3522]) ).
cnf(c_0_3523_0,axiom,
( X1 = X2
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X1))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3523]) ).
cnf(c_0_3523_1,axiom,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X1))
| X1 = X2
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3523]) ).
cnf(c_0_3523_2,axiom,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X1))
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_3523]) ).
cnf(c_0_3524_0,axiom,
( X1 = X2
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X2),X1))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3524]) ).
cnf(c_0_3524_1,axiom,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X2),X1))
| X1 = X2
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3524]) ).
cnf(c_0_3524_2,axiom,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X2),X1))
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_3524]) ).
cnf(c_0_3525_0,axiom,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),sk1_esk3_2(X1,X2)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3525]) ).
cnf(c_0_3525_1,axiom,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),sk1_esk3_2(X1,X2))) ),
inference(literals_permutation,[status(thm)],[c_0_3525]) ).
cnf(c_0_3526_0,axiom,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
| X1 = X2
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(X3,X2),X1))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X2),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_3526]) ).
cnf(c_0_3526_1,axiom,
( X1 = X2
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(X3,X2),X1))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X2),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_3526]) ).
cnf(c_0_3526_2,axiom,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(X3,X2),X1))
| X1 = X2
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X2),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_3526]) ).
cnf(c_0_3526_3,axiom,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X2),X1))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(X3,X2),X1))
| X1 = X2
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3526]) ).
cnf(c_0_3527_0,axiom,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),number_number_of_int(bit0(X1))))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),number_number_of_int(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_3527]) ).
cnf(c_0_3527_1,axiom,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),number_number_of_int(X1)))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),number_number_of_int(bit0(X1)))) ),
inference(literals_permutation,[status(thm)],[c_0_3527]) ).
cnf(c_0_3528_0,axiom,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),number_number_of_int(bit1(X1))))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),number_number_of_int(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_3528]) ).
cnf(c_0_3528_1,axiom,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),number_number_of_int(X1)))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),number_number_of_int(bit1(X1)))) ),
inference(literals_permutation,[status(thm)],[c_0_3528]) ).
cnf(c_0_3529_0,axiom,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),bit1(pls)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,number_number_of_int(X1)),one_one_int)) ),
inference(literals_permutation,[status(thm)],[c_0_3529]) ).
cnf(c_0_3529_1,axiom,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,number_number_of_int(X1)),one_one_int))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),bit1(pls))) ),
inference(literals_permutation,[status(thm)],[c_0_3529]) ).
cnf(c_0_3530_0,axiom,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),bit1(pls)))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,number267125858f_real(X1)),one_one_real)) ),
inference(literals_permutation,[status(thm)],[c_0_3530]) ).
cnf(c_0_3530_1,axiom,
( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,number267125858f_real(X1)),one_one_real))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),bit1(pls))) ),
inference(literals_permutation,[status(thm)],[c_0_3530]) ).
cnf(c_0_3531_0,axiom,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),bit1(pls)))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,number267125858f_real(X1)),one_one_real)) ),
inference(literals_permutation,[status(thm)],[c_0_3531]) ).
cnf(c_0_3531_1,axiom,
( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,number267125858f_real(X1)),one_one_real))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),bit1(pls))) ),
inference(literals_permutation,[status(thm)],[c_0_3531]) ).
cnf(c_0_3532_0,axiom,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),bit1(pls)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(X1)),one_one_int)) ),
inference(literals_permutation,[status(thm)],[c_0_3532]) ).
cnf(c_0_3532_1,axiom,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(X1)),one_one_int))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),bit1(pls))) ),
inference(literals_permutation,[status(thm)],[c_0_3532]) ).
cnf(c_0_3533_0,axiom,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,number_number_of_nat(X1)),number_number_of_nat(X2)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3533]) ).
cnf(c_0_3533_1,axiom,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,number_number_of_nat(X1)),number_number_of_nat(X2))) ),
inference(literals_permutation,[status(thm)],[c_0_3533]) ).
cnf(c_0_3534_0,axiom,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,bit1(X1)),bit0(X2)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3534]) ).
cnf(c_0_3534_1,axiom,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X2))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,bit1(X1)),bit0(X2))) ),
inference(literals_permutation,[status(thm)],[c_0_3534]) ).
cnf(c_0_3535_0,axiom,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,bit1(X1)),bit0(X2)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3535]) ).
cnf(c_0_3535_1,axiom,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X2))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,bit1(X1)),bit0(X2))) ),
inference(literals_permutation,[status(thm)],[c_0_3535]) ).
cnf(c_0_3536_0,axiom,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit0(X1)),bit1(X2)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3536]) ).
cnf(c_0_3536_1,axiom,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit0(X1)),bit1(X2))) ),
inference(literals_permutation,[status(thm)],[c_0_3536]) ).
cnf(c_0_3537_0,axiom,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit0(X1)),bit1(X2)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3537]) ).
cnf(c_0_3537_1,axiom,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit0(X1)),bit1(X2))) ),
inference(literals_permutation,[status(thm)],[c_0_3537]) ).
cnf(c_0_3538_0,axiom,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,bit0(X1)),bit1(X2)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3538]) ).
cnf(c_0_3538_1,axiom,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,bit0(X1)),bit1(X2))) ),
inference(literals_permutation,[status(thm)],[c_0_3538]) ).
cnf(c_0_3539_0,axiom,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,bit0(X1)),bit1(X2)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3539]) ).
cnf(c_0_3539_1,axiom,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,bit0(X1)),bit1(X2))) ),
inference(literals_permutation,[status(thm)],[c_0_3539]) ).
cnf(c_0_3540_0,axiom,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,number_number_of_int(X1)),number_number_of_int(X2)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3540]) ).
cnf(c_0_3540_1,axiom,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,number_number_of_int(X1)),number_number_of_int(X2))) ),
inference(literals_permutation,[status(thm)],[c_0_3540]) ).
cnf(c_0_3541_0,axiom,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,number_number_of_int(X1)),number_number_of_int(X2)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3541]) ).
cnf(c_0_3541_1,axiom,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,number_number_of_int(X1)),number_number_of_int(X2))) ),
inference(literals_permutation,[status(thm)],[c_0_3541]) ).
cnf(c_0_3542_0,axiom,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,number267125858f_real(X1)),number267125858f_real(X2)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3542]) ).
cnf(c_0_3542_1,axiom,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2))
| hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,number267125858f_real(X1)),number267125858f_real(X2))) ),
inference(literals_permutation,[status(thm)],[c_0_3542]) ).
cnf(c_0_3543_0,axiom,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,bit0(X1)),bit0(X2)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3543]) ).
cnf(c_0_3543_1,axiom,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,bit0(X1)),bit0(X2))) ),
inference(literals_permutation,[status(thm)],[c_0_3543]) ).
cnf(c_0_3544_0,axiom,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,bit0(X1)),bit0(X2)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3544]) ).
cnf(c_0_3544_1,axiom,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,bit0(X1)),bit0(X2))) ),
inference(literals_permutation,[status(thm)],[c_0_3544]) ).
cnf(c_0_3545_0,axiom,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,bit1(X1)),bit1(X2)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3545]) ).
cnf(c_0_3545_1,axiom,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,bit1(X1)),bit1(X2))) ),
inference(literals_permutation,[status(thm)],[c_0_3545]) ).
cnf(c_0_3546_0,axiom,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,bit1(X1)),bit1(X2)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3546]) ).
cnf(c_0_3546_1,axiom,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,bit1(X1)),bit1(X2))) ),
inference(literals_permutation,[status(thm)],[c_0_3546]) ).
cnf(c_0_3547_0,axiom,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit1(X1)),bit0(X2)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3547]) ).
cnf(c_0_3547_1,axiom,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X2))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit1(X1)),bit0(X2))) ),
inference(literals_permutation,[status(thm)],[c_0_3547]) ).
cnf(c_0_3548_0,axiom,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit1(X1)),bit0(X2)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3548]) ).
cnf(c_0_3548_1,axiom,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X2))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit1(X1)),bit0(X2))) ),
inference(literals_permutation,[status(thm)],[c_0_3548]) ).
cnf(c_0_3549_0,axiom,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit0(X1)),bit0(X2)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3549]) ).
cnf(c_0_3549_1,axiom,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X2))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit0(X1)),bit0(X2))) ),
inference(literals_permutation,[status(thm)],[c_0_3549]) ).
cnf(c_0_3550_0,axiom,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit0(X1)),bit0(X2)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3550]) ).
cnf(c_0_3550_1,axiom,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X2))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit0(X1)),bit0(X2))) ),
inference(literals_permutation,[status(thm)],[c_0_3550]) ).
cnf(c_0_3551_0,axiom,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit1(X1)),bit1(X2)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3551]) ).
cnf(c_0_3551_1,axiom,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X2))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit1(X1)),bit1(X2))) ),
inference(literals_permutation,[status(thm)],[c_0_3551]) ).
cnf(c_0_3552_0,axiom,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit1(X1)),bit1(X2)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3552]) ).
cnf(c_0_3552_1,axiom,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X2))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit1(X1)),bit1(X2))) ),
inference(literals_permutation,[status(thm)],[c_0_3552]) ).
cnf(c_0_3553_0,axiom,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,number267125858f_real(X1)),number267125858f_real(X2)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3553]) ).
cnf(c_0_3553_1,axiom,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X2))
| hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,number267125858f_real(X1)),number267125858f_real(X2))) ),
inference(literals_permutation,[status(thm)],[c_0_3553]) ).
cnf(c_0_3554_0,axiom,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(X1)),number_number_of_int(X2)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3554]) ).
cnf(c_0_3554_1,axiom,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X2))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(X1)),number_number_of_int(X2))) ),
inference(literals_permutation,[status(thm)],[c_0_3554]) ).
cnf(c_0_3555_0,axiom,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(X1)),number_number_of_int(X2)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3555]) ).
cnf(c_0_3555_1,axiom,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X2))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(X1)),number_number_of_int(X2))) ),
inference(literals_permutation,[status(thm)],[c_0_3555]) ).
cnf(c_0_3556_0,axiom,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),pls))
| hAPP_nat_nat(plus_plus_nat(number_number_of_nat(X1)),number_number_of_nat(X2)) = number_number_of_nat(X1)
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X2),pls)) ),
inference(literals_permutation,[status(thm)],[c_0_3556]) ).
cnf(c_0_3556_1,axiom,
( hAPP_nat_nat(plus_plus_nat(number_number_of_nat(X1)),number_number_of_nat(X2)) = number_number_of_nat(X1)
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),pls))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X2),pls)) ),
inference(literals_permutation,[status(thm)],[c_0_3556]) ).
cnf(c_0_3556_2,axiom,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X2),pls))
| hAPP_nat_nat(plus_plus_nat(number_number_of_nat(X1)),number_number_of_nat(X2)) = number_number_of_nat(X1)
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),pls)) ),
inference(literals_permutation,[status(thm)],[c_0_3556]) ).
cnf(c_0_3557_0,axiom,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,number_number_of_nat(X1)),number_number_of_nat(X2)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),pls)) ),
inference(literals_permutation,[status(thm)],[c_0_3557]) ).
cnf(c_0_3557_1,axiom,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),pls))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,number_number_of_nat(X1)),number_number_of_nat(X2))) ),
inference(literals_permutation,[status(thm)],[c_0_3557]) ).
cnf(c_0_3558_0,axiom,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),pls))
| hAPP_nat_nat(plus_plus_nat(number_number_of_nat(X1)),number_number_of_nat(X2)) = number_number_of_nat(hAPP_int_int(plus_plus_int(X1),X2))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X2),pls)) ),
inference(literals_permutation,[status(thm)],[c_0_3558]) ).
cnf(c_0_3558_1,axiom,
( hAPP_nat_nat(plus_plus_nat(number_number_of_nat(X1)),number_number_of_nat(X2)) = number_number_of_nat(hAPP_int_int(plus_plus_int(X1),X2))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),pls))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X2),pls)) ),
inference(literals_permutation,[status(thm)],[c_0_3558]) ).
cnf(c_0_3558_2,axiom,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X2),pls))
| hAPP_nat_nat(plus_plus_nat(number_number_of_nat(X1)),number_number_of_nat(X2)) = number_number_of_nat(hAPP_int_int(plus_plus_int(X1),X2))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),pls)) ),
inference(literals_permutation,[status(thm)],[c_0_3558]) ).
cnf(c_0_3559_0,axiom,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,number_number_of_int(X1)),one_one_int))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),bit1(pls))) ),
inference(literals_permutation,[status(thm)],[c_0_3559]) ).
cnf(c_0_3559_1,axiom,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),bit1(pls)))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,number_number_of_int(X1)),one_one_int)) ),
inference(literals_permutation,[status(thm)],[c_0_3559]) ).
cnf(c_0_3560_0,axiom,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,number267125858f_real(X1)),one_one_real))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),bit1(pls))) ),
inference(literals_permutation,[status(thm)],[c_0_3560]) ).
cnf(c_0_3560_1,axiom,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),bit1(pls)))
| hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,number267125858f_real(X1)),one_one_real)) ),
inference(literals_permutation,[status(thm)],[c_0_3560]) ).
cnf(c_0_3561_0,axiom,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,number267125858f_real(X1)),one_one_real))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),bit1(pls))) ),
inference(literals_permutation,[status(thm)],[c_0_3561]) ).
cnf(c_0_3561_1,axiom,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),bit1(pls)))
| hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,number267125858f_real(X1)),one_one_real)) ),
inference(literals_permutation,[status(thm)],[c_0_3561]) ).
cnf(c_0_3562_0,axiom,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(X1)),one_one_int))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),bit1(pls))) ),
inference(literals_permutation,[status(thm)],[c_0_3562]) ).
cnf(c_0_3562_1,axiom,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),bit1(pls)))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(X1)),one_one_int)) ),
inference(literals_permutation,[status(thm)],[c_0_3562]) ).
cnf(c_0_3563_0,axiom,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X1),one_one_real))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,sqrt(X1)),one_one_real)) ),
inference(literals_permutation,[status(thm)],[c_0_3563]) ).
cnf(c_0_3563_1,axiom,
( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,sqrt(X1)),one_one_real))
| hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X1),one_one_real)) ),
inference(literals_permutation,[status(thm)],[c_0_3563]) ).
cnf(c_0_3564_0,axiom,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X1),zero_zero_real))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,sqrt(X1)),zero_zero_real)) ),
inference(literals_permutation,[status(thm)],[c_0_3564]) ).
cnf(c_0_3564_1,axiom,
( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,sqrt(X1)),zero_zero_real))
| hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X1),zero_zero_real)) ),
inference(literals_permutation,[status(thm)],[c_0_3564]) ).
cnf(c_0_3565_0,axiom,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),pls))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,bit1(X1)),pls)) ),
inference(literals_permutation,[status(thm)],[c_0_3565]) ).
cnf(c_0_3565_1,axiom,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,bit1(X1)),pls))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),pls)) ),
inference(literals_permutation,[status(thm)],[c_0_3565]) ).
cnf(c_0_3566_0,axiom,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),pls))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,bit0(X1)),pls)) ),
inference(literals_permutation,[status(thm)],[c_0_3566]) ).
cnf(c_0_3566_1,axiom,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,bit0(X1)),pls))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),pls)) ),
inference(literals_permutation,[status(thm)],[c_0_3566]) ).
cnf(c_0_3567_0,axiom,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),pls))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,number_number_of_int(X1)),zero_zero_int)) ),
inference(literals_permutation,[status(thm)],[c_0_3567]) ).
cnf(c_0_3567_1,axiom,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,number_number_of_int(X1)),zero_zero_int))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),pls)) ),
inference(literals_permutation,[status(thm)],[c_0_3567]) ).
cnf(c_0_3568_0,axiom,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),pls))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,number267125858f_real(X1)),zero_zero_real)) ),
inference(literals_permutation,[status(thm)],[c_0_3568]) ).
cnf(c_0_3568_1,axiom,
( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,number267125858f_real(X1)),zero_zero_real))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),pls)) ),
inference(literals_permutation,[status(thm)],[c_0_3568]) ).
cnf(c_0_3569_0,axiom,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),zero_zero_int))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit0(X1)),zero_zero_int)) ),
inference(literals_permutation,[status(thm)],[c_0_3569]) ).
cnf(c_0_3569_1,axiom,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit0(X1)),zero_zero_int))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),zero_zero_int)) ),
inference(literals_permutation,[status(thm)],[c_0_3569]) ).
cnf(c_0_3570_0,axiom,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),zero_zero_int))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit1(X1)),zero_zero_int)) ),
inference(literals_permutation,[status(thm)],[c_0_3570]) ).
cnf(c_0_3570_1,axiom,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit1(X1)),zero_zero_int))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),zero_zero_int)) ),
inference(literals_permutation,[status(thm)],[c_0_3570]) ).
cnf(c_0_3571_0,axiom,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),pls))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit0(X1)),pls)) ),
inference(literals_permutation,[status(thm)],[c_0_3571]) ).
cnf(c_0_3571_1,axiom,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit0(X1)),pls))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),pls)) ),
inference(literals_permutation,[status(thm)],[c_0_3571]) ).
cnf(c_0_3572_0,axiom,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),pls))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit1(X1)),pls)) ),
inference(literals_permutation,[status(thm)],[c_0_3572]) ).
cnf(c_0_3572_1,axiom,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit1(X1)),pls))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),pls)) ),
inference(literals_permutation,[status(thm)],[c_0_3572]) ).
cnf(c_0_3573_0,axiom,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),pls))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,number267125858f_real(X1)),zero_zero_real)) ),
inference(literals_permutation,[status(thm)],[c_0_3573]) ).
cnf(c_0_3573_1,axiom,
( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,number267125858f_real(X1)),zero_zero_real))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),pls)) ),
inference(literals_permutation,[status(thm)],[c_0_3573]) ).
cnf(c_0_3574_0,axiom,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),pls))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(X1)),zero_zero_int)) ),
inference(literals_permutation,[status(thm)],[c_0_3574]) ).
cnf(c_0_3574_1,axiom,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(X1)),zero_zero_int))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),pls)) ),
inference(literals_permutation,[status(thm)],[c_0_3574]) ).
cnf(c_0_3575_0,axiom,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_nat_int(semiri1621563631at_int,X1)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_3575]) ).
cnf(c_0_3575_1,axiom,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_nat_int(semiri1621563631at_int,X1))) ),
inference(literals_permutation,[status(thm)],[c_0_3575]) ).
cnf(c_0_3576_0,axiom,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),hAPP_nat_real(semiri132038758t_real,X1)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_3576]) ).
cnf(c_0_3576_1,axiom,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1))
| hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),hAPP_nat_real(semiri132038758t_real,X1))) ),
inference(literals_permutation,[status(thm)],[c_0_3576]) ).
cnf(c_0_3577_0,axiom,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(semiri984289939at_nat,X1)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_3577]) ).
cnf(c_0_3577_1,axiom,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(semiri984289939at_nat,X1))) ),
inference(literals_permutation,[status(thm)],[c_0_3577]) ).
cnf(c_0_3578_0,axiom,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_nat_int(semiri1621563631at_int,X1)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_3578]) ).
cnf(c_0_3578_1,axiom,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_nat_int(semiri1621563631at_int,X1))) ),
inference(literals_permutation,[status(thm)],[c_0_3578]) ).
cnf(c_0_3579_0,axiom,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,number_number_of_int(X1)),number_number_of_int(X2)))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(X2)),number_number_of_int(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_3579]) ).
cnf(c_0_3579_1,axiom,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(X2)),number_number_of_int(X1)))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,number_number_of_int(X1)),number_number_of_int(X2))) ),
inference(literals_permutation,[status(thm)],[c_0_3579]) ).
cnf(c_0_3580_0,axiom,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,number_number_of_nat(X1)),number_number_of_nat(X2)))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,number_number_of_nat(X2)),number_number_of_nat(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_3580]) ).
cnf(c_0_3580_1,axiom,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,number_number_of_nat(X2)),number_number_of_nat(X1)))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,number_number_of_nat(X1)),number_number_of_nat(X2))) ),
inference(literals_permutation,[status(thm)],[c_0_3580]) ).
cnf(c_0_3581_0,axiom,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,number267125858f_real(X1)),number267125858f_real(X2)))
| hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,number267125858f_real(X2)),number267125858f_real(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_3581]) ).
cnf(c_0_3581_1,axiom,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,number267125858f_real(X2)),number267125858f_real(X1)))
| hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,number267125858f_real(X1)),number267125858f_real(X2))) ),
inference(literals_permutation,[status(thm)],[c_0_3581]) ).
cnf(c_0_3582_0,axiom,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),number_number_of_int(X1)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,bit1(pls)),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_3582]) ).
cnf(c_0_3582_1,axiom,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,bit1(pls)),X1))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),number_number_of_int(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_3582]) ).
cnf(c_0_3583_0,axiom,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,one_one_real),number267125858f_real(X1)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,bit1(pls)),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_3583]) ).
cnf(c_0_3583_1,axiom,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,bit1(pls)),X1))
| hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,one_one_real),number267125858f_real(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_3583]) ).
cnf(c_0_3584_0,axiom,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,one_one_real),number267125858f_real(X1)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit1(pls)),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_3584]) ).
cnf(c_0_3584_1,axiom,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit1(pls)),X1))
| hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,one_one_real),number267125858f_real(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_3584]) ).
cnf(c_0_3585_0,axiom,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),number_number_of_int(X1)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit1(pls)),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_3585]) ).
cnf(c_0_3585_1,axiom,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit1(pls)),X1))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),number_number_of_int(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_3585]) ).
cnf(c_0_3586_0,axiom,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,bit1(pls)),X1))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),number_number_of_int(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_3586]) ).
cnf(c_0_3586_1,axiom,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),number_number_of_int(X1)))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,bit1(pls)),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_3586]) ).
cnf(c_0_3587_0,axiom,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,bit1(pls)),X1))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,one_one_real),number267125858f_real(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_3587]) ).
cnf(c_0_3587_1,axiom,
( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,one_one_real),number267125858f_real(X1)))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,bit1(pls)),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_3587]) ).
cnf(c_0_3588_0,axiom,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit1(pls)),X1))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,one_one_real),number267125858f_real(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_3588]) ).
cnf(c_0_3588_1,axiom,
( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,one_one_real),number267125858f_real(X1)))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit1(pls)),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_3588]) ).
cnf(c_0_3589_0,axiom,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit1(pls)),X1))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),number_number_of_int(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_3589]) ).
cnf(c_0_3589_1,axiom,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),number_number_of_int(X1)))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit1(pls)),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_3589]) ).
cnf(c_0_3590_0,axiom,
( hAPP_int_int(plus_plus_int(X2),hAPP_nat_int(semiri1621563631at_int,sk1_esk10_2(X2,X1))) = X1
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X2),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_3590]) ).
cnf(c_0_3590_1,axiom,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X2),X1))
| hAPP_int_int(plus_plus_int(X2),hAPP_nat_int(semiri1621563631at_int,sk1_esk10_2(X2,X1))) = X1 ),
inference(literals_permutation,[status(thm)],[c_0_3590]) ).
cnf(c_0_3593_0,axiom,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,sqrt(X1)),one_one_real))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X1),one_one_real)) ),
inference(literals_permutation,[status(thm)],[c_0_3593]) ).
cnf(c_0_3593_1,axiom,
( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X1),one_one_real))
| hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,sqrt(X1)),one_one_real)) ),
inference(literals_permutation,[status(thm)],[c_0_3593]) ).
cnf(c_0_3594_0,axiom,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,sqrt(X1)),zero_zero_real))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X1),zero_zero_real)) ),
inference(literals_permutation,[status(thm)],[c_0_3594]) ).
cnf(c_0_3594_1,axiom,
( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X1),zero_zero_real))
| hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,sqrt(X1)),zero_zero_real)) ),
inference(literals_permutation,[status(thm)],[c_0_3594]) ).
cnf(c_0_3595_0,axiom,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,bit1(X1)),pls))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),pls)) ),
inference(literals_permutation,[status(thm)],[c_0_3595]) ).
cnf(c_0_3595_1,axiom,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),pls))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,bit1(X1)),pls)) ),
inference(literals_permutation,[status(thm)],[c_0_3595]) ).
cnf(c_0_3596_0,axiom,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,bit0(X1)),pls))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),pls)) ),
inference(literals_permutation,[status(thm)],[c_0_3596]) ).
cnf(c_0_3596_1,axiom,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),pls))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,bit0(X1)),pls)) ),
inference(literals_permutation,[status(thm)],[c_0_3596]) ).
cnf(c_0_3597_0,axiom,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,number_number_of_int(X1)),zero_zero_int))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),pls)) ),
inference(literals_permutation,[status(thm)],[c_0_3597]) ).
cnf(c_0_3597_1,axiom,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),pls))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,number_number_of_int(X1)),zero_zero_int)) ),
inference(literals_permutation,[status(thm)],[c_0_3597]) ).
cnf(c_0_3598_0,axiom,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,number267125858f_real(X1)),zero_zero_real))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),pls)) ),
inference(literals_permutation,[status(thm)],[c_0_3598]) ).
cnf(c_0_3598_1,axiom,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),pls))
| hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,number267125858f_real(X1)),zero_zero_real)) ),
inference(literals_permutation,[status(thm)],[c_0_3598]) ).
cnf(c_0_3599_0,axiom,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit0(X1)),zero_zero_int))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),zero_zero_int)) ),
inference(literals_permutation,[status(thm)],[c_0_3599]) ).
cnf(c_0_3599_1,axiom,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),zero_zero_int))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit0(X1)),zero_zero_int)) ),
inference(literals_permutation,[status(thm)],[c_0_3599]) ).
cnf(c_0_3600_0,axiom,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit1(X1)),zero_zero_int))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),zero_zero_int)) ),
inference(literals_permutation,[status(thm)],[c_0_3600]) ).
cnf(c_0_3600_1,axiom,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),zero_zero_int))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit1(X1)),zero_zero_int)) ),
inference(literals_permutation,[status(thm)],[c_0_3600]) ).
cnf(c_0_3601_0,axiom,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit0(X1)),pls))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),pls)) ),
inference(literals_permutation,[status(thm)],[c_0_3601]) ).
cnf(c_0_3601_1,axiom,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),pls))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit0(X1)),pls)) ),
inference(literals_permutation,[status(thm)],[c_0_3601]) ).
cnf(c_0_3602_0,axiom,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit1(X1)),pls))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),pls)) ),
inference(literals_permutation,[status(thm)],[c_0_3602]) ).
cnf(c_0_3602_1,axiom,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),pls))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit1(X1)),pls)) ),
inference(literals_permutation,[status(thm)],[c_0_3602]) ).
cnf(c_0_3603_0,axiom,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,number267125858f_real(X1)),zero_zero_real))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),pls)) ),
inference(literals_permutation,[status(thm)],[c_0_3603]) ).
cnf(c_0_3603_1,axiom,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),pls))
| hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,number267125858f_real(X1)),zero_zero_real)) ),
inference(literals_permutation,[status(thm)],[c_0_3603]) ).
cnf(c_0_3604_0,axiom,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(X1)),zero_zero_int))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),pls)) ),
inference(literals_permutation,[status(thm)],[c_0_3604]) ).
cnf(c_0_3604_1,axiom,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),pls))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(X1)),zero_zero_int)) ),
inference(literals_permutation,[status(thm)],[c_0_3604]) ).
cnf(c_0_3605_0,axiom,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),sk1_esk7_1(X1)))
| ~ hBOOL(hAPP_int_bool(X1,hAPP_nat_int(semiri1621563631at_int,X2))) ),
inference(literals_permutation,[status(thm)],[c_0_3605]) ).
cnf(c_0_3605_1,axiom,
( ~ hBOOL(hAPP_int_bool(X1,hAPP_nat_int(semiri1621563631at_int,X2)))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),sk1_esk7_1(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_3605]) ).
cnf(c_0_3606_0,axiom,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X3))
| ~ hBOOL(X1)
| ~ hBOOL(X2)
| ~ hBOOL(X2)
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3606]) ).
cnf(c_0_3606_1,axiom,
( ~ hBOOL(X1)
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X3))
| ~ hBOOL(X2)
| ~ hBOOL(X2)
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3606]) ).
cnf(c_0_3606_2,axiom,
( ~ hBOOL(X2)
| ~ hBOOL(X1)
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X3))
| ~ hBOOL(X2)
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3606]) ).
cnf(c_0_3606_3,axiom,
( ~ hBOOL(X2)
| ~ hBOOL(X2)
| ~ hBOOL(X1)
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X3))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3606]) ).
cnf(c_0_3606_4,axiom,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X3))
| ~ hBOOL(X2)
| ~ hBOOL(X2)
| ~ hBOOL(X1)
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3606]) ).
cnf(c_0_3607_0,axiom,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X3))
| ~ hBOOL(X1)
| ~ hBOOL(X2)
| ~ hBOOL(X1)
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3607]) ).
cnf(c_0_3607_1,axiom,
( ~ hBOOL(X1)
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X3))
| ~ hBOOL(X2)
| ~ hBOOL(X1)
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3607]) ).
cnf(c_0_3607_2,axiom,
( ~ hBOOL(X2)
| ~ hBOOL(X1)
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X3))
| ~ hBOOL(X1)
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3607]) ).
cnf(c_0_3607_3,axiom,
( ~ hBOOL(X1)
| ~ hBOOL(X2)
| ~ hBOOL(X1)
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X3))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3607]) ).
cnf(c_0_3607_4,axiom,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X3))
| ~ hBOOL(X1)
| ~ hBOOL(X2)
| ~ hBOOL(X1)
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3607]) ).
cnf(c_0_3608_0,axiom,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X2),X1))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2))
| X2 != X1 ),
inference(literals_permutation,[status(thm)],[c_0_3608]) ).
cnf(c_0_3608_1,axiom,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X2),X1))
| X2 != X1 ),
inference(literals_permutation,[status(thm)],[c_0_3608]) ).
cnf(c_0_3608_2,axiom,
( X2 != X1
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X2),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_3608]) ).
cnf(c_0_3609_0,axiom,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X1))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
| X2 != X1 ),
inference(literals_permutation,[status(thm)],[c_0_3609]) ).
cnf(c_0_3609_1,axiom,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X1))
| X2 != X1 ),
inference(literals_permutation,[status(thm)],[c_0_3609]) ).
cnf(c_0_3609_2,axiom,
( X2 != X1
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_3609]) ).
cnf(c_0_3610_0,axiom,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X2),X1))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X1),X2))
| X2 != X1 ),
inference(literals_permutation,[status(thm)],[c_0_3610]) ).
cnf(c_0_3610_1,axiom,
( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X1),X2))
| hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X2),X1))
| X2 != X1 ),
inference(literals_permutation,[status(thm)],[c_0_3610]) ).
cnf(c_0_3610_2,axiom,
( X2 != X1
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X1),X2))
| hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X2),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_3610]) ).
cnf(c_0_3611_0,axiom,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X3),X2))
| X1 != X3 ),
inference(literals_permutation,[status(thm)],[c_0_3611]) ).
cnf(c_0_3611_1,axiom,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X3),X2))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2))
| X1 != X3 ),
inference(literals_permutation,[status(thm)],[c_0_3611]) ).
cnf(c_0_3611_2,axiom,
( X1 != X3
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X3),X2))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3611]) ).
cnf(c_0_3612_0,axiom,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X3),X2))
| X1 != X3 ),
inference(literals_permutation,[status(thm)],[c_0_3612]) ).
cnf(c_0_3612_1,axiom,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X3),X2))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
| X1 != X3 ),
inference(literals_permutation,[status(thm)],[c_0_3612]) ).
cnf(c_0_3612_2,axiom,
( X1 != X3
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X3),X2))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3612]) ).
cnf(c_0_3613_0,axiom,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X1),X2))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X3),X2))
| X1 != X3 ),
inference(literals_permutation,[status(thm)],[c_0_3613]) ).
cnf(c_0_3613_1,axiom,
( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X3),X2))
| hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X1),X2))
| X1 != X3 ),
inference(literals_permutation,[status(thm)],[c_0_3613]) ).
cnf(c_0_3613_2,axiom,
( X1 != X3
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X3),X2))
| hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3613]) ).
cnf(c_0_3614_0,axiom,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X3))
| X2 != X3 ),
inference(literals_permutation,[status(thm)],[c_0_3614]) ).
cnf(c_0_3614_1,axiom,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X3))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2))
| X2 != X3 ),
inference(literals_permutation,[status(thm)],[c_0_3614]) ).
cnf(c_0_3614_2,axiom,
( X2 != X3
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X3))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3614]) ).
cnf(c_0_3615_0,axiom,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X3))
| X2 != X3 ),
inference(literals_permutation,[status(thm)],[c_0_3615]) ).
cnf(c_0_3615_1,axiom,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X3))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
| X2 != X3 ),
inference(literals_permutation,[status(thm)],[c_0_3615]) ).
cnf(c_0_3615_2,axiom,
( X2 != X3
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X3))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3615]) ).
cnf(c_0_3616_0,axiom,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X1),X2))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X1),X3))
| X2 != X3 ),
inference(literals_permutation,[status(thm)],[c_0_3616]) ).
cnf(c_0_3616_1,axiom,
( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X1),X3))
| hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X1),X2))
| X2 != X3 ),
inference(literals_permutation,[status(thm)],[c_0_3616]) ).
cnf(c_0_3616_2,axiom,
( X2 != X3
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X1),X3))
| hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3616]) ).
cnf(c_0_3617_0,axiom,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2))
| X3 != X2
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3617]) ).
cnf(c_0_3617_1,axiom,
( X3 != X2
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3617]) ).
cnf(c_0_3617_2,axiom,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X3))
| X3 != X2
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3617]) ).
cnf(c_0_3618_0,axiom,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
| X3 != X2
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3618]) ).
cnf(c_0_3618_1,axiom,
( X3 != X2
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3618]) ).
cnf(c_0_3618_2,axiom,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X3))
| X3 != X2
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3618]) ).
cnf(c_0_3619_0,axiom,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X1),X2))
| X3 != X2
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X1),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3619]) ).
cnf(c_0_3619_1,axiom,
( X3 != X2
| hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X1),X2))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X1),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3619]) ).
cnf(c_0_3619_2,axiom,
( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X1),X3))
| X3 != X2
| hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3619]) ).
cnf(c_0_3620_0,axiom,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2))
| X3 != X1
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X3),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3620]) ).
cnf(c_0_3620_1,axiom,
( X3 != X1
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X3),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3620]) ).
cnf(c_0_3620_2,axiom,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X3),X2))
| X3 != X1
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3620]) ).
cnf(c_0_3621_0,axiom,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
| X3 != X1
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X3),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3621]) ).
cnf(c_0_3621_1,axiom,
( X3 != X1
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X3),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3621]) ).
cnf(c_0_3621_2,axiom,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X3),X2))
| X3 != X1
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3621]) ).
cnf(c_0_3622_0,axiom,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X1),X2))
| X3 != X1
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X3),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3622]) ).
cnf(c_0_3622_1,axiom,
( X3 != X1
| hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X1),X2))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X3),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3622]) ).
cnf(c_0_3622_2,axiom,
( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X3),X2))
| X3 != X1
| hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3622]) ).
cnf(c_0_3623_0,axiom,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,one_one_real),X1))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,one_one_real),sqrt(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_3623]) ).
cnf(c_0_3623_1,axiom,
( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,one_one_real),sqrt(X1)))
| hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,one_one_real),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_3623]) ).
cnf(c_0_3624_0,axiom,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X1))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),sqrt(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_3624]) ).
cnf(c_0_3624_1,axiom,
( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),sqrt(X1)))
| hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_3624]) ).
cnf(c_0_3625_0,axiom,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X1))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),bit1(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_3625]) ).
cnf(c_0_3625_1,axiom,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),bit1(X1)))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_3625]) ).
cnf(c_0_3626_0,axiom,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X1))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),bit0(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_3626]) ).
cnf(c_0_3626_1,axiom,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),bit0(X1)))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_3626]) ).
cnf(c_0_3627_0,axiom,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X1))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),bit1(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_3627]) ).
cnf(c_0_3627_1,axiom,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),bit1(X1)))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_3627]) ).
cnf(c_0_3628_0,axiom,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X1))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),number_number_of_int(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_3628]) ).
cnf(c_0_3628_1,axiom,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),number_number_of_int(X1)))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_3628]) ).
cnf(c_0_3629_0,axiom,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X1))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),number267125858f_real(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_3629]) ).
cnf(c_0_3629_1,axiom,
( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),number267125858f_real(X1)))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_3629]) ).
cnf(c_0_3630_0,axiom,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),X1))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),number_number_of_nat(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_3630]) ).
cnf(c_0_3630_1,axiom,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),number_number_of_nat(X1)))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_3630]) ).
cnf(c_0_3631_0,axiom,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),X1))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),bit0(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_3631]) ).
cnf(c_0_3631_1,axiom,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),bit0(X1)))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_3631]) ).
cnf(c_0_3632_0,axiom,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),X1))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),number267125858f_real(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_3632]) ).
cnf(c_0_3632_1,axiom,
( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),number267125858f_real(X1)))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_3632]) ).
cnf(c_0_3633_0,axiom,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),X1))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),number_number_of_int(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_3633]) ).
cnf(c_0_3633_1,axiom,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),number_number_of_int(X1)))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_3633]) ).
cnf(c_0_3634_0,axiom,
( hBOOL(X1)
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X3))
| ~ hBOOL(X1)
| ~ hBOOL(X2)
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3634]) ).
cnf(c_0_3634_1,axiom,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X3))
| hBOOL(X1)
| ~ hBOOL(X1)
| ~ hBOOL(X2)
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3634]) ).
cnf(c_0_3634_2,axiom,
( ~ hBOOL(X1)
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X3))
| hBOOL(X1)
| ~ hBOOL(X2)
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3634]) ).
cnf(c_0_3634_3,axiom,
( ~ hBOOL(X2)
| ~ hBOOL(X1)
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X3))
| hBOOL(X1)
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3634]) ).
cnf(c_0_3634_4,axiom,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X3))
| ~ hBOOL(X2)
| ~ hBOOL(X1)
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X3))
| hBOOL(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3634]) ).
cnf(c_0_3635_0,axiom,
( hBOOL(X2)
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X3))
| ~ hBOOL(X1)
| ~ hBOOL(X2)
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3635]) ).
cnf(c_0_3635_1,axiom,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X3))
| hBOOL(X2)
| ~ hBOOL(X1)
| ~ hBOOL(X2)
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3635]) ).
cnf(c_0_3635_2,axiom,
( ~ hBOOL(X1)
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X3))
| hBOOL(X2)
| ~ hBOOL(X2)
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3635]) ).
cnf(c_0_3635_3,axiom,
( ~ hBOOL(X2)
| ~ hBOOL(X1)
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X3))
| hBOOL(X2)
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3635]) ).
cnf(c_0_3635_4,axiom,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X3))
| ~ hBOOL(X2)
| ~ hBOOL(X1)
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X3))
| hBOOL(X2) ),
inference(literals_permutation,[status(thm)],[c_0_3635]) ).
cnf(c_0_3636_0,axiom,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X1),X2))
| X1 = X2
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3636]) ).
cnf(c_0_3636_1,axiom,
( X1 = X2
| hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X1),X2))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3636]) ).
cnf(c_0_3636_2,axiom,
( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X1),X2))
| X1 = X2
| hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3636]) ).
cnf(c_0_3637_0,axiom,
( X1 = X2
| hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X1),X2))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3637]) ).
cnf(c_0_3637_1,axiom,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X1),X2))
| X1 = X2
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3637]) ).
cnf(c_0_3637_2,axiom,
( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X1),X2))
| hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X1),X2))
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_3637]) ).
cnf(c_0_3638_0,axiom,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
| X1 = X2
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3638]) ).
cnf(c_0_3638_1,axiom,
( X1 = X2
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3638]) ).
cnf(c_0_3638_2,axiom,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
| X1 = X2
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3638]) ).
cnf(c_0_3639_0,axiom,
( X1 = X2
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3639]) ).
cnf(c_0_3639_1,axiom,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
| X1 = X2
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3639]) ).
cnf(c_0_3639_2,axiom,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_3639]) ).
cnf(c_0_3640_0,axiom,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
| X1 = X2
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3640]) ).
cnf(c_0_3640_1,axiom,
( X1 = X2
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3640]) ).
cnf(c_0_3640_2,axiom,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
| X1 = X2
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3640]) ).
cnf(c_0_3641_0,axiom,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X2))
| X1 = X2
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3641]) ).
cnf(c_0_3641_1,axiom,
( X1 = X2
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X2))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3641]) ).
cnf(c_0_3641_2,axiom,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2))
| X1 = X2
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3641]) ).
cnf(c_0_3642_0,axiom,
( hBOOL(X1)
| hBOOL(X2)
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X3))
| ~ hBOOL(X2)
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3642]) ).
cnf(c_0_3642_1,axiom,
( hBOOL(X2)
| hBOOL(X1)
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X3))
| ~ hBOOL(X2)
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3642]) ).
cnf(c_0_3642_2,axiom,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X3))
| hBOOL(X2)
| hBOOL(X1)
| ~ hBOOL(X2)
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3642]) ).
cnf(c_0_3642_3,axiom,
( ~ hBOOL(X2)
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X3))
| hBOOL(X2)
| hBOOL(X1)
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3642]) ).
cnf(c_0_3642_4,axiom,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X3))
| ~ hBOOL(X2)
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X3))
| hBOOL(X2)
| hBOOL(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3642]) ).
cnf(c_0_3643_0,axiom,
( hBOOL(X1)
| hBOOL(X2)
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X3))
| ~ hBOOL(X1)
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3643]) ).
cnf(c_0_3643_1,axiom,
( hBOOL(X2)
| hBOOL(X1)
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X3))
| ~ hBOOL(X1)
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3643]) ).
cnf(c_0_3643_2,axiom,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X3))
| hBOOL(X2)
| hBOOL(X1)
| ~ hBOOL(X1)
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3643]) ).
cnf(c_0_3643_3,axiom,
( ~ hBOOL(X1)
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X3))
| hBOOL(X2)
| hBOOL(X1)
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3643]) ).
cnf(c_0_3643_4,axiom,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X3))
| ~ hBOOL(X1)
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X3))
| hBOOL(X2)
| hBOOL(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3643]) ).
cnf(c_0_3644_0,axiom,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X1),X2))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3644]) ).
cnf(c_0_3644_1,axiom,
( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X1),X2))
| hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3644]) ).
cnf(c_0_3645_0,axiom,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X1),X2))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3645]) ).
cnf(c_0_3645_1,axiom,
( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X1),X2))
| hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3645]) ).
cnf(c_0_3646_0,axiom,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3646]) ).
cnf(c_0_3646_1,axiom,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3646]) ).
cnf(c_0_3647_0,axiom,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3647]) ).
cnf(c_0_3647_1,axiom,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3647]) ).
cnf(c_0_3648_0,axiom,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3648]) ).
cnf(c_0_3648_1,axiom,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3648]) ).
cnf(c_0_3649_0,axiom,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3649]) ).
cnf(c_0_3649_1,axiom,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3649]) ).
cnf(c_0_3650_0,axiom,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3650]) ).
cnf(c_0_3650_1,axiom,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X2))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3650]) ).
cnf(c_0_3651_0,axiom,
( hBOOL(X1)
| hBOOL(X2)
| hBOOL(X1)
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X3))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3651]) ).
cnf(c_0_3651_1,axiom,
( hBOOL(X2)
| hBOOL(X1)
| hBOOL(X1)
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X3))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3651]) ).
cnf(c_0_3651_2,axiom,
( hBOOL(X1)
| hBOOL(X2)
| hBOOL(X1)
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X3))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3651]) ).
cnf(c_0_3651_3,axiom,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X3))
| hBOOL(X1)
| hBOOL(X2)
| hBOOL(X1)
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3651]) ).
cnf(c_0_3651_4,axiom,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X3))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X3))
| hBOOL(X1)
| hBOOL(X2)
| hBOOL(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3651]) ).
cnf(c_0_3652_0,axiom,
( hBOOL(X1)
| hBOOL(X2)
| hBOOL(X2)
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X3))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3652]) ).
cnf(c_0_3652_1,axiom,
( hBOOL(X2)
| hBOOL(X1)
| hBOOL(X2)
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X3))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3652]) ).
cnf(c_0_3652_2,axiom,
( hBOOL(X2)
| hBOOL(X2)
| hBOOL(X1)
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X3))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3652]) ).
cnf(c_0_3652_3,axiom,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X3))
| hBOOL(X2)
| hBOOL(X2)
| hBOOL(X1)
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3652]) ).
cnf(c_0_3652_4,axiom,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X3))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X3))
| hBOOL(X2)
| hBOOL(X2)
| hBOOL(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3652]) ).
cnf(c_0_3656_0,axiom,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,one_one_real),sqrt(X1)))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,one_one_real),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_3656]) ).
cnf(c_0_3656_1,axiom,
( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,one_one_real),X1))
| hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,one_one_real),sqrt(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_3656]) ).
cnf(c_0_3657_0,axiom,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),sqrt(X1)))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_3657]) ).
cnf(c_0_3657_1,axiom,
( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X1))
| hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),sqrt(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_3657]) ).
cnf(c_0_3658_0,axiom,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),sqrt(X1)))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_3658]) ).
cnf(c_0_3658_1,axiom,
( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X1))
| hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),sqrt(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_3658]) ).
cnf(c_0_3659_0,axiom,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),bit1(X1)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_3659]) ).
cnf(c_0_3659_1,axiom,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X1))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),bit1(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_3659]) ).
cnf(c_0_3660_0,axiom,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),bit0(X1)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_3660]) ).
cnf(c_0_3660_1,axiom,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X1))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),bit0(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_3660]) ).
cnf(c_0_3661_0,axiom,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),bit1(X1)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_3661]) ).
cnf(c_0_3661_1,axiom,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X1))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),bit1(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_3661]) ).
cnf(c_0_3662_0,axiom,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),number_number_of_int(X1)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_3662]) ).
cnf(c_0_3662_1,axiom,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X1))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),number_number_of_int(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_3662]) ).
cnf(c_0_3663_0,axiom,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),number267125858f_real(X1)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_3663]) ).
cnf(c_0_3663_1,axiom,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X1))
| hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),number267125858f_real(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_3663]) ).
cnf(c_0_3664_0,axiom,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),sk1_esk2_1(X1)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_3664]) ).
cnf(c_0_3664_1,axiom,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X1))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),sk1_esk2_1(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_3664]) ).
cnf(c_0_3665_0,axiom,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),number_number_of_nat(X1)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_3665]) ).
cnf(c_0_3665_1,axiom,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),X1))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),number_number_of_nat(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_3665]) ).
cnf(c_0_3666_0,axiom,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),bit0(X1)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_3666]) ).
cnf(c_0_3666_1,axiom,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),X1))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),bit0(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_3666]) ).
cnf(c_0_3667_0,axiom,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),number267125858f_real(X1)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_3667]) ).
cnf(c_0_3667_1,axiom,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),X1))
| hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),number267125858f_real(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_3667]) ).
cnf(c_0_3668_0,axiom,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),number_number_of_int(X1)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_3668]) ).
cnf(c_0_3668_1,axiom,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),X1))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),number_number_of_int(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_3668]) ).
cnf(c_0_3669_0,axiom,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1))
| hBOOL(X2)
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1))
| ~ hBOOL(X3) ),
inference(literals_permutation,[status(thm)],[c_0_3669]) ).
cnf(c_0_3669_1,axiom,
( hBOOL(X2)
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1))
| ~ hBOOL(X3) ),
inference(literals_permutation,[status(thm)],[c_0_3669]) ).
cnf(c_0_3669_2,axiom,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1))
| hBOOL(X2)
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1))
| ~ hBOOL(X3) ),
inference(literals_permutation,[status(thm)],[c_0_3669]) ).
cnf(c_0_3669_3,axiom,
( ~ hBOOL(X3)
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1))
| hBOOL(X2)
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_3669]) ).
cnf(c_0_3670_0,axiom,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1))
| hBOOL(X2)
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1))
| ~ hBOOL(X3) ),
inference(literals_permutation,[status(thm)],[c_0_3670]) ).
cnf(c_0_3670_1,axiom,
( hBOOL(X2)
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1))
| ~ hBOOL(X3) ),
inference(literals_permutation,[status(thm)],[c_0_3670]) ).
cnf(c_0_3670_2,axiom,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1))
| hBOOL(X2)
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1))
| ~ hBOOL(X3) ),
inference(literals_permutation,[status(thm)],[c_0_3670]) ).
cnf(c_0_3670_3,axiom,
( ~ hBOOL(X3)
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1))
| hBOOL(X2)
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_3670]) ).
cnf(c_0_3671_0,axiom,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1))
| hBOOL(X3)
| ~ hBOOL(X2)
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_3671]) ).
cnf(c_0_3671_1,axiom,
( hBOOL(X3)
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1))
| ~ hBOOL(X2)
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_3671]) ).
cnf(c_0_3671_2,axiom,
( ~ hBOOL(X2)
| hBOOL(X3)
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_3671]) ).
cnf(c_0_3671_3,axiom,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1))
| ~ hBOOL(X2)
| hBOOL(X3)
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_3671]) ).
cnf(c_0_3672_0,axiom,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1))
| hBOOL(X3)
| ~ hBOOL(X2)
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_3672]) ).
cnf(c_0_3672_1,axiom,
( hBOOL(X3)
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1))
| ~ hBOOL(X2)
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_3672]) ).
cnf(c_0_3672_2,axiom,
( ~ hBOOL(X2)
| hBOOL(X3)
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_3672]) ).
cnf(c_0_3672_3,axiom,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1))
| ~ hBOOL(X2)
| hBOOL(X3)
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_3672]) ).
cnf(c_0_3673_0,axiom,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X1))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_3673]) ).
cnf(c_0_3673_1,axiom,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),X1))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_3673]) ).
cnf(c_0_3674_0,axiom,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),X1))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_3674]) ).
cnf(c_0_3674_1,axiom,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X1))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_3674]) ).
cnf(c_0_3675_0,axiom,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(power_power_nat(X1),number_number_of_nat(X2))))
| number_number_of_nat(X2) != zero_zero_nat ),
inference(literals_permutation,[status(thm)],[c_0_3675]) ).
cnf(c_0_3675_1,axiom,
( number_number_of_nat(X2) != zero_zero_nat
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(power_power_nat(X1),number_number_of_nat(X2)))) ),
inference(literals_permutation,[status(thm)],[c_0_3675]) ).
cnf(c_0_3676_0,axiom,
( X2 = X3
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),X1))
| hAPP_nat_int(power_power_int(X1),X2) != hAPP_nat_int(power_power_int(X1),X3) ),
inference(literals_permutation,[status(thm)],[c_0_3676]) ).
cnf(c_0_3676_1,axiom,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),X1))
| X2 = X3
| hAPP_nat_int(power_power_int(X1),X2) != hAPP_nat_int(power_power_int(X1),X3) ),
inference(literals_permutation,[status(thm)],[c_0_3676]) ).
cnf(c_0_3676_2,axiom,
( hAPP_nat_int(power_power_int(X1),X2) != hAPP_nat_int(power_power_int(X1),X3)
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),X1))
| X2 = X3 ),
inference(literals_permutation,[status(thm)],[c_0_3676]) ).
cnf(c_0_3677_0,axiom,
( X2 = X3
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,one_one_nat),X1))
| hAPP_nat_nat(power_power_nat(X1),X2) != hAPP_nat_nat(power_power_nat(X1),X3) ),
inference(literals_permutation,[status(thm)],[c_0_3677]) ).
cnf(c_0_3677_1,axiom,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,one_one_nat),X1))
| X2 = X3
| hAPP_nat_nat(power_power_nat(X1),X2) != hAPP_nat_nat(power_power_nat(X1),X3) ),
inference(literals_permutation,[status(thm)],[c_0_3677]) ).
cnf(c_0_3677_2,axiom,
( hAPP_nat_nat(power_power_nat(X1),X2) != hAPP_nat_nat(power_power_nat(X1),X3)
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,one_one_nat),X1))
| X2 = X3 ),
inference(literals_permutation,[status(thm)],[c_0_3677]) ).
cnf(c_0_3678_0,axiom,
( X2 = X3
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,one_one_real),X1))
| hAPP_nat_real(power_power_real(X1),X2) != hAPP_nat_real(power_power_real(X1),X3) ),
inference(literals_permutation,[status(thm)],[c_0_3678]) ).
cnf(c_0_3678_1,axiom,
( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,one_one_real),X1))
| X2 = X3
| hAPP_nat_real(power_power_real(X1),X2) != hAPP_nat_real(power_power_real(X1),X3) ),
inference(literals_permutation,[status(thm)],[c_0_3678]) ).
cnf(c_0_3678_2,axiom,
( hAPP_nat_real(power_power_real(X1),X2) != hAPP_nat_real(power_power_real(X1),X3)
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,one_one_real),X1))
| X2 = X3 ),
inference(literals_permutation,[status(thm)],[c_0_3678]) ).
cnf(c_0_3679_0,axiom,
( hAPP_nat_nat(plus_plus_nat(X2),sk1_esk13_2(X2,X1)) = X1
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_3679]) ).
cnf(c_0_3679_1,axiom,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X1))
| hAPP_nat_nat(plus_plus_nat(X2),sk1_esk13_2(X2,X1)) = X1 ),
inference(literals_permutation,[status(thm)],[c_0_3679]) ).
cnf(c_0_3680_0,axiom,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_nat_int(semiri1621563631at_int,X1)),zero_zero_int))
| X1 != zero_zero_nat ),
inference(literals_permutation,[status(thm)],[c_0_3680]) ).
cnf(c_0_3680_1,axiom,
( X1 != zero_zero_nat
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_nat_int(semiri1621563631at_int,X1)),zero_zero_int)) ),
inference(literals_permutation,[status(thm)],[c_0_3680]) ).
cnf(c_0_3681_0,axiom,
( hAPP_nat_nat(plus_plus_nat(X1),sk1_esk3_2(X1,X2)) = X2
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3681]) ).
cnf(c_0_3681_1,axiom,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
| hAPP_nat_nat(plus_plus_nat(X1),sk1_esk3_2(X1,X2)) = X2 ),
inference(literals_permutation,[status(thm)],[c_0_3681]) ).
cnf(c_0_3682_0,axiom,
( hBOOL(hAPP_int_bool(X1,sk1_esk7_1(X1)))
| ~ hBOOL(hAPP_int_bool(X1,hAPP_nat_int(semiri1621563631at_int,X2))) ),
inference(literals_permutation,[status(thm)],[c_0_3682]) ).
cnf(c_0_3682_1,axiom,
( ~ hBOOL(hAPP_int_bool(X1,hAPP_nat_int(semiri1621563631at_int,X2)))
| hBOOL(hAPP_int_bool(X1,sk1_esk7_1(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_3682]) ).
cnf(c_0_3683_0,axiom,
( hBOOL(hAPP_int_bool(X1,hAPP_nat_int(semiri1621563631at_int,X2)))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),sk1_esk8_1(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_3683]) ).
cnf(c_0_3683_1,axiom,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),sk1_esk8_1(X1)))
| hBOOL(hAPP_int_bool(X1,hAPP_nat_int(semiri1621563631at_int,X2))) ),
inference(literals_permutation,[status(thm)],[c_0_3683]) ).
cnf(c_0_3684_0,axiom,
( hBOOL(hAPP_nat_bool(X1,zero_zero_nat))
| hBOOL(hAPP_nat_bool(X1,sk1_esk19_2(X2,X1)))
| ~ hBOOL(hAPP_nat_bool(X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3684]) ).
cnf(c_0_3684_1,axiom,
( hBOOL(hAPP_nat_bool(X1,sk1_esk19_2(X2,X1)))
| hBOOL(hAPP_nat_bool(X1,zero_zero_nat))
| ~ hBOOL(hAPP_nat_bool(X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3684]) ).
cnf(c_0_3684_2,axiom,
( ~ hBOOL(hAPP_nat_bool(X1,X2))
| hBOOL(hAPP_nat_bool(X1,sk1_esk19_2(X2,X1)))
| hBOOL(hAPP_nat_bool(X1,zero_zero_nat)) ),
inference(literals_permutation,[status(thm)],[c_0_3684]) ).
cnf(c_0_3685_0,axiom,
( hAPP_nat_nat(plus_plus_nat(number_number_of_nat(X1)),number_number_of_nat(X2)) = number_number_of_nat(X2)
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),pls)) ),
inference(literals_permutation,[status(thm)],[c_0_3685]) ).
cnf(c_0_3685_1,axiom,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),pls))
| hAPP_nat_nat(plus_plus_nat(number_number_of_nat(X1)),number_number_of_nat(X2)) = number_number_of_nat(X2) ),
inference(literals_permutation,[status(thm)],[c_0_3685]) ).
cnf(c_0_3696_0,axiom,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X2))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X2),X1))
| X2 = X1 ),
inference(literals_permutation,[status(thm)],[c_0_3696]) ).
cnf(c_0_3696_1,axiom,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X2),X1))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X2))
| X2 = X1 ),
inference(literals_permutation,[status(thm)],[c_0_3696]) ).
cnf(c_0_3696_2,axiom,
( X2 = X1
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X2),X1))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3696]) ).
cnf(c_0_3697_0,axiom,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X1),X2))
| hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X2),X1))
| X2 = X1 ),
inference(literals_permutation,[status(thm)],[c_0_3697]) ).
cnf(c_0_3697_1,axiom,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X2),X1))
| hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X1),X2))
| X2 = X1 ),
inference(literals_permutation,[status(thm)],[c_0_3697]) ).
cnf(c_0_3697_2,axiom,
( X2 = X1
| hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X2),X1))
| hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3697]) ).
cnf(c_0_3698_0,axiom,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X2),X1))
| X2 = X1 ),
inference(literals_permutation,[status(thm)],[c_0_3698]) ).
cnf(c_0_3698_1,axiom,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X2),X1))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
| X2 = X1 ),
inference(literals_permutation,[status(thm)],[c_0_3698]) ).
cnf(c_0_3698_2,axiom,
( X2 = X1
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X2),X1))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3698]) ).
cnf(c_0_3700_0,axiom,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X2),X1))
| X2 = X1 ),
inference(literals_permutation,[status(thm)],[c_0_3700]) ).
cnf(c_0_3700_1,axiom,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X2),X1))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
| X2 = X1 ),
inference(literals_permutation,[status(thm)],[c_0_3700]) ).
cnf(c_0_3700_2,axiom,
( X2 = X1
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X2),X1))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3700]) ).
cnf(c_0_3702_0,axiom,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X2))
| X2 = X1
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X2),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_3702]) ).
cnf(c_0_3702_1,axiom,
( X2 = X1
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X2))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X2),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_3702]) ).
cnf(c_0_3702_2,axiom,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X2),X1))
| X2 = X1
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3702]) ).
cnf(c_0_3703_0,axiom,
( hAPP_nat_int(power_power_int(X1),X2) = hAPP_nat_int(power_power_int(X1),X3)
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),X1))
| X2 != X3 ),
inference(literals_permutation,[status(thm)],[c_0_3703]) ).
cnf(c_0_3703_1,axiom,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),X1))
| hAPP_nat_int(power_power_int(X1),X2) = hAPP_nat_int(power_power_int(X1),X3)
| X2 != X3 ),
inference(literals_permutation,[status(thm)],[c_0_3703]) ).
cnf(c_0_3703_2,axiom,
( X2 != X3
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),X1))
| hAPP_nat_int(power_power_int(X1),X2) = hAPP_nat_int(power_power_int(X1),X3) ),
inference(literals_permutation,[status(thm)],[c_0_3703]) ).
cnf(c_0_3704_0,axiom,
( hAPP_nat_nat(power_power_nat(X1),X2) = hAPP_nat_nat(power_power_nat(X1),X3)
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,one_one_nat),X1))
| X2 != X3 ),
inference(literals_permutation,[status(thm)],[c_0_3704]) ).
cnf(c_0_3704_1,axiom,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,one_one_nat),X1))
| hAPP_nat_nat(power_power_nat(X1),X2) = hAPP_nat_nat(power_power_nat(X1),X3)
| X2 != X3 ),
inference(literals_permutation,[status(thm)],[c_0_3704]) ).
cnf(c_0_3704_2,axiom,
( X2 != X3
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,one_one_nat),X1))
| hAPP_nat_nat(power_power_nat(X1),X2) = hAPP_nat_nat(power_power_nat(X1),X3) ),
inference(literals_permutation,[status(thm)],[c_0_3704]) ).
cnf(c_0_3705_0,axiom,
( hAPP_nat_real(power_power_real(X1),X2) = hAPP_nat_real(power_power_real(X1),X3)
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,one_one_real),X1))
| X2 != X3 ),
inference(literals_permutation,[status(thm)],[c_0_3705]) ).
cnf(c_0_3705_1,axiom,
( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,one_one_real),X1))
| hAPP_nat_real(power_power_real(X1),X2) = hAPP_nat_real(power_power_real(X1),X3)
| X2 != X3 ),
inference(literals_permutation,[status(thm)],[c_0_3705]) ).
cnf(c_0_3705_2,axiom,
( X2 != X3
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,one_one_real),X1))
| hAPP_nat_real(power_power_real(X1),X2) = hAPP_nat_real(power_power_real(X1),X3) ),
inference(literals_permutation,[status(thm)],[c_0_3705]) ).
cnf(c_0_3706_0,axiom,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X2),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_3706]) ).
cnf(c_0_3706_1,axiom,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X2),X1))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3706]) ).
cnf(c_0_3707_0,axiom,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_3707]) ).
cnf(c_0_3707_1,axiom,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X1))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3707]) ).
cnf(c_0_3708_0,axiom,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X1),X2))
| hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X2),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_3708]) ).
cnf(c_0_3708_1,axiom,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X2),X1))
| hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3708]) ).
cnf(c_0_3709_0,axiom,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X1),X2))
| hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X2),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_3709]) ).
cnf(c_0_3709_1,axiom,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X2),X1))
| hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3709]) ).
cnf(c_0_3712_0,axiom,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_3712]) ).
cnf(c_0_3712_1,axiom,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X1))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3712]) ).
cnf(c_0_3713_0,axiom,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X2),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_3713]) ).
cnf(c_0_3713_1,axiom,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X2),X1))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3713]) ).
cnf(c_0_3714_0,axiom,
( hAPP_nat_int(semiri1621563631at_int,number_number_of_nat(X1)) = number_number_of_int(X1)
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),number_number_of_int(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_3714]) ).
cnf(c_0_3714_1,axiom,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),number_number_of_int(X1)))
| hAPP_nat_int(semiri1621563631at_int,number_number_of_nat(X1)) = number_number_of_int(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3714]) ).
cnf(c_0_3715_0,axiom,
( hAPP_nat_real(semiri132038758t_real,number_number_of_nat(X1)) = number267125858f_real(X1)
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),number_number_of_int(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_3715]) ).
cnf(c_0_3715_1,axiom,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),number_number_of_int(X1)))
| hAPP_nat_real(semiri132038758t_real,number_number_of_nat(X1)) = number267125858f_real(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3715]) ).
cnf(c_0_3716_0,axiom,
( hAPP_int_int(plus_plus_int(number_number_of_int(X1)),one_one_int) = number_number_of_int(succ(X1))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_3716]) ).
cnf(c_0_3716_1,axiom,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X1))
| hAPP_int_int(plus_plus_int(number_number_of_int(X1)),one_one_int) = number_number_of_int(succ(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_3716]) ).
cnf(c_0_3717_0,axiom,
( hAPP_nat_nat(plus_plus_nat(number_number_of_nat(X1)),one_one_nat) = number_number_of_nat(succ(X1))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_3717]) ).
cnf(c_0_3717_1,axiom,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X1))
| hAPP_nat_nat(plus_plus_nat(number_number_of_nat(X1)),one_one_nat) = number_number_of_nat(succ(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_3717]) ).
cnf(c_0_3718_0,axiom,
( hAPP_real_real(plus_plus_real(number267125858f_real(X1)),one_one_real) = number267125858f_real(succ(X1))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_3718]) ).
cnf(c_0_3718_1,axiom,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X1))
| hAPP_real_real(plus_plus_real(number267125858f_real(X1)),one_one_real) = number267125858f_real(succ(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_3718]) ).
cnf(c_0_3719_0,axiom,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),hAPP_int_int(plus_plus_int(X2),one_one_int)))
| X1 != X2 ),
inference(literals_permutation,[status(thm)],[c_0_3719]) ).
cnf(c_0_3719_1,axiom,
( X1 != X2
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),hAPP_int_int(plus_plus_int(X2),one_one_int))) ),
inference(literals_permutation,[status(thm)],[c_0_3719]) ).
cnf(c_0_3720_0,axiom,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(power_power_nat(X1),X2)))
| X2 != zero_zero_nat ),
inference(literals_permutation,[status(thm)],[c_0_3720]) ).
cnf(c_0_3720_1,axiom,
( X2 != zero_zero_nat
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(power_power_nat(X1),X2))) ),
inference(literals_permutation,[status(thm)],[c_0_3720]) ).
cnf(c_0_3721_0,axiom,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(power_power_nat(X1),X2)))
| X2 != zero_zero_nat ),
inference(literals_permutation,[status(thm)],[c_0_3721]) ).
cnf(c_0_3721_1,axiom,
( X2 != zero_zero_nat
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(power_power_nat(X1),X2))) ),
inference(literals_permutation,[status(thm)],[c_0_3721]) ).
cnf(c_0_3725_0,axiom,
( hAPP_nat_nat(plus_plus_nat(number_number_of_nat(X1)),one_one_nat) = one_one_nat
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),pls)) ),
inference(literals_permutation,[status(thm)],[c_0_3725]) ).
cnf(c_0_3725_1,axiom,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),pls))
| hAPP_nat_nat(plus_plus_nat(number_number_of_nat(X1)),one_one_nat) = one_one_nat ),
inference(literals_permutation,[status(thm)],[c_0_3725]) ).
cnf(c_0_3726_0,axiom,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2))
| X2 != hAPP_int_int(plus_plus_int(X1),hAPP_nat_int(semiri1621563631at_int,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3726]) ).
cnf(c_0_3726_1,axiom,
( X2 != hAPP_int_int(plus_plus_int(X1),hAPP_nat_int(semiri1621563631at_int,X3))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3726]) ).
cnf(c_0_3727_0,axiom,
( hAPP_int_int(plus_plus_int(one_one_int),number_number_of_int(X1)) = number_number_of_int(succ(X1))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_3727]) ).
cnf(c_0_3727_1,axiom,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X1))
| hAPP_int_int(plus_plus_int(one_one_int),number_number_of_int(X1)) = number_number_of_int(succ(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_3727]) ).
cnf(c_0_3728_0,axiom,
( hAPP_nat_nat(plus_plus_nat(one_one_nat),number_number_of_nat(X1)) = number_number_of_nat(succ(X1))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_3728]) ).
cnf(c_0_3728_1,axiom,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X1))
| hAPP_nat_nat(plus_plus_nat(one_one_nat),number_number_of_nat(X1)) = number_number_of_nat(succ(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_3728]) ).
cnf(c_0_3729_0,axiom,
( hAPP_real_real(plus_plus_real(one_one_real),number267125858f_real(X1)) = number267125858f_real(succ(X1))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_3729]) ).
cnf(c_0_3729_1,axiom,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X1))
| hAPP_real_real(plus_plus_real(one_one_real),number267125858f_real(X1)) = number267125858f_real(succ(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_3729]) ).
cnf(c_0_3730_0,axiom,
( hBOOL(hAPP_int_bool(X1,hAPP_nat_int(semiri1621563631at_int,X2)))
| ~ hBOOL(hAPP_int_bool(X1,sk1_esk8_1(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_3730]) ).
cnf(c_0_3730_1,axiom,
( ~ hBOOL(hAPP_int_bool(X1,sk1_esk8_1(X1)))
| hBOOL(hAPP_int_bool(X1,hAPP_nat_int(semiri1621563631at_int,X2))) ),
inference(literals_permutation,[status(thm)],[c_0_3730]) ).
cnf(c_0_3736_0,axiom,
( hAPP_nat_nat(plus_plus_nat(one_one_nat),number_number_of_nat(X1)) = one_one_nat
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),pls)) ),
inference(literals_permutation,[status(thm)],[c_0_3736]) ).
cnf(c_0_3736_1,axiom,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),pls))
| hAPP_nat_nat(plus_plus_nat(one_one_nat),number_number_of_nat(X1)) = one_one_nat ),
inference(literals_permutation,[status(thm)],[c_0_3736]) ).
cnf(c_0_3737_0,axiom,
( hBOOL(X1)
| ~ hBOOL(X1)
| ~ hBOOL(X2)
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X3))
| ~ hBOOL(X2) ),
inference(literals_permutation,[status(thm)],[c_0_3737]) ).
cnf(c_0_3737_1,axiom,
( ~ hBOOL(X1)
| hBOOL(X1)
| ~ hBOOL(X2)
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X3))
| ~ hBOOL(X2) ),
inference(literals_permutation,[status(thm)],[c_0_3737]) ).
cnf(c_0_3737_2,axiom,
( ~ hBOOL(X2)
| ~ hBOOL(X1)
| hBOOL(X1)
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X3))
| ~ hBOOL(X2) ),
inference(literals_permutation,[status(thm)],[c_0_3737]) ).
cnf(c_0_3737_3,axiom,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X3))
| ~ hBOOL(X2)
| ~ hBOOL(X1)
| hBOOL(X1)
| ~ hBOOL(X2) ),
inference(literals_permutation,[status(thm)],[c_0_3737]) ).
cnf(c_0_3737_4,axiom,
( ~ hBOOL(X2)
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X3))
| ~ hBOOL(X2)
| ~ hBOOL(X1)
| hBOOL(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3737]) ).
cnf(c_0_3738_0,axiom,
( hBOOL(X2)
| ~ hBOOL(X1)
| ~ hBOOL(X2)
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X3))
| ~ hBOOL(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3738]) ).
cnf(c_0_3738_1,axiom,
( ~ hBOOL(X1)
| hBOOL(X2)
| ~ hBOOL(X2)
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X3))
| ~ hBOOL(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3738]) ).
cnf(c_0_3738_2,axiom,
( ~ hBOOL(X2)
| ~ hBOOL(X1)
| hBOOL(X2)
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X3))
| ~ hBOOL(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3738]) ).
cnf(c_0_3738_3,axiom,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X3))
| ~ hBOOL(X2)
| ~ hBOOL(X1)
| hBOOL(X2)
| ~ hBOOL(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3738]) ).
cnf(c_0_3738_4,axiom,
( ~ hBOOL(X1)
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X3))
| ~ hBOOL(X2)
| ~ hBOOL(X1)
| hBOOL(X2) ),
inference(literals_permutation,[status(thm)],[c_0_3738]) ).
cnf(c_0_3739_0,axiom,
( hBOOL(X1)
| ~ hBOOL(X1)
| ~ hBOOL(X2)
| ~ hBOOL(X2)
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3739]) ).
cnf(c_0_3739_1,axiom,
( ~ hBOOL(X1)
| hBOOL(X1)
| ~ hBOOL(X2)
| ~ hBOOL(X2)
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3739]) ).
cnf(c_0_3739_2,axiom,
( ~ hBOOL(X2)
| ~ hBOOL(X1)
| hBOOL(X1)
| ~ hBOOL(X2)
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3739]) ).
cnf(c_0_3739_3,axiom,
( ~ hBOOL(X2)
| ~ hBOOL(X2)
| ~ hBOOL(X1)
| hBOOL(X1)
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3739]) ).
cnf(c_0_3739_4,axiom,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X3))
| ~ hBOOL(X2)
| ~ hBOOL(X2)
| ~ hBOOL(X1)
| hBOOL(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3739]) ).
cnf(c_0_3740_0,axiom,
( hBOOL(X2)
| ~ hBOOL(X1)
| ~ hBOOL(X2)
| ~ hBOOL(X1)
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3740]) ).
cnf(c_0_3740_1,axiom,
( ~ hBOOL(X1)
| hBOOL(X2)
| ~ hBOOL(X2)
| ~ hBOOL(X1)
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3740]) ).
cnf(c_0_3740_2,axiom,
( ~ hBOOL(X2)
| ~ hBOOL(X1)
| hBOOL(X2)
| ~ hBOOL(X1)
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3740]) ).
cnf(c_0_3740_3,axiom,
( ~ hBOOL(X1)
| ~ hBOOL(X2)
| ~ hBOOL(X1)
| hBOOL(X2)
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3740]) ).
cnf(c_0_3740_4,axiom,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X3))
| ~ hBOOL(X1)
| ~ hBOOL(X2)
| ~ hBOOL(X1)
| hBOOL(X2) ),
inference(literals_permutation,[status(thm)],[c_0_3740]) ).
cnf(c_0_3742_0,axiom,
( hBOOL(X1)
| hBOOL(X2)
| hBOOL(X1)
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X3))
| ~ hBOOL(X2) ),
inference(literals_permutation,[status(thm)],[c_0_3742]) ).
cnf(c_0_3742_1,axiom,
( hBOOL(X2)
| hBOOL(X1)
| hBOOL(X1)
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X3))
| ~ hBOOL(X2) ),
inference(literals_permutation,[status(thm)],[c_0_3742]) ).
cnf(c_0_3742_2,axiom,
( hBOOL(X1)
| hBOOL(X2)
| hBOOL(X1)
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X3))
| ~ hBOOL(X2) ),
inference(literals_permutation,[status(thm)],[c_0_3742]) ).
cnf(c_0_3742_3,axiom,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X3))
| hBOOL(X1)
| hBOOL(X2)
| hBOOL(X1)
| ~ hBOOL(X2) ),
inference(literals_permutation,[status(thm)],[c_0_3742]) ).
cnf(c_0_3742_4,axiom,
( ~ hBOOL(X2)
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X3))
| hBOOL(X1)
| hBOOL(X2)
| hBOOL(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3742]) ).
cnf(c_0_3743_0,axiom,
( hBOOL(X1)
| hBOOL(X2)
| hBOOL(X2)
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X3))
| ~ hBOOL(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3743]) ).
cnf(c_0_3743_1,axiom,
( hBOOL(X2)
| hBOOL(X1)
| hBOOL(X2)
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X3))
| ~ hBOOL(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3743]) ).
cnf(c_0_3743_2,axiom,
( hBOOL(X2)
| hBOOL(X2)
| hBOOL(X1)
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X3))
| ~ hBOOL(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3743]) ).
cnf(c_0_3743_3,axiom,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X3))
| hBOOL(X2)
| hBOOL(X2)
| hBOOL(X1)
| ~ hBOOL(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3743]) ).
cnf(c_0_3743_4,axiom,
( ~ hBOOL(X1)
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X3))
| hBOOL(X2)
| hBOOL(X2)
| hBOOL(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3743]) ).
cnf(c_0_3744_0,axiom,
( hBOOL(X1)
| hBOOL(X2)
| hBOOL(X1)
| ~ hBOOL(X2)
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3744]) ).
cnf(c_0_3744_1,axiom,
( hBOOL(X2)
| hBOOL(X1)
| hBOOL(X1)
| ~ hBOOL(X2)
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3744]) ).
cnf(c_0_3744_2,axiom,
( hBOOL(X1)
| hBOOL(X2)
| hBOOL(X1)
| ~ hBOOL(X2)
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3744]) ).
cnf(c_0_3744_3,axiom,
( ~ hBOOL(X2)
| hBOOL(X1)
| hBOOL(X2)
| hBOOL(X1)
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3744]) ).
cnf(c_0_3744_4,axiom,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X3))
| ~ hBOOL(X2)
| hBOOL(X1)
| hBOOL(X2)
| hBOOL(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3744]) ).
cnf(c_0_3745_0,axiom,
( hBOOL(X1)
| hBOOL(X2)
| hBOOL(X2)
| ~ hBOOL(X1)
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3745]) ).
cnf(c_0_3745_1,axiom,
( hBOOL(X2)
| hBOOL(X1)
| hBOOL(X2)
| ~ hBOOL(X1)
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3745]) ).
cnf(c_0_3745_2,axiom,
( hBOOL(X2)
| hBOOL(X2)
| hBOOL(X1)
| ~ hBOOL(X1)
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3745]) ).
cnf(c_0_3745_3,axiom,
( ~ hBOOL(X1)
| hBOOL(X2)
| hBOOL(X2)
| hBOOL(X1)
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3745]) ).
cnf(c_0_3745_4,axiom,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X3))
| ~ hBOOL(X1)
| hBOOL(X2)
| hBOOL(X2)
| hBOOL(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3745]) ).
cnf(c_0_3749_0,axiom,
( hAPP_nat_int(semiri1621563631at_int,sk1_esk15_1(X1)) = X1
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_3749]) ).
cnf(c_0_3749_1,axiom,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1))
| hAPP_nat_int(semiri1621563631at_int,sk1_esk15_1(X1)) = X1 ),
inference(literals_permutation,[status(thm)],[c_0_3749]) ).
cnf(c_0_3750_0,axiom,
( hAPP_nat_int(semiri1621563631at_int,sk1_esk12_1(X1)) = X1
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_3750]) ).
cnf(c_0_3750_1,axiom,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1))
| hAPP_nat_int(semiri1621563631at_int,sk1_esk12_1(X1)) = X1 ),
inference(literals_permutation,[status(thm)],[c_0_3750]) ).
cnf(c_0_3751_0,axiom,
( hAPP_nat_int(semiri1621563631at_int,sk1_esk11_1(X1)) = X1
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_3751]) ).
cnf(c_0_3751_1,axiom,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1))
| hAPP_nat_int(semiri1621563631at_int,sk1_esk11_1(X1)) = X1 ),
inference(literals_permutation,[status(thm)],[c_0_3751]) ).
cnf(c_0_3752_0,axiom,
( hAPP_nat_int(semiri1621563631at_int,sk1_esk2_1(X1)) = X1
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_3752]) ).
cnf(c_0_3752_1,axiom,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X1))
| hAPP_nat_int(semiri1621563631at_int,sk1_esk2_1(X1)) = X1 ),
inference(literals_permutation,[status(thm)],[c_0_3752]) ).
cnf(c_0_3760_0,axiom,
( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X1),X2))
| X1 != X2 ),
inference(literals_permutation,[status(thm)],[c_0_3760]) ).
cnf(c_0_3760_1,axiom,
( X1 != X2
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3760]) ).
cnf(c_0_3761_0,axiom,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
| X1 != X2 ),
inference(literals_permutation,[status(thm)],[c_0_3761]) ).
cnf(c_0_3761_1,axiom,
( X1 != X2
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3761]) ).
cnf(c_0_3762_0,axiom,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X2))
| X1 != X2 ),
inference(literals_permutation,[status(thm)],[c_0_3762]) ).
cnf(c_0_3762_1,axiom,
( X1 != X2
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3762]) ).
cnf(c_0_3763_0,axiom,
( X1 != X2
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3763]) ).
cnf(c_0_3763_1,axiom,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
| X1 != X2 ),
inference(literals_permutation,[status(thm)],[c_0_3763]) ).
cnf(c_0_3764_0,axiom,
( X1 != X2
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X2),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_3764]) ).
cnf(c_0_3764_1,axiom,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X2),X1))
| X1 != X2 ),
inference(literals_permutation,[status(thm)],[c_0_3764]) ).
cnf(c_0_3765_0,axiom,
( X1 != X2
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3765]) ).
cnf(c_0_3765_1,axiom,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
| X1 != X2 ),
inference(literals_permutation,[status(thm)],[c_0_3765]) ).
cnf(c_0_3766_0,axiom,
( X1 != X2
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X2),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_3766]) ).
cnf(c_0_3766_1,axiom,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X2),X1))
| X1 != X2 ),
inference(literals_permutation,[status(thm)],[c_0_3766]) ).
cnf(c_0_3767_0,axiom,
( X1 != zero_zero_nat
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X2),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_3767]) ).
cnf(c_0_3767_1,axiom,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X2),X1))
| X1 != zero_zero_nat ),
inference(literals_permutation,[status(thm)],[c_0_3767]) ).
cnf(c_0_3770_0,axiom,
( number_number_of_nat(X1) = zero_zero_nat
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),pls)) ),
inference(literals_permutation,[status(thm)],[c_0_3770]) ).
cnf(c_0_3770_1,axiom,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),pls))
| number_number_of_nat(X1) = zero_zero_nat ),
inference(literals_permutation,[status(thm)],[c_0_3770]) ).
cnf(c_0_3771_0,axiom,
( number_number_of_nat(X1) = zero_zero_nat
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),pls)) ),
inference(literals_permutation,[status(thm)],[c_0_3771]) ).
cnf(c_0_3771_1,axiom,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),pls))
| number_number_of_nat(X1) = zero_zero_nat ),
inference(literals_permutation,[status(thm)],[c_0_3771]) ).
cnf(c_0_3772_0,axiom,
( sqrt(X1) != zero_zero_real
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_3772]) ).
cnf(c_0_3772_1,axiom,
( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X1))
| sqrt(X1) != zero_zero_real ),
inference(literals_permutation,[status(thm)],[c_0_3772]) ).
cnf(c_0_3784_0,axiom,
( X1 = zero_zero_nat
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),zero_zero_nat)) ),
inference(literals_permutation,[status(thm)],[c_0_3784]) ).
cnf(c_0_3784_1,axiom,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),zero_zero_nat))
| X1 = zero_zero_nat ),
inference(literals_permutation,[status(thm)],[c_0_3784]) ).
cnf(c_0_3796_0,axiom,
( hAPP_nat_nat(plus_plus_nat(number_number_of_nat(X1)),one_one_nat) = number_number_of_nat(succ(X1))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),pls)) ),
inference(literals_permutation,[status(thm)],[c_0_3796]) ).
cnf(c_0_3796_1,axiom,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),pls))
| hAPP_nat_nat(plus_plus_nat(number_number_of_nat(X1)),one_one_nat) = number_number_of_nat(succ(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_3796]) ).
cnf(c_0_3797_0,axiom,
( X1 != zero_zero_nat
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_3797]) ).
cnf(c_0_3797_1,axiom,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1))
| X1 != zero_zero_nat ),
inference(literals_permutation,[status(thm)],[c_0_3797]) ).
cnf(c_0_3798_0,axiom,
( hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(if_nat(X2,X1),X3)) = hAPP_nat_int(semiri1621563631at_int,X1)
| ~ hBOOL(X2) ),
inference(literals_permutation,[status(thm)],[c_0_3798]) ).
cnf(c_0_3798_1,axiom,
( ~ hBOOL(X2)
| hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(if_nat(X2,X1),X3)) = hAPP_nat_int(semiri1621563631at_int,X1) ),
inference(literals_permutation,[status(thm)],[c_0_3798]) ).
cnf(c_0_3799_0,axiom,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
| X2 != hAPP_nat_nat(plus_plus_nat(X1),X3) ),
inference(literals_permutation,[status(thm)],[c_0_3799]) ).
cnf(c_0_3799_1,axiom,
( X2 != hAPP_nat_nat(plus_plus_nat(X1),X3)
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3799]) ).
cnf(c_0_3800_0,axiom,
( hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(if_nat(X2,X3),X1)) = hAPP_nat_int(semiri1621563631at_int,X1)
| hBOOL(X2) ),
inference(literals_permutation,[status(thm)],[c_0_3800]) ).
cnf(c_0_3800_1,axiom,
( hBOOL(X2)
| hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(if_nat(X2,X3),X1)) = hAPP_nat_int(semiri1621563631at_int,X1) ),
inference(literals_permutation,[status(thm)],[c_0_3800]) ).
cnf(c_0_3801_0,axiom,
( hAPP_nat_nat(plus_plus_nat(one_one_nat),number_number_of_nat(X1)) = number_number_of_nat(succ(X1))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),pls)) ),
inference(literals_permutation,[status(thm)],[c_0_3801]) ).
cnf(c_0_3801_1,axiom,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),pls))
| hAPP_nat_nat(plus_plus_nat(one_one_nat),number_number_of_nat(X1)) = number_number_of_nat(succ(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_3801]) ).
cnf(c_0_3810_0,axiom,
( hAPP_nat_int(semiri1621563631at_int,number_number_of_nat(X1)) = zero_zero_int
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),number_number_of_int(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_3810]) ).
cnf(c_0_3810_1,axiom,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),number_number_of_int(X1)))
| hAPP_nat_int(semiri1621563631at_int,number_number_of_nat(X1)) = zero_zero_int ),
inference(literals_permutation,[status(thm)],[c_0_3810]) ).
cnf(c_0_3811_0,axiom,
( hAPP_nat_real(semiri132038758t_real,number_number_of_nat(X1)) = zero_zero_real
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),number_number_of_int(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_3811]) ).
cnf(c_0_3811_1,axiom,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),number_number_of_int(X1)))
| hAPP_nat_real(semiri132038758t_real,number_number_of_nat(X1)) = zero_zero_real ),
inference(literals_permutation,[status(thm)],[c_0_3811]) ).
cnf(c_0_3814_0,axiom,
( X1 = zero_zero_real
| hAPP_nat_real(power_power_real(X1),number_number_of_nat(bit0(bit1(pls)))) != zero_zero_real ),
inference(literals_permutation,[status(thm)],[c_0_3814]) ).
cnf(c_0_3814_1,axiom,
( hAPP_nat_real(power_power_real(X1),number_number_of_nat(bit0(bit1(pls)))) != zero_zero_real
| X1 = zero_zero_real ),
inference(literals_permutation,[status(thm)],[c_0_3814]) ).
cnf(c_0_3815_0,axiom,
( X1 = zero_zero_int
| hAPP_nat_int(power_power_int(X1),number_number_of_nat(bit0(bit1(pls)))) != zero_zero_int ),
inference(literals_permutation,[status(thm)],[c_0_3815]) ).
cnf(c_0_3815_1,axiom,
( hAPP_nat_int(power_power_int(X1),number_number_of_nat(bit0(bit1(pls)))) != zero_zero_int
| X1 = zero_zero_int ),
inference(literals_permutation,[status(thm)],[c_0_3815]) ).
cnf(c_0_3824_0,axiom,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),pls))
| number_number_of_nat(X1) != zero_zero_nat ),
inference(literals_permutation,[status(thm)],[c_0_3824]) ).
cnf(c_0_3824_1,axiom,
( number_number_of_nat(X1) != zero_zero_nat
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),pls)) ),
inference(literals_permutation,[status(thm)],[c_0_3824]) ).
cnf(c_0_3825_0,axiom,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),pls))
| number_number_of_nat(X1) != zero_zero_nat ),
inference(literals_permutation,[status(thm)],[c_0_3825]) ).
cnf(c_0_3825_1,axiom,
( number_number_of_nat(X1) != zero_zero_nat
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),pls)) ),
inference(literals_permutation,[status(thm)],[c_0_3825]) ).
cnf(c_0_3826_0,axiom,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2))
| X1 != X2 ),
inference(literals_permutation,[status(thm)],[c_0_3826]) ).
cnf(c_0_3826_1,axiom,
( X1 != X2
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3826]) ).
cnf(c_0_3827_0,axiom,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X1),X2))
| X1 != X2 ),
inference(literals_permutation,[status(thm)],[c_0_3827]) ).
cnf(c_0_3827_1,axiom,
( X1 != X2
| hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3827]) ).
cnf(c_0_3828_0,axiom,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
| X1 != X2 ),
inference(literals_permutation,[status(thm)],[c_0_3828]) ).
cnf(c_0_3828_1,axiom,
( X1 != X2
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3828]) ).
cnf(c_0_3829_0,axiom,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
| X1 != X2 ),
inference(literals_permutation,[status(thm)],[c_0_3829]) ).
cnf(c_0_3829_1,axiom,
( X1 != X2
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3829]) ).
cnf(c_0_3830_0,axiom,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
| X1 != X2 ),
inference(literals_permutation,[status(thm)],[c_0_3830]) ).
cnf(c_0_3830_1,axiom,
( X1 != X2
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3830]) ).
cnf(c_0_3842_0,axiom,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),zero_zero_nat))
| X1 != zero_zero_nat ),
inference(literals_permutation,[status(thm)],[c_0_3842]) ).
cnf(c_0_3842_1,axiom,
( X1 != zero_zero_nat
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),zero_zero_nat)) ),
inference(literals_permutation,[status(thm)],[c_0_3842]) ).
cnf(c_0_3843_0,axiom,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1))
| X1 = zero_zero_nat ),
inference(literals_permutation,[status(thm)],[c_0_3843]) ).
cnf(c_0_3843_1,axiom,
( X1 = zero_zero_nat
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_3843]) ).
cnf(c_0_3844_0,axiom,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1))
| X1 = zero_zero_nat ),
inference(literals_permutation,[status(thm)],[c_0_3844]) ).
cnf(c_0_3844_1,axiom,
( X1 = zero_zero_nat
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_3844]) ).
cnf(c_0_3861_0,axiom,
( X1 = X2
| hAPP_int_int(plus_plus_int(X3),X1) != hAPP_int_int(plus_plus_int(X3),X2) ),
inference(literals_permutation,[status(thm)],[c_0_3861]) ).
cnf(c_0_3861_1,axiom,
( hAPP_int_int(plus_plus_int(X3),X1) != hAPP_int_int(plus_plus_int(X3),X2)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_3861]) ).
cnf(c_0_3862_0,axiom,
( X1 = X2
| hAPP_nat_nat(plus_plus_nat(X3),X1) != hAPP_nat_nat(plus_plus_nat(X3),X2) ),
inference(literals_permutation,[status(thm)],[c_0_3862]) ).
cnf(c_0_3862_1,axiom,
( hAPP_nat_nat(plus_plus_nat(X3),X1) != hAPP_nat_nat(plus_plus_nat(X3),X2)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_3862]) ).
cnf(c_0_3863_0,axiom,
( X1 = X2
| hAPP_real_real(plus_plus_real(X3),X1) != hAPP_real_real(plus_plus_real(X3),X2) ),
inference(literals_permutation,[status(thm)],[c_0_3863]) ).
cnf(c_0_3863_1,axiom,
( hAPP_real_real(plus_plus_real(X3),X1) != hAPP_real_real(plus_plus_real(X3),X2)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_3863]) ).
cnf(c_0_3864_0,axiom,
( X1 = X2
| hAPP_int_int(plus_plus_int(X1),X3) != hAPP_int_int(plus_plus_int(X2),X3) ),
inference(literals_permutation,[status(thm)],[c_0_3864]) ).
cnf(c_0_3864_1,axiom,
( hAPP_int_int(plus_plus_int(X1),X3) != hAPP_int_int(plus_plus_int(X2),X3)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_3864]) ).
cnf(c_0_3865_0,axiom,
( X1 = X2
| hAPP_nat_nat(plus_plus_nat(X1),X3) != hAPP_nat_nat(plus_plus_nat(X2),X3) ),
inference(literals_permutation,[status(thm)],[c_0_3865]) ).
cnf(c_0_3865_1,axiom,
( hAPP_nat_nat(plus_plus_nat(X1),X3) != hAPP_nat_nat(plus_plus_nat(X2),X3)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_3865]) ).
cnf(c_0_3866_0,axiom,
( X1 = X2
| hAPP_real_real(plus_plus_real(X1),X3) != hAPP_real_real(plus_plus_real(X2),X3) ),
inference(literals_permutation,[status(thm)],[c_0_3866]) ).
cnf(c_0_3866_1,axiom,
( hAPP_real_real(plus_plus_real(X1),X3) != hAPP_real_real(plus_plus_real(X2),X3)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_3866]) ).
cnf(c_0_3867_0,axiom,
( X1 = X2
| hAPP_int_int(plus_plus_int(X3),X1) != hAPP_int_int(plus_plus_int(X3),X2) ),
inference(literals_permutation,[status(thm)],[c_0_3867]) ).
cnf(c_0_3867_1,axiom,
( hAPP_int_int(plus_plus_int(X3),X1) != hAPP_int_int(plus_plus_int(X3),X2)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_3867]) ).
cnf(c_0_3868_0,axiom,
( X1 = X2
| hAPP_nat_nat(plus_plus_nat(X3),X1) != hAPP_nat_nat(plus_plus_nat(X3),X2) ),
inference(literals_permutation,[status(thm)],[c_0_3868]) ).
cnf(c_0_3868_1,axiom,
( hAPP_nat_nat(plus_plus_nat(X3),X1) != hAPP_nat_nat(plus_plus_nat(X3),X2)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_3868]) ).
cnf(c_0_3869_0,axiom,
( X1 = X2
| hAPP_real_real(plus_plus_real(X3),X1) != hAPP_real_real(plus_plus_real(X3),X2) ),
inference(literals_permutation,[status(thm)],[c_0_3869]) ).
cnf(c_0_3869_1,axiom,
( hAPP_real_real(plus_plus_real(X3),X1) != hAPP_real_real(plus_plus_real(X3),X2)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_3869]) ).
cnf(c_0_3870_0,axiom,
( X1 = X2
| hAPP_int_int(plus_plus_int(X3),X1) != hAPP_int_int(plus_plus_int(X3),X2) ),
inference(literals_permutation,[status(thm)],[c_0_3870]) ).
cnf(c_0_3870_1,axiom,
( hAPP_int_int(plus_plus_int(X3),X1) != hAPP_int_int(plus_plus_int(X3),X2)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_3870]) ).
cnf(c_0_3871_0,axiom,
( X1 = X2
| hAPP_nat_nat(plus_plus_nat(X3),X1) != hAPP_nat_nat(plus_plus_nat(X3),X2) ),
inference(literals_permutation,[status(thm)],[c_0_3871]) ).
cnf(c_0_3871_1,axiom,
( hAPP_nat_nat(plus_plus_nat(X3),X1) != hAPP_nat_nat(plus_plus_nat(X3),X2)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_3871]) ).
cnf(c_0_3872_0,axiom,
( X1 = X2
| hAPP_real_real(plus_plus_real(X3),X1) != hAPP_real_real(plus_plus_real(X3),X2) ),
inference(literals_permutation,[status(thm)],[c_0_3872]) ).
cnf(c_0_3872_1,axiom,
( hAPP_real_real(plus_plus_real(X3),X1) != hAPP_real_real(plus_plus_real(X3),X2)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_3872]) ).
cnf(c_0_3873_0,axiom,
( X1 = X2
| hAPP_int_int(plus_plus_int(X1),X3) != hAPP_int_int(plus_plus_int(X2),X3) ),
inference(literals_permutation,[status(thm)],[c_0_3873]) ).
cnf(c_0_3873_1,axiom,
( hAPP_int_int(plus_plus_int(X1),X3) != hAPP_int_int(plus_plus_int(X2),X3)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_3873]) ).
cnf(c_0_3874_0,axiom,
( X1 = X2
| hAPP_nat_nat(plus_plus_nat(X1),X3) != hAPP_nat_nat(plus_plus_nat(X2),X3) ),
inference(literals_permutation,[status(thm)],[c_0_3874]) ).
cnf(c_0_3874_1,axiom,
( hAPP_nat_nat(plus_plus_nat(X1),X3) != hAPP_nat_nat(plus_plus_nat(X2),X3)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_3874]) ).
cnf(c_0_3875_0,axiom,
( X1 = X2
| hAPP_real_real(plus_plus_real(X1),X3) != hAPP_real_real(plus_plus_real(X2),X3) ),
inference(literals_permutation,[status(thm)],[c_0_3875]) ).
cnf(c_0_3875_1,axiom,
( hAPP_real_real(plus_plus_real(X1),X3) != hAPP_real_real(plus_plus_real(X2),X3)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_3875]) ).
cnf(c_0_3876_0,axiom,
( X1 = X2
| hAPP_nat_nat(plus_plus_nat(X1),X3) != hAPP_nat_nat(plus_plus_nat(X2),X3) ),
inference(literals_permutation,[status(thm)],[c_0_3876]) ).
cnf(c_0_3876_1,axiom,
( hAPP_nat_nat(plus_plus_nat(X1),X3) != hAPP_nat_nat(plus_plus_nat(X2),X3)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_3876]) ).
cnf(c_0_3877_0,axiom,
( X1 = X2
| hAPP_nat_nat(plus_plus_nat(X3),X1) != hAPP_nat_nat(plus_plus_nat(X3),X2) ),
inference(literals_permutation,[status(thm)],[c_0_3877]) ).
cnf(c_0_3877_1,axiom,
( hAPP_nat_nat(plus_plus_nat(X3),X1) != hAPP_nat_nat(plus_plus_nat(X3),X2)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_3877]) ).
cnf(c_0_3880_0,axiom,
( hAPP_nat_real(power_power_real(X1),number_number_of_nat(bit0(bit1(pls)))) = zero_zero_real
| X1 != zero_zero_real ),
inference(literals_permutation,[status(thm)],[c_0_3880]) ).
cnf(c_0_3880_1,axiom,
( X1 != zero_zero_real
| hAPP_nat_real(power_power_real(X1),number_number_of_nat(bit0(bit1(pls)))) = zero_zero_real ),
inference(literals_permutation,[status(thm)],[c_0_3880]) ).
cnf(c_0_3881_0,axiom,
( hAPP_nat_int(power_power_int(X1),number_number_of_nat(bit0(bit1(pls)))) = zero_zero_int
| X1 != zero_zero_int ),
inference(literals_permutation,[status(thm)],[c_0_3881]) ).
cnf(c_0_3881_1,axiom,
( X1 != zero_zero_int
| hAPP_nat_int(power_power_int(X1),number_number_of_nat(bit0(bit1(pls)))) = zero_zero_int ),
inference(literals_permutation,[status(thm)],[c_0_3881]) ).
cnf(c_0_3882_0,axiom,
( hAPP_nat_real(power_power_real(X1),number_number_of_nat(X2)) != zero_zero_real
| number_number_of_nat(X2) != zero_zero_nat ),
inference(literals_permutation,[status(thm)],[c_0_3882]) ).
cnf(c_0_3882_1,axiom,
( number_number_of_nat(X2) != zero_zero_nat
| hAPP_nat_real(power_power_real(X1),number_number_of_nat(X2)) != zero_zero_real ),
inference(literals_permutation,[status(thm)],[c_0_3882]) ).
cnf(c_0_3883_0,axiom,
( hAPP_nat_nat(power_power_nat(X1),number_number_of_nat(X2)) != zero_zero_nat
| number_number_of_nat(X2) != zero_zero_nat ),
inference(literals_permutation,[status(thm)],[c_0_3883]) ).
cnf(c_0_3883_1,axiom,
( number_number_of_nat(X2) != zero_zero_nat
| hAPP_nat_nat(power_power_nat(X1),number_number_of_nat(X2)) != zero_zero_nat ),
inference(literals_permutation,[status(thm)],[c_0_3883]) ).
cnf(c_0_3884_0,axiom,
( hAPP_nat_int(power_power_int(X1),number_number_of_nat(X2)) != zero_zero_int
| number_number_of_nat(X2) != zero_zero_nat ),
inference(literals_permutation,[status(thm)],[c_0_3884]) ).
cnf(c_0_3884_1,axiom,
( number_number_of_nat(X2) != zero_zero_nat
| hAPP_nat_int(power_power_int(X1),number_number_of_nat(X2)) != zero_zero_int ),
inference(literals_permutation,[status(thm)],[c_0_3884]) ).
cnf(c_0_3891_0,axiom,
( hAPP_int_int(plus_plus_int(X1),X2) = hAPP_int_int(plus_plus_int(X1),X3)
| X2 != X3 ),
inference(literals_permutation,[status(thm)],[c_0_3891]) ).
cnf(c_0_3891_1,axiom,
( X2 != X3
| hAPP_int_int(plus_plus_int(X1),X2) = hAPP_int_int(plus_plus_int(X1),X3) ),
inference(literals_permutation,[status(thm)],[c_0_3891]) ).
cnf(c_0_3892_0,axiom,
( hAPP_nat_nat(plus_plus_nat(X1),X2) = hAPP_nat_nat(plus_plus_nat(X1),X3)
| X2 != X3 ),
inference(literals_permutation,[status(thm)],[c_0_3892]) ).
cnf(c_0_3892_1,axiom,
( X2 != X3
| hAPP_nat_nat(plus_plus_nat(X1),X2) = hAPP_nat_nat(plus_plus_nat(X1),X3) ),
inference(literals_permutation,[status(thm)],[c_0_3892]) ).
cnf(c_0_3893_0,axiom,
( hAPP_real_real(plus_plus_real(X1),X2) = hAPP_real_real(plus_plus_real(X1),X3)
| X2 != X3 ),
inference(literals_permutation,[status(thm)],[c_0_3893]) ).
cnf(c_0_3893_1,axiom,
( X2 != X3
| hAPP_real_real(plus_plus_real(X1),X2) = hAPP_real_real(plus_plus_real(X1),X3) ),
inference(literals_permutation,[status(thm)],[c_0_3893]) ).
cnf(c_0_3894_0,axiom,
( hAPP_int_int(plus_plus_int(X1),X2) = hAPP_int_int(plus_plus_int(X3),X2)
| X1 != X3 ),
inference(literals_permutation,[status(thm)],[c_0_3894]) ).
cnf(c_0_3894_1,axiom,
( X1 != X3
| hAPP_int_int(plus_plus_int(X1),X2) = hAPP_int_int(plus_plus_int(X3),X2) ),
inference(literals_permutation,[status(thm)],[c_0_3894]) ).
cnf(c_0_3895_0,axiom,
( hAPP_nat_nat(plus_plus_nat(X1),X2) = hAPP_nat_nat(plus_plus_nat(X3),X2)
| X1 != X3 ),
inference(literals_permutation,[status(thm)],[c_0_3895]) ).
cnf(c_0_3895_1,axiom,
( X1 != X3
| hAPP_nat_nat(plus_plus_nat(X1),X2) = hAPP_nat_nat(plus_plus_nat(X3),X2) ),
inference(literals_permutation,[status(thm)],[c_0_3895]) ).
cnf(c_0_3896_0,axiom,
( hAPP_real_real(plus_plus_real(X1),X2) = hAPP_real_real(plus_plus_real(X3),X2)
| X1 != X3 ),
inference(literals_permutation,[status(thm)],[c_0_3896]) ).
cnf(c_0_3896_1,axiom,
( X1 != X3
| hAPP_real_real(plus_plus_real(X1),X2) = hAPP_real_real(plus_plus_real(X3),X2) ),
inference(literals_permutation,[status(thm)],[c_0_3896]) ).
cnf(c_0_3897_0,axiom,
( hAPP_nat_nat(plus_plus_nat(X1),X2) = hAPP_nat_nat(plus_plus_nat(X3),X2)
| X1 != X3 ),
inference(literals_permutation,[status(thm)],[c_0_3897]) ).
cnf(c_0_3897_1,axiom,
( X1 != X3
| hAPP_nat_nat(plus_plus_nat(X1),X2) = hAPP_nat_nat(plus_plus_nat(X3),X2) ),
inference(literals_permutation,[status(thm)],[c_0_3897]) ).
cnf(c_0_3898_0,axiom,
( hAPP_nat_nat(plus_plus_nat(X1),X2) = hAPP_nat_nat(plus_plus_nat(X1),X3)
| X2 != X3 ),
inference(literals_permutation,[status(thm)],[c_0_3898]) ).
cnf(c_0_3898_1,axiom,
( X2 != X3
| hAPP_nat_nat(plus_plus_nat(X1),X2) = hAPP_nat_nat(plus_plus_nat(X1),X3) ),
inference(literals_permutation,[status(thm)],[c_0_3898]) ).
cnf(c_0_3899_0,axiom,
( X1 = zero_zero_real
| hAPP_nat_real(power_power_real(X1),number_number_of_nat(X2)) != zero_zero_real ),
inference(literals_permutation,[status(thm)],[c_0_3899]) ).
cnf(c_0_3899_1,axiom,
( hAPP_nat_real(power_power_real(X1),number_number_of_nat(X2)) != zero_zero_real
| X1 = zero_zero_real ),
inference(literals_permutation,[status(thm)],[c_0_3899]) ).
cnf(c_0_3900_0,axiom,
( X1 = zero_zero_nat
| hAPP_nat_nat(power_power_nat(X1),number_number_of_nat(X2)) != zero_zero_nat ),
inference(literals_permutation,[status(thm)],[c_0_3900]) ).
cnf(c_0_3900_1,axiom,
( hAPP_nat_nat(power_power_nat(X1),number_number_of_nat(X2)) != zero_zero_nat
| X1 = zero_zero_nat ),
inference(literals_permutation,[status(thm)],[c_0_3900]) ).
cnf(c_0_3901_0,axiom,
( X1 = zero_zero_int
| hAPP_nat_int(power_power_int(X1),number_number_of_nat(X2)) != zero_zero_int ),
inference(literals_permutation,[status(thm)],[c_0_3901]) ).
cnf(c_0_3901_1,axiom,
( hAPP_nat_int(power_power_int(X1),number_number_of_nat(X2)) != zero_zero_int
| X1 = zero_zero_int ),
inference(literals_permutation,[status(thm)],[c_0_3901]) ).
cnf(c_0_3902_0,axiom,
( X1 = X2
| hAPP_nat_int(semiri1621563631at_int,X1) != hAPP_nat_int(semiri1621563631at_int,X2) ),
inference(literals_permutation,[status(thm)],[c_0_3902]) ).
cnf(c_0_3902_1,axiom,
( hAPP_nat_int(semiri1621563631at_int,X1) != hAPP_nat_int(semiri1621563631at_int,X2)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_3902]) ).
cnf(c_0_3903_0,axiom,
( X1 = X2
| hAPP_nat_int(semiri1621563631at_int,X1) != hAPP_nat_int(semiri1621563631at_int,X2) ),
inference(literals_permutation,[status(thm)],[c_0_3903]) ).
cnf(c_0_3903_1,axiom,
( hAPP_nat_int(semiri1621563631at_int,X1) != hAPP_nat_int(semiri1621563631at_int,X2)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_3903]) ).
cnf(c_0_3904_0,axiom,
( X1 = X2
| hAPP_nat_nat(semiri984289939at_nat,X1) != hAPP_nat_nat(semiri984289939at_nat,X2) ),
inference(literals_permutation,[status(thm)],[c_0_3904]) ).
cnf(c_0_3904_1,axiom,
( hAPP_nat_nat(semiri984289939at_nat,X1) != hAPP_nat_nat(semiri984289939at_nat,X2)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_3904]) ).
cnf(c_0_3905_0,axiom,
( X1 = X2
| hAPP_nat_real(semiri132038758t_real,X1) != hAPP_nat_real(semiri132038758t_real,X2) ),
inference(literals_permutation,[status(thm)],[c_0_3905]) ).
cnf(c_0_3905_1,axiom,
( hAPP_nat_real(semiri132038758t_real,X1) != hAPP_nat_real(semiri132038758t_real,X2)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_3905]) ).
cnf(c_0_3906_0,axiom,
( X1 = X2
| hAPP_nat_int(semiri1621563631at_int,X1) != hAPP_nat_int(semiri1621563631at_int,X2) ),
inference(literals_permutation,[status(thm)],[c_0_3906]) ).
cnf(c_0_3906_1,axiom,
( hAPP_nat_int(semiri1621563631at_int,X1) != hAPP_nat_int(semiri1621563631at_int,X2)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_3906]) ).
cnf(c_0_3917_0,axiom,
( X1 = zero_zero_nat
| X2 = one_one_nat
| hAPP_nat_nat(power_power_nat(X2),X1) != one_one_nat ),
inference(literals_permutation,[status(thm)],[c_0_3917]) ).
cnf(c_0_3917_1,axiom,
( X2 = one_one_nat
| X1 = zero_zero_nat
| hAPP_nat_nat(power_power_nat(X2),X1) != one_one_nat ),
inference(literals_permutation,[status(thm)],[c_0_3917]) ).
cnf(c_0_3917_2,axiom,
( hAPP_nat_nat(power_power_nat(X2),X1) != one_one_nat
| X2 = one_one_nat
| X1 = zero_zero_nat ),
inference(literals_permutation,[status(thm)],[c_0_3917]) ).
cnf(c_0_3918_0,axiom,
( X1 = zero_zero_int
| hAPP_int_int(plus_plus_int(X2),X1) != X2 ),
inference(literals_permutation,[status(thm)],[c_0_3918]) ).
cnf(c_0_3918_1,axiom,
( hAPP_int_int(plus_plus_int(X2),X1) != X2
| X1 = zero_zero_int ),
inference(literals_permutation,[status(thm)],[c_0_3918]) ).
cnf(c_0_3919_0,axiom,
( X1 = zero_zero_nat
| hAPP_nat_nat(plus_plus_nat(X2),X1) != X2 ),
inference(literals_permutation,[status(thm)],[c_0_3919]) ).
cnf(c_0_3919_1,axiom,
( hAPP_nat_nat(plus_plus_nat(X2),X1) != X2
| X1 = zero_zero_nat ),
inference(literals_permutation,[status(thm)],[c_0_3919]) ).
cnf(c_0_3920_0,axiom,
( X1 = zero_zero_real
| hAPP_real_real(plus_plus_real(X2),X1) != X2 ),
inference(literals_permutation,[status(thm)],[c_0_3920]) ).
cnf(c_0_3920_1,axiom,
( hAPP_real_real(plus_plus_real(X2),X1) != X2
| X1 = zero_zero_real ),
inference(literals_permutation,[status(thm)],[c_0_3920]) ).
cnf(c_0_3921_0,axiom,
( X1 = zero_zero_nat
| hAPP_nat_nat(plus_plus_nat(X2),X1) != X2 ),
inference(literals_permutation,[status(thm)],[c_0_3921]) ).
cnf(c_0_3921_1,axiom,
( hAPP_nat_nat(plus_plus_nat(X2),X1) != X2
| X1 = zero_zero_nat ),
inference(literals_permutation,[status(thm)],[c_0_3921]) ).
cnf(c_0_3922_0,axiom,
( hAPP_nat_nat(power_power_nat(X1),X2) != zero_zero_nat
| X2 != zero_zero_nat ),
inference(literals_permutation,[status(thm)],[c_0_3922]) ).
cnf(c_0_3922_1,axiom,
( X2 != zero_zero_nat
| hAPP_nat_nat(power_power_nat(X1),X2) != zero_zero_nat ),
inference(literals_permutation,[status(thm)],[c_0_3922]) ).
cnf(c_0_3923_0,axiom,
( hAPP_nat_int(power_power_int(X1),X2) != zero_zero_int
| X2 != zero_zero_nat ),
inference(literals_permutation,[status(thm)],[c_0_3923]) ).
cnf(c_0_3923_1,axiom,
( X2 != zero_zero_nat
| hAPP_nat_int(power_power_int(X1),X2) != zero_zero_int ),
inference(literals_permutation,[status(thm)],[c_0_3923]) ).
cnf(c_0_3924_0,axiom,
( hAPP_nat_nat(power_power_nat(X1),X2) != zero_zero_nat
| X2 != zero_zero_nat ),
inference(literals_permutation,[status(thm)],[c_0_3924]) ).
cnf(c_0_3924_1,axiom,
( X2 != zero_zero_nat
| hAPP_nat_nat(power_power_nat(X1),X2) != zero_zero_nat ),
inference(literals_permutation,[status(thm)],[c_0_3924]) ).
cnf(c_0_3925_0,axiom,
( hAPP_nat_real(power_power_real(X1),X2) != zero_zero_real
| X2 != zero_zero_nat ),
inference(literals_permutation,[status(thm)],[c_0_3925]) ).
cnf(c_0_3925_1,axiom,
( X2 != zero_zero_nat
| hAPP_nat_real(power_power_real(X1),X2) != zero_zero_real ),
inference(literals_permutation,[status(thm)],[c_0_3925]) ).
cnf(c_0_3926_0,axiom,
( X1 = zero_zero_nat
| hAPP_nat_nat(power_power_nat(X1),X2) != zero_zero_nat ),
inference(literals_permutation,[status(thm)],[c_0_3926]) ).
cnf(c_0_3926_1,axiom,
( hAPP_nat_nat(power_power_nat(X1),X2) != zero_zero_nat
| X1 = zero_zero_nat ),
inference(literals_permutation,[status(thm)],[c_0_3926]) ).
cnf(c_0_3927_0,axiom,
( X1 = zero_zero_int
| hAPP_int_int(plus_plus_int(X1),X1) != zero_zero_int ),
inference(literals_permutation,[status(thm)],[c_0_3927]) ).
cnf(c_0_3927_1,axiom,
( hAPP_int_int(plus_plus_int(X1),X1) != zero_zero_int
| X1 = zero_zero_int ),
inference(literals_permutation,[status(thm)],[c_0_3927]) ).
cnf(c_0_3928_0,axiom,
( X1 = zero_zero_real
| hAPP_real_real(plus_plus_real(X1),X1) != zero_zero_real ),
inference(literals_permutation,[status(thm)],[c_0_3928]) ).
cnf(c_0_3928_1,axiom,
( hAPP_real_real(plus_plus_real(X1),X1) != zero_zero_real
| X1 = zero_zero_real ),
inference(literals_permutation,[status(thm)],[c_0_3928]) ).
cnf(c_0_3929_0,axiom,
( X1 = zero_zero_int
| hAPP_nat_int(power_power_int(X1),X2) != zero_zero_int ),
inference(literals_permutation,[status(thm)],[c_0_3929]) ).
cnf(c_0_3929_1,axiom,
( hAPP_nat_int(power_power_int(X1),X2) != zero_zero_int
| X1 = zero_zero_int ),
inference(literals_permutation,[status(thm)],[c_0_3929]) ).
cnf(c_0_3930_0,axiom,
( X1 = zero_zero_nat
| hAPP_nat_nat(power_power_nat(X1),X2) != zero_zero_nat ),
inference(literals_permutation,[status(thm)],[c_0_3930]) ).
cnf(c_0_3930_1,axiom,
( hAPP_nat_nat(power_power_nat(X1),X2) != zero_zero_nat
| X1 = zero_zero_nat ),
inference(literals_permutation,[status(thm)],[c_0_3930]) ).
cnf(c_0_3931_0,axiom,
( X1 = zero_zero_real
| hAPP_nat_real(power_power_real(X1),X2) != zero_zero_real ),
inference(literals_permutation,[status(thm)],[c_0_3931]) ).
cnf(c_0_3931_1,axiom,
( hAPP_nat_real(power_power_real(X1),X2) != zero_zero_real
| X1 = zero_zero_real ),
inference(literals_permutation,[status(thm)],[c_0_3931]) ).
cnf(c_0_3932_0,axiom,
( X1 = zero_zero_int
| hAPP_nat_int(power_power_int(X1),X2) != zero_zero_int ),
inference(literals_permutation,[status(thm)],[c_0_3932]) ).
cnf(c_0_3932_1,axiom,
( hAPP_nat_int(power_power_int(X1),X2) != zero_zero_int
| X1 = zero_zero_int ),
inference(literals_permutation,[status(thm)],[c_0_3932]) ).
cnf(c_0_3933_0,axiom,
( X1 = zero_zero_real
| hAPP_nat_real(power_power_real(X1),X2) != zero_zero_real ),
inference(literals_permutation,[status(thm)],[c_0_3933]) ).
cnf(c_0_3933_1,axiom,
( hAPP_nat_real(power_power_real(X1),X2) != zero_zero_real
| X1 = zero_zero_real ),
inference(literals_permutation,[status(thm)],[c_0_3933]) ).
cnf(c_0_3934_0,axiom,
( X1 = zero_zero_nat
| hAPP_nat_nat(plus_plus_nat(X1),X2) != zero_zero_nat ),
inference(literals_permutation,[status(thm)],[c_0_3934]) ).
cnf(c_0_3934_1,axiom,
( hAPP_nat_nat(plus_plus_nat(X1),X2) != zero_zero_nat
| X1 = zero_zero_nat ),
inference(literals_permutation,[status(thm)],[c_0_3934]) ).
cnf(c_0_3935_0,axiom,
( X2 = zero_zero_nat
| hAPP_nat_nat(plus_plus_nat(X1),X2) != zero_zero_nat ),
inference(literals_permutation,[status(thm)],[c_0_3935]) ).
cnf(c_0_3935_1,axiom,
( hAPP_nat_nat(plus_plus_nat(X1),X2) != zero_zero_nat
| X2 = zero_zero_nat ),
inference(literals_permutation,[status(thm)],[c_0_3935]) ).
cnf(c_0_3936_0,axiom,
( X1 = zero_zero_real
| hAPP_real_real(plus_plus_real(X1),X1) != zero_zero_real ),
inference(literals_permutation,[status(thm)],[c_0_3936]) ).
cnf(c_0_3936_1,axiom,
( hAPP_real_real(plus_plus_real(X1),X1) != zero_zero_real
| X1 = zero_zero_real ),
inference(literals_permutation,[status(thm)],[c_0_3936]) ).
cnf(c_0_3937_0,axiom,
( X1 = zero_zero_int
| hAPP_int_int(plus_plus_int(X1),X1) != zero_zero_int ),
inference(literals_permutation,[status(thm)],[c_0_3937]) ).
cnf(c_0_3937_1,axiom,
( hAPP_int_int(plus_plus_int(X1),X1) != zero_zero_int
| X1 = zero_zero_int ),
inference(literals_permutation,[status(thm)],[c_0_3937]) ).
cnf(c_0_3938_0,axiom,
( hAPP_nat_real(power_power_real(X1),number_number_of_nat(X2)) = zero_zero_real
| number_number_of_nat(X2) = zero_zero_nat
| X1 != zero_zero_real ),
inference(literals_permutation,[status(thm)],[c_0_3938]) ).
cnf(c_0_3938_1,axiom,
( number_number_of_nat(X2) = zero_zero_nat
| hAPP_nat_real(power_power_real(X1),number_number_of_nat(X2)) = zero_zero_real
| X1 != zero_zero_real ),
inference(literals_permutation,[status(thm)],[c_0_3938]) ).
cnf(c_0_3938_2,axiom,
( X1 != zero_zero_real
| number_number_of_nat(X2) = zero_zero_nat
| hAPP_nat_real(power_power_real(X1),number_number_of_nat(X2)) = zero_zero_real ),
inference(literals_permutation,[status(thm)],[c_0_3938]) ).
cnf(c_0_3939_0,axiom,
( hAPP_nat_nat(power_power_nat(X1),number_number_of_nat(X2)) = zero_zero_nat
| number_number_of_nat(X2) = zero_zero_nat
| X1 != zero_zero_nat ),
inference(literals_permutation,[status(thm)],[c_0_3939]) ).
cnf(c_0_3939_1,axiom,
( number_number_of_nat(X2) = zero_zero_nat
| hAPP_nat_nat(power_power_nat(X1),number_number_of_nat(X2)) = zero_zero_nat
| X1 != zero_zero_nat ),
inference(literals_permutation,[status(thm)],[c_0_3939]) ).
cnf(c_0_3939_2,axiom,
( X1 != zero_zero_nat
| number_number_of_nat(X2) = zero_zero_nat
| hAPP_nat_nat(power_power_nat(X1),number_number_of_nat(X2)) = zero_zero_nat ),
inference(literals_permutation,[status(thm)],[c_0_3939]) ).
cnf(c_0_3940_0,axiom,
( hAPP_nat_int(power_power_int(X1),number_number_of_nat(X2)) = zero_zero_int
| number_number_of_nat(X2) = zero_zero_nat
| X1 != zero_zero_int ),
inference(literals_permutation,[status(thm)],[c_0_3940]) ).
cnf(c_0_3940_1,axiom,
( number_number_of_nat(X2) = zero_zero_nat
| hAPP_nat_int(power_power_int(X1),number_number_of_nat(X2)) = zero_zero_int
| X1 != zero_zero_int ),
inference(literals_permutation,[status(thm)],[c_0_3940]) ).
cnf(c_0_3940_2,axiom,
( X1 != zero_zero_int
| number_number_of_nat(X2) = zero_zero_nat
| hAPP_nat_int(power_power_int(X1),number_number_of_nat(X2)) = zero_zero_int ),
inference(literals_permutation,[status(thm)],[c_0_3940]) ).
cnf(c_0_3949_0,axiom,
( hAPP_nat_real(power_power_real(zero_zero_real),number_number_of_nat(X1)) = one_one_real
| number_number_of_nat(X1) != zero_zero_nat ),
inference(literals_permutation,[status(thm)],[c_0_3949]) ).
cnf(c_0_3949_1,axiom,
( number_number_of_nat(X1) != zero_zero_nat
| hAPP_nat_real(power_power_real(zero_zero_real),number_number_of_nat(X1)) = one_one_real ),
inference(literals_permutation,[status(thm)],[c_0_3949]) ).
cnf(c_0_3950_0,axiom,
( hAPP_nat_nat(power_power_nat(zero_zero_nat),number_number_of_nat(X1)) = one_one_nat
| number_number_of_nat(X1) != zero_zero_nat ),
inference(literals_permutation,[status(thm)],[c_0_3950]) ).
cnf(c_0_3950_1,axiom,
( number_number_of_nat(X1) != zero_zero_nat
| hAPP_nat_nat(power_power_nat(zero_zero_nat),number_number_of_nat(X1)) = one_one_nat ),
inference(literals_permutation,[status(thm)],[c_0_3950]) ).
cnf(c_0_3951_0,axiom,
( hAPP_nat_int(power_power_int(zero_zero_int),number_number_of_nat(X1)) = one_one_int
| number_number_of_nat(X1) != zero_zero_nat ),
inference(literals_permutation,[status(thm)],[c_0_3951]) ).
cnf(c_0_3951_1,axiom,
( number_number_of_nat(X1) != zero_zero_nat
| hAPP_nat_int(power_power_int(zero_zero_int),number_number_of_nat(X1)) = one_one_int ),
inference(literals_permutation,[status(thm)],[c_0_3951]) ).
cnf(c_0_3955_0,axiom,
( hAPP_nat_int(semiri1621563631at_int,X1) = hAPP_nat_int(semiri1621563631at_int,X2)
| X1 != X2 ),
inference(literals_permutation,[status(thm)],[c_0_3955]) ).
cnf(c_0_3955_1,axiom,
( X1 != X2
| hAPP_nat_int(semiri1621563631at_int,X1) = hAPP_nat_int(semiri1621563631at_int,X2) ),
inference(literals_permutation,[status(thm)],[c_0_3955]) ).
cnf(c_0_3956_0,axiom,
( hAPP_nat_int(semiri1621563631at_int,X1) = hAPP_nat_int(semiri1621563631at_int,X2)
| X1 != X2 ),
inference(literals_permutation,[status(thm)],[c_0_3956]) ).
cnf(c_0_3956_1,axiom,
( X1 != X2
| hAPP_nat_int(semiri1621563631at_int,X1) = hAPP_nat_int(semiri1621563631at_int,X2) ),
inference(literals_permutation,[status(thm)],[c_0_3956]) ).
cnf(c_0_3957_0,axiom,
( hAPP_nat_nat(semiri984289939at_nat,X1) = hAPP_nat_nat(semiri984289939at_nat,X2)
| X1 != X2 ),
inference(literals_permutation,[status(thm)],[c_0_3957]) ).
cnf(c_0_3957_1,axiom,
( X1 != X2
| hAPP_nat_nat(semiri984289939at_nat,X1) = hAPP_nat_nat(semiri984289939at_nat,X2) ),
inference(literals_permutation,[status(thm)],[c_0_3957]) ).
cnf(c_0_3958_0,axiom,
( hAPP_nat_real(semiri132038758t_real,X1) = hAPP_nat_real(semiri132038758t_real,X2)
| X1 != X2 ),
inference(literals_permutation,[status(thm)],[c_0_3958]) ).
cnf(c_0_3958_1,axiom,
( X1 != X2
| hAPP_nat_real(semiri132038758t_real,X1) = hAPP_nat_real(semiri132038758t_real,X2) ),
inference(literals_permutation,[status(thm)],[c_0_3958]) ).
cnf(c_0_3959_0,axiom,
( hAPP_nat_int(semiri1621563631at_int,X1) = hAPP_nat_int(semiri1621563631at_int,X2)
| X1 != X2 ),
inference(literals_permutation,[status(thm)],[c_0_3959]) ).
cnf(c_0_3959_1,axiom,
( X1 != X2
| hAPP_nat_int(semiri1621563631at_int,X1) = hAPP_nat_int(semiri1621563631at_int,X2) ),
inference(literals_permutation,[status(thm)],[c_0_3959]) ).
cnf(c_0_3960_0,axiom,
( hAPP_nat_real(power_power_real(zero_zero_real),number_number_of_nat(X1)) = zero_zero_real
| number_number_of_nat(X1) = zero_zero_nat ),
inference(literals_permutation,[status(thm)],[c_0_3960]) ).
cnf(c_0_3960_1,axiom,
( number_number_of_nat(X1) = zero_zero_nat
| hAPP_nat_real(power_power_real(zero_zero_real),number_number_of_nat(X1)) = zero_zero_real ),
inference(literals_permutation,[status(thm)],[c_0_3960]) ).
cnf(c_0_3961_0,axiom,
( hAPP_nat_nat(power_power_nat(zero_zero_nat),number_number_of_nat(X1)) = zero_zero_nat
| number_number_of_nat(X1) = zero_zero_nat ),
inference(literals_permutation,[status(thm)],[c_0_3961]) ).
cnf(c_0_3961_1,axiom,
( number_number_of_nat(X1) = zero_zero_nat
| hAPP_nat_nat(power_power_nat(zero_zero_nat),number_number_of_nat(X1)) = zero_zero_nat ),
inference(literals_permutation,[status(thm)],[c_0_3961]) ).
cnf(c_0_3962_0,axiom,
( hAPP_nat_int(power_power_int(zero_zero_int),number_number_of_nat(X1)) = zero_zero_int
| number_number_of_nat(X1) = zero_zero_nat ),
inference(literals_permutation,[status(thm)],[c_0_3962]) ).
cnf(c_0_3962_1,axiom,
( number_number_of_nat(X1) = zero_zero_nat
| hAPP_nat_int(power_power_int(zero_zero_int),number_number_of_nat(X1)) = zero_zero_int ),
inference(literals_permutation,[status(thm)],[c_0_3962]) ).
cnf(c_0_3965_0,axiom,
( hAPP_nat_nat(plus_plus_nat(X1),X2) = zero_zero_nat
| X2 != zero_zero_nat
| X1 != zero_zero_nat ),
inference(literals_permutation,[status(thm)],[c_0_3965]) ).
cnf(c_0_3965_1,axiom,
( X2 != zero_zero_nat
| hAPP_nat_nat(plus_plus_nat(X1),X2) = zero_zero_nat
| X1 != zero_zero_nat ),
inference(literals_permutation,[status(thm)],[c_0_3965]) ).
cnf(c_0_3965_2,axiom,
( X1 != zero_zero_nat
| X2 != zero_zero_nat
| hAPP_nat_nat(plus_plus_nat(X1),X2) = zero_zero_nat ),
inference(literals_permutation,[status(thm)],[c_0_3965]) ).
cnf(c_0_3966_0,axiom,
( hAPP_nat_nat(power_power_nat(X1),X2) = zero_zero_nat
| X2 = zero_zero_nat
| X1 != zero_zero_nat ),
inference(literals_permutation,[status(thm)],[c_0_3966]) ).
cnf(c_0_3966_1,axiom,
( X2 = zero_zero_nat
| hAPP_nat_nat(power_power_nat(X1),X2) = zero_zero_nat
| X1 != zero_zero_nat ),
inference(literals_permutation,[status(thm)],[c_0_3966]) ).
cnf(c_0_3966_2,axiom,
( X1 != zero_zero_nat
| X2 = zero_zero_nat
| hAPP_nat_nat(power_power_nat(X1),X2) = zero_zero_nat ),
inference(literals_permutation,[status(thm)],[c_0_3966]) ).
cnf(c_0_3967_0,axiom,
( hAPP_nat_int(power_power_int(X1),X2) = zero_zero_int
| X2 = zero_zero_nat
| X1 != zero_zero_int ),
inference(literals_permutation,[status(thm)],[c_0_3967]) ).
cnf(c_0_3967_1,axiom,
( X2 = zero_zero_nat
| hAPP_nat_int(power_power_int(X1),X2) = zero_zero_int
| X1 != zero_zero_int ),
inference(literals_permutation,[status(thm)],[c_0_3967]) ).
cnf(c_0_3967_2,axiom,
( X1 != zero_zero_int
| X2 = zero_zero_nat
| hAPP_nat_int(power_power_int(X1),X2) = zero_zero_int ),
inference(literals_permutation,[status(thm)],[c_0_3967]) ).
cnf(c_0_3968_0,axiom,
( hAPP_nat_nat(power_power_nat(X1),X2) = zero_zero_nat
| X2 = zero_zero_nat
| X1 != zero_zero_nat ),
inference(literals_permutation,[status(thm)],[c_0_3968]) ).
cnf(c_0_3968_1,axiom,
( X2 = zero_zero_nat
| hAPP_nat_nat(power_power_nat(X1),X2) = zero_zero_nat
| X1 != zero_zero_nat ),
inference(literals_permutation,[status(thm)],[c_0_3968]) ).
cnf(c_0_3968_2,axiom,
( X1 != zero_zero_nat
| X2 = zero_zero_nat
| hAPP_nat_nat(power_power_nat(X1),X2) = zero_zero_nat ),
inference(literals_permutation,[status(thm)],[c_0_3968]) ).
cnf(c_0_3969_0,axiom,
( hAPP_nat_real(power_power_real(X1),X2) = zero_zero_real
| X2 = zero_zero_nat
| X1 != zero_zero_real ),
inference(literals_permutation,[status(thm)],[c_0_3969]) ).
cnf(c_0_3969_1,axiom,
( X2 = zero_zero_nat
| hAPP_nat_real(power_power_real(X1),X2) = zero_zero_real
| X1 != zero_zero_real ),
inference(literals_permutation,[status(thm)],[c_0_3969]) ).
cnf(c_0_3969_2,axiom,
( X1 != zero_zero_real
| X2 = zero_zero_nat
| hAPP_nat_real(power_power_real(X1),X2) = zero_zero_real ),
inference(literals_permutation,[status(thm)],[c_0_3969]) ).
cnf(c_0_3973_0,axiom,
( hAPP_int_int(plus_plus_int(X1),X2) = X1
| X2 != zero_zero_int ),
inference(literals_permutation,[status(thm)],[c_0_3973]) ).
cnf(c_0_3973_1,axiom,
( X2 != zero_zero_int
| hAPP_int_int(plus_plus_int(X1),X2) = X1 ),
inference(literals_permutation,[status(thm)],[c_0_3973]) ).
cnf(c_0_3974_0,axiom,
( hAPP_nat_nat(plus_plus_nat(X1),X2) = X1
| X2 != zero_zero_nat ),
inference(literals_permutation,[status(thm)],[c_0_3974]) ).
cnf(c_0_3974_1,axiom,
( X2 != zero_zero_nat
| hAPP_nat_nat(plus_plus_nat(X1),X2) = X1 ),
inference(literals_permutation,[status(thm)],[c_0_3974]) ).
cnf(c_0_3975_0,axiom,
( hAPP_real_real(plus_plus_real(X1),X2) = X1
| X2 != zero_zero_real ),
inference(literals_permutation,[status(thm)],[c_0_3975]) ).
cnf(c_0_3975_1,axiom,
( X2 != zero_zero_real
| hAPP_real_real(plus_plus_real(X1),X2) = X1 ),
inference(literals_permutation,[status(thm)],[c_0_3975]) ).
cnf(c_0_3976_0,axiom,
( hAPP_int_int(plus_plus_int(X1),X1) = zero_zero_int
| X1 != zero_zero_int ),
inference(literals_permutation,[status(thm)],[c_0_3976]) ).
cnf(c_0_3976_1,axiom,
( X1 != zero_zero_int
| hAPP_int_int(plus_plus_int(X1),X1) = zero_zero_int ),
inference(literals_permutation,[status(thm)],[c_0_3976]) ).
cnf(c_0_3977_0,axiom,
( hAPP_real_real(plus_plus_real(X1),X1) = zero_zero_real
| X1 != zero_zero_real ),
inference(literals_permutation,[status(thm)],[c_0_3977]) ).
cnf(c_0_3977_1,axiom,
( X1 != zero_zero_real
| hAPP_real_real(plus_plus_real(X1),X1) = zero_zero_real ),
inference(literals_permutation,[status(thm)],[c_0_3977]) ).
cnf(c_0_3978_0,axiom,
( hAPP_nat_nat(power_power_nat(X1),X2) = one_one_nat
| X1 != one_one_nat ),
inference(literals_permutation,[status(thm)],[c_0_3978]) ).
cnf(c_0_3978_1,axiom,
( X1 != one_one_nat
| hAPP_nat_nat(power_power_nat(X1),X2) = one_one_nat ),
inference(literals_permutation,[status(thm)],[c_0_3978]) ).
cnf(c_0_3979_0,axiom,
( hAPP_nat_nat(power_power_nat(X1),X2) = one_one_nat
| X2 != zero_zero_nat ),
inference(literals_permutation,[status(thm)],[c_0_3979]) ).
cnf(c_0_3979_1,axiom,
( X2 != zero_zero_nat
| hAPP_nat_nat(power_power_nat(X1),X2) = one_one_nat ),
inference(literals_permutation,[status(thm)],[c_0_3979]) ).
cnf(c_0_3980_0,axiom,
( hAPP_real_real(plus_plus_real(X1),X1) = zero_zero_real
| X1 != zero_zero_real ),
inference(literals_permutation,[status(thm)],[c_0_3980]) ).
cnf(c_0_3980_1,axiom,
( X1 != zero_zero_real
| hAPP_real_real(plus_plus_real(X1),X1) = zero_zero_real ),
inference(literals_permutation,[status(thm)],[c_0_3980]) ).
cnf(c_0_3981_0,axiom,
( hAPP_int_int(plus_plus_int(X1),X1) = zero_zero_int
| X1 != zero_zero_int ),
inference(literals_permutation,[status(thm)],[c_0_3981]) ).
cnf(c_0_3981_1,axiom,
( X1 != zero_zero_int
| hAPP_int_int(plus_plus_int(X1),X1) = zero_zero_int ),
inference(literals_permutation,[status(thm)],[c_0_3981]) ).
cnf(c_0_3983_0,axiom,
( X1 = zero_zero_nat
| hAPP_nat_int(semiri1621563631at_int,X1) != zero_zero_int ),
inference(literals_permutation,[status(thm)],[c_0_3983]) ).
cnf(c_0_3983_1,axiom,
( hAPP_nat_int(semiri1621563631at_int,X1) != zero_zero_int
| X1 = zero_zero_nat ),
inference(literals_permutation,[status(thm)],[c_0_3983]) ).
cnf(c_0_3985_0,axiom,
( hAPP_nat_real(power_power_real(zero_zero_real),X1) = one_one_real
| X1 != zero_zero_nat ),
inference(literals_permutation,[status(thm)],[c_0_3985]) ).
cnf(c_0_3985_1,axiom,
( X1 != zero_zero_nat
| hAPP_nat_real(power_power_real(zero_zero_real),X1) = one_one_real ),
inference(literals_permutation,[status(thm)],[c_0_3985]) ).
cnf(c_0_3986_0,axiom,
( hAPP_nat_nat(power_power_nat(zero_zero_nat),X1) = one_one_nat
| X1 != zero_zero_nat ),
inference(literals_permutation,[status(thm)],[c_0_3986]) ).
cnf(c_0_3986_1,axiom,
( X1 != zero_zero_nat
| hAPP_nat_nat(power_power_nat(zero_zero_nat),X1) = one_one_nat ),
inference(literals_permutation,[status(thm)],[c_0_3986]) ).
cnf(c_0_3987_0,axiom,
( hAPP_nat_int(power_power_int(zero_zero_int),X1) = one_one_int
| X1 != zero_zero_nat ),
inference(literals_permutation,[status(thm)],[c_0_3987]) ).
cnf(c_0_3987_1,axiom,
( X1 != zero_zero_nat
| hAPP_nat_int(power_power_int(zero_zero_int),X1) = one_one_int ),
inference(literals_permutation,[status(thm)],[c_0_3987]) ).
cnf(c_0_4012_0,axiom,
( hAPP_nat_real(power_power_real(zero_zero_real),X1) = zero_zero_real
| X1 = zero_zero_nat ),
inference(literals_permutation,[status(thm)],[c_0_4012]) ).
cnf(c_0_4012_1,axiom,
( X1 = zero_zero_nat
| hAPP_nat_real(power_power_real(zero_zero_real),X1) = zero_zero_real ),
inference(literals_permutation,[status(thm)],[c_0_4012]) ).
cnf(c_0_4013_0,axiom,
( hAPP_nat_nat(power_power_nat(zero_zero_nat),X1) = zero_zero_nat
| X1 = zero_zero_nat ),
inference(literals_permutation,[status(thm)],[c_0_4013]) ).
cnf(c_0_4013_1,axiom,
( X1 = zero_zero_nat
| hAPP_nat_nat(power_power_nat(zero_zero_nat),X1) = zero_zero_nat ),
inference(literals_permutation,[status(thm)],[c_0_4013]) ).
cnf(c_0_4014_0,axiom,
( hAPP_nat_int(power_power_int(zero_zero_int),X1) = zero_zero_int
| X1 = zero_zero_nat ),
inference(literals_permutation,[status(thm)],[c_0_4014]) ).
cnf(c_0_4014_1,axiom,
( X1 = zero_zero_nat
| hAPP_nat_int(power_power_int(zero_zero_int),X1) = zero_zero_int ),
inference(literals_permutation,[status(thm)],[c_0_4014]) ).
cnf(c_0_4030_0,axiom,
( X1 = X2
| bit0(X1) != bit0(X2) ),
inference(literals_permutation,[status(thm)],[c_0_4030]) ).
cnf(c_0_4030_1,axiom,
( bit0(X1) != bit0(X2)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_4030]) ).
cnf(c_0_4031_0,axiom,
( X1 = X2
| bit1(X1) != bit1(X2) ),
inference(literals_permutation,[status(thm)],[c_0_4031]) ).
cnf(c_0_4031_1,axiom,
( bit1(X1) != bit1(X2)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_4031]) ).
cnf(c_0_4032_0,axiom,
( X1 = X2
| number267125858f_real(X1) != number267125858f_real(X2) ),
inference(literals_permutation,[status(thm)],[c_0_4032]) ).
cnf(c_0_4032_1,axiom,
( number267125858f_real(X1) != number267125858f_real(X2)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_4032]) ).
cnf(c_0_4033_0,axiom,
( X1 = X2
| number_number_of_int(X1) != number_number_of_int(X2) ),
inference(literals_permutation,[status(thm)],[c_0_4033]) ).
cnf(c_0_4033_1,axiom,
( number_number_of_int(X1) != number_number_of_int(X2)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_4033]) ).
cnf(c_0_4034_0,axiom,
( hAPP_nat_int(semiri1621563631at_int,X1) = zero_zero_int
| X1 != zero_zero_nat ),
inference(literals_permutation,[status(thm)],[c_0_4034]) ).
cnf(c_0_4034_1,axiom,
( X1 != zero_zero_nat
| hAPP_nat_int(semiri1621563631at_int,X1) = zero_zero_int ),
inference(literals_permutation,[status(thm)],[c_0_4034]) ).
cnf(c_0_4036_0,axiom,
( X1 = number267125858f_real(X2)
| number267125858f_real(X2) != X1 ),
inference(literals_permutation,[status(thm)],[c_0_4036]) ).
cnf(c_0_4036_1,axiom,
( number267125858f_real(X2) != X1
| X1 = number267125858f_real(X2) ),
inference(literals_permutation,[status(thm)],[c_0_4036]) ).
cnf(c_0_4037_0,axiom,
( number267125858f_real(X1) = X2
| X2 != number267125858f_real(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4037]) ).
cnf(c_0_4037_1,axiom,
( X2 != number267125858f_real(X1)
| number267125858f_real(X1) = X2 ),
inference(literals_permutation,[status(thm)],[c_0_4037]) ).
cnf(c_0_4038_0,axiom,
( X1 = number_number_of_int(X2)
| number_number_of_int(X2) != X1 ),
inference(literals_permutation,[status(thm)],[c_0_4038]) ).
cnf(c_0_4038_1,axiom,
( number_number_of_int(X2) != X1
| X1 = number_number_of_int(X2) ),
inference(literals_permutation,[status(thm)],[c_0_4038]) ).
cnf(c_0_4039_0,axiom,
( number_number_of_int(X1) = X2
| X2 != number_number_of_int(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4039]) ).
cnf(c_0_4039_1,axiom,
( X2 != number_number_of_int(X1)
| number_number_of_int(X1) = X2 ),
inference(literals_permutation,[status(thm)],[c_0_4039]) ).
cnf(c_0_4040_0,axiom,
( X1 = number_number_of_nat(X2)
| number_number_of_nat(X2) != X1 ),
inference(literals_permutation,[status(thm)],[c_0_4040]) ).
cnf(c_0_4040_1,axiom,
( number_number_of_nat(X2) != X1
| X1 = number_number_of_nat(X2) ),
inference(literals_permutation,[status(thm)],[c_0_4040]) ).
cnf(c_0_4041_0,axiom,
( number_number_of_nat(X1) = X2
| X2 != number_number_of_nat(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4041]) ).
cnf(c_0_4041_1,axiom,
( X2 != number_number_of_nat(X1)
| number_number_of_nat(X1) = X2 ),
inference(literals_permutation,[status(thm)],[c_0_4041]) ).
cnf(c_0_4044_0,axiom,
( bit0(X1) = bit0(X2)
| X1 != X2 ),
inference(literals_permutation,[status(thm)],[c_0_4044]) ).
cnf(c_0_4044_1,axiom,
( X1 != X2
| bit0(X1) = bit0(X2) ),
inference(literals_permutation,[status(thm)],[c_0_4044]) ).
cnf(c_0_4045_0,axiom,
( bit1(X1) = bit1(X2)
| X1 != X2 ),
inference(literals_permutation,[status(thm)],[c_0_4045]) ).
cnf(c_0_4045_1,axiom,
( X1 != X2
| bit1(X1) = bit1(X2) ),
inference(literals_permutation,[status(thm)],[c_0_4045]) ).
cnf(c_0_4046_0,axiom,
( number267125858f_real(X1) = number267125858f_real(X2)
| X1 != X2 ),
inference(literals_permutation,[status(thm)],[c_0_4046]) ).
cnf(c_0_4046_1,axiom,
( X1 != X2
| number267125858f_real(X1) = number267125858f_real(X2) ),
inference(literals_permutation,[status(thm)],[c_0_4046]) ).
cnf(c_0_4047_0,axiom,
( number_number_of_int(X1) = number_number_of_int(X2)
| X1 != X2 ),
inference(literals_permutation,[status(thm)],[c_0_4047]) ).
cnf(c_0_4047_1,axiom,
( X1 != X2
| number_number_of_int(X1) = number_number_of_int(X2) ),
inference(literals_permutation,[status(thm)],[c_0_4047]) ).
cnf(c_0_4058_0,axiom,
( X1 = fFalse
| X1 = fTrue
| ~ is_bool(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4058]) ).
cnf(c_0_4058_1,axiom,
( X1 = fTrue
| X1 = fFalse
| ~ is_bool(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4058]) ).
cnf(c_0_4058_2,axiom,
( ~ is_bool(X1)
| X1 = fTrue
| X1 = fFalse ),
inference(literals_permutation,[status(thm)],[c_0_4058]) ).
cnf(c_0_4059_0,axiom,
( pls = X1
| bit0(X1) != pls ),
inference(literals_permutation,[status(thm)],[c_0_4059]) ).
cnf(c_0_4059_1,axiom,
( bit0(X1) != pls
| pls = X1 ),
inference(literals_permutation,[status(thm)],[c_0_4059]) ).
cnf(c_0_4060_0,axiom,
( X1 = pls
| bit0(X1) != pls ),
inference(literals_permutation,[status(thm)],[c_0_4060]) ).
cnf(c_0_4060_1,axiom,
( bit0(X1) != pls
| X1 = pls ),
inference(literals_permutation,[status(thm)],[c_0_4060]) ).
cnf(c_0_4073_0,axiom,
( bit0(X1) = pls
| pls != X1 ),
inference(literals_permutation,[status(thm)],[c_0_4073]) ).
cnf(c_0_4073_1,axiom,
( pls != X1
| bit0(X1) = pls ),
inference(literals_permutation,[status(thm)],[c_0_4073]) ).
cnf(c_0_4074_0,axiom,
( bit0(X1) = pls
| X1 != pls ),
inference(literals_permutation,[status(thm)],[c_0_4074]) ).
cnf(c_0_4074_1,axiom,
( X1 != pls
| bit0(X1) = pls ),
inference(literals_permutation,[status(thm)],[c_0_4074]) ).
cnf(c_0_4077_0,axiom,
( X1 = one_one_int
| one_one_int != X1 ),
inference(literals_permutation,[status(thm)],[c_0_4077]) ).
cnf(c_0_4077_1,axiom,
( one_one_int != X1
| X1 = one_one_int ),
inference(literals_permutation,[status(thm)],[c_0_4077]) ).
cnf(c_0_4078_0,axiom,
( one_one_int = X1
| X1 != one_one_int ),
inference(literals_permutation,[status(thm)],[c_0_4078]) ).
cnf(c_0_4078_1,axiom,
( X1 != one_one_int
| one_one_int = X1 ),
inference(literals_permutation,[status(thm)],[c_0_4078]) ).
cnf(c_0_4079_0,axiom,
( X1 = one_one_nat
| one_one_nat != X1 ),
inference(literals_permutation,[status(thm)],[c_0_4079]) ).
cnf(c_0_4079_1,axiom,
( one_one_nat != X1
| X1 = one_one_nat ),
inference(literals_permutation,[status(thm)],[c_0_4079]) ).
cnf(c_0_4080_0,axiom,
( one_one_nat = X1
| X1 != one_one_nat ),
inference(literals_permutation,[status(thm)],[c_0_4080]) ).
cnf(c_0_4080_1,axiom,
( X1 != one_one_nat
| one_one_nat = X1 ),
inference(literals_permutation,[status(thm)],[c_0_4080]) ).
cnf(c_0_4081_0,axiom,
( X1 = one_one_real
| one_one_real != X1 ),
inference(literals_permutation,[status(thm)],[c_0_4081]) ).
cnf(c_0_4081_1,axiom,
( one_one_real != X1
| X1 = one_one_real ),
inference(literals_permutation,[status(thm)],[c_0_4081]) ).
cnf(c_0_4082_0,axiom,
( one_one_real = X1
| X1 != one_one_real ),
inference(literals_permutation,[status(thm)],[c_0_4082]) ).
cnf(c_0_4082_1,axiom,
( X1 != one_one_real
| one_one_real = X1 ),
inference(literals_permutation,[status(thm)],[c_0_4082]) ).
cnf(c_0_4083_0,axiom,
( X1 = zero_zero_int
| zero_zero_int != X1 ),
inference(literals_permutation,[status(thm)],[c_0_4083]) ).
cnf(c_0_4083_1,axiom,
( zero_zero_int != X1
| X1 = zero_zero_int ),
inference(literals_permutation,[status(thm)],[c_0_4083]) ).
cnf(c_0_4084_0,axiom,
( zero_zero_int = X1
| X1 != zero_zero_int ),
inference(literals_permutation,[status(thm)],[c_0_4084]) ).
cnf(c_0_4084_1,axiom,
( X1 != zero_zero_int
| zero_zero_int = X1 ),
inference(literals_permutation,[status(thm)],[c_0_4084]) ).
cnf(c_0_4085_0,axiom,
( X1 = zero_zero_nat
| zero_zero_nat != X1 ),
inference(literals_permutation,[status(thm)],[c_0_4085]) ).
cnf(c_0_4085_1,axiom,
( zero_zero_nat != X1
| X1 = zero_zero_nat ),
inference(literals_permutation,[status(thm)],[c_0_4085]) ).
cnf(c_0_4086_0,axiom,
( zero_zero_nat = X1
| X1 != zero_zero_nat ),
inference(literals_permutation,[status(thm)],[c_0_4086]) ).
cnf(c_0_4086_1,axiom,
( X1 != zero_zero_nat
| zero_zero_nat = X1 ),
inference(literals_permutation,[status(thm)],[c_0_4086]) ).
cnf(c_0_4087_0,axiom,
( X1 = zero_zero_real
| zero_zero_real != X1 ),
inference(literals_permutation,[status(thm)],[c_0_4087]) ).
cnf(c_0_4087_1,axiom,
( zero_zero_real != X1
| X1 = zero_zero_real ),
inference(literals_permutation,[status(thm)],[c_0_4087]) ).
cnf(c_0_4088_0,axiom,
( zero_zero_real = X1
| X1 != zero_zero_real ),
inference(literals_permutation,[status(thm)],[c_0_4088]) ).
cnf(c_0_4088_1,axiom,
( X1 != zero_zero_real
| zero_zero_real = X1 ),
inference(literals_permutation,[status(thm)],[c_0_4088]) ).
cnf(c_0_3120_0,axiom,
~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(plus_plus_real(hAPP_nat_real(power_power_real(X1),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_real(power_power_real(X2),number_number_of_nat(bit0(bit1(pls)))))),zero_zero_real)),
inference(literals_permutation,[status(thm)],[c_0_3120]) ).
cnf(c_0_3121_0,axiom,
~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(X1),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_int(power_power_int(X2),number_number_of_nat(bit0(bit1(pls)))))),zero_zero_int)),
inference(literals_permutation,[status(thm)],[c_0_3121]) ).
cnf(c_0_3148_0,axiom,
~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_nat_real(power_power_real(X1),number_number_of_nat(bit0(bit1(pls))))),zero_zero_real)),
inference(literals_permutation,[status(thm)],[c_0_3148]) ).
cnf(c_0_3149_0,axiom,
~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_nat_int(power_power_int(X1),number_number_of_nat(bit0(bit1(pls))))),zero_zero_int)),
inference(literals_permutation,[status(thm)],[c_0_3149]) ).
cnf(c_0_3362_0,axiom,
~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(X1),X2)),X2)),
inference(literals_permutation,[status(thm)],[c_0_3362]) ).
cnf(c_0_3363_0,axiom,
~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(X1),X2)),X1)),
inference(literals_permutation,[status(thm)],[c_0_3363]) ).
cnf(c_0_3448_0,axiom,
~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_nat_int(semiri1621563631at_int,X1)),zero_zero_int)),
inference(literals_permutation,[status(thm)],[c_0_3448]) ).
cnf(c_0_3449_0,axiom,
~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(semiri984289939at_nat,X1)),zero_zero_nat)),
inference(literals_permutation,[status(thm)],[c_0_3449]) ).
cnf(c_0_3450_0,axiom,
~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_nat_real(semiri132038758t_real,X1)),zero_zero_real)),
inference(literals_permutation,[status(thm)],[c_0_3450]) ).
cnf(c_0_3451_0,axiom,
~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_nat_int(semiri1621563631at_int,X1)),zero_zero_int)),
inference(literals_permutation,[status(thm)],[c_0_3451]) ).
cnf(c_0_3741_0,axiom,
hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),X1)),X1) != zero_zero_int,
inference(literals_permutation,[status(thm)],[c_0_3741]) ).
cnf(c_0_3768_0,axiom,
~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X1)),
inference(literals_permutation,[status(thm)],[c_0_3768]) ).
cnf(c_0_3769_0,axiom,
~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X1)),
inference(literals_permutation,[status(thm)],[c_0_3769]) ).
cnf(c_0_3793_0,axiom,
~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),zero_zero_nat)),
inference(literals_permutation,[status(thm)],[c_0_3793]) ).
cnf(c_0_3794_0,axiom,
~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),zero_zero_nat)),
inference(literals_permutation,[status(thm)],[c_0_3794]) ).
cnf(c_0_3795_0,axiom,
~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),zero_zero_nat)),
inference(literals_permutation,[status(thm)],[c_0_3795]) ).
cnf(c_0_3802_0,axiom,
~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),zero_zero_int)),
inference(literals_permutation,[status(thm)],[c_0_3802]) ).
cnf(c_0_3803_0,axiom,
~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,one_one_nat),zero_zero_nat)),
inference(literals_permutation,[status(thm)],[c_0_3803]) ).
cnf(c_0_3804_0,axiom,
~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,one_one_real),zero_zero_real)),
inference(literals_permutation,[status(thm)],[c_0_3804]) ).
cnf(c_0_3805_0,axiom,
~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),zero_zero_int)),
inference(literals_permutation,[status(thm)],[c_0_3805]) ).
cnf(c_0_3806_0,axiom,
~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,one_one_nat),zero_zero_nat)),
inference(literals_permutation,[status(thm)],[c_0_3806]) ).
cnf(c_0_3807_0,axiom,
~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,one_one_real),zero_zero_real)),
inference(literals_permutation,[status(thm)],[c_0_3807]) ).
cnf(c_0_3808_0,axiom,
~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),zero_zero_int)),
inference(literals_permutation,[status(thm)],[c_0_3808]) ).
cnf(c_0_3809_0,axiom,
~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),pls)),
inference(literals_permutation,[status(thm)],[c_0_3809]) ).
cnf(c_0_4042_0,axiom,
bit0(X1) != bit1(X2),
inference(literals_permutation,[status(thm)],[c_0_4042]) ).
cnf(c_0_4043_0,axiom,
bit1(X1) != bit0(X2),
inference(literals_permutation,[status(thm)],[c_0_4043]) ).
cnf(c_0_4071_0,axiom,
bit1(X1) != pls,
inference(literals_permutation,[status(thm)],[c_0_4071]) ).
cnf(c_0_4072_0,axiom,
bit1(X1) != pls,
inference(literals_permutation,[status(thm)],[c_0_4072]) ).
cnf(c_0_4102_0,axiom,
one_one_int != zero_zero_int,
inference(literals_permutation,[status(thm)],[c_0_4102]) ).
cnf(c_0_4103_0,axiom,
zero_zero_nat != one_one_nat,
inference(literals_permutation,[status(thm)],[c_0_4103]) ).
cnf(c_0_4104_0,axiom,
one_one_real != zero_zero_real,
inference(literals_permutation,[status(thm)],[c_0_4104]) ).
cnf(c_0_4105_0,axiom,
one_one_int != zero_zero_int,
inference(literals_permutation,[status(thm)],[c_0_4105]) ).
cnf(c_0_4106_0,axiom,
zero_zero_nat != one_one_nat,
inference(literals_permutation,[status(thm)],[c_0_4106]) ).
cnf(c_0_4107_0,axiom,
one_one_real != zero_zero_real,
inference(literals_permutation,[status(thm)],[c_0_4107]) ).
cnf(c_0_4108_0,axiom,
one_one_real != zero_zero_real,
inference(literals_permutation,[status(thm)],[c_0_4108]) ).
cnf(c_0_4109_0,axiom,
one_one_int != zero_zero_int,
inference(literals_permutation,[status(thm)],[c_0_4109]) ).
cnf(c_0_3124_0,axiom,
hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),sqrt(hAPP_real_real(plus_plus_real(hAPP_nat_real(power_power_real(X1),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_real(power_power_real(X2),number_number_of_nat(bit0(bit1(pls)))))))),
inference(literals_permutation,[status(thm)],[c_0_3124]) ).
cnf(c_0_3129_0,axiom,
hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(X1),number_number_of_nat(bit0(bit1(pls))))),times_times_int(times_times_int(number_number_of_int(bit0(bit1(pls))),X1),X2))),hAPP_nat_int(power_power_int(X2),number_number_of_nat(bit0(bit1(pls))))) = hAPP_nat_int(power_power_int(hAPP_int_int(plus_plus_int(X1),X2)),number_number_of_nat(bit0(bit1(pls)))),
inference(literals_permutation,[status(thm)],[c_0_3129]) ).
cnf(c_0_3137_0,axiom,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(X1),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_int(power_power_int(X2),number_number_of_nat(bit0(bit1(pls))))))),
inference(literals_permutation,[status(thm)],[c_0_3137]) ).
cnf(c_0_3138_0,axiom,
hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),hAPP_real_real(plus_plus_real(hAPP_nat_real(power_power_real(X1),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_real(power_power_real(X2),number_number_of_nat(bit0(bit1(pls))))))),
inference(literals_permutation,[status(thm)],[c_0_3138]) ).
cnf(c_0_3240_0,axiom,
hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_nat_real(semiri132038758t_real,X1)),hAPP_nat_real(power_power_real(number267125858f_real(bit0(bit1(pls)))),X1))),
inference(literals_permutation,[status(thm)],[c_0_3240]) ).
cnf(c_0_3241_0,axiom,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_nat_int(semiri1621563631at_int,X1)),hAPP_nat_int(power_power_int(number_number_of_int(bit0(bit1(pls)))),X1))),
inference(literals_permutation,[status(thm)],[c_0_3241]) ).
cnf(c_0_3303_0,axiom,
hAPP_int_int(plus_plus_int(hAPP_nat_int(semiri1621563631at_int,X1)),hAPP_int_int(plus_plus_int(hAPP_nat_int(semiri1621563631at_int,X2)),X3)) = hAPP_int_int(plus_plus_int(hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(plus_plus_nat(X1),X2))),X3),
inference(literals_permutation,[status(thm)],[c_0_3303]) ).
cnf(c_0_3322_0,axiom,
hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,one_one_real),hAPP_nat_real(power_power_real(number267125858f_real(bit0(bit1(pls)))),X1))),
inference(literals_permutation,[status(thm)],[c_0_3322]) ).
cnf(c_0_3381_0,axiom,
hAPP_nat_int(power_power_int(hAPP_nat_int(power_power_int(X1),number_number_of_nat(bit0(bit1(pls))))),number_number_of_nat(bit0(bit1(pls)))) = hAPP_nat_int(power_power_int(X1),number_number_of_nat(bit0(bit0(bit1(pls))))),
inference(literals_permutation,[status(thm)],[c_0_3381]) ).
cnf(c_0_3429_0,axiom,
hAPP_real_real(plus_plus_real(number267125858f_real(X1)),hAPP_real_real(plus_plus_real(number267125858f_real(X2)),X3)) = hAPP_real_real(plus_plus_real(number267125858f_real(hAPP_int_int(plus_plus_int(X1),X2))),X3),
inference(literals_permutation,[status(thm)],[c_0_3429]) ).
cnf(c_0_3430_0,axiom,
hAPP_int_int(plus_plus_int(number_number_of_int(X1)),hAPP_int_int(plus_plus_int(number_number_of_int(X2)),X3)) = hAPP_int_int(plus_plus_int(number_number_of_int(hAPP_int_int(plus_plus_int(X1),X2))),X3),
inference(literals_permutation,[status(thm)],[c_0_3430]) ).
cnf(c_0_3431_0,axiom,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),hAPP_nat_int(power_power_int(X1),number_number_of_nat(bit0(bit1(pls)))))),
inference(literals_permutation,[status(thm)],[c_0_3431]) ).
cnf(c_0_3438_0,axiom,
hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(X1),X2)),hAPP_int_int(plus_plus_int(X3),X4)) = hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(X1),X3)),hAPP_int_int(plus_plus_int(X2),X4)),
inference(literals_permutation,[status(thm)],[c_0_3438]) ).
cnf(c_0_3439_0,axiom,
hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(plus_plus_nat(X1),X2)),hAPP_nat_nat(plus_plus_nat(X3),X4)) = hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(plus_plus_nat(X1),X3)),hAPP_nat_nat(plus_plus_nat(X2),X4)),
inference(literals_permutation,[status(thm)],[c_0_3439]) ).
cnf(c_0_3440_0,axiom,
hAPP_real_real(plus_plus_real(hAPP_real_real(plus_plus_real(X1),X2)),hAPP_real_real(plus_plus_real(X3),X4)) = hAPP_real_real(plus_plus_real(hAPP_real_real(plus_plus_real(X1),X3)),hAPP_real_real(plus_plus_real(X2),X4)),
inference(literals_permutation,[status(thm)],[c_0_3440]) ).
cnf(c_0_3441_0,axiom,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_nat_int(power_power_int(X1),number_number_of_nat(bit0(bit1(pls)))))),
inference(literals_permutation,[status(thm)],[c_0_3441]) ).
cnf(c_0_3442_0,axiom,
hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),hAPP_nat_real(power_power_real(X1),number_number_of_nat(bit0(bit1(pls)))))),
inference(literals_permutation,[status(thm)],[c_0_3442]) ).
cnf(c_0_3591_0,axiom,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,m1),hAPP_int_int(plus_plus_int(one_one_int),hAPP_nat_int(semiri1621563631at_int,n)))),
inference(literals_permutation,[status(thm)],[c_0_3591]) ).
cnf(c_0_3592_0,axiom,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_int_int(plus_plus_int(one_one_int),hAPP_nat_int(semiri1621563631at_int,n)))),
inference(literals_permutation,[status(thm)],[c_0_3592]) ).
cnf(c_0_3653_0,axiom,
hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(X1),X2)),X3) = hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(X1),X3)),X2),
inference(literals_permutation,[status(thm)],[c_0_3653]) ).
cnf(c_0_3654_0,axiom,
hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(plus_plus_nat(X1),X2)),X3) = hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(plus_plus_nat(X1),X3)),X2),
inference(literals_permutation,[status(thm)],[c_0_3654]) ).
cnf(c_0_3655_0,axiom,
hAPP_real_real(plus_plus_real(hAPP_real_real(plus_plus_real(X1),X2)),X3) = hAPP_real_real(plus_plus_real(hAPP_real_real(plus_plus_real(X1),X3)),X2),
inference(literals_permutation,[status(thm)],[c_0_3655]) ).
cnf(c_0_3686_0,axiom,
hAPP_int_int(plus_plus_int(bit0(times_times_int(X1,X2))),X2) = times_times_int(bit1(X1),X2),
inference(literals_permutation,[status(thm)],[c_0_3686]) ).
cnf(c_0_3687_0,axiom,
hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(X1),X2)),X3) = hAPP_int_int(plus_plus_int(X1),hAPP_int_int(plus_plus_int(X2),X3)),
inference(literals_permutation,[status(thm)],[c_0_3687]) ).
cnf(c_0_3688_0,axiom,
hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(plus_plus_nat(X1),X2)),X3) = hAPP_nat_nat(plus_plus_nat(X1),hAPP_nat_nat(plus_plus_nat(X2),X3)),
inference(literals_permutation,[status(thm)],[c_0_3688]) ).
cnf(c_0_3689_0,axiom,
hAPP_real_real(plus_plus_real(hAPP_real_real(plus_plus_real(X1),X2)),X3) = hAPP_real_real(plus_plus_real(X1),hAPP_real_real(plus_plus_real(X2),X3)),
inference(literals_permutation,[status(thm)],[c_0_3689]) ).
cnf(c_0_3690_0,axiom,
hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(X1),X2)),X3) = hAPP_int_int(plus_plus_int(X1),hAPP_int_int(plus_plus_int(X2),X3)),
inference(literals_permutation,[status(thm)],[c_0_3690]) ).
cnf(c_0_3691_0,axiom,
hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(plus_plus_nat(X1),X2)),X3) = hAPP_nat_nat(plus_plus_nat(X1),hAPP_nat_nat(plus_plus_nat(X2),X3)),
inference(literals_permutation,[status(thm)],[c_0_3691]) ).
cnf(c_0_3692_0,axiom,
hAPP_real_real(plus_plus_real(hAPP_real_real(plus_plus_real(X1),X2)),X3) = hAPP_real_real(plus_plus_real(X1),hAPP_real_real(plus_plus_real(X2),X3)),
inference(literals_permutation,[status(thm)],[c_0_3692]) ).
cnf(c_0_3693_0,axiom,
hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(X1),X2)),X3) = hAPP_int_int(plus_plus_int(X1),hAPP_int_int(plus_plus_int(X2),X3)),
inference(literals_permutation,[status(thm)],[c_0_3693]) ).
cnf(c_0_3694_0,axiom,
hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(plus_plus_nat(X1),X2)),X3) = hAPP_nat_nat(plus_plus_nat(X1),hAPP_nat_nat(plus_plus_nat(X2),X3)),
inference(literals_permutation,[status(thm)],[c_0_3694]) ).
cnf(c_0_3695_0,axiom,
hAPP_real_real(plus_plus_real(hAPP_real_real(plus_plus_real(X1),X2)),X3) = hAPP_real_real(plus_plus_real(X1),hAPP_real_real(plus_plus_real(X2),X3)),
inference(literals_permutation,[status(thm)],[c_0_3695]) ).
cnf(c_0_3699_0,axiom,
hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(plus_plus_nat(X1),X2)),X3) = hAPP_nat_nat(plus_plus_nat(X1),hAPP_nat_nat(plus_plus_nat(X2),X3)),
inference(literals_permutation,[status(thm)],[c_0_3699]) ).
cnf(c_0_3701_0,axiom,
hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(X1),X2)),X3) = hAPP_int_int(plus_plus_int(X1),hAPP_int_int(plus_plus_int(X2),X3)),
inference(literals_permutation,[status(thm)],[c_0_3701]) ).
cnf(c_0_3710_0,axiom,
hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),hAPP_nat_nat(plus_plus_nat(X1),X2))),
inference(literals_permutation,[status(thm)],[c_0_3710]) ).
cnf(c_0_3711_0,axiom,
hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),hAPP_nat_nat(plus_plus_nat(X2),X1))),
inference(literals_permutation,[status(thm)],[c_0_3711]) ).
cnf(c_0_3722_0,axiom,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),hAPP_int_int(plus_plus_int(X1),one_one_int))),
inference(literals_permutation,[status(thm)],[c_0_3722]) ).
cnf(c_0_3723_0,axiom,
hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),hAPP_nat_nat(plus_plus_nat(X1),one_one_nat))),
inference(literals_permutation,[status(thm)],[c_0_3723]) ).
cnf(c_0_3724_0,axiom,
hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X1),hAPP_real_real(plus_plus_real(X1),one_one_real))),
inference(literals_permutation,[status(thm)],[c_0_3724]) ).
cnf(c_0_3731_0,axiom,
hAPP_int_int(plus_plus_int(hAPP_nat_int(semiri1621563631at_int,X1)),hAPP_nat_int(semiri1621563631at_int,X2)) = hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(plus_plus_nat(X1),X2)),
inference(literals_permutation,[status(thm)],[c_0_3731]) ).
cnf(c_0_3732_0,axiom,
hAPP_int_int(plus_plus_int(hAPP_nat_int(semiri1621563631at_int,X1)),hAPP_nat_int(semiri1621563631at_int,X2)) = hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(plus_plus_nat(X1),X2)),
inference(literals_permutation,[status(thm)],[c_0_3732]) ).
cnf(c_0_3733_0,axiom,
hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(semiri984289939at_nat,X1)),hAPP_nat_nat(semiri984289939at_nat,X2)) = hAPP_nat_nat(semiri984289939at_nat,hAPP_nat_nat(plus_plus_nat(X1),X2)),
inference(literals_permutation,[status(thm)],[c_0_3733]) ).
cnf(c_0_3734_0,axiom,
hAPP_real_real(plus_plus_real(hAPP_nat_real(semiri132038758t_real,X1)),hAPP_nat_real(semiri132038758t_real,X2)) = hAPP_nat_real(semiri132038758t_real,hAPP_nat_nat(plus_plus_nat(X1),X2)),
inference(literals_permutation,[status(thm)],[c_0_3734]) ).
cnf(c_0_3735_0,axiom,
hAPP_int_int(plus_plus_int(hAPP_nat_int(semiri1621563631at_int,X1)),hAPP_nat_int(semiri1621563631at_int,X2)) = hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(plus_plus_nat(X1),X2)),
inference(literals_permutation,[status(thm)],[c_0_3735]) ).
cnf(c_0_3746_0,axiom,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),number_number_of_int(bit0(bit1(pls))))),
inference(literals_permutation,[status(thm)],[c_0_3746]) ).
cnf(c_0_3747_0,axiom,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),number_number_of_int(bit1(bit1(pls))))),
inference(literals_permutation,[status(thm)],[c_0_3747]) ).
cnf(c_0_3748_0,axiom,
hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),number_number_of_nat(bit0(bit1(pls))))),
inference(literals_permutation,[status(thm)],[c_0_3748]) ).
cnf(c_0_3753_0,axiom,
hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),hAPP_real_real(plus_plus_real(one_one_real),one_one_real))),
inference(literals_permutation,[status(thm)],[c_0_3753]) ).
cnf(c_0_3754_0,axiom,
hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(plus_plus_nat(one_one_nat),one_one_nat))),
inference(literals_permutation,[status(thm)],[c_0_3754]) ).
cnf(c_0_3755_0,axiom,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_int_int(plus_plus_int(one_one_int),one_one_int))),
inference(literals_permutation,[status(thm)],[c_0_3755]) ).
cnf(c_0_3756_0,axiom,
hAPP_real_real(plus_plus_real(hAPP_real_real(plus_plus_real(one_one_real),number267125858f_real(X1))),number267125858f_real(X1)) = number267125858f_real(bit1(X1)),
inference(literals_permutation,[status(thm)],[c_0_3756]) ).
cnf(c_0_3757_0,axiom,
hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),number_number_of_int(X1))),number_number_of_int(X1)) = number_number_of_int(bit1(X1)),
inference(literals_permutation,[status(thm)],[c_0_3757]) ).
cnf(c_0_3758_0,axiom,
hAPP_real_real(plus_plus_real(hAPP_real_real(plus_plus_real(zero_zero_real),number267125858f_real(X1))),number267125858f_real(X1)) = number267125858f_real(bit0(X1)),
inference(literals_permutation,[status(thm)],[c_0_3758]) ).
cnf(c_0_3759_0,axiom,
hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(zero_zero_int),number_number_of_int(X1))),number_number_of_int(X1)) = number_number_of_int(bit0(X1)),
inference(literals_permutation,[status(thm)],[c_0_3759]) ).
cnf(c_0_3773_0,axiom,
hAPP_int_int(plus_plus_int(X1),hAPP_int_int(plus_plus_int(X2),X3)) = hAPP_int_int(plus_plus_int(X2),hAPP_int_int(plus_plus_int(X1),X3)),
inference(literals_permutation,[status(thm)],[c_0_3773]) ).
cnf(c_0_3774_0,axiom,
hAPP_nat_nat(plus_plus_nat(X1),hAPP_nat_nat(plus_plus_nat(X2),X3)) = hAPP_nat_nat(plus_plus_nat(X2),hAPP_nat_nat(plus_plus_nat(X1),X3)),
inference(literals_permutation,[status(thm)],[c_0_3774]) ).
cnf(c_0_3775_0,axiom,
hAPP_real_real(plus_plus_real(X1),hAPP_real_real(plus_plus_real(X2),X3)) = hAPP_real_real(plus_plus_real(X2),hAPP_real_real(plus_plus_real(X1),X3)),
inference(literals_permutation,[status(thm)],[c_0_3775]) ).
cnf(c_0_3776_0,axiom,
hAPP_nat_int(power_power_int(hAPP_nat_int(semiri1621563631at_int,X1)),X2) = hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(power_power_nat(X1),X2)),
inference(literals_permutation,[status(thm)],[c_0_3776]) ).
cnf(c_0_3777_0,axiom,
hAPP_nat_int(power_power_int(hAPP_nat_int(semiri1621563631at_int,X1)),X2) = hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(power_power_nat(X1),X2)),
inference(literals_permutation,[status(thm)],[c_0_3777]) ).
cnf(c_0_3778_0,axiom,
hAPP_nat_nat(power_power_nat(hAPP_nat_nat(semiri984289939at_nat,X1)),X2) = hAPP_nat_nat(semiri984289939at_nat,hAPP_nat_nat(power_power_nat(X1),X2)),
inference(literals_permutation,[status(thm)],[c_0_3778]) ).
cnf(c_0_3779_0,axiom,
hAPP_nat_real(power_power_real(hAPP_nat_real(semiri132038758t_real,X1)),X2) = hAPP_nat_real(semiri132038758t_real,hAPP_nat_nat(power_power_nat(X1),X2)),
inference(literals_permutation,[status(thm)],[c_0_3779]) ).
cnf(c_0_3780_0,axiom,
hAPP_nat_nat(plus_plus_nat(X1),hAPP_nat_nat(plus_plus_nat(X2),X3)) = hAPP_nat_nat(plus_plus_nat(X2),hAPP_nat_nat(plus_plus_nat(X1),X3)),
inference(literals_permutation,[status(thm)],[c_0_3780]) ).
cnf(c_0_3781_0,axiom,
hAPP_int_int(plus_plus_int(X1),hAPP_int_int(plus_plus_int(X2),X3)) = hAPP_int_int(plus_plus_int(X2),hAPP_int_int(plus_plus_int(X1),X3)),
inference(literals_permutation,[status(thm)],[c_0_3781]) ).
cnf(c_0_3782_0,axiom,
hAPP_nat_int(power_power_int(hAPP_nat_int(semiri1621563631at_int,X1)),X2) = hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(power_power_nat(X1),X2)),
inference(literals_permutation,[status(thm)],[c_0_3782]) ).
cnf(c_0_3783_0,axiom,
hAPP_nat_int(power_power_int(hAPP_nat_int(semiri1621563631at_int,X1)),X2) = hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(power_power_nat(X1),X2)),
inference(literals_permutation,[status(thm)],[c_0_3783]) ).
cnf(c_0_3785_0,axiom,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_nat_int(semiri1621563631at_int,X1))),
inference(literals_permutation,[status(thm)],[c_0_3785]) ).
cnf(c_0_3786_0,axiom,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_nat_int(semiri1621563631at_int,X1))),
inference(literals_permutation,[status(thm)],[c_0_3786]) ).
cnf(c_0_3787_0,axiom,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_nat_int(semiri1621563631at_int,X1))),
inference(literals_permutation,[status(thm)],[c_0_3787]) ).
cnf(c_0_3788_0,axiom,
hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),hAPP_nat_nat(semiri984289939at_nat,X1))),
inference(literals_permutation,[status(thm)],[c_0_3788]) ).
cnf(c_0_3789_0,axiom,
hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),hAPP_nat_real(semiri132038758t_real,X1))),
inference(literals_permutation,[status(thm)],[c_0_3789]) ).
cnf(c_0_3790_0,axiom,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_nat_int(semiri1621563631at_int,X1))),
inference(literals_permutation,[status(thm)],[c_0_3790]) ).
cnf(c_0_3791_0,axiom,
hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),hAPP_nat_nat(semiri984289939at_nat,X1))),
inference(literals_permutation,[status(thm)],[c_0_3791]) ).
cnf(c_0_3792_0,axiom,
hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),hAPP_nat_real(semiri132038758t_real,X1))),
inference(literals_permutation,[status(thm)],[c_0_3792]) ).
cnf(c_0_3812_0,axiom,
bit0(hAPP_int_int(plus_plus_int(X1),succ(X2))) = hAPP_int_int(plus_plus_int(bit1(X1)),bit1(X2)),
inference(literals_permutation,[status(thm)],[c_0_3812]) ).
cnf(c_0_3813_0,axiom,
hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),X1)),X1) = bit1(X1),
inference(literals_permutation,[status(thm)],[c_0_3813]) ).
cnf(c_0_3816_0,axiom,
hAPP_int_int(plus_plus_int(bit0(X1)),bit1(X2)) = bit1(hAPP_int_int(plus_plus_int(X1),X2)),
inference(literals_permutation,[status(thm)],[c_0_3816]) ).
cnf(c_0_3817_0,axiom,
hAPP_int_int(plus_plus_int(bit1(X1)),bit0(X2)) = bit1(hAPP_int_int(plus_plus_int(X1),X2)),
inference(literals_permutation,[status(thm)],[c_0_3817]) ).
cnf(c_0_3818_0,axiom,
hAPP_real_real(plus_plus_real(number267125858f_real(X1)),number267125858f_real(X2)) = number267125858f_real(hAPP_int_int(plus_plus_int(X1),X2)),
inference(literals_permutation,[status(thm)],[c_0_3818]) ).
cnf(c_0_3819_0,axiom,
hAPP_int_int(plus_plus_int(number_number_of_int(X1)),number_number_of_int(X2)) = number_number_of_int(hAPP_int_int(plus_plus_int(X1),X2)),
inference(literals_permutation,[status(thm)],[c_0_3819]) ).
cnf(c_0_3820_0,axiom,
hAPP_real_real(plus_plus_real(number267125858f_real(X1)),number267125858f_real(X2)) = number267125858f_real(hAPP_int_int(plus_plus_int(X1),X2)),
inference(literals_permutation,[status(thm)],[c_0_3820]) ).
cnf(c_0_3821_0,axiom,
hAPP_int_int(plus_plus_int(number_number_of_int(X1)),number_number_of_int(X2)) = number_number_of_int(hAPP_int_int(plus_plus_int(X1),X2)),
inference(literals_permutation,[status(thm)],[c_0_3821]) ).
cnf(c_0_3822_0,axiom,
hAPP_int_int(plus_plus_int(bit0(X1)),bit0(X2)) = bit0(hAPP_int_int(plus_plus_int(X1),X2)),
inference(literals_permutation,[status(thm)],[c_0_3822]) ).
cnf(c_0_3823_0,axiom,
hAPP_int_int(plus_plus_int(number_number_of_int(X1)),number_number_of_int(X2)) = number_number_of_int(hAPP_int_int(plus_plus_int(X1),X2)),
inference(literals_permutation,[status(thm)],[c_0_3823]) ).
cnf(c_0_3831_0,axiom,
number267125858f_real(hAPP_int_int(plus_plus_int(X1),bit1(pls))) = hAPP_real_real(plus_plus_real(number267125858f_real(X1)),one_one_real),
inference(literals_permutation,[status(thm)],[c_0_3831]) ).
cnf(c_0_3832_0,axiom,
number_number_of_int(hAPP_int_int(plus_plus_int(X1),bit1(pls))) = hAPP_int_int(plus_plus_int(number_number_of_int(X1)),one_one_int),
inference(literals_permutation,[status(thm)],[c_0_3832]) ).
cnf(c_0_3833_0,axiom,
number267125858f_real(hAPP_int_int(plus_plus_int(bit1(pls)),X1)) = hAPP_real_real(plus_plus_real(one_one_real),number267125858f_real(X1)),
inference(literals_permutation,[status(thm)],[c_0_3833]) ).
cnf(c_0_3834_0,axiom,
number_number_of_int(hAPP_int_int(plus_plus_int(bit1(pls)),X1)) = hAPP_int_int(plus_plus_int(one_one_int),number_number_of_int(X1)),
inference(literals_permutation,[status(thm)],[c_0_3834]) ).
cnf(c_0_3835_0,axiom,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X1)),
inference(literals_permutation,[status(thm)],[c_0_3835]) ).
cnf(c_0_3836_0,axiom,
hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X1)),
inference(literals_permutation,[status(thm)],[c_0_3836]) ).
cnf(c_0_3837_0,axiom,
hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X1),X1)),
inference(literals_permutation,[status(thm)],[c_0_3837]) ).
cnf(c_0_3838_0,axiom,
hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X1),X1)),
inference(literals_permutation,[status(thm)],[c_0_3838]) ).
cnf(c_0_3839_0,axiom,
hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X1)),
inference(literals_permutation,[status(thm)],[c_0_3839]) ).
cnf(c_0_3840_0,axiom,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),number_number_of_int(pls))),
inference(literals_permutation,[status(thm)],[c_0_3840]) ).
cnf(c_0_3841_0,axiom,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X1)),
inference(literals_permutation,[status(thm)],[c_0_3841]) ).
cnf(c_0_3845_0,axiom,
hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),X1)),
inference(literals_permutation,[status(thm)],[c_0_3845]) ).
cnf(c_0_3846_0,axiom,
hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),X1)),
inference(literals_permutation,[status(thm)],[c_0_3846]) ).
cnf(c_0_3847_0,axiom,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),one_one_int)),
inference(literals_permutation,[status(thm)],[c_0_3847]) ).
cnf(c_0_3848_0,axiom,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),one_one_int)),
inference(literals_permutation,[status(thm)],[c_0_3848]) ).
cnf(c_0_3849_0,axiom,
hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),one_one_nat)),
inference(literals_permutation,[status(thm)],[c_0_3849]) ).
cnf(c_0_3850_0,axiom,
hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),one_one_real)),
inference(literals_permutation,[status(thm)],[c_0_3850]) ).
cnf(c_0_3851_0,axiom,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),zero_zero_int)),
inference(literals_permutation,[status(thm)],[c_0_3851]) ).
cnf(c_0_3852_0,axiom,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),pls)),
inference(literals_permutation,[status(thm)],[c_0_3852]) ).
cnf(c_0_3853_0,axiom,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),t)),
inference(literals_permutation,[status(thm)],[c_0_3853]) ).
cnf(c_0_3854_0,axiom,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),one_one_int)),
inference(literals_permutation,[status(thm)],[c_0_3854]) ).
cnf(c_0_3855_0,axiom,
hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),one_one_nat)),
inference(literals_permutation,[status(thm)],[c_0_3855]) ).
cnf(c_0_3856_0,axiom,
hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),one_one_real)),
inference(literals_permutation,[status(thm)],[c_0_3856]) ).
cnf(c_0_3857_0,axiom,
hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),tn)),
inference(literals_permutation,[status(thm)],[c_0_3857]) ).
cnf(c_0_3858_0,axiom,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),one_one_int)),
inference(literals_permutation,[status(thm)],[c_0_3858]) ).
cnf(c_0_3859_0,axiom,
hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),n)),
inference(literals_permutation,[status(thm)],[c_0_3859]) ).
cnf(c_0_3860_0,axiom,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),t)),
inference(literals_permutation,[status(thm)],[c_0_3860]) ).
cnf(c_0_3878_0,axiom,
hAPP_nat_int(semiri1621563631at_int,number_number_of_nat(bit1(bit1(pls)))) = number_number_of_int(bit1(bit1(pls))),
inference(literals_permutation,[status(thm)],[c_0_3878]) ).
cnf(c_0_3879_0,axiom,
hAPP_nat_int(semiri1621563631at_int,number_number_of_nat(bit0(bit1(pls)))) = number_number_of_int(bit0(bit1(pls))),
inference(literals_permutation,[status(thm)],[c_0_3879]) ).
cnf(c_0_3885_0,axiom,
hAPP_nat_real(power_power_real(zero_zero_real),number_number_of_nat(bit0(bit1(pls)))) = zero_zero_real,
inference(literals_permutation,[status(thm)],[c_0_3885]) ).
cnf(c_0_3886_0,axiom,
hAPP_nat_nat(power_power_nat(zero_zero_nat),number_number_of_nat(bit0(bit1(pls)))) = zero_zero_nat,
inference(literals_permutation,[status(thm)],[c_0_3886]) ).
cnf(c_0_3887_0,axiom,
hAPP_nat_int(power_power_int(zero_zero_int),number_number_of_nat(bit0(bit1(pls)))) = zero_zero_int,
inference(literals_permutation,[status(thm)],[c_0_3887]) ).
cnf(c_0_3888_0,axiom,
hAPP_nat_real(power_power_real(one_one_real),number_number_of_nat(bit0(bit1(pls)))) = one_one_real,
inference(literals_permutation,[status(thm)],[c_0_3888]) ).
cnf(c_0_3889_0,axiom,
hAPP_nat_nat(power_power_nat(one_one_nat),number_number_of_nat(bit0(bit1(pls)))) = one_one_nat,
inference(literals_permutation,[status(thm)],[c_0_3889]) ).
cnf(c_0_3890_0,axiom,
hAPP_nat_int(power_power_int(one_one_int),number_number_of_nat(bit0(bit1(pls)))) = one_one_int,
inference(literals_permutation,[status(thm)],[c_0_3890]) ).
cnf(c_0_3907_0,axiom,
hAPP_int_int(plus_plus_int(X1),X2) = hAPP_int_int(plus_plus_int(X2),X1),
inference(literals_permutation,[status(thm)],[c_0_3907]) ).
cnf(c_0_3908_0,axiom,
hAPP_nat_nat(plus_plus_nat(X1),X2) = hAPP_nat_nat(plus_plus_nat(X2),X1),
inference(literals_permutation,[status(thm)],[c_0_3908]) ).
cnf(c_0_3909_0,axiom,
hAPP_real_real(plus_plus_real(X1),X2) = hAPP_real_real(plus_plus_real(X2),X1),
inference(literals_permutation,[status(thm)],[c_0_3909]) ).
cnf(c_0_3910_0,axiom,
hAPP_nat_nat(plus_plus_nat(X1),X2) = hAPP_nat_nat(plus_plus_nat(X2),X1),
inference(literals_permutation,[status(thm)],[c_0_3910]) ).
cnf(c_0_3911_0,axiom,
hAPP_int_int(plus_plus_int(X1),X2) = hAPP_int_int(plus_plus_int(X2),X1),
inference(literals_permutation,[status(thm)],[c_0_3911]) ).
cnf(c_0_3912_0,axiom,
number267125858f_real(hAPP_nat_int(semiri1621563631at_int,X1)) = hAPP_nat_real(semiri132038758t_real,X1),
inference(literals_permutation,[status(thm)],[c_0_3912]) ).
cnf(c_0_3913_0,axiom,
number_number_of_int(hAPP_nat_int(semiri1621563631at_int,X1)) = hAPP_nat_int(semiri1621563631at_int,X1),
inference(literals_permutation,[status(thm)],[c_0_3913]) ).
cnf(c_0_3914_0,axiom,
number_number_of_nat(hAPP_nat_int(semiri1621563631at_int,X1)) = hAPP_nat_nat(semiri984289939at_nat,X1),
inference(literals_permutation,[status(thm)],[c_0_3914]) ).
cnf(c_0_3915_0,axiom,
hAPP_nat_nat(if_nat(fFalse,X1),X2) = X2,
inference(literals_permutation,[status(thm)],[c_0_3915]) ).
cnf(c_0_3916_0,axiom,
hAPP_nat_nat(if_nat(fTrue,X1),X2) = X1,
inference(literals_permutation,[status(thm)],[c_0_3916]) ).
cnf(c_0_3941_0,axiom,
hAPP_int_int(plus_plus_int(one_one_int),number_number_of_int(X1)) = number_number_of_int(succ(X1)),
inference(literals_permutation,[status(thm)],[c_0_3941]) ).
cnf(c_0_3942_0,axiom,
hAPP_real_real(plus_plus_real(one_one_real),number267125858f_real(X1)) = number267125858f_real(succ(X1)),
inference(literals_permutation,[status(thm)],[c_0_3942]) ).
cnf(c_0_3943_0,axiom,
number_number_of_nat(bit0(bit1(pls))) = hAPP_nat_nat(plus_plus_nat(one_one_nat),one_one_nat),
inference(literals_permutation,[status(thm)],[c_0_3943]) ).
cnf(c_0_3944_0,axiom,
number267125858f_real(bit0(bit1(pls))) = hAPP_real_real(plus_plus_real(one_one_real),one_one_real),
inference(literals_permutation,[status(thm)],[c_0_3944]) ).
cnf(c_0_3945_0,axiom,
number_number_of_nat(bit0(bit1(pls))) = hAPP_nat_nat(plus_plus_nat(one_one_nat),one_one_nat),
inference(literals_permutation,[status(thm)],[c_0_3945]) ).
cnf(c_0_3946_0,axiom,
number_number_of_int(bit0(bit1(pls))) = hAPP_int_int(plus_plus_int(one_one_int),one_one_int),
inference(literals_permutation,[status(thm)],[c_0_3946]) ).
cnf(c_0_3947_0,axiom,
number267125858f_real(bit0(bit1(pls))) = hAPP_real_real(plus_plus_real(one_one_real),one_one_real),
inference(literals_permutation,[status(thm)],[c_0_3947]) ).
cnf(c_0_3948_0,axiom,
number_number_of_int(bit0(bit1(pls))) = hAPP_int_int(plus_plus_int(one_one_int),one_one_int),
inference(literals_permutation,[status(thm)],[c_0_3948]) ).
cnf(c_0_3952_0,axiom,
is_bool(hAPP_real_bool(X1,X2)),
inference(literals_permutation,[status(thm)],[c_0_3952]) ).
cnf(c_0_3953_0,axiom,
is_bool(hAPP_nat_bool(X1,X2)),
inference(literals_permutation,[status(thm)],[c_0_3953]) ).
cnf(c_0_3954_0,axiom,
is_bool(hAPP_int_bool(X1,X2)),
inference(literals_permutation,[status(thm)],[c_0_3954]) ).
cnf(c_0_3963_0,axiom,
hAPP_real_real(plus_plus_real(number267125858f_real(pls)),X1) = X1,
inference(literals_permutation,[status(thm)],[c_0_3963]) ).
cnf(c_0_3964_0,axiom,
hAPP_int_int(plus_plus_int(number_number_of_int(pls)),X1) = X1,
inference(literals_permutation,[status(thm)],[c_0_3964]) ).
cnf(c_0_3970_0,axiom,
hAPP_real_real(plus_plus_real(X1),number267125858f_real(pls)) = X1,
inference(literals_permutation,[status(thm)],[c_0_3970]) ).
cnf(c_0_3971_0,axiom,
hAPP_int_int(plus_plus_int(X1),number_number_of_int(pls)) = X1,
inference(literals_permutation,[status(thm)],[c_0_3971]) ).
cnf(c_0_3972_0,axiom,
hAPP_int_int(plus_plus_int(X1),X1) = bit0(X1),
inference(literals_permutation,[status(thm)],[c_0_3972]) ).
cnf(c_0_3982_0,axiom,
hAPP_int_int(plus_plus_int(X1),one_one_int) = succ(X1),
inference(literals_permutation,[status(thm)],[c_0_3982]) ).
cnf(c_0_3984_0,axiom,
succ(bit1(X1)) = bit0(succ(X1)),
inference(literals_permutation,[status(thm)],[c_0_3984]) ).
cnf(c_0_3988_0,axiom,
hAPP_nat_int(power_power_int(X1),one_one_nat) = X1,
inference(literals_permutation,[status(thm)],[c_0_3988]) ).
cnf(c_0_3989_0,axiom,
hAPP_nat_nat(power_power_nat(X1),one_one_nat) = X1,
inference(literals_permutation,[status(thm)],[c_0_3989]) ).
cnf(c_0_3990_0,axiom,
hAPP_nat_real(power_power_real(X1),one_one_nat) = X1,
inference(literals_permutation,[status(thm)],[c_0_3990]) ).
cnf(c_0_3991_0,axiom,
hAPP_int_int(plus_plus_int(X1),zero_zero_int) = X1,
inference(literals_permutation,[status(thm)],[c_0_3991]) ).
cnf(c_0_3992_0,axiom,
hAPP_nat_nat(plus_plus_nat(X1),zero_zero_nat) = X1,
inference(literals_permutation,[status(thm)],[c_0_3992]) ).
cnf(c_0_3993_0,axiom,
hAPP_real_real(plus_plus_real(X1),zero_zero_real) = X1,
inference(literals_permutation,[status(thm)],[c_0_3993]) ).
cnf(c_0_3994_0,axiom,
hAPP_int_int(plus_plus_int(X1),zero_zero_int) = X1,
inference(literals_permutation,[status(thm)],[c_0_3994]) ).
cnf(c_0_3995_0,axiom,
hAPP_nat_nat(plus_plus_nat(X1),zero_zero_nat) = X1,
inference(literals_permutation,[status(thm)],[c_0_3995]) ).
cnf(c_0_3996_0,axiom,
hAPP_real_real(plus_plus_real(X1),zero_zero_real) = X1,
inference(literals_permutation,[status(thm)],[c_0_3996]) ).
cnf(c_0_3997_0,axiom,
hAPP_int_int(plus_plus_int(X1),zero_zero_int) = X1,
inference(literals_permutation,[status(thm)],[c_0_3997]) ).
cnf(c_0_3998_0,axiom,
hAPP_nat_nat(plus_plus_nat(X1),zero_zero_nat) = X1,
inference(literals_permutation,[status(thm)],[c_0_3998]) ).
cnf(c_0_3999_0,axiom,
hAPP_real_real(plus_plus_real(X1),zero_zero_real) = X1,
inference(literals_permutation,[status(thm)],[c_0_3999]) ).
cnf(c_0_4000_0,axiom,
hAPP_nat_int(power_power_int(X1),one_one_nat) = X1,
inference(literals_permutation,[status(thm)],[c_0_4000]) ).
cnf(c_0_4001_0,axiom,
hAPP_nat_nat(power_power_nat(X1),one_one_nat) = X1,
inference(literals_permutation,[status(thm)],[c_0_4001]) ).
cnf(c_0_4002_0,axiom,
hAPP_nat_real(power_power_real(X1),one_one_nat) = X1,
inference(literals_permutation,[status(thm)],[c_0_4002]) ).
cnf(c_0_4003_0,axiom,
hAPP_nat_nat(plus_plus_nat(X1),zero_zero_nat) = X1,
inference(literals_permutation,[status(thm)],[c_0_4003]) ).
cnf(c_0_4004_0,axiom,
hAPP_int_int(plus_plus_int(X1),zero_zero_int) = X1,
inference(literals_permutation,[status(thm)],[c_0_4004]) ).
cnf(c_0_4005_0,axiom,
hAPP_int_int(plus_plus_int(X1),pls) = X1,
inference(literals_permutation,[status(thm)],[c_0_4005]) ).
cnf(c_0_4006_0,axiom,
hAPP_nat_int(power_power_int(X1),zero_zero_nat) = one_one_int,
inference(literals_permutation,[status(thm)],[c_0_4006]) ).
cnf(c_0_4007_0,axiom,
hAPP_nat_nat(power_power_nat(X1),zero_zero_nat) = one_one_nat,
inference(literals_permutation,[status(thm)],[c_0_4007]) ).
cnf(c_0_4008_0,axiom,
hAPP_nat_real(power_power_real(X1),zero_zero_nat) = one_one_real,
inference(literals_permutation,[status(thm)],[c_0_4008]) ).
cnf(c_0_4009_0,axiom,
hAPP_nat_int(power_power_int(X1),zero_zero_nat) = one_one_int,
inference(literals_permutation,[status(thm)],[c_0_4009]) ).
cnf(c_0_4010_0,axiom,
hAPP_nat_nat(power_power_nat(X1),zero_zero_nat) = one_one_nat,
inference(literals_permutation,[status(thm)],[c_0_4010]) ).
cnf(c_0_4011_0,axiom,
hAPP_nat_real(power_power_real(X1),zero_zero_nat) = one_one_real,
inference(literals_permutation,[status(thm)],[c_0_4011]) ).
cnf(c_0_4015_0,axiom,
hAPP_int_int(plus_plus_int(zero_zero_int),X1) = X1,
inference(literals_permutation,[status(thm)],[c_0_4015]) ).
cnf(c_0_4016_0,axiom,
hAPP_nat_nat(plus_plus_nat(zero_zero_nat),X1) = X1,
inference(literals_permutation,[status(thm)],[c_0_4016]) ).
cnf(c_0_4017_0,axiom,
hAPP_real_real(plus_plus_real(zero_zero_real),X1) = X1,
inference(literals_permutation,[status(thm)],[c_0_4017]) ).
cnf(c_0_4018_0,axiom,
hAPP_int_int(plus_plus_int(zero_zero_int),X1) = X1,
inference(literals_permutation,[status(thm)],[c_0_4018]) ).
cnf(c_0_4019_0,axiom,
hAPP_nat_nat(plus_plus_nat(zero_zero_nat),X1) = X1,
inference(literals_permutation,[status(thm)],[c_0_4019]) ).
cnf(c_0_4020_0,axiom,
hAPP_real_real(plus_plus_real(zero_zero_real),X1) = X1,
inference(literals_permutation,[status(thm)],[c_0_4020]) ).
cnf(c_0_4021_0,axiom,
hAPP_int_int(plus_plus_int(zero_zero_int),X1) = X1,
inference(literals_permutation,[status(thm)],[c_0_4021]) ).
cnf(c_0_4022_0,axiom,
hAPP_nat_nat(plus_plus_nat(zero_zero_nat),X1) = X1,
inference(literals_permutation,[status(thm)],[c_0_4022]) ).
cnf(c_0_4023_0,axiom,
hAPP_real_real(plus_plus_real(zero_zero_real),X1) = X1,
inference(literals_permutation,[status(thm)],[c_0_4023]) ).
cnf(c_0_4024_0,axiom,
hAPP_nat_nat(plus_plus_nat(zero_zero_nat),X1) = X1,
inference(literals_permutation,[status(thm)],[c_0_4024]) ).
cnf(c_0_4025_0,axiom,
hAPP_int_int(plus_plus_int(zero_zero_int),X1) = X1,
inference(literals_permutation,[status(thm)],[c_0_4025]) ).
cnf(c_0_4026_0,axiom,
hAPP_int_int(plus_plus_int(pls),X1) = X1,
inference(literals_permutation,[status(thm)],[c_0_4026]) ).
cnf(c_0_4027_0,axiom,
hAPP_nat_int(power_power_int(one_one_int),X1) = one_one_int,
inference(literals_permutation,[status(thm)],[c_0_4027]) ).
cnf(c_0_4028_0,axiom,
hAPP_nat_nat(power_power_nat(one_one_nat),X1) = one_one_nat,
inference(literals_permutation,[status(thm)],[c_0_4028]) ).
cnf(c_0_4029_0,axiom,
hAPP_nat_real(power_power_real(one_one_real),X1) = one_one_real,
inference(literals_permutation,[status(thm)],[c_0_4029]) ).
cnf(c_0_4035_0,axiom,
succ(bit0(X1)) = bit1(X1),
inference(literals_permutation,[status(thm)],[c_0_4035]) ).
cnf(c_0_4048_0,axiom,
hAPP_nat_int(semiri1621563631at_int,zero_zero_nat) = zero_zero_int,
inference(literals_permutation,[status(thm)],[c_0_4048]) ).
cnf(c_0_4049_0,axiom,
hAPP_nat_int(semiri1621563631at_int,zero_zero_nat) = zero_zero_int,
inference(literals_permutation,[status(thm)],[c_0_4049]) ).
cnf(c_0_4050_0,axiom,
hAPP_nat_nat(semiri984289939at_nat,zero_zero_nat) = zero_zero_nat,
inference(literals_permutation,[status(thm)],[c_0_4050]) ).
cnf(c_0_4051_0,axiom,
hAPP_nat_real(semiri132038758t_real,zero_zero_nat) = zero_zero_real,
inference(literals_permutation,[status(thm)],[c_0_4051]) ).
cnf(c_0_4052_0,axiom,
hAPP_nat_int(semiri1621563631at_int,one_one_nat) = one_one_int,
inference(literals_permutation,[status(thm)],[c_0_4052]) ).
cnf(c_0_4053_0,axiom,
hAPP_nat_int(semiri1621563631at_int,one_one_nat) = one_one_int,
inference(literals_permutation,[status(thm)],[c_0_4053]) ).
cnf(c_0_4054_0,axiom,
hAPP_nat_nat(semiri984289939at_nat,one_one_nat) = one_one_nat,
inference(literals_permutation,[status(thm)],[c_0_4054]) ).
cnf(c_0_4055_0,axiom,
hAPP_nat_real(semiri132038758t_real,one_one_nat) = one_one_real,
inference(literals_permutation,[status(thm)],[c_0_4055]) ).
cnf(c_0_4056_0,axiom,
hAPP_nat_int(semiri1621563631at_int,zero_zero_nat) = zero_zero_int,
inference(literals_permutation,[status(thm)],[c_0_4056]) ).
cnf(c_0_4057_0,axiom,
hAPP_nat_int(semiri1621563631at_int,one_one_nat) = one_one_int,
inference(literals_permutation,[status(thm)],[c_0_4057]) ).
cnf(c_0_4061_0,axiom,
number267125858f_real(bit1(pls)) = one_one_real,
inference(literals_permutation,[status(thm)],[c_0_4061]) ).
cnf(c_0_4062_0,axiom,
number_number_of_nat(bit1(pls)) = one_one_nat,
inference(literals_permutation,[status(thm)],[c_0_4062]) ).
cnf(c_0_4063_0,axiom,
number_number_of_int(bit1(pls)) = one_one_int,
inference(literals_permutation,[status(thm)],[c_0_4063]) ).
cnf(c_0_4064_0,axiom,
number_number_of_nat(bit1(pls)) = one_one_nat,
inference(literals_permutation,[status(thm)],[c_0_4064]) ).
cnf(c_0_4065_0,axiom,
number_number_of_nat(bit1(pls)) = one_one_nat,
inference(literals_permutation,[status(thm)],[c_0_4065]) ).
cnf(c_0_4066_0,axiom,
number_number_of_int(bit1(pls)) = one_one_int,
inference(literals_permutation,[status(thm)],[c_0_4066]) ).
cnf(c_0_4067_0,axiom,
number267125858f_real(bit1(pls)) = one_one_real,
inference(literals_permutation,[status(thm)],[c_0_4067]) ).
cnf(c_0_4068_0,axiom,
number_number_of_int(bit1(pls)) = one_one_int,
inference(literals_permutation,[status(thm)],[c_0_4068]) ).
cnf(c_0_4069_0,axiom,
number267125858f_real(bit1(pls)) = one_one_real,
inference(literals_permutation,[status(thm)],[c_0_4069]) ).
cnf(c_0_4070_0,axiom,
number_number_of_int(bit1(pls)) = one_one_int,
inference(literals_permutation,[status(thm)],[c_0_4070]) ).
cnf(c_0_4075_0,axiom,
succ(pls) = bit1(pls),
inference(literals_permutation,[status(thm)],[c_0_4075]) ).
cnf(c_0_4076_0,axiom,
number_number_of_int(X1) = X1,
inference(literals_permutation,[status(thm)],[c_0_4076]) ).
cnf(c_0_4089_0,axiom,
number267125858f_real(pls) = zero_zero_real,
inference(literals_permutation,[status(thm)],[c_0_4089]) ).
cnf(c_0_4090_0,axiom,
number_number_of_int(pls) = zero_zero_int,
inference(literals_permutation,[status(thm)],[c_0_4090]) ).
cnf(c_0_4091_0,axiom,
number267125858f_real(pls) = zero_zero_real,
inference(literals_permutation,[status(thm)],[c_0_4091]) ).
cnf(c_0_4092_0,axiom,
number_number_of_int(pls) = zero_zero_int,
inference(literals_permutation,[status(thm)],[c_0_4092]) ).
cnf(c_0_4093_0,axiom,
number267125858f_real(pls) = zero_zero_real,
inference(literals_permutation,[status(thm)],[c_0_4093]) ).
cnf(c_0_4094_0,axiom,
number_number_of_nat(pls) = zero_zero_nat,
inference(literals_permutation,[status(thm)],[c_0_4094]) ).
cnf(c_0_4095_0,axiom,
number_number_of_int(pls) = zero_zero_int,
inference(literals_permutation,[status(thm)],[c_0_4095]) ).
cnf(c_0_4096_0,axiom,
bit0(pls) = pls,
inference(literals_permutation,[status(thm)],[c_0_4096]) ).
cnf(c_0_4097_0,axiom,
number_number_of_nat(pls) = zero_zero_nat,
inference(literals_permutation,[status(thm)],[c_0_4097]) ).
cnf(c_0_4098_0,axiom,
number_number_of_nat(pls) = zero_zero_nat,
inference(literals_permutation,[status(thm)],[c_0_4098]) ).
cnf(c_0_4099_0,axiom,
number_number_of_int(pls) = zero_zero_int,
inference(literals_permutation,[status(thm)],[c_0_4099]) ).
cnf(c_0_4100_0,axiom,
is_bool(fTrue),
inference(literals_permutation,[status(thm)],[c_0_4100]) ).
cnf(c_0_4101_0,axiom,
is_bool(fFalse),
inference(literals_permutation,[status(thm)],[c_0_4101]) ).
cnf(c_0_4110_0,axiom,
pls = zero_zero_int,
inference(literals_permutation,[status(thm)],[c_0_4110]) ).
% CNF of non-axioms
% Start CNF derivation
fof(c_0_0_001,conjecture,
hAPP_nat_int(power_power_int(hAPP_int_int(plus_plus_int(one_one_int),hAPP_nat_int(semiri1621563631at_int,n))),number_number_of_nat(bit0(bit1(pls)))) != zero_zero_int,
file('<stdin>',conj_0) ).
fof(c_0_1_002,negated_conjecture,
hAPP_nat_int(power_power_int(hAPP_int_int(plus_plus_int(one_one_int),hAPP_nat_int(semiri1621563631at_int,n))),number_number_of_nat(bit0(bit1(pls)))) = zero_zero_int,
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[c_0_0])]) ).
fof(c_0_2_003,negated_conjecture,
hAPP_nat_int(power_power_int(hAPP_int_int(plus_plus_int(one_one_int),hAPP_nat_int(semiri1621563631at_int,n))),number_number_of_nat(bit0(bit1(pls)))) = zero_zero_int,
c_0_1 ).
cnf(c_0_3_004,negated_conjecture,
hAPP_nat_int(power_power_int(hAPP_int_int(plus_plus_int(one_one_int),hAPP_nat_int(semiri1621563631at_int,n))),number_number_of_nat(bit0(bit1(pls)))) = zero_zero_int,
inference(split_conjunct,[status(thm)],[c_0_2]) ).
cnf(c_0_4_005,negated_conjecture,
hAPP_nat_int(power_power_int(hAPP_int_int(plus_plus_int(one_one_int),hAPP_nat_int(semiri1621563631at_int,n))),number_number_of_nat(bit0(bit1(pls)))) = zero_zero_int,
c_0_3,
[final] ).
% End CNF derivation
%-------------------------------------------------------------
% Proof by iprover
cnf(c_2082,negated_conjecture,
hAPP_nat_int(power_power_int(hAPP_int_int(plus_plus_int(one_one_int),hAPP_nat_int(semiri1621563631at_int,n))),number_number_of_nat(bit0(bit1(pls)))) = zero_zero_int,
file('/export/starexec/sandbox/tmp/iprover_modulo_ad02e3.p',c_0_4) ).
cnf(c_2645,negated_conjecture,
hAPP_nat_int(power_power_int(hAPP_int_int(plus_plus_int(one_one_int),hAPP_nat_int(semiri1621563631at_int,n))),number_number_of_nat(bit0(bit1(pls)))) = zero_zero_int,
inference(copy,[status(esa)],[c_2082]) ).
cnf(c_2649,negated_conjecture,
hAPP_nat_int(power_power_int(hAPP_int_int(plus_plus_int(one_one_int),hAPP_nat_int(semiri1621563631at_int,n))),number_number_of_nat(bit0(bit1(pls)))) = zero_zero_int,
inference(copy,[status(esa)],[c_2645]) ).
cnf(c_2650,negated_conjecture,
hAPP_nat_int(power_power_int(hAPP_int_int(plus_plus_int(one_one_int),hAPP_nat_int(semiri1621563631at_int,n))),number_number_of_nat(bit0(bit1(pls)))) = zero_zero_int,
inference(copy,[status(esa)],[c_2649]) ).
cnf(c_2651,negated_conjecture,
hAPP_nat_int(power_power_int(hAPP_int_int(plus_plus_int(one_one_int),hAPP_nat_int(semiri1621563631at_int,n))),number_number_of_nat(bit0(bit1(pls)))) = zero_zero_int,
inference(copy,[status(esa)],[c_2650]) ).
cnf(c_8751,negated_conjecture,
hAPP_nat_int(power_power_int(hAPP_int_int(plus_plus_int(one_one_int),hAPP_nat_int(semiri1621563631at_int,n))),number_number_of_nat(bit0(bit1(pls)))) = zero_zero_int,
inference(copy,[status(esa)],[c_2651]) ).
cnf(c_8752,plain,
hAPP_nat_int(power_power_int(hAPP_int_int(plus_plus_int(one_one_int),hAPP_nat_int(semiri1621563631at_int,n))),number_number_of_nat(bit0(bit1(zero_zero_int)))) = zero_zero_int,
inference(rewriting,[status(thm)],[c_8751]) ).
cnf(c_411,plain,
( X0 = zero_zero_int
| hAPP_nat_int(power_power_int(X0),X1) != zero_zero_int ),
file('/export/starexec/sandbox/tmp/iprover_modulo_ad02e3.p',c_0_3932_1) ).
cnf(c_5409,plain,
( X0 = zero_zero_int
| hAPP_nat_int(power_power_int(X0),X1) != zero_zero_int ),
inference(copy,[status(esa)],[c_411]) ).
cnf(c_5410,plain,
( hAPP_nat_int(power_power_int(X0),X1) != zero_zero_int
| X0 = zero_zero_int ),
inference(rewriting,[status(thm)],[c_5409]) ).
cnf(c_8815,plain,
hAPP_int_int(plus_plus_int(one_one_int),hAPP_nat_int(semiri1621563631at_int,n)) = zero_zero_int,
inference(resolution,[status(thm)],[c_8752,c_5410]) ).
cnf(c_8816,plain,
hAPP_int_int(plus_plus_int(one_one_int),hAPP_nat_int(semiri1621563631at_int,n)) = zero_zero_int,
inference(rewriting,[status(thm)],[c_8815]) ).
cnf(c_266,plain,
( zero_zero_int = X0
| X0 != zero_zero_int ),
file('/export/starexec/sandbox/tmp/iprover_modulo_ad02e3.p',c_0_4084_1) ).
cnf(c_5119,plain,
( zero_zero_int = X0
| X0 != zero_zero_int ),
inference(copy,[status(esa)],[c_266]) ).
cnf(c_8873,plain,
zero_zero_int = hAPP_int_int(plus_plus_int(one_one_int),hAPP_nat_int(semiri1621563631at_int,n)),
inference(resolution,[status(thm)],[c_8816,c_5119]) ).
cnf(c_8874,plain,
zero_zero_int = hAPP_int_int(plus_plus_int(one_one_int),hAPP_nat_int(semiri1621563631at_int,n)),
inference(rewriting,[status(thm)],[c_8873]) ).
cnf(c_578,plain,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X1))
| X0 != X1 ),
file('/export/starexec/sandbox/tmp/iprover_modulo_ad02e3.p',c_0_3762_1) ).
cnf(c_5743,plain,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X1))
| X0 != X1 ),
inference(copy,[status(esa)],[c_578]) ).
cnf(c_12644,plain,
~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_int_int(plus_plus_int(one_one_int),hAPP_nat_int(semiri1621563631at_int,n)))),
inference(resolution,[status(thm)],[c_8874,c_5743]) ).
cnf(c_12665,plain,
~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_int_int(plus_plus_int(one_one_int),hAPP_nat_int(semiri1621563631at_int,n)))),
inference(rewriting,[status(thm)],[c_12644]) ).
cnf(c_203,plain,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_int_int(plus_plus_int(one_one_int),hAPP_nat_int(semiri1621563631at_int,n)))),
file('/export/starexec/sandbox/tmp/iprover_modulo_ad02e3.p',c_0_3592_0) ).
cnf(c_4998,plain,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_int_int(plus_plus_int(one_one_int),hAPP_nat_int(semiri1621563631at_int,n)))),
inference(copy,[status(esa)],[c_203]) ).
cnf(c_172180,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_12665,c_4998]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : NUM925+2 : TPTP v8.1.0. Released v5.3.0.
% 0.07/0.13 % Command : iprover_modulo %s %d
% 0.13/0.34 % Computer : n006.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Wed Jul 6 19:17:21 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.35 % Running in mono-core mode
% 0.20/0.55 % Orienting using strategy Equiv(ClausalAll)
% 0.20/0.55 % FOF problem with conjecture
% 0.20/0.55 % Executing iprover_moduloopt --modulo true --schedule none --sub_typing false --res_to_prop_solver none --res_prop_simpl_given false --res_lit_sel kbo_max --large_theory_mode false --res_time_limit 1000 --res_orphan_elimination false --prep_sem_filter none --prep_unflatten false --comb_res_mult 1000 --comb_inst_mult 300 --clausifier .//eprover --clausifier_options "--tstp-format " --proof_out_file /export/starexec/sandbox/tmp/iprover_proof_d5c530.s --tptp_safe_out true --time_out_real 150 /export/starexec/sandbox/tmp/iprover_modulo_ad02e3.p | tee /export/starexec/sandbox/tmp/iprover_modulo_out_8dd8e0 | grep -v "SZS"
% 0.20/0.57
% 0.20/0.57 %---------------- iProver v2.5 (CASC-J8 2016) ----------------%
% 0.20/0.57
% 0.20/0.57 %
% 0.20/0.57 % ------ iProver source info
% 0.20/0.57
% 0.20/0.57 % git: sha1: 57accf6c58032223c7708532cf852a99fa48c1b3
% 0.20/0.57 % git: non_committed_changes: true
% 0.20/0.57 % git: last_make_outside_of_git: true
% 0.20/0.57
% 0.20/0.57 %
% 0.20/0.57 % ------ Input Options
% 0.20/0.57
% 0.20/0.57 % --out_options all
% 0.20/0.57 % --tptp_safe_out true
% 0.20/0.57 % --problem_path ""
% 0.20/0.57 % --include_path ""
% 0.20/0.57 % --clausifier .//eprover
% 0.20/0.57 % --clausifier_options --tstp-format
% 0.20/0.57 % --stdin false
% 0.20/0.57 % --dbg_backtrace false
% 0.20/0.57 % --dbg_dump_prop_clauses false
% 0.20/0.57 % --dbg_dump_prop_clauses_file -
% 0.20/0.57 % --dbg_out_stat false
% 0.20/0.57
% 0.20/0.57 % ------ General Options
% 0.20/0.57
% 0.20/0.57 % --fof false
% 0.20/0.57 % --time_out_real 150.
% 0.20/0.57 % --time_out_prep_mult 0.2
% 0.20/0.57 % --time_out_virtual -1.
% 0.20/0.57 % --schedule none
% 0.20/0.57 % --ground_splitting input
% 0.20/0.57 % --splitting_nvd 16
% 0.20/0.57 % --non_eq_to_eq false
% 0.20/0.57 % --prep_gs_sim true
% 0.20/0.57 % --prep_unflatten false
% 0.20/0.57 % --prep_res_sim true
% 0.20/0.57 % --prep_upred true
% 0.20/0.57 % --res_sim_input true
% 0.20/0.57 % --clause_weak_htbl true
% 0.20/0.57 % --gc_record_bc_elim false
% 0.20/0.57 % --symbol_type_check false
% 0.20/0.57 % --clausify_out false
% 0.20/0.57 % --large_theory_mode false
% 0.20/0.57 % --prep_sem_filter none
% 0.20/0.57 % --prep_sem_filter_out false
% 0.20/0.57 % --preprocessed_out false
% 0.20/0.57 % --sub_typing false
% 0.20/0.57 % --brand_transform false
% 0.20/0.57 % --pure_diseq_elim true
% 0.20/0.57 % --min_unsat_core false
% 0.20/0.57 % --pred_elim true
% 0.20/0.57 % --add_important_lit false
% 0.20/0.57 % --soft_assumptions false
% 0.20/0.57 % --reset_solvers false
% 0.20/0.57 % --bc_imp_inh []
% 0.20/0.57 % --conj_cone_tolerance 1.5
% 0.20/0.57 % --prolific_symb_bound 500
% 0.20/0.57 % --lt_threshold 2000
% 0.20/0.57
% 0.20/0.57 % ------ SAT Options
% 0.20/0.57
% 0.20/0.57 % --sat_mode false
% 0.20/0.57 % --sat_fm_restart_options ""
% 0.20/0.57 % --sat_gr_def false
% 0.20/0.57 % --sat_epr_types true
% 0.20/0.57 % --sat_non_cyclic_types false
% 0.20/0.57 % --sat_finite_models false
% 0.20/0.57 % --sat_fm_lemmas false
% 0.20/0.57 % --sat_fm_prep false
% 0.20/0.57 % --sat_fm_uc_incr true
% 0.20/0.57 % --sat_out_model small
% 0.20/0.57 % --sat_out_clauses false
% 0.20/0.57
% 0.20/0.57 % ------ QBF Options
% 0.20/0.57
% 0.20/0.57 % --qbf_mode false
% 0.20/0.57 % --qbf_elim_univ true
% 0.20/0.57 % --qbf_sk_in true
% 0.20/0.57 % --qbf_pred_elim true
% 0.20/0.57 % --qbf_split 32
% 0.20/0.57
% 0.20/0.57 % ------ BMC1 Options
% 0.20/0.57
% 0.20/0.57 % --bmc1_incremental false
% 0.20/0.57 % --bmc1_axioms reachable_all
% 0.20/0.57 % --bmc1_min_bound 0
% 0.20/0.57 % --bmc1_max_bound -1
% 0.20/0.57 % --bmc1_max_bound_default -1
% 0.20/0.57 % --bmc1_symbol_reachability true
% 0.20/0.57 % --bmc1_property_lemmas false
% 0.20/0.57 % --bmc1_k_induction false
% 0.20/0.57 % --bmc1_non_equiv_states false
% 0.20/0.57 % --bmc1_deadlock false
% 0.20/0.57 % --bmc1_ucm false
% 0.20/0.57 % --bmc1_add_unsat_core none
% 0.20/0.57 % --bmc1_unsat_core_children false
% 0.20/0.57 % --bmc1_unsat_core_extrapolate_axioms false
% 0.20/0.57 % --bmc1_out_stat full
% 0.20/0.57 % --bmc1_ground_init false
% 0.20/0.57 % --bmc1_pre_inst_next_state false
% 0.20/0.57 % --bmc1_pre_inst_state false
% 0.20/0.57 % --bmc1_pre_inst_reach_state false
% 0.20/0.57 % --bmc1_out_unsat_core false
% 0.20/0.57 % --bmc1_aig_witness_out false
% 0.20/0.57 % --bmc1_verbose false
% 0.20/0.57 % --bmc1_dump_clauses_tptp false
% 0.20/0.59 % --bmc1_dump_unsat_core_tptp false
% 0.20/0.59 % --bmc1_dump_file -
% 0.20/0.59 % --bmc1_ucm_expand_uc_limit 128
% 0.20/0.59 % --bmc1_ucm_n_expand_iterations 6
% 0.20/0.59 % --bmc1_ucm_extend_mode 1
% 0.20/0.59 % --bmc1_ucm_init_mode 2
% 0.20/0.59 % --bmc1_ucm_cone_mode none
% 0.20/0.59 % --bmc1_ucm_reduced_relation_type 0
% 0.20/0.59 % --bmc1_ucm_relax_model 4
% 0.20/0.59 % --bmc1_ucm_full_tr_after_sat true
% 0.20/0.59 % --bmc1_ucm_expand_neg_assumptions false
% 0.20/0.59 % --bmc1_ucm_layered_model none
% 0.20/0.59 % --bmc1_ucm_max_lemma_size 10
% 0.20/0.59
% 0.20/0.59 % ------ AIG Options
% 0.20/0.59
% 0.20/0.59 % --aig_mode false
% 0.20/0.59
% 0.20/0.59 % ------ Instantiation Options
% 0.20/0.59
% 0.20/0.59 % --instantiation_flag true
% 0.20/0.59 % --inst_lit_sel [+prop;+sign;+ground;-num_var;-num_symb]
% 0.20/0.59 % --inst_solver_per_active 750
% 0.20/0.59 % --inst_solver_calls_frac 0.5
% 0.20/0.59 % --inst_passive_queue_type priority_queues
% 0.20/0.59 % --inst_passive_queues [[-conj_dist;+conj_symb;-num_var];[+age;-num_symb]]
% 0.20/0.59 % --inst_passive_queues_freq [25;2]
% 0.20/0.59 % --inst_dismatching true
% 0.20/0.59 % --inst_eager_unprocessed_to_passive true
% 0.20/0.59 % --inst_prop_sim_given true
% 0.20/0.59 % --inst_prop_sim_new false
% 0.20/0.59 % --inst_orphan_elimination true
% 0.20/0.59 % --inst_learning_loop_flag true
% 0.20/0.59 % --inst_learning_start 3000
% 0.20/0.59 % --inst_learning_factor 2
% 0.20/0.59 % --inst_start_prop_sim_after_learn 3
% 0.20/0.59 % --inst_sel_renew solver
% 0.20/0.59 % --inst_lit_activity_flag true
% 0.20/0.59 % --inst_out_proof true
% 0.20/0.59
% 0.20/0.59 % ------ Resolution Options
% 0.20/0.59
% 0.20/0.59 % --resolution_flag true
% 0.20/0.59 % --res_lit_sel kbo_max
% 0.20/0.59 % --res_to_prop_solver none
% 0.20/0.59 % --res_prop_simpl_new false
% 0.20/0.59 % --res_prop_simpl_given false
% 0.20/0.59 % --res_passive_queue_type priority_queues
% 0.20/0.59 % --res_passive_queues [[-conj_dist;+conj_symb;-num_symb];[+age;-num_symb]]
% 0.20/0.59 % --res_passive_queues_freq [15;5]
% 0.20/0.59 % --res_forward_subs full
% 0.20/0.59 % --res_backward_subs full
% 0.20/0.59 % --res_forward_subs_resolution true
% 0.20/0.59 % --res_backward_subs_resolution true
% 0.20/0.59 % --res_orphan_elimination false
% 0.20/0.59 % --res_time_limit 1000.
% 0.20/0.59 % --res_out_proof true
% 0.20/0.59 % --proof_out_file /export/starexec/sandbox/tmp/iprover_proof_d5c530.s
% 0.20/0.59 % --modulo true
% 0.20/0.59
% 0.20/0.59 % ------ Combination Options
% 0.20/0.59
% 0.20/0.59 % --comb_res_mult 1000
% 0.20/0.59 % --comb_inst_mult 300
% 0.20/0.59 % ------
% 0.20/0.59
% 0.20/0.59 % ------ Parsing...%
% 0.20/0.59
% 0.20/0.59
% 0.20/0.59 % ------ Statistics
% 0.20/0.59
% 0.20/0.59 % ------ General
% 0.20/0.59
% 0.20/0.59 % num_of_input_clauses: 560
% 0.20/0.59 % num_of_input_neg_conjectures: 0
% 0.20/0.59 % num_of_splits: 0
% 0.20/0.59 % num_of_split_atoms: 0
% 0.20/0.59 % num_of_sem_filtered_clauses: 0
% 0.20/0.59 % num_of_subtypes: 0
% 0.20/0.59 % monotx_restored_types: 0
% 0.20/0.59 % sat_num_of_epr_types: 0
% 0.20/0.59 % sat_num_of_non_cyclic_types: 0
% 0.20/0.59 % sat_guarded_non_collapsed_types: 0
% 0.20/0.59 % is_epr: 0
% 0.20/0.59 % is_horn: 0
% 0.20/0.59 % has_eq: 0
% 0.20/0.59 % num_pure_diseq_elim: 0
% 0.20/0.59 % simp_replaced_by: 0
% 0.20/0.59 % res_preprocessed: 0
% 0.20/0.59 % prep_upred: 0
% 0.20/0.59 % prep_unflattend: 0
% 0.20/0.59 % pred_elim_cands: 0
% 0.20/0.59 % pred_elim: 0
% 0.20/0.59 % pred_elim_cl: 0
% 0.20/0.59 % pred_elim_cycles: 0
% 0.20/0.59 % forced_gc_time: 0
% 0.20/0.59 % gc_basic_clause_elim: 0
% 0.20/0.59 % parsing_time: 0.
% 0.20/0.59 % sem_filter_time: 0.
% 0.20/0.59 % pred_elim_time: 0.
% 0.20/0.59 % out_proof_time: 0.
% 0.20/0.59 % monotx_time: 0.
% 0.20/0.59 % subtype_inf_time: 0.
% 0.20/0.59 % unif_index_cands_time: 0.
% 0.20/0.59 % uFatal error: exception Failure("Parse error in: /export/starexec/sandbox/tmp/iprover_modulo_ad02e3.p line: 563 near token: '!='")
% 0.20/0.60 nif_index_add_time: 0.
% 0.20/0.60 % total_time: 0.041
% 0.20/0.60 % num_of_symbols: 81
% 0.20/0.60 % num_of_terms: 1128
% 0.20/0.60
% 0.20/0.60 % ------ Propositional Solver
% 0.20/0.60
% 0.20/0.60 % prop_solver_calls: 0
% 0.20/0.60 % prop_fast_solver_calls: 0
% 0.20/0.60 % prop_num_of_clauses: 0
% 0.20/0.60 % prop_preprocess_simplified: 0
% 0.20/0.60 % prop_fo_subsumed: 0
% 0.20/0.60 % prop_solver_time: 0.
% 0.20/0.60 % prop_fast_solver_time: 0.
% 0.20/0.60 % prop_unsat_core_time: 0.
% 0.20/0.60
% 0.20/0.60 % ------ QBF
% 0.20/0.60
% 0.20/0.60 % qbf_q_res: 0
% 0.20/0.60 % qbf_num_tautologies: 0
% 0.20/0.60 % qbf_prep_cycles: 0
% 0.20/0.60
% 0.20/0.60 % ------ BMC1
% 0.20/0.60
% 0.20/0.60 % bmc1_current_bound: -1
% 0.20/0.60 % bmc1_last_solved_bound: -1
% 0.20/0.60 % bmc1_unsat_core_size: -1
% 0.20/0.60 % bmc1_unsat_core_parents_size: -1
% 0.20/0.60 % bmc1_merge_next_fun: 0
% 0.20/0.60 % bmc1_unsat_core_clauses_time: 0.
% 0.20/0.60
% 0.20/0.60 % ------ Instantiation
% 0.20/0.60
% 0.20/0.60 % inst_num_of_clauses: undef
% 0.20/0.60 % inst_num_in_passive: undef
% 0.20/0.60 % inst_num_in_active: 0
% 0.20/0.60 % inst_num_in_unprocessed: 0
% 0.20/0.60 % inst_num_of_loops: 0
% 0.20/0.60 % inst_num_of_learning_restarts: 0
% 0.20/0.60 % inst_num_moves_active_passive: 0
% 0.20/0.60 % inst_lit_activity: 0
% 0.20/0.60 % inst_lit_activity_moves: 0
% 0.20/0.60 % inst_num_tautologies: 0
% 0.20/0.60 % inst_num_prop_implied: 0
% 0.20/0.60 % inst_num_existing_simplified: 0
% 0.20/0.60 % inst_num_eq_res_simplified: 0
% 0.20/0.60 % inst_num_child_elim: 0
% 0.20/0.60 % inst_num_of_dismatching_blockings: 0
% 0.20/0.60 % inst_num_of_non_proper_insts: 0
% 0.20/0.60 % inst_num_of_duplicates: 0
% 0.20/0.60 % inst_inst_num_from_inst_to_res: 0
% 0.20/0.60 % inst_dismatching_checking_time: 0.
% 0.20/0.60
% 0.20/0.60 % ------ Resolution
% 0.20/0.60
% 0.20/0.60 % res_num_of_clauses: undef
% 0.20/0.60 % res_num_in_passive: undef
% 0.20/0.60 % res_num_in_active: 0
% 0.20/0.60 % res_num_of_loops: 0
% 0.20/0.60 % res_forward_subset_subsumed: 0
% 0.20/0.60 % res_backward_subset_subsumed: 0
% 0.20/0.60 % res_forward_subsumed: 0
% 0.20/0.60 % res_backward_subsumed: 0
% 0.20/0.60 % res_forward_subsumption_resolution: 0
% 0.20/0.60 % res_backward_subsumption_resolution: 0
% 0.20/0.60 % res_clause_to_clause_subsumption: 0
% 0.20/0.60 % res_orphan_elimination: 0
% 0.20/0.60 % res_tautology_del: 0
% 0.20/0.60 % res_num_eq_res_simplified: 0
% 0.20/0.60 % res_num_sel_changes: 0
% 0.20/0.60 % res_moves_from_active_to_pass: 0
% 0.20/0.60
% 0.20/0.60 % Status Unknown
% 0.45/0.78 % Orienting using strategy ClausalAll
% 0.45/0.78 % FOF problem with conjecture
% 0.45/0.78 % Executing iprover_moduloopt --modulo true --schedule none --sub_typing false --res_to_prop_solver none --res_prop_simpl_given false --res_lit_sel kbo_max --large_theory_mode false --res_time_limit 1000 --res_orphan_elimination false --prep_sem_filter none --prep_unflatten false --comb_res_mult 1000 --comb_inst_mult 300 --clausifier .//eprover --clausifier_options "--tstp-format " --proof_out_file /export/starexec/sandbox/tmp/iprover_proof_d5c530.s --tptp_safe_out true --time_out_real 150 /export/starexec/sandbox/tmp/iprover_modulo_ad02e3.p | tee /export/starexec/sandbox/tmp/iprover_modulo_out_14e995 | grep -v "SZS"
% 0.45/0.80
% 0.45/0.80 %---------------- iProver v2.5 (CASC-J8 2016) ----------------%
% 0.45/0.80
% 0.45/0.80 %
% 0.45/0.80 % ------ iProver source info
% 0.45/0.80
% 0.45/0.80 % git: sha1: 57accf6c58032223c7708532cf852a99fa48c1b3
% 0.45/0.80 % git: non_committed_changes: true
% 0.45/0.80 % git: last_make_outside_of_git: true
% 0.45/0.80
% 0.45/0.80 %
% 0.45/0.80 % ------ Input Options
% 0.45/0.80
% 0.45/0.80 % --out_options all
% 0.45/0.80 % --tptp_safe_out true
% 0.45/0.80 % --problem_path ""
% 0.45/0.80 % --include_path ""
% 0.45/0.80 % --clausifier .//eprover
% 0.45/0.80 % --clausifier_options --tstp-format
% 0.45/0.80 % --stdin false
% 0.45/0.80 % --dbg_backtrace false
% 0.45/0.80 % --dbg_dump_prop_clauses false
% 0.45/0.80 % --dbg_dump_prop_clauses_file -
% 0.45/0.80 % --dbg_out_stat false
% 0.45/0.80
% 0.45/0.80 % ------ General Options
% 0.45/0.80
% 0.45/0.80 % --fof false
% 0.45/0.80 % --time_out_real 150.
% 0.45/0.80 % --time_out_prep_mult 0.2
% 0.45/0.80 % --time_out_virtual -1.
% 0.45/0.80 % --schedule none
% 0.45/0.80 % --ground_splitting input
% 0.45/0.80 % --splitting_nvd 16
% 0.45/0.80 % --non_eq_to_eq false
% 0.45/0.80 % --prep_gs_sim true
% 0.45/0.80 % --prep_unflatten false
% 0.45/0.80 % --prep_res_sim true
% 0.45/0.80 % --prep_upred true
% 0.45/0.80 % --res_sim_input true
% 0.45/0.80 % --clause_weak_htbl true
% 0.45/0.80 % --gc_record_bc_elim false
% 0.45/0.80 % --symbol_type_check false
% 0.45/0.80 % --clausify_out false
% 0.45/0.80 % --large_theory_mode false
% 0.45/0.80 % --prep_sem_filter none
% 0.45/0.80 % --prep_sem_filter_out false
% 0.45/0.80 % --preprocessed_out false
% 0.45/0.80 % --sub_typing false
% 0.45/0.80 % --brand_transform false
% 0.45/0.80 % --pure_diseq_elim true
% 0.45/0.80 % --min_unsat_core false
% 0.45/0.80 % --pred_elim true
% 0.45/0.80 % --add_important_lit false
% 0.45/0.80 % --soft_assumptions false
% 0.45/0.80 % --reset_solvers false
% 0.45/0.80 % --bc_imp_inh []
% 0.45/0.80 % --conj_cone_tolerance 1.5
% 0.45/0.80 % --prolific_symb_bound 500
% 0.45/0.80 % --lt_threshold 2000
% 0.45/0.80
% 0.45/0.80 % ------ SAT Options
% 0.45/0.80
% 0.45/0.80 % --sat_mode false
% 0.45/0.80 % --sat_fm_restart_options ""
% 0.45/0.80 % --sat_gr_def false
% 0.45/0.80 % --sat_epr_types true
% 0.45/0.80 % --sat_non_cyclic_types false
% 0.45/0.80 % --sat_finite_models false
% 0.45/0.80 % --sat_fm_lemmas false
% 0.45/0.80 % --sat_fm_prep false
% 0.45/0.80 % --sat_fm_uc_incr true
% 0.45/0.80 % --sat_out_model small
% 0.45/0.80 % --sat_out_clauses false
% 0.45/0.80
% 0.45/0.80 % ------ QBF Options
% 0.45/0.80
% 0.45/0.80 % --qbf_mode false
% 0.45/0.80 % --qbf_elim_univ true
% 0.45/0.80 % --qbf_sk_in true
% 0.45/0.80 % --qbf_pred_elim true
% 0.45/0.80 % --qbf_split 32
% 0.45/0.80
% 0.45/0.80 % ------ BMC1 Options
% 0.45/0.81
% 0.45/0.81 % --bmc1_incremental false
% 0.45/0.81 % --bmc1_axioms reachable_all
% 0.45/0.81 % --bmc1_min_bound 0
% 0.45/0.81 % --bmc1_max_bound -1
% 0.45/0.81 % --bmc1_max_bound_default -1
% 0.45/0.81 % --bmc1_symbol_reachability true
% 0.45/0.81 % --bmc1_property_lemmas false
% 0.45/0.81 % --bmc1_k_induction false
% 0.45/0.81 % --bmc1_non_equiv_states false
% 0.45/0.81 % --bmc1_deadlock false
% 0.45/0.81 % --bmc1_ucm false
% 0.45/0.81 % --bmc1_add_unsat_core none
% 0.45/0.81 % --bmc1_unsat_core_children false
% 0.45/0.81 % --bmc1_unsat_core_extrapolate_axioms false
% 0.45/0.81 % --bmc1_out_stat full
% 0.45/0.81 % --bmc1_ground_init false
% 0.45/0.81 % --bmc1_pre_inst_next_state false
% 0.45/0.81 % --bmc1_pre_inst_state false
% 0.45/0.81 % --bmc1_pre_inst_reach_state false
% 0.45/0.81 % --bmc1_out_unsat_core false
% 0.45/0.81 % --bmc1_aig_witness_out false
% 0.45/0.81 % --bmc1_verbose false
% 0.45/0.81 % --bmc1_dump_clauses_tptp false
% 3.28/3.55 % --bmc1_dump_unsat_core_tptp false
% 3.28/3.55 % --bmc1_dump_file -
% 3.28/3.55 % --bmc1_ucm_expand_uc_limit 128
% 3.28/3.55 % --bmc1_ucm_n_expand_iterations 6
% 3.28/3.55 % --bmc1_ucm_extend_mode 1
% 3.28/3.55 % --bmc1_ucm_init_mode 2
% 3.28/3.55 % --bmc1_ucm_cone_mode none
% 3.28/3.55 % --bmc1_ucm_reduced_relation_type 0
% 3.28/3.55 % --bmc1_ucm_relax_model 4
% 3.28/3.55 % --bmc1_ucm_full_tr_after_sat true
% 3.28/3.55 % --bmc1_ucm_expand_neg_assumptions false
% 3.28/3.55 % --bmc1_ucm_layered_model none
% 3.28/3.55 % --bmc1_ucm_max_lemma_size 10
% 3.28/3.55
% 3.28/3.55 % ------ AIG Options
% 3.28/3.55
% 3.28/3.55 % --aig_mode false
% 3.28/3.55
% 3.28/3.55 % ------ Instantiation Options
% 3.28/3.55
% 3.28/3.55 % --instantiation_flag true
% 3.28/3.55 % --inst_lit_sel [+prop;+sign;+ground;-num_var;-num_symb]
% 3.28/3.55 % --inst_solver_per_active 750
% 3.28/3.55 % --inst_solver_calls_frac 0.5
% 3.28/3.55 % --inst_passive_queue_type priority_queues
% 3.28/3.55 % --inst_passive_queues [[-conj_dist;+conj_symb;-num_var];[+age;-num_symb]]
% 3.28/3.55 % --inst_passive_queues_freq [25;2]
% 3.28/3.55 % --inst_dismatching true
% 3.28/3.55 % --inst_eager_unprocessed_to_passive true
% 3.28/3.55 % --inst_prop_sim_given true
% 3.28/3.55 % --inst_prop_sim_new false
% 3.28/3.55 % --inst_orphan_elimination true
% 3.28/3.55 % --inst_learning_loop_flag true
% 3.28/3.55 % --inst_learning_start 3000
% 3.28/3.55 % --inst_learning_factor 2
% 3.28/3.55 % --inst_start_prop_sim_after_learn 3
% 3.28/3.55 % --inst_sel_renew solver
% 3.28/3.55 % --inst_lit_activity_flag true
% 3.28/3.55 % --inst_out_proof true
% 3.28/3.55
% 3.28/3.55 % ------ Resolution Options
% 3.28/3.55
% 3.28/3.55 % --resolution_flag true
% 3.28/3.55 % --res_lit_sel kbo_max
% 3.28/3.55 % --res_to_prop_solver none
% 3.28/3.55 % --res_prop_simpl_new false
% 3.28/3.55 % --res_prop_simpl_given false
% 3.28/3.55 % --res_passive_queue_type priority_queues
% 3.28/3.55 % --res_passive_queues [[-conj_dist;+conj_symb;-num_symb];[+age;-num_symb]]
% 3.28/3.55 % --res_passive_queues_freq [15;5]
% 3.28/3.55 % --res_forward_subs full
% 3.28/3.55 % --res_backward_subs full
% 3.28/3.55 % --res_forward_subs_resolution true
% 3.28/3.55 % --res_backward_subs_resolution true
% 3.28/3.55 % --res_orphan_elimination false
% 3.28/3.55 % --res_time_limit 1000.
% 3.28/3.55 % --res_out_proof true
% 3.28/3.55 % --proof_out_file /export/starexec/sandbox/tmp/iprover_proof_d5c530.s
% 3.28/3.55 % --modulo true
% 3.28/3.55
% 3.28/3.55 % ------ Combination Options
% 3.28/3.55
% 3.28/3.55 % --comb_res_mult 1000
% 3.28/3.55 % --comb_inst_mult 300
% 3.28/3.55 % ------
% 3.28/3.55
% 3.28/3.55 % ------ Parsing...% successful
% 3.28/3.55
% 3.28/3.55 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e pe_s pe_e snvd_s sp: 0 0s snvd_e %
% 3.28/3.55
% 3.28/3.55 % ------ Proving...
% 3.28/3.55 % ------ Problem Properties
% 3.28/3.55
% 3.28/3.55 %
% 3.28/3.55 % EPR false
% 3.28/3.55 % Horn false
% 3.28/3.55 % Has equality true
% 3.28/3.55
% 3.28/3.55 % % ------ Input Options Time Limit: Unbounded
% 3.28/3.55
% 3.28/3.55
% 3.28/3.55 Compiling...
% 3.28/3.55 Loading plugin: done.
% 3.28/3.55 Compiling...
% 3.28/3.55 Loading plugin: done.
% 3.28/3.55 Compiling...
% 3.28/3.55 Loading plugin: done.
% 3.28/3.55 Compiling...
% 3.28/3.55 Loading plugin: done.
% 3.28/3.55 Compiling...
% 3.28/3.55 Loading plugin: done.
% 3.28/3.55 Compiling...
% 3.28/3.55 Loading plugin: done.
% 3.28/3.55 Compiling...
% 3.28/3.55 Loading plugin: done.
% 3.28/3.55 Compiling...
% 3.28/3.55 Loading plugin: done.
% 3.28/3.55 Compiling...
% 3.28/3.55 Loading plugin: done.
% 3.28/3.55 Compiling...
% 3.28/3.55 Loading plugin: done.
% 3.28/3.55 Compiling...
% 3.28/3.55 Loading plugin: done.
% 3.28/3.55 Compiling...
% 3.28/3.55 Loading plugin: done.
% 3.28/3.55 Compiling...
% 3.28/3.55 Loading plugin: done.
% 3.28/3.55 % % ------ Current options:
% 3.28/3.55
% 3.28/3.55 % ------ Input Options
% 3.28/3.55
% 3.28/3.55 % --out_options all
% 3.28/3.55 % --tptp_safe_out true
% 3.28/3.55 % --problem_path ""
% 3.28/3.55 % --include_path ""
% 3.28/3.55 % --clausifier .//eprover
% 3.28/3.55 % --clausifier_options --tstp-format
% 3.28/3.55 % --stdin false
% 3.28/3.55 % --dbg_backtrace false
% 3.28/3.55 % --dbg_dump_prop_clauses false
% 3.28/3.55 % --dbg_dump_prop_clauses_file -
% 3.28/3.55 % --dbg_out_stat false
% 3.28/3.55
% 3.28/3.55 % ------ General Options
% 3.28/3.55
% 3.28/3.55 % --fof false
% 3.28/3.55 % --time_out_real 150.
% 3.28/3.55 % --time_out_prep_mult 0.2
% 3.28/3.55 % --time_out_virtual -1.
% 3.28/3.55 % --schedule none
% 3.28/3.55 % --ground_splitting input
% 3.28/3.55 % --splitting_nvd 16
% 3.28/3.55 % --non_eq_to_eq false
% 3.28/3.55 % --prep_gs_sim true
% 3.28/3.55 % --prep_unflatten false
% 3.28/3.55 % --prep_res_sim true
% 3.28/3.55 % --prep_upred true
% 3.28/3.55 % --res_sim_input true
% 3.28/3.55 % --clause_weak_htbl true
% 3.28/3.55 % --gc_record_bc_elim false
% 3.28/3.55 % --symbol_type_check false
% 3.28/3.55 % --clausify_out false
% 3.28/3.55 % --large_theory_mode false
% 3.28/3.55 % --prep_sem_filter none
% 3.28/3.55 % --prep_sem_filter_out false
% 3.28/3.55 % --preprocessed_out false
% 3.28/3.55 % --sub_typing false
% 3.28/3.55 % --brand_transform false
% 3.28/3.55 % --pure_diseq_elim true
% 3.28/3.55 % --min_unsat_core false
% 3.28/3.55 % --pred_elim true
% 3.28/3.55 % --add_important_lit false
% 3.28/3.55 % --soft_assumptions false
% 3.28/3.55 % --reset_solvers false
% 3.28/3.55 % --bc_imp_inh []
% 3.28/3.55 % --conj_cone_tolerance 1.5
% 3.28/3.55 % --prolific_symb_bound 500
% 3.28/3.55 % --lt_threshold 2000
% 3.28/3.55
% 3.28/3.55 % ------ SAT Options
% 3.28/3.55
% 3.28/3.55 % --sat_mode false
% 3.28/3.55 % --sat_fm_restart_options ""
% 3.28/3.55 % --sat_gr_def false
% 3.28/3.55 % --sat_epr_types true
% 3.28/3.55 % --sat_non_cyclic_types false
% 3.28/3.55 % --sat_finite_models false
% 3.28/3.55 % --sat_fm_lemmas false
% 3.28/3.55 % --sat_fm_prep false
% 3.28/3.55 % --sat_fm_uc_incr true
% 3.28/3.55 % --sat_out_model small
% 3.28/3.55 % --sat_out_clauses false
% 3.28/3.55
% 3.28/3.55 % ------ QBF Options
% 3.28/3.55
% 3.28/3.55 % --qbf_mode false
% 3.28/3.55 % --qbf_elim_univ true
% 3.28/3.55 % --qbf_sk_in true
% 3.28/3.55 % --qbf_pred_elim true
% 3.28/3.55 % --qbf_split 32
% 3.28/3.55
% 3.28/3.55 % ------ BMC1 Options
% 3.28/3.55
% 3.28/3.55 % --bmc1_incremental false
% 3.28/3.55 % --bmc1_axioms reachable_all
% 3.28/3.55 % --bmc1_min_bound 0
% 3.28/3.55 % --bmc1_max_bound -1
% 3.28/3.55 % --bmc1_max_bound_default -1
% 3.28/3.55 % --bmc1_symbol_reachability true
% 3.28/3.55 % --bmc1_property_lemmas false
% 3.28/3.55 % --bmc1_k_induction false
% 3.28/3.55 % --bmc1_non_equiv_states false
% 3.28/3.55 % --bmc1_deadlock false
% 3.28/3.55 % --bmc1_ucm false
% 3.28/3.55 % --bmc1_add_unsat_core none
% 3.28/3.55 % --bmc1_unsat_core_children false
% 3.28/3.55 % --bmc1_unsat_core_extrapolate_axioms false
% 3.28/3.55 % --bmc1_out_stat full
% 3.28/3.55 % --bmc1_ground_init false
% 3.28/3.55 % --bmc1_pre_inst_next_state false
% 3.28/3.55 % --bmc1_pre_inst_state false
% 3.28/3.55 % --bmc1_pre_inst_reach_state false
% 3.28/3.55 % --bmc1_out_unsat_core false
% 3.28/3.55 % --bmc1_aig_witness_out false
% 3.28/3.55 % --bmc1_verbose false
% 3.28/3.55 % --bmc1_dump_clauses_tptp false
% 3.28/3.55 % --bmc1_dump_unsat_core_tptp false
% 3.28/3.55 % --bmc1_dump_file -
% 3.28/3.55 % --bmc1_ucm_expand_uc_limit 128
% 3.28/3.55 % --bmc1_ucm_n_expand_iterations 6
% 3.28/3.55 % --bmc1_ucm_extend_mode 1
% 3.28/3.55 % --bmc1_ucm_init_mode 2
% 3.28/3.55 % --bmc1_ucm_cone_mode none
% 3.28/3.55 % --bmc1_ucm_reduced_relation_type 0
% 3.28/3.55 % --bmc1_ucm_relax_model 4
% 3.28/3.55 % --bmc1_ucm_full_tr_after_sat true
% 3.28/3.55 % --bmc1_ucm_expand_neg_assumptions false
% 3.28/3.55 % --bmc1_ucm_layered_model none
% 3.28/3.55 % --bmc1_ucm_max_lemma_size 10
% 3.28/3.55
% 3.28/3.55 % ------ AIG Options
% 3.28/3.55
% 3.28/3.55 % --aig_mode false
% 3.28/3.55
% 3.28/3.55 % ------ Instantiation Options
% 3.28/3.55
% 3.28/3.55 % --instantiation_flag true
% 3.28/3.55 % --inst_lit_sel [+prop;+sign;+ground;-num_var;-num_symb]
% 7.43/7.62 % --inst_solver_per_active 750
% 7.43/7.62 % --inst_solver_calls_frac 0.5
% 7.43/7.62 % --inst_passive_queue_type priority_queues
% 7.43/7.62 % --inst_passive_queues [[-conj_dist;+conj_symb;-num_var];[+age;-num_symb]]
% 7.43/7.62 % --inst_passive_queues_freq [25;2]
% 7.43/7.62 % --inst_dismatching true
% 7.43/7.62 % --inst_eager_unprocessed_to_passive true
% 7.43/7.62 % --inst_prop_sim_given true
% 7.43/7.62 % --inst_prop_sim_new false
% 7.43/7.62 % --inst_orphan_elimination true
% 7.43/7.62 % --inst_learning_loop_flag true
% 7.43/7.62 % --inst_learning_start 3000
% 7.43/7.62 % --inst_learning_factor 2
% 7.43/7.62 % --inst_start_prop_sim_after_learn 3
% 7.43/7.62 % --inst_sel_renew solver
% 7.43/7.62 % --inst_lit_activity_flag true
% 7.43/7.62 % --inst_out_proof true
% 7.43/7.62
% 7.43/7.62 % ------ Resolution Options
% 7.43/7.62
% 7.43/7.62 % --resolution_flag true
% 7.43/7.62 % --res_lit_sel kbo_max
% 7.43/7.62 % --res_to_prop_solver none
% 7.43/7.62 % --res_prop_simpl_new false
% 7.43/7.62 % --res_prop_simpl_given false
% 7.43/7.62 % --res_passive_queue_type priority_queues
% 7.43/7.62 % --res_passive_queues [[-conj_dist;+conj_symb;-num_symb];[+age;-num_symb]]
% 7.43/7.62 % --res_passive_queues_freq [15;5]
% 7.43/7.62 % --res_forward_subs full
% 7.43/7.62 % --res_backward_subs full
% 7.43/7.62 % --res_forward_subs_resolution true
% 7.43/7.62 % --res_backward_subs_resolution true
% 7.43/7.62 % --res_orphan_elimination false
% 7.43/7.62 % --res_time_limit 1000.
% 7.43/7.62 % --res_out_proof true
% 7.43/7.62 % --proof_out_file /export/starexec/sandbox/tmp/iprover_proof_d5c530.s
% 7.43/7.62 % --modulo true
% 7.43/7.62
% 7.43/7.62 % ------ Combination Options
% 7.43/7.62
% 7.43/7.62 % --comb_res_mult 1000
% 7.43/7.62 % --comb_inst_mult 300
% 7.43/7.62 % ------
% 7.43/7.62
% 7.43/7.62
% 7.43/7.62
% 7.43/7.62 % ------ Proving...
% 7.43/7.62 %
% 7.43/7.62
% 7.43/7.62
% 7.43/7.62 % Resolution empty clause
% 7.43/7.62
% 7.43/7.62 % ------ Statistics
% 7.43/7.62
% 7.43/7.62 % ------ General
% 7.43/7.62
% 7.43/7.62 % num_of_input_clauses: 2083
% 7.43/7.62 % num_of_input_neg_conjectures: 1
% 7.43/7.62 % num_of_splits: 0
% 7.43/7.62 % num_of_split_atoms: 0
% 7.43/7.62 % num_of_sem_filtered_clauses: 0
% 7.43/7.62 % num_of_subtypes: 0
% 7.43/7.62 % monotx_restored_types: 0
% 7.43/7.62 % sat_num_of_epr_types: 0
% 7.43/7.62 % sat_num_of_non_cyclic_types: 0
% 7.43/7.62 % sat_guarded_non_collapsed_types: 0
% 7.43/7.62 % is_epr: 0
% 7.43/7.62 % is_horn: 0
% 7.43/7.62 % has_eq: 1
% 7.43/7.62 % num_pure_diseq_elim: 0
% 7.43/7.62 % simp_replaced_by: 0
% 7.43/7.62 % res_preprocessed: 2
% 7.43/7.62 % prep_upred: 0
% 7.43/7.62 % prep_unflattend: 0
% 7.43/7.62 % pred_elim_cands: 0
% 7.43/7.62 % pred_elim: 0
% 7.43/7.62 % pred_elim_cl: 0
% 7.43/7.62 % pred_elim_cycles: 0
% 7.43/7.62 % forced_gc_time: 0
% 7.43/7.62 % gc_basic_clause_elim: 0
% 7.43/7.62 % parsing_time: 0.08
% 7.43/7.62 % sem_filter_time: 0.
% 7.43/7.62 % pred_elim_time: 0.
% 7.43/7.62 % out_proof_time: 0.
% 7.43/7.62 % monotx_time: 0.
% 7.43/7.62 % subtype_inf_time: 0.
% 7.43/7.62 % unif_index_cands_time: 0.018
% 7.43/7.62 % unif_index_add_time: 0.008
% 7.43/7.62 % total_time: 6.831
% 7.43/7.62 % num_of_symbols: 97
% 7.43/7.62 % num_of_terms: 178014
% 7.43/7.62
% 7.43/7.62 % ------ Propositional Solver
% 7.43/7.62
% 7.43/7.62 % prop_solver_calls: 3
% 7.43/7.62 % prop_fast_solver_calls: 3
% 7.43/7.62 % prop_num_of_clauses: 2567
% 7.43/7.62 % prop_preprocess_simplified: 11933
% 7.43/7.62 % prop_fo_subsumed: 0
% 7.43/7.62 % prop_solver_time: 0.
% 7.43/7.62 % prop_fast_solver_time: 0.
% 7.43/7.62 % prop_unsat_core_time: 0.
% 7.43/7.62
% 7.43/7.62 % ------ QBF
% 7.43/7.62
% 7.43/7.62 % qbf_q_res: 0
% 7.43/7.62 % qbf_num_tautologies: 0
% 7.43/7.62 % qbf_prep_cycles: 0
% 7.43/7.62
% 7.43/7.62 % ------ BMC1
% 7.43/7.62
% 7.43/7.62 % bmc1_current_bound: -1
% 7.43/7.62 % bmc1_last_solved_bound: -1
% 7.43/7.62 % bmc1_unsat_core_size: -1
% 7.43/7.62 % bmc1_unsat_core_parents_size: -1
% 7.43/7.62 % bmc1_merge_next_fun: 0
% 7.43/7.62 % bmc1_unsat_core_clauses_time: 0.
% 7.43/7.62
% 7.43/7.62 % ------ Instantiation
% 7.43/7.62
% 7.43/7.62 % inst_num_of_clauses: 2573
% 7.43/7.62 % inst_num_in_passive: 1865
% 7.43/7.62 % inst_num_in_active: 599
% 7.43/7.62 % inst_num_in_unprocessed: 109
% 7.43/7.62 % inst_num_of_loops: 600
% 7.43/7.62 % inst_num_of_learning_restarts: 0
% 7.43/7.62 % inst_num_moves_active_passive: 0
% 7.43/7.62 % inst_lit_activity: 48
% 7.43/7.62 % inst_lit_activity_moves: 0
% 7.43/7.62 % inst_num_tautologies: 0
% 7.43/7.62 % inst_num_prop_implied: 0
% 7.43/7.62 % inst_num_existing_simplified: 0
% 7.43/7.62 % inst_num_eq_res_simplified: 0
% 7.43/7.62 % inst_num_child_elim: 0
% 7.43/7.62 % inst_num_of_dismatching_blockings: 34
% 7.43/7.62 % inst_num_of_non_proper_insts: 752
% 7.43/7.62 % inst_num_of_duplicates: 1643
% 7.43/7.62 % inst_inst_num_from_inst_to_res: 0
% 7.43/7.62 % inst_dismatching_checking_time: 0.
% 7.43/7.62
% 7.43/7.62 % ------ Resolution
% 7.43/7.62
% 7.43/7.62 % res_num_of_clauses: 67068
% 7.43/7.62 % res_num_in_passive: 63472
% 7.43/7.62 % res_num_in_active: 2544
% 7.43/7.62 % res_num_of_loops: 2087
% 7.43/7.62 % res_forward_subset_subsumed: 12047
% 7.43/7.62 % res_backward_subset_subsumed: 147
% 7.43/7.62 % res_forward_subsumed: 180
% 7.43/7.62 % res_backward_subsumed: 59
% 7.43/7.62 % res_forward_subsumption_resolution: 55
% 7.43/7.62 % res_backward_subsumption_resolution: 8
% 7.43/7.62 % res_clause_to_clause_subsumption: 10579
% 7.43/7.62 % res_orphan_elimination: 0
% 7.43/7.62 % res_tautology_del: 711
% 7.43/7.62 % res_num_eq_res_simplified: 49
% 7.43/7.62 % res_num_sel_changes: 0
% 7.43/7.62 % res_moves_from_active_to_pass: 0
% 7.43/7.62
% 7.43/7.62 % Status Unsatisfiable
% 7.43/7.62 % SZS status Theorem
% 7.43/7.62 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------