%------------------------------------------------------------------------------
% File : iProverMo---2.5-0.1
% Problem : NUM925+6 : TPTP v8.1.0. Released v5.3.0.
% Transfm : none
% Format : tptp:raw
% Command : iprover_modulo %s %d
% Computer : n012.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 11:03:23 EDT 2022
% Result : Theorem 7.61s 7.84s
% Output : CNFRefutation 7.68s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 668
% Syntax : Number of formulae : 6061 (1382 unt; 0 def)
% Number of atoms : 17014 (3168 equ)
% Maximal formula atoms : 56 ( 2 avg)
% Number of connectives : 19428 (8475 ~;8949 |; 382 &)
% ( 292 <=>;1330 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 4 avg)
% Maximal term depth : 11 ( 2 avg)
% Number of predicates : 42 ( 40 usr; 1 prp; 0-2 aty)
% Number of functors : 121 ( 121 usr; 15 con; 0-6 aty)
% Number of variables : 13908 ( 556 sgn4140 !; 32 ?)
% Comments :
%------------------------------------------------------------------------------
% Axioms transformation by autotheo
% Orienting (remaining) axiom formulas using strategy ClausalAll
% CNF of (remaining) axioms:
% Start CNF derivation
fof(c_0_0,axiom,
! [X31,X40] : hAPP(nat,int,power_power(int,hAPP(int,int,plus_plus(int,X31),X40)),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) = hAPP(int,int,plus_plus(int,hAPP(int,int,plus_plus(int,hAPP(nat,int,power_power(int,X31),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),number_number_of(int,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),X31)),X40))),hAPP(nat,int,power_power(int,X40),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),
file('<stdin>',fact_463_zadd__power2) ).
fof(c_0_1,axiom,
! [X1] :
( linordered_idom(X1)
=> ! [X5,X6] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,plus_plus(X1,hAPP(nat,X1,power_power(X1,X5),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,X1,power_power(X1,X6),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),zero_zero(X1)))
<=> ( ti(X1,X5) = zero_zero(X1)
& ti(X1,X6) = zero_zero(X1) ) ) ),
file('<stdin>',fact_336_sum__power2__le__zero__iff) ).
fof(c_0_2,axiom,
! [X1] :
( linordered_idom(X1)
=> ! [X10,X11] : ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,plus_plus(X1,hAPP(nat,X1,power_power(X1,X10),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,X1,power_power(X1,X11),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),zero_zero(X1))) ),
file('<stdin>',fact_98_not__sum__power2__lt__zero) ).
fof(c_0_3,axiom,
! [X3,X1] :
( ( order(X1)
& order(X3) )
=> ! [X46,X54,X42,X7] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X3,X1,X54,X42)),X7))
=> ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X46),X42))
=> ( ! [X47,X48] :
( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X48),X47))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X3,X1,X54,X48)),hAPP(X3,X1,X54,X47))) )
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X3,X1,X54,X46)),X7)) ) ) ) ),
file('<stdin>',fact_460_xt4) ).
fof(c_0_4,axiom,
! [X1,X3] :
( ( order(X3)
& order(X1) )
=> ! [X54,X46,X7,X42] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X7),X42))
=> ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),hAPP(X1,X3,X54,X42)),X46))
=> ( ! [X47,X48] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X47),X48))
=> hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),hAPP(X1,X3,X54,X47)),hAPP(X1,X3,X54,X48))) )
=> hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),hAPP(X1,X3,X54,X7)),X46)) ) ) ) ),
file('<stdin>',fact_458_order__le__less__subst2) ).
fof(c_0_5,axiom,
! [X3,X1] :
( ( order(X1)
& ord(X3) )
=> ! [X46,X54,X42,X7] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X3,X1,X54,X42)),X7))
=> ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X46),X42))
=> ( ! [X47,X48] :
( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X48),X47))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X3,X1,X54,X48)),hAPP(X3,X1,X54,X47))) )
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X3,X1,X54,X46)),X7)) ) ) ) ),
file('<stdin>',fact_457_xt6) ).
fof(c_0_6,axiom,
! [X1,X3] :
( ( order(X3)
& order(X1) )
=> ! [X54,X46,X7,X42] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X7),X42))
=> ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),hAPP(X1,X3,X54,X42)),X46))
=> ( ! [X47,X48] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X47),X48))
=> hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),hAPP(X1,X3,X54,X47)),hAPP(X1,X3,X54,X48))) )
=> hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),hAPP(X1,X3,X54,X7)),X46)) ) ) ) ),
file('<stdin>',fact_455_order__less__le__subst2) ).
fof(c_0_7,axiom,
! [X1,X3] :
( ( order(X3)
& order(X1) )
=> ! [X46,X7,X54,X42] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X7),hAPP(X3,X1,X54,X42)))
=> ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X42),X46))
=> ( ! [X47,X48] :
( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X47),X48))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X3,X1,X54,X47)),hAPP(X3,X1,X54,X48))) )
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X7),hAPP(X3,X1,X54,X46))) ) ) ) ),
file('<stdin>',fact_461_order__le__less__subst1) ).
fof(c_0_8,axiom,
! [X1,X3] :
( ( order(X3)
& order(X1) )
=> ! [X46,X7,X54,X42] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X7),hAPP(X3,X1,X54,X42)))
=> ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X42),X46))
=> ( ! [X47,X48] :
( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X47),X48))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X3,X1,X54,X47)),hAPP(X3,X1,X54,X48))) )
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X7),hAPP(X3,X1,X54,X46))) ) ) ) ),
file('<stdin>',fact_459_order__less__le__subst1) ).
fof(c_0_9,axiom,
! [X3,X1] :
( ( order(X1)
& order(X3) )
=> ! [X46,X54,X42,X7] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X42),X7))
=> ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X46),hAPP(X1,X3,X54,X42)))
=> ( ! [X47,X48] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X48),X47))
=> hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),hAPP(X1,X3,X54,X48)),hAPP(X1,X3,X54,X47))) )
=> hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X46),hAPP(X1,X3,X54,X7))) ) ) ) ),
file('<stdin>',fact_454_xt7) ).
fof(c_0_10,axiom,
! [X3,X1] :
( ( order(X1)
& order(X3) )
=> ! [X46,X54,X42,X7] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X42),X7))
=> ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X46),hAPP(X1,X3,X54,X42)))
=> ( ! [X47,X48] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X48),X47))
=> hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),hAPP(X1,X3,X54,X48)),hAPP(X1,X3,X54,X47))) )
=> hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X46),hAPP(X1,X3,X54,X7))) ) ) ) ),
file('<stdin>',fact_451_xt5) ).
fof(c_0_11,axiom,
! [X10,X11] : hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),hAPP(real,real,sqrt,hAPP(real,real,plus_plus(real,hAPP(nat,real,power_power(real,X10),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,real,power_power(real,X11),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))))),
file('<stdin>',fact_462_real__sqrt__sum__squares__ge__zero) ).
fof(c_0_12,axiom,
! [X1] :
( linordered_idom(X1)
=> ! [X5,X6] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),hAPP(X1,X1,plus_plus(X1,hAPP(nat,X1,power_power(X1,X5),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,X1,power_power(X1,X6),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))))
<=> ( ti(X1,X5) != zero_zero(X1)
| ti(X1,X6) != zero_zero(X1) ) ) ),
file('<stdin>',fact_97_sum__power2__gt__zero__iff) ).
fof(c_0_13,axiom,
! [X1] :
( linordered_idom(X1)
=> ! [X10,X11] : hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),hAPP(X1,X1,plus_plus(X1,hAPP(nat,X1,power_power(X1,X10),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,X1,power_power(X1,X11),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))) ),
file('<stdin>',fact_335_sum__power2__ge__zero) ).
fof(c_0_14,axiom,
! [X1] :
( linordered_semidom(X1)
=> ! [X10,X11] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(nat,X1,power_power(X1,X10),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,X1,power_power(X1,X11),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X11))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X10),X11)) ) ) ),
file('<stdin>',fact_334_power2__less__imp__less) ).
fof(c_0_15,axiom,
! [X1] :
( linordered_semidom(X1)
=> ! [X10,X11] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(nat,X1,power_power(X1,X10),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,X1,power_power(X1,X11),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X11))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X10),X11)) ) ) ),
file('<stdin>',fact_331_power2__le__imp__le) ).
fof(c_0_16,axiom,
! [X1] :
( linordered_ring(X1)
=> ! [X10,X11] : ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,plus_plus(X1,hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X10),X10)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X11),X11))),zero_zero(X1))) ),
file('<stdin>',fact_478_not__sum__squares__lt__zero) ).
fof(c_0_17,axiom,
! [X1] :
( linordered_idom(X1)
=> ! [X31] : ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(nat,X1,power_power(X1,X31),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),zero_zero(X1))) ),
file('<stdin>',fact_96_power2__less__0) ).
fof(c_0_18,axiom,
! [X1] :
( linord581940658strict(X1)
=> ! [X5,X6] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),hAPP(X1,X1,plus_plus(X1,hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X5),X5)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X6),X6))))
<=> ( ti(X1,X5) != zero_zero(X1)
| ti(X1,X6) != zero_zero(X1) ) ) ),
file('<stdin>',fact_477_sum__squares__gt__zero__iff) ).
fof(c_0_19,axiom,
! [X1] :
( linordered_idom(X1)
=> ! [X5,X6] :
( hAPP(X1,X1,plus_plus(X1,hAPP(nat,X1,power_power(X1,X5),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,X1,power_power(X1,X6),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) = zero_zero(X1)
<=> ( ti(X1,X5) = zero_zero(X1)
& ti(X1,X6) = zero_zero(X1) ) ) ),
file('<stdin>',fact_2_sum__power2__eq__zero__iff) ).
fof(c_0_20,axiom,
! [X5,X6] :
( hAPP(real,real,plus_plus(real,hAPP(nat,real,power_power(real,X5),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,real,power_power(real,X6),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) = zero_zero(real)
<=> ( X5 = zero_zero(real)
& X6 = zero_zero(real) ) ),
file('<stdin>',fact_106_realpow__two__sum__zero__iff) ).
fof(c_0_21,axiom,
! [X1] :
( ( number_ring(X1)
& linordered_idom(X1) )
=> ! [X15] : hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(nat,X1,semiring_1_of_nat(X1),X15)),hAPP(nat,X1,power_power(X1,number_number_of(X1,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),X15))) ),
file('<stdin>',fact_103_of__nat__less__two__power) ).
fof(c_0_22,axiom,
! [X15] : hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),one_one(real)),hAPP(nat,real,power_power(real,number_number_of(real,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),X15))),
file('<stdin>',fact_372_two__realpow__ge__one) ).
fof(c_0_23,axiom,
! [X28,X12,X54] :
( ! [X53,X43] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X53),X43))
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,X54,X53)),hAPP(nat,nat,X54,X43))) )
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,plus_plus(nat,hAPP(nat,nat,X54,X28)),X12)),hAPP(nat,nat,X54,hAPP(nat,nat,plus_plus(nat,X28),X12)))) ),
file('<stdin>',fact_377_mono__nat__linear__lb) ).
fof(c_0_24,axiom,
! [X10] : hAPP(nat,int,power_power(int,hAPP(nat,int,power_power(int,X10),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) = hAPP(nat,int,power_power(int,X10),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),
file('<stdin>',fact_10_quartic__square__square) ).
fof(c_0_25,axiom,
! [X1] :
( linordered_idom(X1)
=> ! [X7] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),hAPP(nat,X1,power_power(X1,X7),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))
<=> ti(X1,X7) != zero_zero(X1) ) ),
file('<stdin>',fact_95_zero__less__power2) ).
fof(c_0_26,axiom,
! [X1] :
( linord581940658strict(X1)
=> ! [X7,X42,X46] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X46))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X46),X7)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X46),X42)))
<=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X7),X42)) ) ) ),
file('<stdin>',fact_476_mult__le__cancel__left__pos) ).
fof(c_0_27,axiom,
! [X1] :
( linordered_semiring(X1)
=> ! [X31,X41,X40] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X31),X41)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X40),X41)))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X41))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X31),X40)) ) ) ),
file('<stdin>',fact_470_mult__right__less__imp__less) ).
fof(c_0_28,axiom,
! [X1] :
( linord20386208strict(X1)
=> ! [X31,X41,X40] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X31),X41)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X40),X41)))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X41))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X31),X40)) ) ) ),
file('<stdin>',fact_469_mult__less__imp__less__right) ).
fof(c_0_29,axiom,
! [X1] :
( linordered_semiring(X1)
=> ! [X41,X31,X40] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X41),X31)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X41),X40)))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X41))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X31),X40)) ) ) ),
file('<stdin>',fact_468_mult__left__less__imp__less) ).
fof(c_0_30,axiom,
! [X1] :
( linord20386208strict(X1)
=> ! [X41,X31,X40] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X41),X31)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X41),X40)))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X41))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X31),X40)) ) ) ),
file('<stdin>',fact_467_mult__less__imp__less__left) ).
fof(c_0_31,axiom,
! [X1] :
( linord20386208strict(X1)
=> ! [X31,X41,X40] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X31),X41)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X40),X41)))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X41))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X31),X40)) ) ) ),
file('<stdin>',fact_466_mult__right__le__imp__le) ).
fof(c_0_32,axiom,
! [X1] :
( linord20386208strict(X1)
=> ! [X41,X31,X40] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X41),X31)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X41),X40)))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X41))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X31),X40)) ) ) ),
file('<stdin>',fact_465_mult__left__le__imp__le) ).
fof(c_0_33,axiom,
! [X1] :
( linord581940658strict(X1)
=> ! [X7,X42,X46] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X46),zero_zero(X1)))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X46),X7)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X46),X42)))
<=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X42),X7)) ) ) ),
file('<stdin>',fact_494_mult__less__cancel__left__neg) ).
fof(c_0_34,axiom,
! [X1] :
( linord581940658strict(X1)
=> ! [X7,X42,X46] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X46),zero_zero(X1)))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X46),X7)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X46),X42)))
<=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X42),X7)) ) ) ),
file('<stdin>',fact_475_mult__le__cancel__left__neg) ).
fof(c_0_35,axiom,
! [X1] :
( linord20386208strict(X1)
=> ! [X41,X45,X31,X40] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X31),X40))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X41),X45))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X40))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X41))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X31),X41)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X40),X45))) ) ) ) ) ),
file('<stdin>',fact_474_mult__strict__mono) ).
fof(c_0_36,axiom,
! [X1] :
( linord20386208strict(X1)
=> ! [X41,X45,X31,X40] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X31),X40))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X41),X45))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X31))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X41))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X31),X41)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X40),X45))) ) ) ) ) ),
file('<stdin>',fact_473_mult__strict__mono_H) ).
fof(c_0_37,axiom,
! [X1] :
( linord20386208strict(X1)
=> ! [X41,X45,X31,X40] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X31),X40))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X41),X45))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X31))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X41))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X31),X41)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X40),X45))) ) ) ) ) ),
file('<stdin>',fact_472_mult__less__le__imp__less) ).
fof(c_0_38,axiom,
! [X1] :
( linord20386208strict(X1)
=> ! [X41,X45,X31,X40] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X31),X40))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X41),X45))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X31))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X41))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X31),X41)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X40),X45))) ) ) ) ) ),
file('<stdin>',fact_471_mult__le__less__imp__less) ).
fof(c_0_39,axiom,
! [X29] :
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,plus_plus(int,hAPP(int,int,plus_plus(int,one_one(int)),X29)),X29)),zero_zero(int)))
<=> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X29),zero_zero(int))) ),
file('<stdin>',fact_64_odd__less__0) ).
fof(c_0_40,axiom,
! [X1,X3] :
( ord(X3)
=> ! [X54,X57] :
( ! [X47] : hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),hAPP(X1,X3,X54,X47)),hAPP(X1,X3,X57,X47)))
=> hBOOL(hAPP(fun(X1,X3),bool,hAPP(fun(X1,X3),fun(fun(X1,X3),bool),ord_less_eq(fun(X1,X3)),X54),X57)) ) ),
file('<stdin>',fact_448_le__funI) ).
fof(c_0_41,axiom,
! [X1,X3] :
( ord(X3)
=> ! [X54,X57] :
( hBOOL(hAPP(fun(X1,X3),bool,hAPP(fun(X1,X3),fun(fun(X1,X3),bool),ord_less_eq(fun(X1,X3)),X54),X57))
<=> ! [X47] : hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),hAPP(X1,X3,X54,X47)),hAPP(X1,X3,X57,X47))) ) ),
file('<stdin>',fact_401_le__fun__def) ).
fof(c_0_42,axiom,
! [X1] :
( linord20386208strict(X1)
=> ! [X41,X31,X40] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X31),X40))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X41))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X31),X41)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X40),X41))) ) ) ),
file('<stdin>',fact_491_mult__strict__right__mono) ).
fof(c_0_43,axiom,
! [X1] :
( linord20386208strict(X1)
=> ! [X41,X31,X40] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X31),X40))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X41))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X41),X31)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X41),X40))) ) ) ),
file('<stdin>',fact_490_mult__strict__left__mono) ).
fof(c_0_44,axiom,
! [X1] :
( linord893533164strict(X1)
=> ! [X41,X31,X40] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X31),X40))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X41))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X41),X31)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X41),X40))) ) ) ),
file('<stdin>',fact_489_comm__mult__strict__left__mono) ).
fof(c_0_45,axiom,
! [X1] :
( linord581940658strict(X1)
=> ! [X41,X40,X31] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X40),X31))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X41),zero_zero(X1)))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X31),X41)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X40),X41))) ) ) ),
file('<stdin>',fact_488_mult__strict__right__mono__neg) ).
fof(c_0_46,axiom,
! [X1] :
( linord581940658strict(X1)
=> ! [X41,X40,X31] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X40),X31))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X41),zero_zero(X1)))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X41),X31)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X41),X40))) ) ) ),
file('<stdin>',fact_487_mult__strict__left__mono__neg) ).
fof(c_0_47,axiom,
! [X34,X55,X54] :
( ! [X35,X56] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X35),X56))
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,X54,X35)),hAPP(nat,nat,X54,X56))) )
=> ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X34),X55))
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,X54,X34)),hAPP(nat,nat,X54,X55))) ) ),
file('<stdin>',fact_384_less__mono__imp__le__mono) ).
fof(c_0_48,axiom,
! [X1] :
( linordered_semidom(X1)
=> ! [X10,X11] :
( hAPP(nat,X1,power_power(X1,X10),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) = hAPP(nat,X1,power_power(X1,X11),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X10))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X11))
=> ti(X1,X10) = ti(X1,X11) ) ) ) ),
file('<stdin>',fact_332_power2__eq__imp__eq) ).
fof(c_0_49,axiom,
! [X1] :
( linordered_idom(X1)
=> ! [X31] : hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),hAPP(nat,X1,power_power(X1,X31),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))) ),
file('<stdin>',fact_330_zero__le__power2) ).
fof(c_0_50,axiom,
! [X10] : hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X10),hAPP(nat,int,power_power(int,X10),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),
file('<stdin>',fact_329_power2__ge__self) ).
fof(c_0_51,axiom,
! [X10] :
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X10))
=> ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X10),number_number_of(int,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))
=> ( X10 = zero_zero(int)
| X10 = one_one(int) ) ) ),
file('<stdin>',fact_337_int__pos__lt__two__imp__zero__or__one) ).
fof(c_0_52,axiom,
! [X1] :
( linord20386208strict(X1)
=> ! [X40,X31] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X31),zero_zero(X1)))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X40))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X31),X40)),zero_zero(X1))) ) ) ),
file('<stdin>',fact_493_mult__neg__pos) ).
fof(c_0_53,axiom,
! [X1] :
( linordered_semidom(X1)
=> ! [X15,X31,X40] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X31),X40))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X31))
=> ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X15))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(nat,X1,power_power(X1,X31),X15)),hAPP(nat,X1,power_power(X1,X40),X15))) ) ) ) ),
file('<stdin>',fact_327_power__strict__mono) ).
fof(c_0_54,axiom,
! [X1] :
( linordered_semidom(X1)
=> ! [X31,X15,X32] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X15),X32))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X31))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X31),one_one(X1)))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(nat,X1,power_power(X1,X31),X32)),hAPP(nat,X1,power_power(X1,X31),X15))) ) ) ) ),
file('<stdin>',fact_259_power__decreasing) ).
fof(c_0_55,axiom,
! [X1] :
( linordered_semidom(X1)
=> ! [X31,X15,X32] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X15),X32))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X31))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X31),one_one(X1)))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(nat,X1,power_power(X1,X31),X32)),hAPP(nat,X1,power_power(X1,X31),X15))) ) ) ) ),
file('<stdin>',fact_110_power__strict__decreasing) ).
fof(c_0_56,axiom,
! [X1] :
( linord20386208strict(X1)
=> ! [X40,X31] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X40),X31)))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X31))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X40)) ) ) ),
file('<stdin>',fact_495_zero__less__mult__pos2) ).
fof(c_0_57,axiom,
! [X1] :
( linordered_semidom(X1)
=> ! [X31,X15,X40] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(nat,X1,power_power(X1,X31),X15)),hAPP(nat,X1,power_power(X1,X40),X15)))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X40))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X31),X40)) ) ) ),
file('<stdin>',fact_303_power__less__imp__less__base) ).
fof(c_0_58,axiom,
! [X1] :
( linordered_semidom(X1)
=> ! [X14,X15,X31] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),one_one(X1)),X31))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(nat,X1,power_power(X1,X31),X14)),hAPP(nat,X1,power_power(X1,X31),X15)))
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X14),X15)) ) ) ),
file('<stdin>',fact_261_power__le__imp__le__exp) ).
fof(c_0_59,axiom,
! [X1] :
( linordered_semidom(X1)
=> ! [X5,X6,X42] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),one_one(X1)),X42))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(nat,X1,power_power(X1,X42),X5)),hAPP(nat,X1,power_power(X1,X42),X6)))
<=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X5),X6)) ) ) ),
file('<stdin>',fact_260_power__increasing__iff) ).
fof(c_0_60,axiom,
! [X1] :
( linordered_semidom(X1)
=> ! [X14,X15,X31] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),one_one(X1)),X31))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(nat,X1,power_power(X1,X31),X14)),hAPP(nat,X1,power_power(X1,X31),X15)))
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X14),X15)) ) ) ),
file('<stdin>',fact_182_power__less__imp__less__exp) ).
fof(c_0_61,axiom,
! [X1] :
( linordered_semidom(X1)
=> ! [X5,X6,X42] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),one_one(X1)),X42))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(nat,X1,power_power(X1,X42),X5)),hAPP(nat,X1,power_power(X1,X42),X6)))
<=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X5),X6)) ) ) ),
file('<stdin>',fact_181_power__strict__increasing__iff) ).
fof(c_0_62,axiom,
! [X1] :
( linordered_semidom(X1)
=> ! [X15,X31] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),one_one(X1)),X31))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(nat,X1,power_power(X1,X31),X15)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X31),hAPP(nat,X1,power_power(X1,X31),X15)))) ) ),
file('<stdin>',fact_479_power__less__power__Suc) ).
fof(c_0_63,axiom,
! [X14,X15,X21] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X21))
=> ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,power_power(nat,X21),X14)),hAPP(nat,nat,power_power(nat,X21),X15)))
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X14),X15)) ) ),
file('<stdin>',fact_140_nat__power__less__imp__less) ).
fof(c_0_64,axiom,
! [X1] :
( linordered_semidom(X1)
=> ! [X15,X31,X40] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X31),X40))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X31))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(nat,X1,power_power(X1,X31),X15)),hAPP(nat,X1,power_power(X1,X40),X15))) ) ) ),
file('<stdin>',fact_277_power__mono) ).
fof(c_0_65,axiom,
! [X1] :
( linord581940658strict(X1)
=> ! [X40,X31] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X31),zero_zero(X1)))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X40),zero_zero(X1)))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X31),X40))) ) ) ),
file('<stdin>',fact_492_mult__neg__neg) ).
fof(c_0_66,axiom,
! [X1] :
( ordere223160158up_add(X1)
=> ! [X41,X45,X31,X40] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X31),X40))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X41),X45))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,plus_plus(X1,X31),X41)),hAPP(X1,X1,plus_plus(X1,X40),X45))) ) ) ),
file('<stdin>',fact_272_add__le__less__mono) ).
fof(c_0_67,axiom,
! [X1] :
( ordere223160158up_add(X1)
=> ! [X41,X45,X31,X40] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X31),X40))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X41),X45))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,plus_plus(X1,X31),X41)),hAPP(X1,X1,plus_plus(X1,X40),X45))) ) ) ),
file('<stdin>',fact_271_add__less__le__mono) ).
fof(c_0_68,axiom,
! [X1] :
( ordere779506340up_add(X1)
=> ! [X41,X45,X31,X40] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X31),X40))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X41),X45))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,plus_plus(X1,X31),X41)),hAPP(X1,X1,plus_plus(X1,X40),X45))) ) ) ),
file('<stdin>',fact_238_add__mono) ).
fof(c_0_69,axiom,
! [X1] :
( ordere223160158up_add(X1)
=> ! [X41,X45,X31,X40] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X31),X40))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X41),X45))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,plus_plus(X1,X31),X41)),hAPP(X1,X1,plus_plus(X1,X40),X45))) ) ) ),
file('<stdin>',fact_220_add__strict__mono) ).
fof(c_0_70,axiom,
! [X1] :
( linordered_semidom(X1)
=> ! [X31,X15,X32] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X15),X32))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),one_one(X1)),X31))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(nat,X1,power_power(X1,X31),X15)),hAPP(nat,X1,power_power(X1,X31),X32))) ) ) ),
file('<stdin>',fact_241_power__increasing) ).
fof(c_0_71,axiom,
! [X1] :
( linordered_semidom(X1)
=> ! [X31,X15,X32] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X15),X32))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),one_one(X1)),X31))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(nat,X1,power_power(X1,X31),X15)),hAPP(nat,X1,power_power(X1,X31),X32))) ) ) ),
file('<stdin>',fact_183_power__strict__increasing) ).
fof(c_0_72,axiom,
! [X1] :
( dense_linorder(X1)
=> ! [X16,X10,X11] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X10),X11))
=> ( ! [X62] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X10),X62))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X62),X11))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X62),X16)) ) )
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X11),X16)) ) ) ),
file('<stdin>',fact_450_dense__le__bounded) ).
fof(c_0_73,axiom,
! [X20,X30,X21,X22] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X21),X22))
=> ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X20),X30))
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,plus_plus(nat,X21),X20)),hAPP(nat,nat,plus_plus(nat,X22),X30))) ) ),
file('<stdin>',fact_364_add__le__mono) ).
fof(c_0_74,axiom,
! [X50,X16,X51,X8] :
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X51),X8))
=> ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X50),X16))
=> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,plus_plus(int,X51),X50)),hAPP(int,int,plus_plus(int,X8),X16))) ) ),
file('<stdin>',fact_288_zadd__zless__mono) ).
fof(c_0_75,axiom,
! [X20,X30,X21,X22] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X21),X22))
=> ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X20),X30))
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,plus_plus(nat,X21),X20)),hAPP(nat,nat,plus_plus(nat,X22),X30))) ) ),
file('<stdin>',fact_134_add__less__mono) ).
fof(c_0_76,axiom,
! [X1] :
( linordered_semidom(X1)
=> ! [X15,X31] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),one_one(X1)),X31))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),one_one(X1)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X31),hAPP(nat,X1,power_power(X1,X31),X15)))) ) ),
file('<stdin>',fact_480_power__gt1__lemma) ).
fof(c_0_77,axiom,
! [X1] :
( ordere236663937imp_le(X1)
=> ! [X41,X31,X40] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,plus_plus(X1,X41),X31)),hAPP(X1,X1,plus_plus(X1,X41),X40)))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X31),X40)) ) ),
file('<stdin>',fact_240_add__le__imp__le__left) ).
fof(c_0_78,axiom,
! [X1] :
( ordere236663937imp_le(X1)
=> ! [X31,X41,X40] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,plus_plus(X1,X31),X41)),hAPP(X1,X1,plus_plus(X1,X40),X41)))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X31),X40)) ) ),
file('<stdin>',fact_239_add__le__imp__le__right) ).
fof(c_0_79,axiom,
! [X1] :
( ordere236663937imp_le(X1)
=> ! [X46,X7,X42] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,plus_plus(X1,X46),X7)),hAPP(X1,X1,plus_plus(X1,X46),X42)))
<=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X7),X42)) ) ),
file('<stdin>',fact_235_add__le__cancel__left) ).
fof(c_0_80,axiom,
! [X1] :
( ordere236663937imp_le(X1)
=> ! [X7,X46,X42] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,plus_plus(X1,X7),X46)),hAPP(X1,X1,plus_plus(X1,X42),X46)))
<=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X7),X42)) ) ),
file('<stdin>',fact_234_add__le__cancel__right) ).
fof(c_0_81,axiom,
! [X1] :
( ordere236663937imp_le(X1)
=> ! [X7,X46,X42] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,plus_plus(X1,X7),X46)),hAPP(X1,X1,plus_plus(X1,X42),X46)))
<=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X7),X42)) ) ),
file('<stdin>',fact_224_add__less__cancel__right) ).
fof(c_0_82,axiom,
! [X1] :
( ordere236663937imp_le(X1)
=> ! [X46,X7,X42] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,plus_plus(X1,X46),X7)),hAPP(X1,X1,plus_plus(X1,X46),X42)))
<=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X7),X42)) ) ),
file('<stdin>',fact_223_add__less__cancel__left) ).
fof(c_0_83,axiom,
! [X1] :
( ordere236663937imp_le(X1)
=> ! [X31,X41,X40] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,plus_plus(X1,X31),X41)),hAPP(X1,X1,plus_plus(X1,X40),X41)))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X31),X40)) ) ),
file('<stdin>',fact_219_add__less__imp__less__right) ).
fof(c_0_84,axiom,
! [X1] :
( ordere236663937imp_le(X1)
=> ! [X41,X31,X40] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,plus_plus(X1,X41),X31)),hAPP(X1,X1,plus_plus(X1,X41),X40)))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X31),X40)) ) ),
file('<stdin>',fact_218_add__less__imp__less__left) ).
fof(c_0_85,axiom,
! [X33,X12,X34] :
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X12),X34))
=> ( hBOOL(hAPP(int,bool,X33,hAPP(int,int,plus_plus(int,X12),one_one(int))))
=> ( ! [X35] :
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X12),X35))
=> ( hBOOL(hAPP(int,bool,X33,X35))
=> hBOOL(hAPP(int,bool,X33,hAPP(int,int,plus_plus(int,X35),one_one(int)))) ) )
=> hBOOL(hAPP(int,bool,X33,X34)) ) ) ),
file('<stdin>',fact_112_int__gr__induct) ).
fof(c_0_86,axiom,
! [X20,X30] : hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,bit1,X20)),X30) = hAPP(int,int,plus_plus(int,hAPP(int,int,bit0,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),X20),X30))),X30),
file('<stdin>',fact_464_mult__Bit1) ).
fof(c_0_87,axiom,
! [X12,X28,X17] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,plus_plus(nat,X12),X28)),hAPP(nat,nat,plus_plus(nat,X12),X17)))
<=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X28),X17)) ),
file('<stdin>',fact_360_nat__add__left__cancel__le) ).
fof(c_0_88,axiom,
! [X12,X28,X17] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,plus_plus(nat,X12),X28)),hAPP(nat,nat,plus_plus(nat,X12),X17)))
<=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X28),X17)) ),
file('<stdin>',fact_126_nat__add__left__cancel__less) ).
fof(c_0_89,axiom,
! [X33,X28,X17] :
( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X28),X17))
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X33,X17),X28)) )
=> ( ( X28 = X17
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X33,X17),X28)) )
=> ( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X17),X28))
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X33,X17),X28)) )
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X33,X17),X28)) ) ) ),
file('<stdin>',fact_137_nat__less__cases) ).
fof(c_0_90,axiom,
! [X1] :
( ordere216010020id_add(X1)
=> ! [X40,X31] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X31),zero_zero(X1)))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X40),zero_zero(X1)))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,plus_plus(X1,X31),X40)),zero_zero(X1))) ) ) ),
file('<stdin>',fact_302_add__nonpos__neg) ).
fof(c_0_91,axiom,
! [X1] :
( ordere216010020id_add(X1)
=> ! [X40,X31] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X31),zero_zero(X1)))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X40),zero_zero(X1)))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,plus_plus(X1,X31),X40)),zero_zero(X1))) ) ) ),
file('<stdin>',fact_301_add__neg__nonpos) ).
fof(c_0_92,axiom,
! [X1] :
( ordere216010020id_add(X1)
=> ! [X40,X31] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X31),zero_zero(X1)))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X40),zero_zero(X1)))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,plus_plus(X1,X31),X40)),zero_zero(X1))) ) ) ),
file('<stdin>',fact_270_add__nonpos__nonpos) ).
fof(c_0_93,axiom,
! [X1] :
( ordere216010020id_add(X1)
=> ! [X40,X31] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X31),zero_zero(X1)))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X40),zero_zero(X1)))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,plus_plus(X1,X31),X40)),zero_zero(X1))) ) ) ),
file('<stdin>',fact_227_add__neg__neg) ).
fof(c_0_94,axiom,
! [X1] :
( linordered_semidom(X1)
=> ! [X28,X17] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(nat,X1,semiring_1_of_nat(X1),X28)),hAPP(nat,X1,semiring_1_of_nat(X1),X17)))
<=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X28),X17)) ) ),
file('<stdin>',fact_253_of__nat__le__iff) ).
fof(c_0_95,axiom,
! [X1] :
( linordered_semidom(X1)
=> ! [X14,X15] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(nat,X1,semiring_1_of_nat(X1),X14)),hAPP(nat,X1,semiring_1_of_nat(X1),X15)))
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X14),X15)) ) ),
file('<stdin>',fact_168_of__nat__less__imp__less) ).
fof(c_0_96,axiom,
! [X1] :
( linordered_semidom(X1)
=> ! [X28,X17] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(nat,X1,semiring_1_of_nat(X1),X28)),hAPP(nat,X1,semiring_1_of_nat(X1),X17)))
<=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X28),X17)) ) ),
file('<stdin>',fact_166_of__nat__less__iff) ).
fof(c_0_97,axiom,
! [X28,X17] :
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(nat,int,semiring_1_of_nat(int),X28)),hAPP(nat,int,semiring_1_of_nat(int),X17)))
<=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X28),X17)) ),
file('<stdin>',fact_370_zle__int) ).
fof(c_0_98,axiom,
! [X5,X6] :
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(nat,int,semiring_1_of_nat(int),X5)),hAPP(nat,int,semiring_1_of_nat(int),X6)))
<=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X5),X6)) ),
file('<stdin>',fact_369_Nat__Transfer_Otransfer__int__nat__relations_I3_J) ).
fof(c_0_99,axiom,
! [X28,X17] :
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(nat,int,semiring_1_of_nat(int),X28)),hAPP(nat,int,semiring_1_of_nat(int),X17)))
<=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X28),X17)) ),
file('<stdin>',fact_149_zless__int) ).
fof(c_0_100,axiom,
! [X5,X6] :
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(nat,int,semiring_1_of_nat(int),X5)),hAPP(nat,int,semiring_1_of_nat(int),X6)))
<=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X5),X6)) ),
file('<stdin>',fact_147_Nat__Transfer_Otransfer__int__nat__relations_I2_J) ).
fof(c_0_101,axiom,
! [X18,X19] :
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,bit1,X18)),hAPP(int,int,bit0,X19)))
<=> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X18),X19)) ),
file('<stdin>',fact_311_less__eq__int__code_I15_J) ).
fof(c_0_102,axiom,
! [X12,X13] :
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,bit1,X12)),hAPP(int,int,bit0,X13)))
<=> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X12),X13)) ),
file('<stdin>',fact_310_rel__simps_I33_J) ).
fof(c_0_103,axiom,
! [X18,X19] :
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit0,X18)),hAPP(int,int,bit1,X19)))
<=> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X18),X19)) ),
file('<stdin>',fact_309_less__int__code_I14_J) ).
fof(c_0_104,axiom,
! [X12,X13] :
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit0,X12)),hAPP(int,int,bit1,X13)))
<=> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X12),X13)) ),
file('<stdin>',fact_308_rel__simps_I15_J) ).
fof(c_0_105,axiom,
! [X18,X19] :
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,bit0,X18)),hAPP(int,int,bit1,X19)))
<=> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X18),X19)) ),
file('<stdin>',fact_283_less__eq__int__code_I14_J) ).
fof(c_0_106,axiom,
! [X12,X13] :
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,bit0,X12)),hAPP(int,int,bit1,X13)))
<=> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X12),X13)) ),
file('<stdin>',fact_282_rel__simps_I32_J) ).
fof(c_0_107,axiom,
! [X12,X13] :
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,bit0,X12)),hAPP(int,int,bit0,X13)))
<=> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X12),X13)) ),
file('<stdin>',fact_246_rel__simps_I31_J) ).
fof(c_0_108,axiom,
! [X18,X19] :
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,bit0,X18)),hAPP(int,int,bit0,X19)))
<=> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X18),X19)) ),
file('<stdin>',fact_245_less__eq__int__code_I13_J) ).
fof(c_0_109,axiom,
! [X12,X13] :
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,bit1,X12)),hAPP(int,int,bit1,X13)))
<=> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X12),X13)) ),
file('<stdin>',fact_243_rel__simps_I34_J) ).
fof(c_0_110,axiom,
! [X18,X19] :
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,bit1,X18)),hAPP(int,int,bit1,X19)))
<=> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X18),X19)) ),
file('<stdin>',fact_242_less__eq__int__code_I16_J) ).
fof(c_0_111,axiom,
! [X12,X13] :
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit1,X12)),hAPP(int,int,bit0,X13)))
<=> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X12),X13)) ),
file('<stdin>',fact_53_rel__simps_I16_J) ).
fof(c_0_112,axiom,
! [X18,X19] :
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit1,X18)),hAPP(int,int,bit0,X19)))
<=> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X18),X19)) ),
file('<stdin>',fact_52_less__int__code_I15_J) ).
fof(c_0_113,axiom,
! [X12,X13] :
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit0,X12)),hAPP(int,int,bit0,X13)))
<=> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X12),X13)) ),
file('<stdin>',fact_34_rel__simps_I14_J) ).
fof(c_0_114,axiom,
! [X18,X19] :
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit0,X18)),hAPP(int,int,bit0,X19)))
<=> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X18),X19)) ),
file('<stdin>',fact_33_less__int__code_I13_J) ).
fof(c_0_115,axiom,
! [X12,X13] :
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit1,X12)),hAPP(int,int,bit1,X13)))
<=> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X12),X13)) ),
file('<stdin>',fact_31_rel__simps_I17_J) ).
fof(c_0_116,axiom,
! [X18,X19] :
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit1,X18)),hAPP(int,int,bit1,X19)))
<=> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X18),X19)) ),
file('<stdin>',fact_30_less__int__code_I16_J) ).
fof(c_0_117,axiom,
! [X1] :
( linordered_semidom(X1)
=> ! [X31,X15,X40] :
( hAPP(nat,X1,power_power(X1,X31),X15) = hAPP(nat,X1,power_power(X1,X40),X15)
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X31))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X40))
=> ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X15))
=> ti(X1,X31) = ti(X1,X40) ) ) ) ) ),
file('<stdin>',fact_321_power__eq__imp__eq__base) ).
fof(c_0_118,axiom,
! [X1,X3] :
( ord(X3)
=> ! [X5,X54,X57] :
( hBOOL(hAPP(fun(X1,X3),bool,hAPP(fun(X1,X3),fun(fun(X1,X3),bool),ord_less_eq(fun(X1,X3)),X54),X57))
=> hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),hAPP(X1,X3,X54,X5)),hAPP(X1,X3,X57,X5))) ) ),
file('<stdin>',fact_397_le__funD) ).
fof(c_0_119,axiom,
! [X1,X3] :
( ord(X3)
=> ! [X5,X54,X57] :
( hBOOL(hAPP(fun(X1,X3),bool,hAPP(fun(X1,X3),fun(fun(X1,X3),bool),ord_less_eq(fun(X1,X3)),X54),X57))
=> hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),hAPP(X1,X3,X54,X5)),hAPP(X1,X3,X57,X5))) ) ),
file('<stdin>',fact_387_le__funE) ).
fof(c_0_120,axiom,
! [X31,X15] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X15))
=> ( hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X31))
=> ? [X47] :
( hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X47))
& hAPP(nat,real,power_power(real,X47),X15) = X31
& ! [X48] :
( ( hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X48))
& hAPP(nat,real,power_power(real,X48),X15) = X31 )
=> X48 = X47 ) ) ) ),
file('<stdin>',fact_229_realpow__pos__nth__unique) ).
fof(c_0_121,axiom,
! [X1] :
( ordere216010020id_add(X1)
=> ! [X40,X31] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X31))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X40))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),hAPP(X1,X1,plus_plus(X1,X31),X40))) ) ) ),
file('<stdin>',fact_298_add__nonneg__pos) ).
fof(c_0_122,axiom,
! [X1] :
( ordere216010020id_add(X1)
=> ! [X40,X31] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X31))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X40))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),hAPP(X1,X1,plus_plus(X1,X31),X40))) ) ) ),
file('<stdin>',fact_297_add__pos__nonneg) ).
fof(c_0_123,axiom,
! [X1] :
( ordere216010020id_add(X1)
=> ! [X40,X31] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X31))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X40))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),hAPP(X1,X1,plus_plus(X1,X31),X40))) ) ) ),
file('<stdin>',fact_266_add__nonneg__nonneg) ).
fof(c_0_124,axiom,
! [X1] :
( ordere216010020id_add(X1)
=> ! [X40,X31] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X31))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X40))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),hAPP(X1,X1,plus_plus(X1,X31),X40))) ) ) ),
file('<stdin>',fact_228_add__pos__pos) ).
fof(c_0_125,axiom,
! [X1] :
( ordere216010020id_add(X1)
=> ! [X40,X41,X31] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X31))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X40),X41))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X40),hAPP(X1,X1,plus_plus(X1,X31),X41))) ) ) ),
file('<stdin>',fact_300_add__strict__increasing2) ).
fof(c_0_126,axiom,
! [X1] :
( ordere216010020id_add(X1)
=> ! [X40,X41,X31] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X31))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X40),X41))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X40),hAPP(X1,X1,plus_plus(X1,X31),X41))) ) ) ),
file('<stdin>',fact_299_add__strict__increasing) ).
fof(c_0_127,axiom,
! [X1] :
( ordere216010020id_add(X1)
=> ! [X40,X31,X41] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X41))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X40),X31))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X40),hAPP(X1,X1,plus_plus(X1,X31),X41))) ) ) ),
file('<stdin>',fact_269_add__increasing2) ).
fof(c_0_128,axiom,
! [X1] :
( ordere216010020id_add(X1)
=> ! [X40,X41,X31] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X31))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X40),X41))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X40),hAPP(X1,X1,plus_plus(X1,X31),X41))) ) ) ),
file('<stdin>',fact_268_add__increasing) ).
fof(c_0_129,axiom,
! [X1] :
( linordered_semidom(X1)
=> ! [X40,X41,X31] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X31))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X40),X41))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X40),hAPP(X1,X1,plus_plus(X1,X31),X41))) ) ) ),
file('<stdin>',fact_175_pos__add__strict) ).
fof(c_0_130,axiom,
! [X1,X3] :
( ord(X3)
=> ! [X54,X57] :
( hBOOL(hAPP(fun(X1,X3),bool,hAPP(fun(X1,X3),fun(fun(X1,X3),bool),ord_less(fun(X1,X3)),X54),X57))
<=> ( hBOOL(hAPP(fun(X1,X3),bool,hAPP(fun(X1,X3),fun(fun(X1,X3),bool),ord_less_eq(fun(X1,X3)),X54),X57))
& ~ hBOOL(hAPP(fun(X1,X3),bool,hAPP(fun(X1,X3),fun(fun(X1,X3),bool),ord_less_eq(fun(X1,X3)),X57),X54)) ) ) ),
file('<stdin>',fact_447_less__fun__def) ).
fof(c_0_131,axiom,
! [X1] :
( linordered_semidom(X1)
=> ! [X15,X31] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),one_one(X1)),X31))
=> ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X15))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),one_one(X1)),hAPP(nat,X1,power_power(X1,X31),X15))) ) ) ),
file('<stdin>',fact_108_one__less__power) ).
fof(c_0_132,axiom,
! [X11,X10] :
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X10))
=> ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X11))
=> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,plus_plus(int,X10),X11))) ) ),
file('<stdin>',fact_287_Nat__Transfer_Otransfer__nat__int__function__closures_I1_J) ).
fof(c_0_133,axiom,
! [X1] :
( linord219039673up_add(X1)
=> ! [X7] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,plus_plus(X1,X7),X7)),zero_zero(X1)))
<=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X7),zero_zero(X1))) ) ),
file('<stdin>',fact_265_double__add__le__zero__iff__single__add__le__zero) ).
fof(c_0_134,axiom,
! [X1] :
( linord219039673up_add(X1)
=> ! [X7] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,plus_plus(X1,X7),X7)),zero_zero(X1)))
<=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X7),zero_zero(X1))) ) ),
file('<stdin>',fact_195_double__add__less__zero__iff__single__add__less__zero) ).
fof(c_0_135,axiom,
! [X1] :
( linordered_idom(X1)
=> ! [X7] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,plus_plus(X1,X7),X7)),zero_zero(X1)))
<=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X7),zero_zero(X1))) ) ),
file('<stdin>',fact_44_even__less__0__iff) ).
fof(c_0_136,axiom,
! [X33,X12,X34] :
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X12),X34))
=> ( hBOOL(hAPP(int,bool,X33,X12))
=> ( ! [X35] :
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X12),X35))
=> ( hBOOL(hAPP(int,bool,X33,X35))
=> hBOOL(hAPP(int,bool,X33,hAPP(int,int,plus_plus(int,X35),one_one(int)))) ) )
=> hBOOL(hAPP(int,bool,X33,X34)) ) ) ),
file('<stdin>',fact_382_int__ge__induct) ).
fof(c_0_137,axiom,
! [X24,X29] :
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,plus_plus(int,X24),one_one(int))),X29))
<=> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X24),X29)) ),
file('<stdin>',fact_318_add1__zle__eq) ).
fof(c_0_138,axiom,
hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),number_number_of(int,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),
file('<stdin>',fact_328_Nat__Transfer_Otransfer__nat__int__function__closures_I7_J) ).
fof(c_0_139,axiom,
hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),number_number_of(int,hAPP(int,int,bit1,hAPP(int,int,bit1,pls))))),
file('<stdin>',fact_323_Nat__Transfer_Otransfer__nat__int__function__closures_I8_J) ).
fof(c_0_140,axiom,
hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),
file('<stdin>',fact_189_pos2) ).
fof(c_0_141,axiom,
! [X1] :
( ordere779506340up_add(X1)
=> ! [X41,X31,X40] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X31),X40))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,plus_plus(X1,X41),X31)),hAPP(X1,X1,plus_plus(X1,X41),X40))) ) ),
file('<stdin>',fact_237_add__left__mono) ).
fof(c_0_142,axiom,
! [X1] :
( ordere779506340up_add(X1)
=> ! [X41,X31,X40] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X31),X40))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,plus_plus(X1,X31),X41)),hAPP(X1,X1,plus_plus(X1,X40),X41))) ) ),
file('<stdin>',fact_236_add__right__mono) ).
fof(c_0_143,axiom,
! [X1] :
( ordere223160158up_add(X1)
=> ! [X41,X31,X40] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X31),X40))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,plus_plus(X1,X31),X41)),hAPP(X1,X1,plus_plus(X1,X40),X41))) ) ),
file('<stdin>',fact_222_add__strict__right__mono) ).
fof(c_0_144,axiom,
! [X1] :
( ordere223160158up_add(X1)
=> ! [X41,X31,X40] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X31),X40))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,plus_plus(X1,X41),X31)),hAPP(X1,X1,plus_plus(X1,X41),X40))) ) ),
file('<stdin>',fact_221_add__strict__left__mono) ).
fof(c_0_145,axiom,
! [X14,X20,X15] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,plus_plus(nat,X14),X20)),X15))
=> ~ ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X14),X15))
=> ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X20),X15)) ) ),
file('<stdin>',fact_367_add__leE) ).
fof(c_0_146,axiom,
! [X14,X20,X15] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,plus_plus(nat,X14),X20)),X15))
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X14),X15)) ),
file('<stdin>',fact_366_add__leD1) ).
fof(c_0_147,axiom,
! [X14,X20,X15] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,plus_plus(nat,X14),X20)),X15))
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X20),X15)) ),
file('<stdin>',fact_365_add__leD2) ).
fof(c_0_148,axiom,
! [X21,X22,X20] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,plus_plus(nat,X21),X22)),X20))
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X21),X20)) ),
file('<stdin>',fact_136_add__lessD1) ).
fof(c_0_149,axiom,
! [X28,X17] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,plus_plus(nat,X28),X17)))
<=> ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X28))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X17)) ) ),
file('<stdin>',fact_143_add__gr__0) ).
fof(c_0_150,axiom,
! [X16,X10,X11] :
( hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X10),X11))
=> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,plus_plus(real,X16),X10)),hAPP(real,real,plus_plus(real,X16),X11))) ),
file('<stdin>',fact_368_real__add__left__mono) ).
fof(c_0_151,axiom,
! [X20,X21,X22] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X21),X22))
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,plus_plus(nat,X21),X20)),hAPP(nat,nat,plus_plus(nat,X22),X20))) ),
file('<stdin>',fact_363_add__le__mono1) ).
fof(c_0_152,axiom,
! [X20,X21,X22] :
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X21),X22))
=> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,plus_plus(int,X20),X21)),hAPP(int,int,plus_plus(int,X20),X22))) ),
file('<stdin>',fact_255_zadd__left__mono) ).
fof(c_0_153,axiom,
! [X20,X21,X22] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X21),X22))
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,plus_plus(nat,X21),X20)),hAPP(nat,nat,plus_plus(nat,X22),X20))) ),
file('<stdin>',fact_133_add__less__mono1) ).
fof(c_0_154,axiom,
! [X20,X21,X22] :
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X21),X22))
=> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,plus_plus(int,X21),X20)),hAPP(int,int,plus_plus(int,X22),X20))) ),
file('<stdin>',fact_35_zadd__strict__right__mono) ).
fof(c_0_155,axiom,
! [X1] :
( ( number_ring(X1)
& linordered_idom(X1) )
=> ! [X6] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),one_one(X1)),number_number_of(X1,X6)))
<=> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,bit1,pls)),X6)) ) ),
file('<stdin>',fact_262_le__special_I2_J) ).
fof(c_0_156,axiom,
! [X1] :
( ( number_ring(X1)
& linordered_idom(X1) )
=> ! [X6] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),one_one(X1)),number_number_of(X1,X6)))
<=> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit1,pls)),X6)) ) ),
file('<stdin>',fact_63_less__special_I2_J) ).
fof(c_0_157,axiom,
! [X14,X15,X16] : hAPP(int,int,plus_plus(int,hAPP(nat,int,semiring_1_of_nat(int),X14)),hAPP(int,int,plus_plus(int,hAPP(nat,int,semiring_1_of_nat(int),X15)),X16)) = hAPP(int,int,plus_plus(int,hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,plus_plus(nat,X14),X15))),X16),
file('<stdin>',fact_22_zadd__int__left) ).
fof(c_0_158,axiom,
! [X5] :
( hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,sqrt,X5)),one_one(real)))
<=> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X5),one_one(real))) ),
file('<stdin>',fact_485_real__sqrt__lt__1__iff) ).
fof(c_0_159,axiom,
! [X5] :
( hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,sqrt,X5)),zero_zero(real)))
<=> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X5),zero_zero(real))) ),
file('<stdin>',fact_483_real__sqrt__lt__0__iff) ).
fof(c_0_160,axiom,
! [X24] :
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit0,X24)),zero_zero(int)))
<=> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X24),zero_zero(int))) ),
file('<stdin>',fact_58_bin__less__0__simps_I3_J) ).
fof(c_0_161,axiom,
! [X24] :
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit1,X24)),zero_zero(int)))
<=> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X24),zero_zero(int))) ),
file('<stdin>',fact_56_bin__less__0__simps_I4_J) ).
fof(c_0_162,axiom,
! [X1] :
( linordered_semidom(X1)
=> ! [X14,X15] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X14),X15))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(nat,X1,semiring_1_of_nat(X1),X14)),hAPP(nat,X1,semiring_1_of_nat(X1),X15))) ) ),
file('<stdin>',fact_167_less__imp__of__nat__less) ).
fof(c_0_163,axiom,
! [X12] :
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,bit1,X12)),pls))
<=> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X12),pls)) ),
file('<stdin>',fact_307_rel__simps_I29_J) ).
fof(c_0_164,axiom,
! [X12] :
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,bit0,X12)),pls))
<=> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X12),pls)) ),
file('<stdin>',fact_285_rel__simps_I27_J) ).
fof(c_0_165,axiom,
! [X12] :
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit0,X12)),pls))
<=> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X12),pls)) ),
file('<stdin>',fact_54_rel__simps_I10_J) ).
fof(c_0_166,axiom,
! [X12] :
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit1,X12)),pls))
<=> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X12),pls)) ),
file('<stdin>',fact_51_rel__simps_I12_J) ).
fof(c_0_167,axiom,
! [X38,X39] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),number_number_of(nat,X38)),number_number_of(nat,X39)))
<=> ( ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X38),X39))
=> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),X39)) )
& hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X38),X39)) ) ),
file('<stdin>',fact_150_less__nat__number__of) ).
fof(c_0_168,axiom,
! [X1] :
( order(X1)
=> ! [X16,X11,X10] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X11),X10))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X16),X11))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X16),X10)) ) ) ),
file('<stdin>',fact_444_xt1_I8_J) ).
fof(c_0_169,axiom,
! [X1] :
( preorder(X1)
=> ! [X16,X10,X11] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X10),X11))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X11),X16))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X10),X16)) ) ) ),
file('<stdin>',fact_443_order__le__less__trans) ).
fof(c_0_170,axiom,
! [X1] :
( order(X1)
=> ! [X16,X11,X10] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X11),X10))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X16),X11))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X16),X10)) ) ) ),
file('<stdin>',fact_442_xt1_I7_J) ).
fof(c_0_171,axiom,
! [X1] :
( preorder(X1)
=> ! [X16,X10,X11] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X10),X11))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X11),X16))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X10),X16)) ) ) ),
file('<stdin>',fact_441_order__less__le__trans) ).
fof(c_0_172,axiom,
! [X1] :
( preorder(X1)
=> ! [X16,X10,X11] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X10),X11))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X11),X16))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X10),X16)) ) ) ),
file('<stdin>',fact_405_order__less__trans) ).
fof(c_0_173,axiom,
! [X1] :
( order(X1)
=> ! [X16,X11,X10] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X11),X10))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X16),X11))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X16),X10)) ) ) ),
file('<stdin>',fact_404_xt1_I10_J) ).
fof(c_0_174,axiom,
! [X1] :
( preorder(X1)
=> ! [X16,X10,X11] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X10),X11))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X11),X16))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X10),X16)) ) ) ),
file('<stdin>',fact_390_order__trans) ).
fof(c_0_175,axiom,
! [X1] :
( order(X1)
=> ! [X16,X11,X10] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X11),X10))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X16),X11))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X16),X10)) ) ) ),
file('<stdin>',fact_388_xt1_I6_J) ).
fof(c_0_176,axiom,
! [X58,X59] :
( hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X59))
=> ( hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X58))
=> ? [X60] :
( hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X60))
& hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X60),X59))
& hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X60),X58)) ) ) ),
file('<stdin>',fact_445_real__lbound__gt__zero) ).
fof(c_0_177,axiom,
! [X31,X15] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X15))
=> ( hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X31))
=> ? [X49] :
( hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X49))
& hAPP(nat,real,power_power(real,X49),X15) = X31 ) ) ),
file('<stdin>',fact_230_realpow__pos__nth) ).
fof(c_0_178,axiom,
! [X20,X21,X22] :
( hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X21),X22))
=> ( hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X22),X20))
=> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X21),X20)) ) ),
file('<stdin>',fact_380_real__le__trans) ).
fof(c_0_179,axiom,
! [X20,X21,X22] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X21),X22))
=> ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X22),X20))
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X21),X20)) ) ),
file('<stdin>',fact_353_le__trans) ).
fof(c_0_180,axiom,
! [X20,X21,X22] :
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X21),X22))
=> ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X22),X20))
=> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X21),X20)) ) ),
file('<stdin>',fact_250_zle__trans) ).
fof(c_0_181,axiom,
! [X8,X16] :
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X8),X16))
=> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,plus_plus(int,X8),one_one(int))),X16)) ),
file('<stdin>',fact_319_zless__imp__add1__zle) ).
fof(c_0_182,axiom,
! [X15] :
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),number_number_of(int,X15)))
=> ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),number_number_of(int,hAPP(int,int,bit0,X15))))
& hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),number_number_of(int,hAPP(int,int,bit1,X15)))) ) ),
file('<stdin>',fact_338_number__of1) ).
fof(c_0_183,axiom,
! [X1] :
( linord219039673up_add(X1)
=> ! [X7] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),hAPP(X1,X1,plus_plus(X1,X7),X7)))
<=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X7)) ) ),
file('<stdin>',fact_264_zero__le__double__add__iff__zero__le__single__add) ).
fof(c_0_184,axiom,
! [X1] :
( linord219039673up_add(X1)
=> ! [X7] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),hAPP(X1,X1,plus_plus(X1,X7),X7)))
<=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X7)) ) ),
file('<stdin>',fact_194_zero__less__double__add__iff__zero__less__single__add) ).
fof(c_0_185,axiom,
! [X5,X24] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,power_power(nat,X5),number_number_of(nat,X24))))
<=> ( number_number_of(nat,X24) = zero_zero(nat)
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X5)) ) ),
file('<stdin>',fact_148_zero__less__power__nat__eq__number__of) ).
fof(c_0_186,axiom,
! [X22,X21] : ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,plus_plus(nat,X22),X21)),X21)),
file('<stdin>',fact_118_not__add__less2) ).
fof(c_0_187,axiom,
! [X21,X22] : ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,plus_plus(nat,X21),X22)),X21)),
file('<stdin>',fact_117_not__add__less1) ).
fof(c_0_188,axiom,
! [X1] :
( number_semiring(X1)
=> ! [X23,X9] :
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),X9))
=> ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),X23))
=> hAPP(X1,X1,plus_plus(X1,number_number_of(X1,X9)),number_number_of(X1,X23)) = number_number_of(X1,hAPP(int,int,plus_plus(int,X9),X23)) ) ) ),
file('<stdin>',fact_322_semiring__add__number__of) ).
fof(c_0_189,axiom,
! [X38,X39] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),number_number_of(nat,X38)),number_number_of(nat,X39)))
<=> ( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X38),X39))
=> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X38),pls)) ) ),
file('<stdin>',fact_371_le__nat__number__of) ).
fof(c_0_190,axiom,
! [X5,X17] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,power_power(nat,X5),X17)))
<=> ( X17 = zero_zero(nat)
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X5)) ) ),
file('<stdin>',fact_146_zero__less__power__nat__eq) ).
fof(c_0_191,axiom,
! [X5,X17] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,power_power(nat,X5),X17)))
<=> ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X5))
| X17 = zero_zero(nat) ) ),
file('<stdin>',fact_142_nat__zero__less__power__iff) ).
fof(c_0_192,axiom,
! [X24,X29] :
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X24),hAPP(int,int,plus_plus(int,X29),one_one(int))))
<=> ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X24),X29))
| X24 = X29 ) ),
file('<stdin>',fact_60_zless__add1__eq) ).
fof(c_0_193,axiom,
! [X24,X29] :
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X24),hAPP(int,int,plus_plus(int,X29),one_one(int))))
<=> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X24),X29)) ),
file('<stdin>',fact_317_zle__add1__eq__le) ).
fof(c_0_194,axiom,
! [X1] :
( preorder(X1)
=> ! [X5,X6] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X5),X6))
<=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X5),X6))
& ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X6),X5)) ) ) ),
file('<stdin>',fact_428_less__le__not__le) ).
fof(c_0_195,axiom,
! [X1] :
( linordered_semidom(X1)
=> ! [X17] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),hAPP(nat,X1,semiring_1_of_nat(X1),X17)))
<=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X17)) ) ),
file('<stdin>',fact_107_of__nat__0__less__iff) ).
fof(c_0_196,axiom,
! [X1] :
( ( number_ring(X1)
& linordered_idom(X1) )
=> ! [X5] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),number_number_of(X1,X5)),one_one(X1)))
<=> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X5),hAPP(int,int,bit1,pls))) ) ),
file('<stdin>',fact_263_le__special_I4_J) ).
fof(c_0_197,axiom,
! [X1] :
( ( number_ring(X1)
& linordered_idom(X1) )
=> ! [X5] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),number_number_of(X1,X5)),one_one(X1)))
<=> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X5),hAPP(int,int,bit1,pls))) ) ),
file('<stdin>',fact_62_less__special_I4_J) ).
fof(c_0_198,axiom,
! [X1] :
( linordered_semidom(X1)
=> ! [X14] : ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(nat,X1,semiring_1_of_nat(X1),X14)),zero_zero(X1))) ),
file('<stdin>',fact_185_of__nat__less__0__iff) ).
fof(c_0_199,axiom,
! [X52,X33,X5] :
( ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X5))
=> ( hBOOL(X33)
<=> hBOOL(X52) ) )
=> ( ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X5))
& hBOOL(X33) )
<=> ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X5))
& hBOOL(X52) ) ) ),
file('<stdin>',fact_373_conj__le__cong) ).
fof(c_0_200,axiom,
! [X52,X33,X5] :
( ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X5))
=> ( hBOOL(X33)
<=> hBOOL(X52) ) )
=> ( ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X5))
=> hBOOL(X33) )
<=> ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X5))
=> hBOOL(X52) ) ) ),
file('<stdin>',fact_374_imp__le__cong) ).
fof(c_0_201,axiom,
! [X17] :
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(nat,int,semiring_1_of_nat(int),X17)))
<=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X17)) ),
file('<stdin>',fact_161_zero__less__int__conv) ).
fof(c_0_202,axiom,
! [X6] :
( hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),one_one(real)),hAPP(real,real,sqrt,X6)))
<=> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),one_one(real)),X6)) ),
file('<stdin>',fact_486_real__sqrt__gt__1__iff) ).
fof(c_0_203,axiom,
! [X6] :
( hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(real,real,sqrt,X6)))
<=> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X6)) ),
file('<stdin>',fact_484_real__sqrt__gt__0__iff) ).
fof(c_0_204,axiom,
! [X17] :
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(nat,int,semiring_1_of_nat(int),X17)),zero_zero(int)))
<=> X17 = zero_zero(nat) ),
file('<stdin>',fact_313_int__le__0__conv) ).
fof(c_0_205,axiom,
! [X20] : ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(nat,int,semiring_1_of_nat(int),X20)),zero_zero(int))),
file('<stdin>',fact_61_int__less__0__conv) ).
fof(c_0_206,axiom,
! [X1] :
( ordere216010020id_add(X1)
=> ! [X6,X5] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X5))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X6))
=> ( hAPP(X1,X1,plus_plus(X1,X5),X6) = zero_zero(X1)
<=> ( ti(X1,X5) = zero_zero(X1)
& ti(X1,X6) = zero_zero(X1) ) ) ) ) ),
file('<stdin>',fact_267_add__nonneg__eq__0__iff) ).
fof(c_0_207,axiom,
! [X12] :
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),hAPP(int,int,bit1,X12)))
<=> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),X12)) ),
file('<stdin>',fact_306_rel__simps_I5_J) ).
fof(c_0_208,axiom,
! [X12] :
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),hAPP(int,int,bit0,X12)))
<=> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),X12)) ),
file('<stdin>',fact_284_rel__simps_I21_J) ).
fof(c_0_209,axiom,
! [X12] :
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),hAPP(int,int,bit1,X12)))
<=> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),X12)) ),
file('<stdin>',fact_281_rel__simps_I22_J) ).
fof(c_0_210,axiom,
! [X12] :
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),hAPP(int,int,bit0,X12)))
<=> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),X12)) ),
file('<stdin>',fact_55_rel__simps_I4_J) ).
fof(c_0_211,axiom,
! [X1] :
( ( number(X1)
& linorder(X1) )
=> ! [X38,X24] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),number_number_of(X1,X38)),number_number_of(X1,X24)))
<=> ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),number_number_of(X1,X24)),number_number_of(X1,X38))) ) ),
file('<stdin>',fact_275_le__number__of__eq__not__less) ).
fof(c_0_212,axiom,
! [X33] :
( ! [X47] :
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X47))
=> hBOOL(hAPP(int,bool,X33,X47)) )
<=> ! [X47] : hBOOL(hAPP(int,bool,X33,hAPP(nat,int,semiring_1_of_nat(int),X47))) ),
file('<stdin>',fact_291_transfer__int__nat__quantifiers_I1_J) ).
fof(c_0_213,axiom,
! [X1] :
( linordered_semidom(X1)
=> ! [X15,X31] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),one_one(X1)),X31))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),one_one(X1)),hAPP(nat,X1,power_power(X1,X31),X15))) ) ),
file('<stdin>',fact_278_one__le__power) ).
fof(c_0_214,axiom,
! [X1] :
( linordered_semidom(X1)
=> ! [X15,X31] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X31))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),hAPP(nat,X1,power_power(X1,X31),X15))) ) ),
file('<stdin>',fact_276_zero__le__power) ).
fof(c_0_215,axiom,
! [X1] :
( linordered_semidom(X1)
=> ! [X15,X31] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X31))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),hAPP(nat,X1,power_power(X1,X31),X15))) ) ),
file('<stdin>',fact_178_zero__less__power) ).
fof(c_0_216,axiom,
! [X1] :
( linorder(X1)
=> ! [X37] :
? [X61] :
! [X47] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X61),X47))
=> ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X47),X37)) ) ),
file('<stdin>',fact_449_pinf_I6_J) ).
fof(c_0_217,axiom,
! [X16] :
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X16))
=> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(int,int,plus_plus(int,one_one(int)),X16))) ),
file('<stdin>',fact_324_le__imp__0__less) ).
fof(c_0_218,axiom,
! [X15,X10] :
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X10))
=> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(nat,int,power_power(int,X10),X15))) ),
file('<stdin>',fact_293_Nat__Transfer_Otransfer__nat__int__function__closures_I4_J) ).
fof(c_0_219,axiom,
! [X1] :
( linorder(X1)
=> ! [X37] :
? [X61] :
! [X47] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X47),X61))
=> ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X37),X47)) ) ),
file('<stdin>',fact_456_minf_I8_J) ).
fof(c_0_220,axiom,
! [X14,X21,X22] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X21),X22))
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X21),hAPP(nat,nat,plus_plus(nat,X14),X22))) ),
file('<stdin>',fact_362_trans__le__add2) ).
fof(c_0_221,axiom,
! [X14,X21,X22] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X21),X22))
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X21),hAPP(nat,nat,plus_plus(nat,X22),X14))) ),
file('<stdin>',fact_361_trans__le__add1) ).
fof(c_0_222,axiom,
! [X14,X21,X22] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X21),X22))
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X21),hAPP(nat,nat,plus_plus(nat,X14),X22))) ),
file('<stdin>',fact_132_trans__less__add2) ).
fof(c_0_223,axiom,
! [X14,X21,X22] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X21),X22))
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X21),hAPP(nat,nat,plus_plus(nat,X22),X14))) ),
file('<stdin>',fact_131_trans__less__add1) ).
fof(c_0_224,axiom,
! [X1] :
( linorder(X1)
=> ! [X5,X6] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X5),X6))
=> ( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X5),X6))
<=> ti(X1,X5) = ti(X1,X6) ) ) ),
file('<stdin>',fact_437_linorder__antisym__conv2) ).
fof(c_0_225,axiom,
! [X1] :
( order(X1)
=> ! [X5,X6] :
( ti(X1,X5) = ti(X1,X6)
<=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X5),X6))
& hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X6),X5)) ) ) ),
file('<stdin>',fact_399_order__eq__iff) ).
fof(c_0_226,axiom,
! [X1] :
( order(X1)
=> ! [X6,X5] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X6),X5))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X5),X6))
<=> ti(X1,X5) = ti(X1,X6) ) ) ),
file('<stdin>',fact_396_order__antisym__conv) ).
fof(c_0_227,axiom,
! [X1] :
( order(X1)
=> ! [X10,X11] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X10),X11))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X11),X10))
=> ti(X1,X10) = ti(X1,X11) ) ) ),
file('<stdin>',fact_391_order__antisym) ).
fof(c_0_228,axiom,
! [X1] :
( order(X1)
=> ! [X11,X10] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X11),X10))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X10),X11))
=> ti(X1,X10) = ti(X1,X11) ) ) ),
file('<stdin>',fact_389_xt1_I5_J) ).
fof(c_0_229,axiom,
! [X1] :
( ring_11004092258visors(X1)
=> ! [X7] :
( hAPP(nat,X1,power_power(X1,X7),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) = zero_zero(X1)
<=> ti(X1,X7) = zero_zero(X1) ) ),
file('<stdin>',fact_5_zero__eq__power2) ).
fof(c_0_230,axiom,
! [X1] :
( preorder(X1)
=> ! [X33,X5,X6] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X5),X6))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X6),X5))
=> hBOOL(X33) ) ) ),
file('<stdin>',fact_412_order__less__imp__triv) ).
fof(c_0_231,axiom,
! [X1] :
( linorder(X1)
=> ! [X11,X10] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X11),X10))
=> ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X10),X11)) ) ),
file('<stdin>',fact_435_leD) ).
fof(c_0_232,axiom,
! [X1] :
( linorder(X1)
=> ! [X5,X6] :
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X5),X6))
<=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X6),X5)) ) ),
file('<stdin>',fact_425_linorder__not__le) ).
fof(c_0_233,axiom,
! [X1] :
( linorder(X1)
=> ! [X5,X6] :
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X5),X6))
<=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X6),X5)) ) ),
file('<stdin>',fact_424_linorder__not__less) ).
fof(c_0_234,axiom,
! [X1] :
( linorder(X1)
=> ! [X5,X6] :
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X5),X6))
<=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X6),X5))
| ti(X1,X5) = ti(X1,X6) ) ) ),
file('<stdin>',fact_421_not__less__iff__gr__or__eq) ).
fof(c_0_235,axiom,
! [X1] :
( preorder(X1)
=> ! [X10,X11] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X10),X11))
=> ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X11),X10)) ) ),
file('<stdin>',fact_416_order__less__not__sym) ).
fof(c_0_236,axiom,
! [X1] :
( preorder(X1)
=> ! [X10,X11] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X10),X11))
=> ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X11),X10)) ) ),
file('<stdin>',fact_415_order__less__imp__not__less) ).
fof(c_0_237,axiom,
! [X1] :
( preorder(X1)
=> ! [X31,X40] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X31),X40))
=> ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X40),X31)) ) ),
file('<stdin>',fact_411_order__less__asym_H) ).
fof(c_0_238,axiom,
! [X1] :
( order(X1)
=> ! [X40,X31] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X40),X31))
=> ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X31),X40)) ) ),
file('<stdin>',fact_410_xt1_I9_J) ).
fof(c_0_239,axiom,
! [X1] :
( preorder(X1)
=> ! [X10,X11] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X10),X11))
=> ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X11),X10)) ) ),
file('<stdin>',fact_403_order__less__asym) ).
fof(c_0_240,axiom,
! [X10] :
( hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X10))
=> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(real,real,sqrt,X10))) ),
file('<stdin>',fact_481_real__sqrt__gt__zero) ).
fof(c_0_241,axiom,
! [X16,X8] :
( hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X16),X8))
=> ( hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X8),X16))
=> X16 = X8 ) ),
file('<stdin>',fact_381_real__le__antisym) ).
fof(c_0_242,axiom,
! [X14,X15] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X14),X15))
=> ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X15),X14))
=> X14 = X15 ) ),
file('<stdin>',fact_354_le__antisym) ).
fof(c_0_243,axiom,
! [X16,X8] :
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X16),X8))
=> ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X8),X16))
=> X16 = X8 ) ),
file('<stdin>',fact_251_zle__antisym) ).
fof(c_0_244,axiom,
! [X14,X15,X20,X30] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X20),X30))
=> ( hAPP(nat,nat,plus_plus(nat,X14),X30) = hAPP(nat,nat,plus_plus(nat,X20),X15)
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X14),X15)) ) ),
file('<stdin>',fact_135_less__add__eq__less) ).
fof(c_0_245,axiom,
! [X1] :
( dense_linorder(X1)
=> ! [X16,X11] :
( ! [X47] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X47),X11))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X47),X16)) )
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X11),X16)) ) ),
file('<stdin>',fact_446_dense__le) ).
fof(c_0_246,axiom,
! [X33] :
( ? [X47] :
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X47))
& hBOOL(hAPP(int,bool,X33,X47)) )
<=> ? [X47] : hBOOL(hAPP(int,bool,X33,hAPP(nat,int,semiring_1_of_nat(int),X47))) ),
file('<stdin>',fact_290_transfer__int__nat__quantifiers_I2_J) ).
fof(c_0_247,axiom,
hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(int,int,plus_plus(int,one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),n)))),
file('<stdin>',fact_0_n1pos) ).
fof(c_0_248,axiom,
number_number_of(int,hAPP(int,int,bit1,hAPP(int,int,bit1,pls))) = hAPP(nat,int,semiring_1_of_nat(int),number_number_of(nat,hAPP(int,int,bit1,hAPP(int,int,bit1,pls)))),
file('<stdin>',fact_105_transfer__int__nat__numerals_I4_J) ).
fof(c_0_249,axiom,
number_number_of(int,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))) = hAPP(nat,int,semiring_1_of_nat(int),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),
file('<stdin>',fact_104_transfer__int__nat__numerals_I3_J) ).
fof(c_0_250,axiom,
hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),m1),hAPP(int,int,plus_plus(int,one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),n)))),
file('<stdin>',fact_102_mn) ).
fof(c_0_251,axiom,
! [X17,X33] :
( ~ hBOOL(hAPP(nat,bool,X33,zero_zero(nat)))
=> ( hBOOL(hAPP(nat,bool,X33,X17))
=> ? [X44] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X44),X17))
& ! [X35] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X35),X44))
=> ~ hBOOL(hAPP(nat,bool,X33,X35)) )
& hBOOL(hAPP(nat,bool,X33,X44)) ) ) ),
file('<stdin>',fact_383_ex__least__nat__le) ).
fof(c_0_252,axiom,
! [X17,X33] :
( ~ hBOOL(hAPP(nat,bool,X33,zero_zero(nat)))
=> ( hBOOL(hAPP(nat,bool,X33,X17))
=> ? [X44] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X44),X17))
& ! [X35] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X35),X44))
=> ~ hBOOL(hAPP(nat,bool,X33,X35)) )
& hBOOL(hAPP(nat,bool,X33,hAPP(nat,nat,plus_plus(nat,X44),one_one(nat)))) ) ) ),
file('<stdin>',fact_375_ex__least__nat__less) ).
fof(c_0_253,axiom,
! [X5,X6,X33] :
( ( hBOOL(X33)
=> hAPP(nat,int,semiring_1_of_nat(int),X5) = hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),hAPP(bool,fun(nat,fun(nat,nat)),if(nat),X33),X5),X6)) )
& ( ~ hBOOL(X33)
=> hAPP(nat,int,semiring_1_of_nat(int),X6) = hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),hAPP(bool,fun(nat,fun(nat,nat)),if(nat),X33),X5),X6)) ) ),
file('<stdin>',fact_159_int__if__cong) ).
fof(c_0_254,axiom,
! [X23,X9] :
( ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X9),pls))
=> hAPP(nat,nat,plus_plus(nat,number_number_of(nat,X9)),number_number_of(nat,X23)) = number_number_of(nat,X23) )
& ( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X9),pls))
=> ( ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X23),pls))
=> hAPP(nat,nat,plus_plus(nat,number_number_of(nat,X9)),number_number_of(nat,X23)) = number_number_of(nat,X9) )
& ( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X23),pls))
=> hAPP(nat,nat,plus_plus(nat,number_number_of(nat,X9)),number_number_of(nat,X23)) = number_number_of(nat,hAPP(int,int,plus_plus(int,X9),X23)) ) ) ) ),
file('<stdin>',fact_36_add__nat__number__of) ).
fof(c_0_255,axiom,
! [X1] :
( ( number_ring(X1)
& linordered_idom(X1) )
=> ! [X5,X6] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),number_number_of(X1,X5)),number_number_of(X1,X6)))
<=> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X5),X6)) ) ),
file('<stdin>',fact_252_le__number__of) ).
fof(c_0_256,axiom,
! [X1] :
( ( number_ring(X1)
& linordered_idom(X1) )
=> ! [X5,X6] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),number_number_of(X1,X5)),number_number_of(X1,X6)))
<=> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X5),X6)) ) ),
file('<stdin>',fact_18_less__number__of) ).
fof(c_0_257,axiom,
! [X1] :
( linorder(X1)
=> ! [X37] :
? [X61] :
! [X47] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X61),X47))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X37),X47)) ) ),
file('<stdin>',fact_453_pinf_I8_J) ).
fof(c_0_258,axiom,
! [X1] :
( ( number_ring(X1)
& linordered_idom(X1) )
=> ! [X5] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),number_number_of(X1,X5)),zero_zero(X1)))
<=> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X5),pls)) ) ),
file('<stdin>',fact_258_le__special_I3_J) ).
fof(c_0_259,axiom,
! [X1] :
( ( number_ring(X1)
& linordered_idom(X1) )
=> ! [X5] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),number_number_of(X1,X5)),zero_zero(X1)))
<=> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X5),pls)) ) ),
file('<stdin>',fact_49_less__special_I3_J) ).
fof(c_0_260,axiom,
! [X12,X13] :
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),number_number_of(int,X12)),number_number_of(int,X13)))
<=> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X12),X13)) ),
file('<stdin>',fact_256_less__eq__number__of__int__code) ).
fof(c_0_261,axiom,
! [X12,X13] :
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),number_number_of(int,X12)),number_number_of(int,X13)))
<=> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X12),X13)) ),
file('<stdin>',fact_16_less__number__of__int__code) ).
fof(c_0_262,axiom,
! [X1] :
( ( number_ring(X1)
& linordered_idom(X1) )
=> ! [X6] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),number_number_of(X1,X6)))
<=> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),X6)) ) ),
file('<stdin>',fact_257_le__special_I1_J) ).
fof(c_0_263,axiom,
! [X1] :
( ( number_ring(X1)
& linordered_idom(X1) )
=> ! [X6] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),number_number_of(X1,X6)))
<=> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),X6)) ) ),
file('<stdin>',fact_50_less__special_I1_J) ).
fof(c_0_264,axiom,
! [X1] :
( linorder(X1)
=> ! [X37] :
? [X61] :
! [X47] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X47),X61))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X47),X37)) ) ),
file('<stdin>',fact_452_minf_I6_J) ).
fof(c_0_265,axiom,
! [X1] :
( linorder(X1)
=> ! [X6,X5] :
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X6),X5))
=> ( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X5),X6))
<=> ti(X1,X5) = ti(X1,X6) ) ) ),
file('<stdin>',fact_419_linorder__antisym__conv3) ).
fof(c_0_266,axiom,
! [X1] :
( order(X1)
=> ! [X41,X31,X40] :
( ti(X1,X31) = ti(X1,X40)
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X41),X40))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X41),X31)) ) ) ),
file('<stdin>',fact_408_xt1_I1_J) ).
fof(c_0_267,axiom,
! [X1] :
( order(X1)
=> ! [X41,X40,X31] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X40),X31))
=> ( ti(X1,X40) = ti(X1,X41)
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X41),X31)) ) ) ),
file('<stdin>',fact_406_xt1_I2_J) ).
fof(c_0_268,axiom,
! [X1] :
( order(X1)
=> ! [X41,X31,X40] :
( ti(X1,X31) = ti(X1,X40)
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X41),X40))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X41),X31)) ) ) ),
file('<stdin>',fact_394_xt1_I3_J) ).
fof(c_0_269,axiom,
! [X1] :
( order(X1)
=> ! [X41,X40,X31] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X40),X31))
=> ( ti(X1,X40) = ti(X1,X41)
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X41),X31)) ) ) ),
file('<stdin>',fact_392_xt1_I4_J) ).
fof(c_0_270,axiom,
! [X1] :
( order(X1)
=> ! [X40,X31] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X40),X31))
=> ( ti(X1,X31) != ti(X1,X40)
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X40),X31)) ) ) ),
file('<stdin>',fact_440_xt1_I11_J) ).
fof(c_0_271,axiom,
! [X1] :
( order(X1)
=> ! [X31,X40] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X31),X40))
=> ( ti(X1,X31) != ti(X1,X40)
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X31),X40)) ) ) ),
file('<stdin>',fact_439_order__le__neq__trans) ).
fof(c_0_272,axiom,
! [X1] :
( order(X1)
=> ! [X10,X11] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X10),X11))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X10),X11))
| ti(X1,X10) = ti(X1,X11) ) ) ),
file('<stdin>',fact_438_order__le__imp__less__or__eq) ).
fof(c_0_273,axiom,
! [X1] :
( order(X1)
=> ! [X31,X40] :
( ti(X1,X31) != ti(X1,X40)
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X40),X31))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X40),X31)) ) ) ),
file('<stdin>',fact_434_xt1_I12_J) ).
fof(c_0_274,axiom,
! [X1] :
( order(X1)
=> ! [X31,X40] :
( ti(X1,X31) != ti(X1,X40)
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X31),X40))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X31),X40)) ) ) ),
file('<stdin>',fact_433_order__neq__le__trans) ).
fof(c_0_275,axiom,
! [X1] :
( linorder(X1)
=> ! [X5,X6] :
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X5),X6))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X5),X6))
<=> ti(X1,X5) = ti(X1,X6) ) ) ),
file('<stdin>',fact_432_linorder__antisym__conv1) ).
fof(c_0_276,axiom,
! [X1] :
( order(X1)
=> ! [X5,X6] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X5),X6))
<=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X5),X6))
| ti(X1,X5) = ti(X1,X6) ) ) ),
file('<stdin>',fact_429_order__le__less) ).
fof(c_0_277,axiom,
! [X1] :
( order(X1)
=> ! [X5,X6] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X5),X6))
<=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X5),X6))
& ti(X1,X5) != ti(X1,X6) ) ) ),
file('<stdin>',fact_427_order__less__le) ).
fof(c_0_278,axiom,
! [X1] :
( ord(X1)
=> ! [X41,X31,X40] :
( X31 = X40
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X40),X41))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X31),X41)) ) ) ),
file('<stdin>',fact_409_ord__eq__less__trans) ).
fof(c_0_279,axiom,
! [X1] :
( ord(X1)
=> ! [X41,X31,X40] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X31),X40))
=> ( X40 = X41
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X31),X41)) ) ) ),
file('<stdin>',fact_407_ord__less__eq__trans) ).
fof(c_0_280,axiom,
! [X1] :
( ord(X1)
=> ! [X41,X31,X40] :
( X31 = X40
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X40),X41))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X31),X41)) ) ) ),
file('<stdin>',fact_395_ord__eq__le__trans) ).
fof(c_0_281,axiom,
! [X1] :
( ord(X1)
=> ! [X41,X31,X40] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X31),X40))
=> ( X40 = X41
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X31),X41)) ) ) ),
file('<stdin>',fact_393_ord__le__eq__trans) ).
fof(c_0_282,axiom,
! [X1] :
( preorder(X1)
=> ! [X10,X11] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X10),X11))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X10),X11)) ) ),
file('<stdin>',fact_436_order__less__imp__le) ).
fof(c_0_283,axiom,
! [X38] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),number_number_of(nat,X38)))
<=> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),X38)) ),
file('<stdin>',fact_160_less__0__number__of) ).
fof(c_0_284,axiom,
! [X21,X22] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X21),X22))
=> ? [X44] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X44))
& hAPP(nat,nat,plus_plus(nat,X21),X44) = X22 ) ),
file('<stdin>',fact_191_less__imp__add__positive) ).
fof(c_0_285,axiom,
! [X20] :
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),X20))
=> ? [X43] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X43))
& X20 = hAPP(nat,int,semiring_1_of_nat(int),X43) ) ),
file('<stdin>',fact_190_zero__less__imp__eq__int) ).
fof(c_0_286,axiom,
! [X29] :
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),one_one(int)),X29))
<=> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),X29)) ),
file('<stdin>',fact_312_int__one__le__iff__zero__less) ).
fof(c_0_287,axiom,
! [X5,X6] :
( hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X5),X6))
<=> ( hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X5),X6))
& X5 != X6 ) ),
file('<stdin>',fact_356_real__less__def) ).
fof(c_0_288,axiom,
! [X5,X6] :
( hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X5),X6))
<=> ( hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X5),X6))
| X5 = X6 ) ),
file('<stdin>',fact_355_less__eq__real__def) ).
fof(c_0_289,axiom,
! [X28,X17] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X28),X17))
<=> ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X28),X17))
& X28 != X17 ) ),
file('<stdin>',fact_349_nat__less__le) ).
fof(c_0_290,axiom,
! [X28,X17] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X28),X17))
<=> ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X28),X17))
| X28 = X17 ) ),
file('<stdin>',fact_348_le__eq__less__or__eq) ).
fof(c_0_291,axiom,
! [X14,X15] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X14),X15))
=> ( X14 != X15
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X14),X15)) ) ),
file('<stdin>',fact_346_le__neq__implies__less) ).
fof(c_0_292,axiom,
! [X29,X24] :
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X29),X24))
<=> ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X29),X24))
& X29 != X24 ) ),
file('<stdin>',fact_254_zless__le) ).
fof(c_0_293,axiom,
! [X14,X15] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X14),X15))
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X14),X15)) ),
file('<stdin>',fact_347_less__imp__le__nat) ).
fof(c_0_294,axiom,
! [X14,X15] :
( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X14),X15))
| X14 = X15 )
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X14),X15)) ),
file('<stdin>',fact_345_less__or__eq__imp__le) ).
fof(c_0_295,axiom,
! [X1] :
( comm_semiring_1(X1)
=> ! [X31,X40,X41,X45] : hAPP(X1,X1,plus_plus(X1,hAPP(X1,X1,plus_plus(X1,X31),X40)),hAPP(X1,X1,plus_plus(X1,X41),X45)) = hAPP(X1,X1,plus_plus(X1,hAPP(X1,X1,plus_plus(X1,X31),X41)),hAPP(X1,X1,plus_plus(X1,X40),X45)) ),
file('<stdin>',fact_200_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J) ).
fof(c_0_296,axiom,
! [X20,X30] : hAPP(int,int,plus_plus(int,hAPP(int,int,bit1,X20)),hAPP(int,int,bit1,X30)) = hAPP(int,int,bit0,hAPP(int,int,plus_plus(int,X20),hAPP(int,int,succ,X30))),
file('<stdin>',fact_326_add__Bit1__Bit1) ).
fof(c_0_297,axiom,
! [X1] :
( number_ring(X1)
=> ! [X9,X8,X16] : hAPP(X1,X1,plus_plus(X1,number_number_of(X1,X9)),hAPP(X1,X1,plus_plus(X1,number_number_of(X1,X8)),X16)) = hAPP(X1,X1,plus_plus(X1,number_number_of(X1,hAPP(int,int,plus_plus(int,X9),X8))),X16) ),
file('<stdin>',fact_87_add__number__of__left) ).
fof(c_0_298,axiom,
! [X1] :
( linordered_semidom(X1)
=> ! [X28,X17,X7] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),one_one(X1)),X7))
=> ( hAPP(nat,X1,power_power(X1,X7),X28) = hAPP(nat,X1,power_power(X1,X7),X17)
<=> X28 = X17 ) ) ),
file('<stdin>',fact_180_power__inject__exp) ).
fof(c_0_299,axiom,
! [X1] :
( number_semiring(X1)
=> ! [X9] :
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),X9))
=> hAPP(X1,X1,plus_plus(X1,number_number_of(X1,X9)),one_one(X1)) = number_number_of(X1,hAPP(int,int,succ,X9)) ) ),
file('<stdin>',fact_296_semiring__number__of__add__1) ).
fof(c_0_300,axiom,
! [X24,X29] :
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X24),X29))
<=> ? [X43] : X29 = hAPP(int,int,plus_plus(int,X24),hAPP(nat,int,semiring_1_of_nat(int),X43)) ),
file('<stdin>',fact_294_zle__iff__zadd) ).
fof(c_0_301,axiom,
! [X1] :
( number_semiring(X1)
=> ! [X9] :
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),X9))
=> hAPP(X1,X1,plus_plus(X1,one_one(X1)),number_number_of(X1,X9)) = number_number_of(X1,hAPP(int,int,succ,X9)) ) ),
file('<stdin>',fact_295_semiring__1__add__number__of) ).
fof(c_0_302,axiom,
! [X1] :
( linorder(X1)
=> ! [X5,X6] :
( ti(X1,X5) != ti(X1,X6)
<=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X5),X6))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X6),X5)) ) ) ),
file('<stdin>',fact_422_linorder__neq__iff) ).
fof(c_0_303,axiom,
! [X1] :
( linorder(X1)
=> ! [X10,X11] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X10),X11))
| ti(X1,X10) = ti(X1,X11)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X11),X10)) ) ),
file('<stdin>',fact_420_linorder__less__linear) ).
fof(c_0_304,axiom,
! [X1] :
( linorder(X1)
=> ! [X10,X11] :
( ti(X1,X10) != ti(X1,X11)
=> ( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X10),X11))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X11),X10)) ) ) ),
file('<stdin>',fact_418_linorder__neqE) ).
fof(c_0_305,axiom,
! [X1] :
( linorder(X1)
=> ! [X10,X11] :
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X10),X11))
=> ( ti(X1,X10) != ti(X1,X11)
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X11),X10)) ) ) ),
file('<stdin>',fact_402_linorder__cases) ).
fof(c_0_306,axiom,
! [X1] :
( linordered_idom(X1)
=> ! [X10,X11] :
( ti(X1,X10) != ti(X1,X11)
=> ( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X10),X11))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X11),X10)) ) ) ),
file('<stdin>',fact_151_linorder__neqE__linordered__idom) ).
fof(c_0_307,axiom,
! [X1] :
( semiring_1(X1)
=> hAPP(nat,X1,power_power(X1,zero_zero(X1)),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) = zero_zero(X1) ),
file('<stdin>',fact_4_zero__power2) ).
fof(c_0_308,axiom,
! [X1] :
( semiring_1(X1)
=> hAPP(nat,X1,power_power(X1,one_one(X1)),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) = one_one(X1) ),
file('<stdin>',fact_3_one__power2) ).
fof(c_0_309,axiom,
! [X1] :
( linorder(X1)
=> ! [X11,X10] :
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X11),X10))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X10),X11)) ) ),
file('<stdin>',fact_431_not__leE) ).
fof(c_0_310,axiom,
! [X1] :
( linorder(X1)
=> ! [X10,X11] :
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X10),X11))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X11),X10)) ) ),
file('<stdin>',fact_430_leI) ).
fof(c_0_311,axiom,
! [X1] :
( linorder(X1)
=> ! [X10,X11] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X10),X11))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X11),X10)) ) ),
file('<stdin>',fact_426_linorder__le__less__linear) ).
fof(c_0_312,axiom,
! [X1] :
( linorder(X1)
=> ! [X10,X11] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X10),X11))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X11),X10)) ) ),
file('<stdin>',fact_400_linorder__linear) ).
fof(c_0_313,axiom,
! [X1] :
( linorder(X1)
=> ! [X10,X11] :
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X10),X11))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X11),X10)) ) ),
file('<stdin>',fact_386_linorder__le__cases) ).
fof(c_0_314,axiom,
! [X10,X11] :
( X10 != X11
=> ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X10),X11))
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X11),X10)) ) ),
file('<stdin>',fact_127_linorder__neqE__nat) ).
fof(c_0_315,axiom,
! [X28,X17] :
( X28 != X17
<=> ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X28),X17))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X17),X28)) ) ),
file('<stdin>',fact_120_nat__neq__iff) ).
fof(c_0_316,axiom,
! [X10,X11] :
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X10),X11))
| X10 = X11
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X11),X10)) ),
file('<stdin>',fact_15_zless__linear) ).
fof(c_0_317,axiom,
! [X16,X8] :
( hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X16),X8))
| hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X8),X16)) ),
file('<stdin>',fact_379_real__le__linear) ).
fof(c_0_318,axiom,
! [X14,X15] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X14),X15))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X15),X14)) ),
file('<stdin>',fact_351_nat__le__linear) ).
fof(c_0_319,axiom,
! [X16,X8] :
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X16),X8))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X8),X16)) ),
file('<stdin>',fact_249_zle__linear) ).
fof(c_0_320,axiom,
! [X10] :
( hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X10))
=> hAPP(real,real,sqrt,X10) != zero_zero(real) ),
file('<stdin>',fact_482_real__sqrt__not__eq__zero) ).
fof(c_0_321,axiom,
! [X1] :
( number_ring(X1)
=> ! [X9] :
( ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),number_number_of(int,X9)))
=> hAPP(nat,X1,semiring_1_of_nat(X1),number_number_of(nat,X9)) = number_number_of(X1,X9) )
& ( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),number_number_of(int,X9)))
=> hAPP(nat,X1,semiring_1_of_nat(X1),number_number_of(nat,X9)) = zero_zero(X1) ) ) ),
file('<stdin>',fact_333_of__nat__number__of__lemma) ).
fof(c_0_322,axiom,
! [X1] :
( linordered_semidom(X1)
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),hAPP(X1,X1,plus_plus(X1,one_one(X1)),one_one(X1)))) ),
file('<stdin>',fact_111_zero__less__two) ).
fof(c_0_323,axiom,
! [X1] :
( number_ring(X1)
=> ! [X8] : hAPP(X1,X1,plus_plus(X1,one_one(X1)),number_number_of(X1,X8)) = number_number_of(X1,hAPP(int,int,plus_plus(int,hAPP(int,int,bit1,pls)),X8)) ),
file('<stdin>',fact_6_add__special_I2_J) ).
fof(c_0_324,axiom,
! [X9] :
( ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X9),pls))
=> hAPP(nat,nat,plus_plus(nat,number_number_of(nat,X9)),one_one(nat)) = one_one(nat) )
& ( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X9),pls))
=> hAPP(nat,nat,plus_plus(nat,number_number_of(nat,X9)),one_one(nat)) = number_number_of(nat,hAPP(int,int,succ,X9)) ) ),
file('<stdin>',fact_232_nat__number__of__add__1) ).
fof(c_0_325,axiom,
! [X28,X17] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X28),X17))
<=> ? [X44] : X17 = hAPP(nat,nat,plus_plus(nat,X28),X44) ),
file('<stdin>',fact_359_le__iff__add) ).
fof(c_0_326,axiom,
! [X9] :
( ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X9),pls))
=> hAPP(nat,nat,plus_plus(nat,one_one(nat)),number_number_of(nat,X9)) = one_one(nat) )
& ( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X9),pls))
=> hAPP(nat,nat,plus_plus(nat,one_one(nat)),number_number_of(nat,X9)) = number_number_of(nat,hAPP(int,int,succ,X9)) ) ),
file('<stdin>',fact_233_nat__1__add__number__of) ).
fof(c_0_327,axiom,
! [X1] :
( comm_semiring_1(X1)
=> ! [X31,X40,X41] : hAPP(X1,X1,plus_plus(X1,hAPP(X1,X1,plus_plus(X1,X31),X40)),X41) = hAPP(X1,X1,plus_plus(X1,hAPP(X1,X1,plus_plus(X1,X31),X41)),X40) ),
file('<stdin>',fact_203_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J) ).
fof(c_0_328,axiom,
! [X16] :
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X16))
=> ~ ! [X53] : X16 != hAPP(nat,int,semiring_1_of_nat(int),X53) ),
file('<stdin>',fact_376_nonneg__eq__int) ).
fof(c_0_329,axiom,
! [X20] :
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X20))
=> ~ ! [X43] : X20 != hAPP(nat,int,semiring_1_of_nat(int),X43) ),
file('<stdin>',fact_341_nonneg__int__cases) ).
fof(c_0_330,axiom,
! [X20] :
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X20))
=> ? [X43] : X20 = hAPP(nat,int,semiring_1_of_nat(int),X43) ),
file('<stdin>',fact_340_zero__le__imp__eq__int) ).
fof(c_0_331,axiom,
! [X1] :
( linordered_semidom(X1)
=> ! [X31] : hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X31),hAPP(X1,X1,plus_plus(X1,X31),one_one(X1)))) ),
file('<stdin>',fact_179_less__add__one) ).
fof(c_0_332,axiom,
! [X1] :
( linordered_semidom(X1)
=> ! [X15] : hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),hAPP(nat,X1,semiring_1_of_nat(X1),X15))) ),
file('<stdin>',fact_280_of__nat__0__le__iff) ).
fof(c_0_333,axiom,
! [X1] :
( linordered_semidom(X1)
=> ! [X14] : hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),hAPP(nat,X1,semiring_1_of_nat(X1),X14))) ),
file('<stdin>',fact_279_zero__le__imp__of__nat) ).
fof(c_0_334,axiom,
! [X15,X14] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X15),hAPP(nat,nat,plus_plus(nat,X15),X14))),
file('<stdin>',fact_358_le__add1) ).
fof(c_0_335,axiom,
! [X15,X14] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X15),hAPP(nat,nat,plus_plus(nat,X14),X15))),
file('<stdin>',fact_357_le__add2) ).
fof(c_0_336,axiom,
! [X1] :
( linordered_semidom(X1)
=> ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),one_one(X1)),zero_zero(X1))) ),
file('<stdin>',fact_273_not__one__le__zero) ).
fof(c_0_337,axiom,
! [X1] :
( linordered_semidom(X1)
=> ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),one_one(X1)),zero_zero(X1))) ),
file('<stdin>',fact_176_not__one__less__zero) ).
fof(c_0_338,axiom,
! [X1] :
( semiring_1(X1)
=> ! [X14,X15] : hAPP(nat,X1,semiring_1_of_nat(X1),hAPP(nat,nat,plus_plus(nat,X14),X15)) = hAPP(X1,X1,plus_plus(X1,hAPP(nat,X1,semiring_1_of_nat(X1),X14)),hAPP(nat,X1,semiring_1_of_nat(X1),X15)) ),
file('<stdin>',fact_169_of__nat__add) ).
fof(c_0_339,axiom,
! [X15] : hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(nat,int,semiring_1_of_nat(int),X15))),
file('<stdin>',fact_292_zero__zle__int) ).
fof(c_0_340,axiom,
! [X16] : hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(nat,int,semiring_1_of_nat(int),X16))),
file('<stdin>',fact_289_Nat__Transfer_Otransfer__nat__int__function__closures_I9_J) ).
fof(c_0_341,axiom,
! [X1] :
( order(X1)
=> ! [X10,X11] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X10),X11))
=> ti(X1,X10) != ti(X1,X11) ) ),
file('<stdin>',fact_417_less__imp__neq) ).
fof(c_0_342,axiom,
! [X1] :
( order(X1)
=> ! [X10,X11] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X10),X11))
=> ti(X1,X10) != ti(X1,X11) ) ),
file('<stdin>',fact_414_order__less__imp__not__eq) ).
fof(c_0_343,axiom,
! [X1] :
( order(X1)
=> ! [X10,X11] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X10),X11))
=> ti(X1,X11) != ti(X1,X10) ) ),
file('<stdin>',fact_413_order__less__imp__not__eq2) ).
fof(c_0_344,axiom,
! [X10,X11] : hAPP(int,int,plus_plus(int,hAPP(nat,int,semiring_1_of_nat(int),X10)),hAPP(nat,int,semiring_1_of_nat(int),X11)) = hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,plus_plus(nat,X10),X11)),
file('<stdin>',fact_173_Nat__Transfer_Otransfer__int__nat__functions_I1_J) ).
fof(c_0_345,axiom,
! [X14,X15] : hAPP(int,int,plus_plus(int,hAPP(nat,int,semiring_1_of_nat(int),X14)),hAPP(nat,int,semiring_1_of_nat(int),X15)) = hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,plus_plus(nat,X14),X15)),
file('<stdin>',fact_23_zadd__int) ).
fof(c_0_346,axiom,
! [X1] :
( preorder(X1)
=> ! [X10] : ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X10),X10)) ),
file('<stdin>',fact_423_order__less__irrefl) ).
fof(c_0_347,axiom,
! [X20,X30] : hAPP(int,int,plus_plus(int,hAPP(int,int,bit0,X20)),hAPP(int,int,bit1,X30)) = hAPP(int,int,bit1,hAPP(int,int,plus_plus(int,X20),X30)),
file('<stdin>',fact_91_add__Bit0__Bit1) ).
fof(c_0_348,axiom,
! [X20,X30] : hAPP(int,int,plus_plus(int,hAPP(int,int,bit1,X20)),hAPP(int,int,bit0,X30)) = hAPP(int,int,bit1,hAPP(int,int,plus_plus(int,X20),X30)),
file('<stdin>',fact_90_add__Bit1__Bit0) ).
fof(c_0_349,axiom,
! [X20,X30] : hAPP(int,int,plus_plus(int,hAPP(int,int,bit0,X20)),hAPP(int,int,bit0,X30)) = hAPP(int,int,bit0,hAPP(int,int,plus_plus(int,X20),X30)),
file('<stdin>',fact_77_add__Bit0__Bit0) ).
fof(c_0_350,axiom,
! [X17] :
( X17 != zero_zero(nat)
<=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X17)) ),
file('<stdin>',fact_144_neq0__conv) ).
fof(c_0_351,axiom,
! [X17] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X17),zero_zero(nat)))
<=> X17 = zero_zero(nat) ),
file('<stdin>',fact_344_le__0__eq) ).
fof(c_0_352,axiom,
! [X38] :
( number_number_of(nat,X38) = zero_zero(nat)
<=> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X38),pls)) ),
file('<stdin>',fact_305_eq__number__of__0) ).
fof(c_0_353,axiom,
! [X38] :
( zero_zero(nat) = number_number_of(nat,X38)
<=> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X38),pls)) ),
file('<stdin>',fact_304_eq__0__number__of) ).
fof(c_0_354,axiom,
! [X15] : ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X15),zero_zero(nat))),
file('<stdin>',fact_145_not__less0) ).
fof(c_0_355,axiom,
! [X15] : ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X15),zero_zero(nat))),
file('<stdin>',fact_141_less__nat__zero__code) ).
fof(c_0_356,axiom,
! [X15] : ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X15),zero_zero(nat))),
file('<stdin>',fact_114_less__zeroE) ).
fof(c_0_357,axiom,
! [X14,X15] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X14),X15))
=> X15 != zero_zero(nat) ),
file('<stdin>',fact_139_gr__implies__not0) ).
fof(c_0_358,axiom,
! [X36,X37] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X36),X37))
=> X36 != X37 ),
file('<stdin>',fact_130_less__not__refl3) ).
fof(c_0_359,axiom,
! [X15,X14] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X15),X14))
=> X14 != X15 ),
file('<stdin>',fact_129_less__not__refl2) ).
fof(c_0_360,axiom,
! [X15] : ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X15),X15)),
file('<stdin>',fact_128_less__irrefl__nat) ).
fof(c_0_361,axiom,
! [X15] : ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X15),X15)),
file('<stdin>',fact_116_less__not__refl) ).
fof(c_0_362,axiom,
~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),zero_zero(int))),
file('<stdin>',fact_57_bin__less__0__simps_I1_J) ).
fof(c_0_363,axiom,
~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),pls)),
file('<stdin>',fact_32_rel__simps_I2_J) ).
fof(c_0_364,axiom,
! [X1] :
( comm_semiring_1(X1)
=> ! [X31,X41,X45] : hAPP(X1,X1,plus_plus(X1,X31),hAPP(X1,X1,plus_plus(X1,X41),X45)) = hAPP(X1,X1,plus_plus(X1,hAPP(X1,X1,plus_plus(X1,X31),X41)),X45) ),
file('<stdin>',fact_206_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J) ).
fof(c_0_365,axiom,
! [X1] :
( comm_semiring_1(X1)
=> ! [X31,X40,X41] : hAPP(X1,X1,plus_plus(X1,hAPP(X1,X1,plus_plus(X1,X31),X40)),X41) = hAPP(X1,X1,plus_plus(X1,X31),hAPP(X1,X1,plus_plus(X1,X40),X41)) ),
file('<stdin>',fact_205_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J) ).
fof(c_0_366,axiom,
! [X1] :
( ab_semigroup_add(X1)
=> ! [X31,X40,X41] : hAPP(X1,X1,plus_plus(X1,hAPP(X1,X1,plus_plus(X1,X31),X40)),X41) = hAPP(X1,X1,plus_plus(X1,X31),hAPP(X1,X1,plus_plus(X1,X40),X41)) ),
file('<stdin>',fact_204_ab__semigroup__add__class_Oadd__ac_I1_J) ).
fof(c_0_367,axiom,
! [X16] : hAPP(int,int,plus_plus(int,hAPP(int,int,plus_plus(int,one_one(int)),X16)),X16) != zero_zero(int),
file('<stdin>',fact_93_odd__nonzero) ).
fof(c_0_368,axiom,
! [X14,X15,X20] : hAPP(nat,nat,plus_plus(nat,hAPP(nat,nat,plus_plus(nat,X14),X15)),X20) = hAPP(nat,nat,plus_plus(nat,X14),hAPP(nat,nat,plus_plus(nat,X15),X20)),
file('<stdin>',fact_123_nat__add__assoc) ).
fof(c_0_369,axiom,
! [X25,X26,X27] : hAPP(int,int,plus_plus(int,hAPP(int,int,plus_plus(int,X25),X26)),X27) = hAPP(int,int,plus_plus(int,X25),hAPP(int,int,plus_plus(int,X26),X27)),
file('<stdin>',fact_45_zadd__assoc) ).
fof(c_0_370,axiom,
! [X1,X10,X11] : hAPP(X1,X1,hAPP(X1,fun(X1,X1),hAPP(bool,fun(X1,fun(X1,X1)),if(X1),fFalse),X10),X11) = ti(X1,X11),
file('<stdin>',help_If_2_1_T) ).
fof(c_0_371,axiom,
! [X1,X10,X11] : hAPP(X1,X1,hAPP(X1,fun(X1,X1),hAPP(bool,fun(X1,fun(X1,X1)),if(X1),fTrue),X10),X11) = ti(X1,X10),
file('<stdin>',help_If_1_1_T) ).
fof(c_0_372,axiom,
! [X1] :
( semiring_1(X1)
=> ! [X14,X15] : hAPP(nat,X1,semiring_1_of_nat(X1),hAPP(nat,nat,power_power(nat,X14),X15)) = hAPP(nat,X1,power_power(X1,hAPP(nat,X1,semiring_1_of_nat(X1),X14)),X15) ),
file('<stdin>',fact_171_of__nat__power) ).
fof(c_0_373,axiom,
! [X1] :
( number_ring(X1)
=> ! [X8] : number_number_of(X1,hAPP(int,int,bit1,X8)) = hAPP(X1,X1,plus_plus(X1,hAPP(X1,X1,plus_plus(X1,one_one(X1)),number_number_of(X1,X8))),number_number_of(X1,X8)) ),
file('<stdin>',fact_100_number__of__Bit1) ).
fof(c_0_374,axiom,
! [X1] :
( number_ring(X1)
=> ! [X8] : number_number_of(X1,hAPP(int,int,bit0,X8)) = hAPP(X1,X1,plus_plus(X1,hAPP(X1,X1,plus_plus(X1,zero_zero(X1)),number_number_of(X1,X8))),number_number_of(X1,X8)) ),
file('<stdin>',fact_99_number__of__Bit0) ).
fof(c_0_375,axiom,
! [X10,X15] : hAPP(nat,int,power_power(int,hAPP(nat,int,semiring_1_of_nat(int),X10)),X15) = hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,power_power(nat,X10),X15)),
file('<stdin>',fact_174_Nat__Transfer_Otransfer__int__nat__functions_I4_J) ).
fof(c_0_376,axiom,
! [X14,X15] : hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,power_power(nat,X14),X15)) = hAPP(nat,int,power_power(int,hAPP(nat,int,semiring_1_of_nat(int),X14)),X15),
file('<stdin>',fact_21_int__power) ).
fof(c_0_377,axiom,
! [X14,X15] : hAPP(nat,int,power_power(int,hAPP(nat,int,semiring_1_of_nat(int),X14)),X15) = hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,power_power(nat,X14),X15)),
file('<stdin>',fact_20_zpower__int) ).
fof(c_0_378,axiom,
! [X1] :
( number_ring(X1)
=> ! [X9] : hAPP(X1,X1,plus_plus(X1,number_number_of(X1,X9)),one_one(X1)) = number_number_of(X1,hAPP(int,int,plus_plus(int,X9),hAPP(int,int,bit1,pls))) ),
file('<stdin>',fact_7_add__special_I3_J) ).
fof(c_0_379,axiom,
! [X1] :
( number_semiring(X1)
=> hAPP(X1,X1,plus_plus(X1,one_one(X1)),one_one(X1)) = number_number_of(X1,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))) ),
file('<stdin>',fact_9_semiring__one__add__one__is__two) ).
fof(c_0_380,axiom,
! [X1] :
( number_ring(X1)
=> hAPP(X1,X1,plus_plus(X1,one_one(X1)),one_one(X1)) = number_number_of(X1,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))) ),
file('<stdin>',fact_8_one__add__one__is__two) ).
fof(c_0_381,axiom,
hAPP(nat,nat,plus_plus(nat,one_one(nat)),one_one(nat)) = number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))),
file('<stdin>',fact_29_nat__1__add__1) ).
fof(c_0_382,axiom,
! [X1] :
( comm_semiring_1(X1)
=> ! [X31,X41,X45] : hAPP(X1,X1,plus_plus(X1,X31),hAPP(X1,X1,plus_plus(X1,X41),X45)) = hAPP(X1,X1,plus_plus(X1,X41),hAPP(X1,X1,plus_plus(X1,X31),X45)) ),
file('<stdin>',fact_207_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J) ).
fof(c_0_383,axiom,
! [X1] :
( linordered_semidom(X1)
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),one_one(X1))) ),
file('<stdin>',fact_274_zero__le__one) ).
fof(c_0_384,axiom,
! [X1] :
( linordered_semidom(X1)
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),one_one(X1))) ),
file('<stdin>',fact_177_zero__less__one) ).
fof(c_0_385,axiom,
hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),number_number_of(int,pls))),
file('<stdin>',fact_339_number__of2) ).
fof(c_0_386,axiom,
! [X1] :
( preorder(X1)
=> ! [X10,X11] :
( X10 = X11
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X10),X11)) ) ),
file('<stdin>',fact_398_order__eq__refl) ).
fof(c_0_387,axiom,
! [X1] :
( preorder(X1)
=> ! [X10] : hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X10),X10)) ),
file('<stdin>',fact_385_order__refl) ).
fof(c_0_388,axiom,
! [X10,X11,X16] : hAPP(nat,nat,plus_plus(nat,X10),hAPP(nat,nat,plus_plus(nat,X11),X16)) = hAPP(nat,nat,plus_plus(nat,X11),hAPP(nat,nat,plus_plus(nat,X10),X16)),
file('<stdin>',fact_122_nat__add__left__commute) ).
fof(c_0_389,axiom,
! [X20] : hAPP(int,int,bit1,X20) = hAPP(int,int,plus_plus(int,hAPP(int,int,plus_plus(int,one_one(int)),X20)),X20),
file('<stdin>',fact_92_Bit1__def) ).
fof(c_0_390,axiom,
! [X10,X11,X16] : hAPP(int,int,plus_plus(int,X10),hAPP(int,int,plus_plus(int,X11),X16)) = hAPP(int,int,plus_plus(int,X11),hAPP(int,int,plus_plus(int,X10),X16)),
file('<stdin>',fact_46_zadd__left__commute) ).
fof(c_0_391,axiom,
hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),one_one(int))),
file('<stdin>',fact_286_Nat__Transfer_Otransfer__nat__int__function__closures_I6_J) ).
fof(c_0_392,axiom,
hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),zero_zero(int))),
file('<stdin>',fact_247_Nat__Transfer_Otransfer__nat__int__function__closures_I5_J) ).
fof(c_0_393,axiom,
hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),one_one(int))),
file('<stdin>',fact_59_int__0__less__1) ).
fof(c_0_394,axiom,
! [X15] :
( X15 != zero_zero(nat)
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X15)) ),
file('<stdin>',fact_138_gr0I) ).
fof(c_0_395,axiom,
! [X15] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),zero_zero(nat)),X15)),
file('<stdin>',fact_343_less__eq__nat_Osimps_I1_J) ).
fof(c_0_396,axiom,
! [X15] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),zero_zero(nat)),X15)),
file('<stdin>',fact_342_le0) ).
fof(c_0_397,axiom,
hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),one_one(int)),t)),
file('<stdin>',fact_231_tpos) ).
fof(c_0_398,axiom,
hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),tn)),
file('<stdin>',fact_113_tn0) ).
fof(c_0_399,axiom,
hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),n)),
file('<stdin>',fact_14_n0) ).
fof(c_0_400,axiom,
hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),t)),
file('<stdin>',fact_1_t1) ).
fof(c_0_401,axiom,
! [X14,X15] :
( X14 = X15
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X14),X15)) ),
file('<stdin>',fact_352_eq__imp__le) ).
fof(c_0_402,axiom,
! [X8] : hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X8),X8)),
file('<stdin>',fact_378_real__le__refl) ).
fof(c_0_403,axiom,
! [X15] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X15),X15)),
file('<stdin>',fact_350_le__refl) ).
fof(c_0_404,axiom,
! [X8] : hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X8),X8)),
file('<stdin>',fact_248_zle__refl) ).
fof(c_0_405,axiom,
hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),pls)),
file('<stdin>',fact_244_rel__simps_I19_J) ).
fof(c_0_406,axiom,
! [X20] : hAPP(int,int,succ,hAPP(int,int,bit1,X20)) = hAPP(int,int,bit0,hAPP(int,int,succ,X20)),
file('<stdin>',fact_316_succ__Bit1) ).
fof(c_0_407,axiom,
! [X1,X2,X4] : ti(fun(X1,fun(X1,X1)),hAPP(bool,fun(X1,fun(X1,X1)),X2,X4)) = hAPP(bool,fun(X1,fun(X1,X1)),X2,X4),
file('<stdin>',tsy_c_hAPP_2_res) ).
fof(c_0_408,axiom,
! [X1,X2,X4] : hAPP(bool,fun(X1,fun(X1,X1)),ti(fun(bool,fun(X1,fun(X1,X1))),X2),X4) = hAPP(bool,fun(X1,fun(X1,X1)),X2,X4),
file('<stdin>',tsy_c_hAPP_2_arg1) ).
fof(c_0_409,axiom,
! [X20] : hAPP(int,int,succ,hAPP(int,int,bit0,X20)) = hAPP(int,int,bit1,X20),
file('<stdin>',fact_315_succ__Bit0) ).
fof(c_0_410,axiom,
! [X1] :
( number_ring(X1)
=> ! [X9,X8] : number_number_of(X1,hAPP(int,int,plus_plus(int,X9),X8)) = hAPP(X1,X1,plus_plus(X1,number_number_of(X1,X9)),number_number_of(X1,X8)) ),
file('<stdin>',fact_89_number__of__add) ).
fof(c_0_411,axiom,
! [X1] :
( number_ring(X1)
=> ! [X9,X8] : hAPP(X1,X1,plus_plus(X1,number_number_of(X1,X9)),number_number_of(X1,X8)) = number_number_of(X1,hAPP(int,int,plus_plus(int,X9),X8)) ),
file('<stdin>',fact_88_add__number__of__eq) ).
fof(c_0_412,axiom,
! [X1] :
( cancel_semigroup_add(X1)
=> ! [X7,X42,X46] :
( hAPP(X1,X1,plus_plus(X1,X7),X42) = hAPP(X1,X1,plus_plus(X1,X7),X46)
<=> ti(X1,X42) = ti(X1,X46) ) ),
file('<stdin>',fact_202_add__left__cancel) ).
fof(c_0_413,axiom,
! [X1] :
( cancel_semigroup_add(X1)
=> ! [X42,X7,X46] :
( hAPP(X1,X1,plus_plus(X1,X42),X7) = hAPP(X1,X1,plus_plus(X1,X46),X7)
<=> ti(X1,X42) = ti(X1,X46) ) ),
file('<stdin>',fact_201_add__right__cancel) ).
fof(c_0_414,axiom,
! [X1] :
( cancel_semigroup_add(X1)
=> ! [X31,X40,X41] :
( hAPP(X1,X1,plus_plus(X1,X31),X40) = hAPP(X1,X1,plus_plus(X1,X31),X41)
=> ti(X1,X40) = ti(X1,X41) ) ),
file('<stdin>',fact_199_add__left__imp__eq) ).
fof(c_0_415,axiom,
! [X1] :
( cancel146912293up_add(X1)
=> ! [X31,X40,X41] :
( hAPP(X1,X1,plus_plus(X1,X31),X40) = hAPP(X1,X1,plus_plus(X1,X31),X41)
=> ti(X1,X40) = ti(X1,X41) ) ),
file('<stdin>',fact_198_add__imp__eq) ).
fof(c_0_416,axiom,
! [X1] :
( cancel_semigroup_add(X1)
=> ! [X40,X31,X41] :
( hAPP(X1,X1,plus_plus(X1,X40),X31) = hAPP(X1,X1,plus_plus(X1,X41),X31)
=> ti(X1,X40) = ti(X1,X41) ) ),
file('<stdin>',fact_197_add__right__imp__eq) ).
fof(c_0_417,axiom,
! [X9,X8] : hAPP(int,int,plus_plus(int,number_number_of(int,X9)),number_number_of(int,X8)) = number_number_of(int,hAPP(int,int,plus_plus(int,X9),X8)),
file('<stdin>',fact_17_plus__numeral__code_I9_J) ).
fof(c_0_418,axiom,
! [X1,X2,X4] : ti(fun(X1,X1),hAPP(X1,fun(X1,X1),X2,X4)) = hAPP(X1,fun(X1,X1),X2,X4),
file('<stdin>',tsy_c_hAPP_3_res) ).
fof(c_0_419,axiom,
! [X28,X12,X17] :
( hAPP(nat,nat,plus_plus(nat,X28),X12) = hAPP(nat,nat,plus_plus(nat,X17),X12)
<=> X28 = X17 ),
file('<stdin>',fact_125_nat__add__right__cancel) ).
fof(c_0_420,axiom,
! [X12,X28,X17] :
( hAPP(nat,nat,plus_plus(nat,X12),X28) = hAPP(nat,nat,plus_plus(nat,X12),X17)
<=> X28 = X17 ),
file('<stdin>',fact_124_nat__add__left__cancel) ).
fof(c_0_421,axiom,
! [X1] :
( number_ring(X1)
=> ! [X20] : number_number_of(X1,hAPP(int,int,succ,X20)) = hAPP(X1,X1,plus_plus(X1,one_one(X1)),number_number_of(X1,X20)) ),
file('<stdin>',fact_325_number__of__succ) ).
fof(c_0_422,axiom,
! [X1] :
( semiring_char_0(X1)
=> ! [X28,X17] :
( hAPP(nat,X1,semiring_1_of_nat(X1),X28) = hAPP(nat,X1,semiring_1_of_nat(X1),X17)
<=> X28 = X17 ) ),
file('<stdin>',fact_157_of__nat__eq__iff) ).
fof(c_0_423,axiom,
! [X5,X6] :
( hAPP(nat,int,semiring_1_of_nat(int),X5) = hAPP(nat,int,semiring_1_of_nat(int),X6)
<=> X5 = X6 ),
file('<stdin>',fact_158_Nat__Transfer_Otransfer__int__nat__relations_I1_J) ).
fof(c_0_424,axiom,
! [X28,X17] :
( hAPP(nat,int,semiring_1_of_nat(int),X28) = hAPP(nat,int,semiring_1_of_nat(int),X17)
<=> X28 = X17 ),
file('<stdin>',fact_48_int__int__eq) ).
fof(c_0_425,axiom,
! [X1] :
( number_semiring(X1)
=> ! [X15] : number_number_of(X1,hAPP(nat,int,semiring_1_of_nat(int),X15)) = hAPP(nat,X1,semiring_1_of_nat(X1),X15) ),
file('<stdin>',fact_94_number__of__int) ).
fof(c_0_426,axiom,
! [X12,X13] :
( hAPP(int,int,bit0,X12) = hAPP(int,int,bit0,X13)
<=> X12 = X13 ),
file('<stdin>',fact_43_rel__simps_I48_J) ).
fof(c_0_427,axiom,
! [X12,X13] :
( hAPP(int,int,bit1,X12) = hAPP(int,int,bit1,X13)
<=> X12 = X13 ),
file('<stdin>',fact_42_rel__simps_I51_J) ).
fof(c_0_428,axiom,
! [X20,X30] : hAPP(int,int,bit0,X20) != hAPP(int,int,bit1,X30),
file('<stdin>',fact_69_rel__simps_I49_J) ).
fof(c_0_429,axiom,
! [X20,X30] : hAPP(int,int,bit1,X20) != hAPP(int,int,bit0,X30),
file('<stdin>',fact_68_rel__simps_I50_J) ).
fof(c_0_430,axiom,
! [X1,X2,X4,X3] :
( ord(X3)
=> ti(X3,hAPP(X1,X3,X2,X4)) = hAPP(X1,X3,X2,X4) ),
file('<stdin>',tsy_c_hAPP_0_res) ).
fof(c_0_431,axiom,
! [X2,X4,X1] :
( power(X1)
=> ti(X1,hAPP(nat,X1,X2,X4)) = hAPP(nat,X1,X2,X4) ),
file('<stdin>',tsy_c_hAPP_1_res) ).
fof(c_0_432,axiom,
! [X1,X2,X4] : ti(X1,hAPP(X1,X1,X2,X4)) = hAPP(X1,X1,X2,X4),
file('<stdin>',tsy_c_hAPP_4_res) ).
fof(c_0_433,axiom,
! [X1,X2,X4] : hAPP(X1,fun(X1,X1),ti(fun(X1,fun(X1,X1)),X2),X4) = hAPP(X1,fun(X1,X1),X2,X4),
file('<stdin>',tsy_c_hAPP_3_arg1) ).
fof(c_0_434,axiom,
! [X1,X2,X4] : hAPP(bool,fun(X1,fun(X1,X1)),X2,ti(bool,X4)) = hAPP(bool,fun(X1,fun(X1,X1)),X2,X4),
file('<stdin>',tsy_c_hAPP_2_arg2) ).
fof(c_0_435,axiom,
! [X1,X2,X4,X3] :
( ord(X3)
=> hAPP(X1,X3,ti(fun(X1,X3),X2),X4) = hAPP(X1,X3,X2,X4) ),
file('<stdin>',tsy_c_hAPP_0_arg1) ).
fof(c_0_436,axiom,
! [X1,X2,X4] : hAPP(X1,X1,ti(fun(X1,X1),X2),X4) = hAPP(X1,X1,X2,X4),
file('<stdin>',tsy_c_hAPP_4_arg1) ).
fof(c_0_437,axiom,
! [X1,X2,X4] : hAPP(X1,fun(X1,X1),X2,ti(X1,X4)) = hAPP(X1,fun(X1,X1),X2,X4),
file('<stdin>',tsy_c_hAPP_3_arg2) ).
fof(c_0_438,axiom,
! [X2,X4,X1] :
( power(X1)
=> hAPP(nat,X1,ti(fun(nat,X1),X2),X4) = hAPP(nat,X1,X2,X4) ),
file('<stdin>',tsy_c_hAPP_1_arg1) ).
fof(c_0_439,axiom,
! [X1] :
( comm_semiring_1(X1)
=> ! [X31,X41] : hAPP(X1,X1,plus_plus(X1,X31),X41) = hAPP(X1,X1,plus_plus(X1,X41),X31) ),
file('<stdin>',fact_208_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J) ).
fof(c_0_440,axiom,
! [X14,X15] : hAPP(nat,nat,plus_plus(nat,X14),X15) = hAPP(nat,nat,plus_plus(nat,X15),X14),
file('<stdin>',fact_121_nat__add__commute) ).
fof(c_0_441,axiom,
! [X16,X8] : hAPP(int,int,plus_plus(int,X16),X8) = hAPP(int,int,plus_plus(int,X8),X16),
file('<stdin>',fact_47_zadd__commute) ).
fof(c_0_442,axiom,
! [X1,X2,X4,X3] :
( ord(X3)
=> hAPP(X1,X3,X2,ti(X1,X4)) = hAPP(X1,X3,X2,X4) ),
file('<stdin>',tsy_c_hAPP_0_arg2) ).
fof(c_0_443,axiom,
! [X1] :
( ( power(X1)
& mult_zero(X1)
& no_zero_divisors(X1)
& zero_neq_one(X1) )
=> ! [X7,X24] :
( hAPP(nat,X1,power_power(X1,X7),number_number_of(nat,X24)) = zero_zero(X1)
<=> ( ti(X1,X7) = zero_zero(X1)
& number_number_of(nat,X24) != zero_zero(nat) ) ) ),
file('<stdin>',fact_86_power__eq__0__iff__number__of) ).
fof(c_0_444,axiom,
! [X2,X4,X1] :
( power(X1)
=> hAPP(nat,X1,X2,ti(nat,X4)) = hAPP(nat,X1,X2,X4) ),
file('<stdin>',tsy_c_hAPP_1_arg2) ).
fof(c_0_445,axiom,
! [X1,X2,X4] : hAPP(X1,X1,X2,ti(X1,X4)) = hAPP(X1,X1,X2,X4),
file('<stdin>',tsy_c_hAPP_4_arg2) ).
fof(c_0_446,axiom,
! [X20] : hAPP(int,int,succ,X20) = hAPP(int,int,plus_plus(int,X20),one_one(int)),
file('<stdin>',fact_320_succ__def) ).
fof(c_0_447,axiom,
! [X20] : hAPP(int,int,bit0,X20) = hAPP(int,int,plus_plus(int,X20),X20),
file('<stdin>',fact_78_Bit0__def) ).
fof(c_0_448,axiom,
! [X1] :
( number_semiring(X1)
=> number_number_of(X1,hAPP(int,int,bit1,pls)) = one_one(X1) ),
file('<stdin>',fact_101_semiring__numeral__1__eq__1) ).
fof(c_0_449,axiom,
! [X1] :
( number_ring(X1)
=> number_number_of(X1,hAPP(int,int,bit1,pls)) = one_one(X1) ),
file('<stdin>',fact_13_numeral__1__eq__1) ).
fof(c_0_450,axiom,
! [X1] :
( number_ring(X1)
=> one_one(X1) = number_number_of(X1,hAPP(int,int,bit1,pls)) ),
file('<stdin>',fact_12_semiring__norm_I110_J) ).
fof(c_0_451,axiom,
one_one(nat) = number_number_of(nat,hAPP(int,int,bit1,pls)),
file('<stdin>',fact_39_Numeral1__eq1__nat) ).
fof(c_0_452,axiom,
number_number_of(nat,hAPP(int,int,bit1,pls)) = one_one(nat),
file('<stdin>',fact_38_nat__numeral__1__eq__1) ).
fof(c_0_453,axiom,
one_one(int) = number_number_of(int,hAPP(int,int,bit1,pls)),
file('<stdin>',fact_37_one__is__num__one) ).
fof(c_0_454,axiom,
hAPP(int,int,succ,pls) = hAPP(int,int,bit1,pls),
file('<stdin>',fact_314_succ__Pls) ).
fof(c_0_455,axiom,
! [X1] :
( ( power(X1)
& mult_zero(X1)
& no_zero_divisors(X1)
& zero_neq_one(X1) )
=> ! [X7,X17] :
( hAPP(nat,X1,power_power(X1,X7),X17) = zero_zero(X1)
<=> ( ti(X1,X7) = zero_zero(X1)
& X17 != zero_zero(nat) ) ) ),
file('<stdin>',fact_184_power__eq__0__iff) ).
fof(c_0_456,axiom,
! [X1] :
( semiri456707255roduct(X1)
=> ! [X42,X7] :
( ti(X1,X42) = hAPP(X1,X1,plus_plus(X1,X42),X7)
<=> ti(X1,X7) = zero_zero(X1) ) ),
file('<stdin>',fact_210_add__0__iff) ).
fof(c_0_457,axiom,
! [X1] :
( linord219039673up_add(X1)
=> ! [X7] :
( zero_zero(X1) = hAPP(X1,X1,plus_plus(X1,X7),X7)
<=> ti(X1,X7) = zero_zero(X1) ) ),
file('<stdin>',fact_214_double__zero__sym) ).
fof(c_0_458,axiom,
! [X1] :
( linord219039673up_add(X1)
=> ! [X7] :
( hAPP(X1,X1,plus_plus(X1,X7),X7) = zero_zero(X1)
<=> ti(X1,X7) = zero_zero(X1) ) ),
file('<stdin>',fact_65_double__eq__0__iff) ).
fof(c_0_459,axiom,
! [X1] :
( ring_11004092258visors(X1)
=> ! [X15,X31] :
( ti(X1,X31) != zero_zero(X1)
=> hAPP(nat,X1,power_power(X1,X31),X15) != zero_zero(X1) ) ),
file('<stdin>',fact_164_field__power__not__zero) ).
fof(c_0_460,axiom,
! [X5,X17] :
( hAPP(nat,nat,power_power(nat,X5),X17) = one_one(nat)
<=> ( X5 = one_one(nat)
| X17 = zero_zero(nat) ) ),
file('<stdin>',fact_192_exp__eq__1) ).
fof(c_0_461,axiom,
! [X28,X17] :
( hAPP(nat,nat,power_power(nat,X28),X17) = zero_zero(nat)
<=> ( X17 != zero_zero(nat)
& X28 = zero_zero(nat) ) ),
file('<stdin>',fact_226_nat__power__eq__0__iff) ).
fof(c_0_462,axiom,
! [X28,X17] :
( hAPP(nat,nat,plus_plus(nat,X28),X17) = zero_zero(nat)
<=> ( X28 = zero_zero(nat)
& X17 = zero_zero(nat) ) ),
file('<stdin>',fact_153_add__is__0) ).
fof(c_0_463,axiom,
! [X14,X15] :
( hAPP(nat,nat,plus_plus(nat,X14),X15) = X14
=> X15 = zero_zero(nat) ),
file('<stdin>',fact_152_add__eq__self__zero) ).
fof(c_0_464,axiom,
! [X17] :
( hAPP(nat,int,semiring_1_of_nat(int),X17) = zero_zero(int)
<=> X17 = zero_zero(nat) ),
file('<stdin>',fact_27_int__eq__0__conv) ).
fof(c_0_465,axiom,
! [X13] :
( pls = hAPP(int,int,bit0,X13)
<=> pls = X13 ),
file('<stdin>',fact_71_rel__simps_I38_J) ).
fof(c_0_466,axiom,
! [X12] :
( hAPP(int,int,bit0,X12) = pls
<=> X12 = pls ),
file('<stdin>',fact_70_rel__simps_I44_J) ).
fof(c_0_467,axiom,
! [X30] : pls != hAPP(int,int,bit1,X30),
file('<stdin>',fact_67_rel__simps_I39_J) ).
fof(c_0_468,axiom,
! [X20] : hAPP(int,int,bit1,X20) != pls,
file('<stdin>',fact_66_rel__simps_I46_J) ).
fof(c_0_469,axiom,
! [X1] :
( ( power(X1)
& semiring_0(X1) )
=> ! [X8] :
( ( number_number_of(nat,X8) = zero_zero(nat)
=> hAPP(nat,X1,power_power(X1,zero_zero(X1)),number_number_of(nat,X8)) = one_one(X1) )
& ( number_number_of(nat,X8) != zero_zero(nat)
=> hAPP(nat,X1,power_power(X1,zero_zero(X1)),number_number_of(nat,X8)) = zero_zero(X1) ) ) ),
file('<stdin>',fact_11_power__0__left__number__of) ).
fof(c_0_470,axiom,
! [X1] :
( number_ring(X1)
=> ! [X31] : hAPP(X1,X1,plus_plus(X1,number_number_of(X1,pls)),X31) = ti(X1,X31) ),
file('<stdin>',fact_84_add__numeral__0) ).
fof(c_0_471,axiom,
! [X1] :
( number_ring(X1)
=> ! [X31] : hAPP(X1,X1,plus_plus(X1,X31),number_number_of(X1,pls)) = ti(X1,X31) ),
file('<stdin>',fact_85_add__numeral__0__right) ).
fof(c_0_472,axiom,
! [X1] :
( ( power(X1)
& semiring_0(X1) )
=> ! [X15] :
( ( X15 = zero_zero(nat)
=> hAPP(nat,X1,power_power(X1,zero_zero(X1)),X15) = one_one(X1) )
& ( X15 != zero_zero(nat)
=> hAPP(nat,X1,power_power(X1,zero_zero(X1)),X15) = zero_zero(X1) ) ) ),
file('<stdin>',fact_109_power__0__left) ).
fof(c_0_473,axiom,
! [X1] :
( monoid_add(X1)
=> ! [X31] : hAPP(X1,X1,plus_plus(X1,zero_zero(X1)),X31) = ti(X1,X31) ),
file('<stdin>',fact_217_add__0__left) ).
fof(c_0_474,axiom,
! [X1] :
( comm_semiring_1(X1)
=> ! [X31] : hAPP(X1,X1,plus_plus(X1,zero_zero(X1)),X31) = ti(X1,X31) ),
file('<stdin>',fact_216_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J) ).
fof(c_0_475,axiom,
! [X1] :
( comm_monoid_add(X1)
=> ! [X31] : hAPP(X1,X1,plus_plus(X1,zero_zero(X1)),X31) = ti(X1,X31) ),
file('<stdin>',fact_215_add__0) ).
fof(c_0_476,axiom,
! [X1] :
( monoid_add(X1)
=> ! [X31] : hAPP(X1,X1,plus_plus(X1,X31),zero_zero(X1)) = ti(X1,X31) ),
file('<stdin>',fact_213_add__0__right) ).
fof(c_0_477,axiom,
! [X1] :
( comm_semiring_1(X1)
=> ! [X31] : hAPP(X1,X1,plus_plus(X1,X31),zero_zero(X1)) = ti(X1,X31) ),
file('<stdin>',fact_212_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J) ).
fof(c_0_478,axiom,
! [X1] :
( comm_monoid_add(X1)
=> ! [X31] : hAPP(X1,X1,plus_plus(X1,X31),zero_zero(X1)) = ti(X1,X31) ),
file('<stdin>',fact_211_add_Ocomm__neutral) ).
fof(c_0_479,axiom,
! [X1] :
( comm_semiring_1(X1)
=> ! [X10] : hAPP(nat,X1,power_power(X1,X10),one_one(nat)) = ti(X1,X10) ),
file('<stdin>',fact_225_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J) ).
fof(c_0_480,axiom,
! [X1] :
( monoid_mult(X1)
=> ! [X31] : hAPP(nat,X1,power_power(X1,X31),one_one(nat)) = ti(X1,X31) ),
file('<stdin>',fact_156_power__one__right) ).
fof(c_0_481,axiom,
! [X1] :
( monoid_mult(X1)
=> ! [X15] : hAPP(nat,X1,power_power(X1,one_one(X1)),X15) = one_one(X1) ),
file('<stdin>',fact_165_power__one) ).
fof(c_0_482,axiom,
! [X1] :
( comm_semiring_1(X1)
=> ! [X10] : hAPP(nat,X1,power_power(X1,X10),zero_zero(nat)) = one_one(X1) ),
file('<stdin>',fact_193_comm__semiring__1__class_Onormalizing__semiring__rules_I32_J) ).
fof(c_0_483,axiom,
! [X1] :
( power(X1)
=> ! [X31] : hAPP(nat,X1,power_power(X1,X31),zero_zero(nat)) = one_one(X1) ),
file('<stdin>',fact_186_power__0) ).
fof(c_0_484,axiom,
! [X15] : hAPP(nat,nat,plus_plus(nat,zero_zero(nat)),X15) = X15,
file('<stdin>',fact_155_plus__nat_Oadd__0) ).
fof(c_0_485,axiom,
! [X16] : hAPP(int,int,plus_plus(int,zero_zero(int)),X16) = X16,
file('<stdin>',fact_80_zadd__0) ).
fof(c_0_486,axiom,
! [X14] : hAPP(nat,nat,plus_plus(nat,X14),zero_zero(nat)) = X14,
file('<stdin>',fact_154_Nat_Oadd__0__right) ).
fof(c_0_487,axiom,
! [X16] : hAPP(int,int,plus_plus(int,X16),zero_zero(int)) = X16,
file('<stdin>',fact_79_zadd__0__right) ).
fof(c_0_488,axiom,
! [X20] : hAPP(int,int,plus_plus(int,X20),pls) = X20,
file('<stdin>',fact_75_add__Pls__right) ).
fof(c_0_489,axiom,
! [X1] :
( semiring_1(X1)
=> hAPP(nat,X1,semiring_1_of_nat(X1),zero_zero(nat)) = zero_zero(X1) ),
file('<stdin>',fact_187_of__nat__0) ).
fof(c_0_490,axiom,
! [X1] :
( semiring_1(X1)
=> hAPP(nat,X1,semiring_1_of_nat(X1),one_one(nat)) = one_one(X1) ),
file('<stdin>',fact_170_of__nat__1) ).
fof(c_0_491,axiom,
! [X20] : hAPP(int,int,plus_plus(int,pls),X20) = X20,
file('<stdin>',fact_76_add__Pls) ).
fof(c_0_492,axiom,
zero_zero(int) = hAPP(nat,int,semiring_1_of_nat(int),zero_zero(nat)),
file('<stdin>',fact_188_transfer__int__nat__numerals_I1_J) ).
fof(c_0_493,axiom,
one_one(int) = hAPP(nat,int,semiring_1_of_nat(int),one_one(nat)),
file('<stdin>',fact_172_transfer__int__nat__numerals_I2_J) ).
fof(c_0_494,axiom,
hAPP(nat,int,semiring_1_of_nat(int),zero_zero(nat)) = zero_zero(int),
file('<stdin>',fact_28_int__0) ).
fof(c_0_495,axiom,
hAPP(nat,int,semiring_1_of_nat(int),one_one(nat)) = one_one(int),
file('<stdin>',fact_24_int__1) ).
fof(c_0_496,axiom,
hAPP(int,int,bit0,pls) = pls,
file('<stdin>',fact_72_Bit0__Pls) ).
fof(c_0_497,axiom,
! [X1] : ti(fun(bool,fun(X1,fun(X1,X1))),if(X1)) = if(X1),
file('<stdin>',tsy_c_If_res) ).
fof(c_0_498,axiom,
! [X1] :
( linordered_semiring(X1)
=> ti(fun(X1,fun(X1,X1)),times_times(X1)) = times_times(X1) ),
file('<stdin>',tsy_c_Groups_Otimes__class_Otimes_res) ).
fof(c_0_499,axiom,
! [X3] :
( ord(X3)
=> ti(fun(X3,fun(X3,bool)),ord_less_eq(X3)) = ord_less_eq(X3) ),
file('<stdin>',tsy_c_Orderings_Oord__class_Oless__eq_res) ).
fof(c_0_500,axiom,
! [X1] :
( ord(X1)
=> ti(fun(X1,fun(X1,bool)),ord_less(X1)) = ord_less(X1) ),
file('<stdin>',tsy_c_Orderings_Oord__class_Oless_res) ).
fof(c_0_501,axiom,
! [X2,X1] :
( cancel_semigroup_add(X1)
=> ti(fun(X1,X1),plus_plus(X1,X2)) = plus_plus(X1,X2) ),
file('<stdin>',tsy_c_Groups_Oplus__class_Oplus_2_res) ).
fof(c_0_502,axiom,
! [X2,X1] :
( ab_semigroup_add(X1)
=> ti(fun(X1,X1),plus_plus(X1,X2)) = plus_plus(X1,X2) ),
file('<stdin>',tsy_c_Groups_Oplus__class_Oplus_1_res) ).
fof(c_0_503,axiom,
! [X2,X1] :
( monoid_add(X1)
=> ti(fun(X1,X1),plus_plus(X1,X2)) = plus_plus(X1,X2) ),
file('<stdin>',tsy_c_Groups_Oplus__class_Oplus_0_res) ).
fof(c_0_504,axiom,
! [X2,X1] :
( power(X1)
=> ti(fun(nat,X1),power_power(X1,X2)) = power_power(X1,X2) ),
file('<stdin>',tsy_c_Power_Opower__class_Opower_res) ).
fof(c_0_505,axiom,
! [X1] :
( number(X1)
=> ! [X24,X5] :
( number_number_of(X1,X24) = ti(X1,X5)
<=> ti(X1,X5) = number_number_of(X1,X24) ) ),
file('<stdin>',fact_41_number__of__reorient) ).
fof(c_0_506,axiom,
! [X2,X1] :
( power(X1)
=> power_power(X1,ti(X1,X2)) = power_power(X1,X2) ),
file('<stdin>',tsy_c_Power_Opower__class_Opower_arg1) ).
fof(c_0_507,axiom,
! [X2,X1] :
( number(X1)
=> ti(X1,number_number_of(X1,X2)) = number_number_of(X1,X2) ),
file('<stdin>',tsy_c_Int_Onumber__class_Onumber__of_res) ).
fof(c_0_508,axiom,
! [X2,X1] :
( cancel_semigroup_add(X1)
=> plus_plus(X1,ti(X1,X2)) = plus_plus(X1,X2) ),
file('<stdin>',tsy_c_Groups_Oplus__class_Oplus_2_arg1) ).
fof(c_0_509,axiom,
! [X2,X1] :
( ab_semigroup_add(X1)
=> plus_plus(X1,ti(X1,X2)) = plus_plus(X1,X2) ),
file('<stdin>',tsy_c_Groups_Oplus__class_Oplus_1_arg1) ).
fof(c_0_510,axiom,
! [X2,X1] :
( monoid_add(X1)
=> plus_plus(X1,ti(X1,X2)) = plus_plus(X1,X2) ),
file('<stdin>',tsy_c_Groups_Oplus__class_Oplus_0_arg1) ).
fof(c_0_511,axiom,
! [X1] :
( ( number_ring(X1)
& ring_char_0(X1) )
=> ! [X5,X6] :
( number_number_of(X1,X5) = number_number_of(X1,X6)
<=> X5 = X6 ) ),
file('<stdin>',fact_40_eq__number__of) ).
fof(c_0_512,axiom,
! [X2,X1] :
( number(X1)
=> number_number_of(X1,ti(int,X2)) = number_number_of(X1,X2) ),
file('<stdin>',tsy_c_Int_Onumber__class_Onumber__of_arg1) ).
fof(c_0_513,axiom,
! [X1] :
( semiring_1(X1)
=> ti(fun(nat,X1),semiring_1_of_nat(X1)) = semiring_1_of_nat(X1) ),
file('<stdin>',tsy_c_Nat_Osemiring__1__class_Oof__nat_res) ).
fof(c_0_514,axiom,
! [X1] :
( one(X1)
=> ! [X5] :
( one_one(X1) = ti(X1,X5)
<=> ti(X1,X5) = one_one(X1) ) ),
file('<stdin>',fact_209_one__reorient) ).
fof(c_0_515,axiom,
! [X1] :
( zero(X1)
=> ! [X5] :
( zero_zero(X1) = ti(X1,X5)
<=> ti(X1,X5) = zero_zero(X1) ) ),
file('<stdin>',fact_196_zero__reorient) ).
fof(c_0_516,axiom,
! [X65,X66] : ti(X65,ti(X65,X66)) = ti(X65,X66),
file('<stdin>',help_ti_idem) ).
fof(c_0_517,axiom,
! [X2] :
( hBOOL(ti(bool,X2))
<=> hBOOL(X2) ),
file('<stdin>',tsy_c_hBOOL_arg1) ).
fof(c_0_518,axiom,
! [X63,X64] :
( ord(X64)
=> ord(fun(X63,X64)) ),
file('<stdin>',arity_fun___Orderings_Oord) ).
fof(c_0_519,axiom,
! [X63,X64] :
( order(X64)
=> order(fun(X63,X64)) ),
file('<stdin>',arity_fun___Orderings_Oorder) ).
fof(c_0_520,axiom,
! [X63,X64] :
( preorder(X64)
=> preorder(fun(X63,X64)) ),
file('<stdin>',arity_fun___Orderings_Opreorder) ).
fof(c_0_521,axiom,
ti(fun(real,real),sqrt) = sqrt,
file('<stdin>',tsy_c_NthRoot_Osqrt_res) ).
fof(c_0_522,axiom,
ti(fun(int,int),succ) = succ,
file('<stdin>',tsy_c_Int_Osucc_res) ).
fof(c_0_523,axiom,
! [X1] :
( zero(X1)
=> ti(X1,zero_zero(X1)) = zero_zero(X1) ),
file('<stdin>',tsy_c_Groups_Ozero__class_Ozero_res) ).
fof(c_0_524,axiom,
! [X1] :
( one(X1)
=> ti(X1,one_one(X1)) = one_one(X1) ),
file('<stdin>',tsy_c_Groups_Oone__class_Oone_res) ).
fof(c_0_525,axiom,
! [X67] :
( ti(bool,X67) = fTrue
| ti(bool,X67) = fFalse ),
file('<stdin>',help_If_3_1_T) ).
fof(c_0_526,axiom,
! [X1] : ti(X1,undefined(X1)) = undefined(X1),
file('<stdin>',tsy_c_HOL_Oundefined_res) ).
fof(c_0_527,axiom,
! [X1] :
( number_ring(X1)
=> zero_zero(X1) = number_number_of(X1,pls) ),
file('<stdin>',fact_83_semiring__norm_I112_J) ).
fof(c_0_528,axiom,
! [X1] :
( number_ring(X1)
=> number_number_of(X1,pls) = zero_zero(X1) ),
file('<stdin>',fact_82_number__of__Pls) ).
fof(c_0_529,axiom,
! [X1] :
( number_semiring(X1)
=> number_number_of(X1,pls) = zero_zero(X1) ),
file('<stdin>',fact_81_semiring__numeral__0__eq__0) ).
fof(c_0_530,axiom,
! [X1] :
( zero_neq_one(X1)
=> zero_zero(X1) != one_one(X1) ),
file('<stdin>',fact_163_zero__neq__one) ).
fof(c_0_531,axiom,
! [X1] :
( zero_neq_one(X1)
=> one_one(X1) != zero_zero(X1) ),
file('<stdin>',fact_162_one__neq__zero) ).
fof(c_0_532,axiom,
! [X20] : number_number_of(int,X20) = X20,
file('<stdin>',fact_119_number__of__is__id) ).
fof(c_0_533,axiom,
zero_zero(nat) = number_number_of(nat,pls),
file('<stdin>',fact_26_semiring__norm_I113_J) ).
fof(c_0_534,axiom,
number_number_of(nat,pls) = zero_zero(nat),
file('<stdin>',fact_25_nat__number__of__Pls) ).
fof(c_0_535,axiom,
zero_zero(int) = number_number_of(int,pls),
file('<stdin>',fact_19_zero__is__num__zero) ).
fof(c_0_536,axiom,
ti(nat,tn) = tn,
file('<stdin>',tsy_v_tn_____res) ).
fof(c_0_537,axiom,
ti(int,t) = t,
file('<stdin>',tsy_v_t_____res) ).
fof(c_0_538,axiom,
ti(int,m1) = m1,
file('<stdin>',tsy_v_m1_____res) ).
fof(c_0_539,axiom,
ti(bool,fTrue) = fTrue,
file('<stdin>',tsy_c_fTrue_res) ).
fof(c_0_540,axiom,
ti(bool,fFalse) = fFalse,
file('<stdin>',tsy_c_fFalse_res) ).
fof(c_0_541,axiom,
zero_zero(real) != one_one(real),
file('<stdin>',fact_115_real__zero__not__eq__one) ).
fof(c_0_542,axiom,
zero_zero(int) != one_one(int),
file('<stdin>',fact_74_int__0__neq__1) ).
fof(c_0_543,axiom,
one(real),
file('<stdin>',arity_RealDef_Oreal___Groups_Oone) ).
fof(c_0_544,axiom,
number(real),
file('<stdin>',arity_RealDef_Oreal___Int_Onumber) ).
fof(c_0_545,axiom,
zero(real),
file('<stdin>',arity_RealDef_Oreal___Groups_Ozero) ).
fof(c_0_546,axiom,
power(real),
file('<stdin>',arity_RealDef_Oreal___Power_Opower) ).
fof(c_0_547,axiom,
ord(real),
file('<stdin>',arity_RealDef_Oreal___Orderings_Oord) ).
fof(c_0_548,axiom,
number_ring(real),
file('<stdin>',arity_RealDef_Oreal___Int_Onumber__ring) ).
fof(c_0_549,axiom,
ring_char_0(real),
file('<stdin>',arity_RealDef_Oreal___Int_Oring__char__0) ).
fof(c_0_550,axiom,
order(real),
file('<stdin>',arity_RealDef_Oreal___Orderings_Oorder) ).
fof(c_0_551,axiom,
mult_zero(real),
file('<stdin>',arity_RealDef_Oreal___Rings_Omult__zero) ).
fof(c_0_552,axiom,
semiring_0(real),
file('<stdin>',arity_RealDef_Oreal___Rings_Osemiring__0) ).
fof(c_0_553,axiom,
semiring_1(real),
file('<stdin>',arity_RealDef_Oreal___Rings_Osemiring__1) ).
fof(c_0_554,axiom,
monoid_add(real),
file('<stdin>',arity_RealDef_Oreal___Groups_Omonoid__add) ).
fof(c_0_555,axiom,
monoid_mult(real),
file('<stdin>',arity_RealDef_Oreal___Groups_Omonoid__mult) ).
fof(c_0_556,axiom,
linorder(real),
file('<stdin>',arity_RealDef_Oreal___Orderings_Olinorder) ).
fof(c_0_557,axiom,
preorder(real),
file('<stdin>',arity_RealDef_Oreal___Orderings_Opreorder) ).
fof(c_0_558,axiom,
zero_neq_one(real),
file('<stdin>',arity_RealDef_Oreal___Rings_Ozero__neq__one) ).
fof(c_0_559,axiom,
number_semiring(real),
file('<stdin>',arity_RealDef_Oreal___Int_Onumber__semiring) ).
fof(c_0_560,axiom,
semiring_char_0(real),
file('<stdin>',arity_RealDef_Oreal___Nat_Osemiring__char__0) ).
fof(c_0_561,axiom,
comm_semiring_1(real),
file('<stdin>',arity_RealDef_Oreal___Rings_Ocomm__semiring__1) ).
fof(c_0_562,axiom,
linordered_idom(real),
file('<stdin>',arity_RealDef_Oreal___Rings_Olinordered__idom) ).
fof(c_0_563,axiom,
linordered_ring(real),
file('<stdin>',arity_RealDef_Oreal___Rings_Olinordered__ring) ).
fof(c_0_564,axiom,
comm_monoid_add(real),
file('<stdin>',arity_RealDef_Oreal___Groups_Ocomm__monoid__add) ).
fof(c_0_565,axiom,
no_zero_divisors(real),
file('<stdin>',arity_RealDef_Oreal___Rings_Ono__zero__divisors) ).
fof(c_0_566,axiom,
ab_semigroup_add(real),
file('<stdin>',arity_RealDef_Oreal___Groups_Oab__semigroup__add) ).
fof(c_0_567,axiom,
dense_linorder(real),
file('<stdin>',arity_RealDef_Oreal___Orderings_Odense__linorder) ).
fof(c_0_568,axiom,
linordered_semidom(real),
file('<stdin>',arity_RealDef_Oreal___Rings_Olinordered__semidom) ).
fof(c_0_569,axiom,
linordered_semiring(real),
file('<stdin>',arity_RealDef_Oreal___Rings_Olinordered__semiring) ).
fof(c_0_570,axiom,
cancel_semigroup_add(real),
file('<stdin>',arity_RealDef_Oreal___Groups_Ocancel__semigroup__add) ).
fof(c_0_571,axiom,
linord581940658strict(real),
file('<stdin>',arity_RealDef_Oreal___Rings_Olinordered__ring__strict) ).
fof(c_0_572,axiom,
ring_11004092258visors(real),
file('<stdin>',arity_RealDef_Oreal___Rings_Oring__1__no__zero__divisors) ).
fof(c_0_573,axiom,
cancel146912293up_add(real),
file('<stdin>',arity_RealDef_Oreal___Groups_Ocancel__ab__semigroup__add) ).
fof(c_0_574,axiom,
linord219039673up_add(real),
file('<stdin>',arity_RealDef_Oreal___Groups_Olinordered__ab__group__add) ).
fof(c_0_575,axiom,
ordere216010020id_add(real),
file('<stdin>',arity_RealDef_Oreal___Groups_Oordered__comm__monoid__add) ).
fof(c_0_576,axiom,
ordere779506340up_add(real),
file('<stdin>',arity_RealDef_Oreal___Groups_Oordered__ab__semigroup__add) ).
fof(c_0_577,axiom,
linord20386208strict(real),
file('<stdin>',arity_RealDef_Oreal___Rings_Olinordered__semiring__strict) ).
fof(c_0_578,axiom,
linord893533164strict(real),
file('<stdin>',arity_RealDef_Oreal___Rings_Olinordered__comm__semiring__strict) ).
fof(c_0_579,axiom,
ordere236663937imp_le(real),
file('<stdin>',arity_RealDef_Oreal___Groups_Oordered__ab__semigroup__add__imp__le) ).
fof(c_0_580,axiom,
ordere223160158up_add(real),
file('<stdin>',arity_RealDef_Oreal___Groups_Oordered__cancel__ab__semigroup__add) ).
fof(c_0_581,axiom,
semiri456707255roduct(real),
file('<stdin>',arity_RealDef_Oreal___Semiring__Normalization_Ocomm__semiring__1__cancel__crossp) ).
fof(c_0_582,axiom,
ord(bool),
file('<stdin>',arity_HOL_Obool___Orderings_Oord) ).
fof(c_0_583,axiom,
order(bool),
file('<stdin>',arity_HOL_Obool___Orderings_Oorder) ).
fof(c_0_584,axiom,
preorder(bool),
file('<stdin>',arity_HOL_Obool___Orderings_Opreorder) ).
fof(c_0_585,axiom,
one(nat),
file('<stdin>',arity_Nat_Onat___Groups_Oone) ).
fof(c_0_586,axiom,
number(nat),
file('<stdin>',arity_Nat_Onat___Int_Onumber) ).
fof(c_0_587,axiom,
zero(nat),
file('<stdin>',arity_Nat_Onat___Groups_Ozero) ).
fof(c_0_588,axiom,
power(nat),
file('<stdin>',arity_Nat_Onat___Power_Opower) ).
fof(c_0_589,axiom,
ord(nat),
file('<stdin>',arity_Nat_Onat___Orderings_Oord) ).
fof(c_0_590,axiom,
order(nat),
file('<stdin>',arity_Nat_Onat___Orderings_Oorder) ).
fof(c_0_591,axiom,
mult_zero(nat),
file('<stdin>',arity_Nat_Onat___Rings_Omult__zero) ).
fof(c_0_592,axiom,
semiring_0(nat),
file('<stdin>',arity_Nat_Onat___Rings_Osemiring__0) ).
fof(c_0_593,axiom,
semiring_1(nat),
file('<stdin>',arity_Nat_Onat___Rings_Osemiring__1) ).
fof(c_0_594,axiom,
monoid_add(nat),
file('<stdin>',arity_Nat_Onat___Groups_Omonoid__add) ).
fof(c_0_595,axiom,
monoid_mult(nat),
file('<stdin>',arity_Nat_Onat___Groups_Omonoid__mult) ).
fof(c_0_596,axiom,
linorder(nat),
file('<stdin>',arity_Nat_Onat___Orderings_Olinorder) ).
fof(c_0_597,axiom,
preorder(nat),
file('<stdin>',arity_Nat_Onat___Orderings_Opreorder) ).
fof(c_0_598,axiom,
zero_neq_one(nat),
file('<stdin>',arity_Nat_Onat___Rings_Ozero__neq__one) ).
fof(c_0_599,axiom,
number_semiring(nat),
file('<stdin>',arity_Nat_Onat___Int_Onumber__semiring) ).
fof(c_0_600,axiom,
semiring_char_0(nat),
file('<stdin>',arity_Nat_Onat___Nat_Osemiring__char__0) ).
fof(c_0_601,axiom,
comm_semiring_1(nat),
file('<stdin>',arity_Nat_Onat___Rings_Ocomm__semiring__1) ).
fof(c_0_602,axiom,
comm_monoid_add(nat),
file('<stdin>',arity_Nat_Onat___Groups_Ocomm__monoid__add) ).
fof(c_0_603,axiom,
no_zero_divisors(nat),
file('<stdin>',arity_Nat_Onat___Rings_Ono__zero__divisors) ).
fof(c_0_604,axiom,
ab_semigroup_add(nat),
file('<stdin>',arity_Nat_Onat___Groups_Oab__semigroup__add) ).
fof(c_0_605,axiom,
linordered_semidom(nat),
file('<stdin>',arity_Nat_Onat___Rings_Olinordered__semidom) ).
fof(c_0_606,axiom,
linordered_semiring(nat),
file('<stdin>',arity_Nat_Onat___Rings_Olinordered__semiring) ).
fof(c_0_607,axiom,
cancel_semigroup_add(nat),
file('<stdin>',arity_Nat_Onat___Groups_Ocancel__semigroup__add) ).
fof(c_0_608,axiom,
cancel146912293up_add(nat),
file('<stdin>',arity_Nat_Onat___Groups_Ocancel__ab__semigroup__add) ).
fof(c_0_609,axiom,
ordere216010020id_add(nat),
file('<stdin>',arity_Nat_Onat___Groups_Oordered__comm__monoid__add) ).
fof(c_0_610,axiom,
ordere779506340up_add(nat),
file('<stdin>',arity_Nat_Onat___Groups_Oordered__ab__semigroup__add) ).
fof(c_0_611,axiom,
linord20386208strict(nat),
file('<stdin>',arity_Nat_Onat___Rings_Olinordered__semiring__strict) ).
fof(c_0_612,axiom,
linord893533164strict(nat),
file('<stdin>',arity_Nat_Onat___Rings_Olinordered__comm__semiring__strict) ).
fof(c_0_613,axiom,
ordere236663937imp_le(nat),
file('<stdin>',arity_Nat_Onat___Groups_Oordered__ab__semigroup__add__imp__le) ).
fof(c_0_614,axiom,
ordere223160158up_add(nat),
file('<stdin>',arity_Nat_Onat___Groups_Oordered__cancel__ab__semigroup__add) ).
fof(c_0_615,axiom,
semiri456707255roduct(nat),
file('<stdin>',arity_Nat_Onat___Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduc) ).
fof(c_0_616,axiom,
one(int),
file('<stdin>',arity_Int_Oint___Groups_Oone) ).
fof(c_0_617,axiom,
number(int),
file('<stdin>',arity_Int_Oint___Int_Onumber) ).
fof(c_0_618,axiom,
zero(int),
file('<stdin>',arity_Int_Oint___Groups_Ozero) ).
fof(c_0_619,axiom,
power(int),
file('<stdin>',arity_Int_Oint___Power_Opower) ).
fof(c_0_620,axiom,
ord(int),
file('<stdin>',arity_Int_Oint___Orderings_Oord) ).
fof(c_0_621,axiom,
number_ring(int),
file('<stdin>',arity_Int_Oint___Int_Onumber__ring) ).
fof(c_0_622,axiom,
ring_char_0(int),
file('<stdin>',arity_Int_Oint___Int_Oring__char__0) ).
fof(c_0_623,axiom,
order(int),
file('<stdin>',arity_Int_Oint___Orderings_Oorder) ).
fof(c_0_624,axiom,
mult_zero(int),
file('<stdin>',arity_Int_Oint___Rings_Omult__zero) ).
fof(c_0_625,axiom,
semiring_0(int),
file('<stdin>',arity_Int_Oint___Rings_Osemiring__0) ).
fof(c_0_626,axiom,
semiring_1(int),
file('<stdin>',arity_Int_Oint___Rings_Osemiring__1) ).
fof(c_0_627,axiom,
monoid_add(int),
file('<stdin>',arity_Int_Oint___Groups_Omonoid__add) ).
fof(c_0_628,axiom,
monoid_mult(int),
file('<stdin>',arity_Int_Oint___Groups_Omonoid__mult) ).
fof(c_0_629,axiom,
linorder(int),
file('<stdin>',arity_Int_Oint___Orderings_Olinorder) ).
fof(c_0_630,axiom,
preorder(int),
file('<stdin>',arity_Int_Oint___Orderings_Opreorder) ).
fof(c_0_631,axiom,
zero_neq_one(int),
file('<stdin>',arity_Int_Oint___Rings_Ozero__neq__one) ).
fof(c_0_632,axiom,
number_semiring(int),
file('<stdin>',arity_Int_Oint___Int_Onumber__semiring) ).
fof(c_0_633,axiom,
semiring_char_0(int),
file('<stdin>',arity_Int_Oint___Nat_Osemiring__char__0) ).
fof(c_0_634,axiom,
comm_semiring_1(int),
file('<stdin>',arity_Int_Oint___Rings_Ocomm__semiring__1) ).
fof(c_0_635,axiom,
linordered_idom(int),
file('<stdin>',arity_Int_Oint___Rings_Olinordered__idom) ).
fof(c_0_636,axiom,
linordered_ring(int),
file('<stdin>',arity_Int_Oint___Rings_Olinordered__ring) ).
fof(c_0_637,axiom,
comm_monoid_add(int),
file('<stdin>',arity_Int_Oint___Groups_Ocomm__monoid__add) ).
fof(c_0_638,axiom,
no_zero_divisors(int),
file('<stdin>',arity_Int_Oint___Rings_Ono__zero__divisors) ).
fof(c_0_639,axiom,
ab_semigroup_add(int),
file('<stdin>',arity_Int_Oint___Groups_Oab__semigroup__add) ).
fof(c_0_640,axiom,
linordered_semidom(int),
file('<stdin>',arity_Int_Oint___Rings_Olinordered__semidom) ).
fof(c_0_641,axiom,
linordered_semiring(int),
file('<stdin>',arity_Int_Oint___Rings_Olinordered__semiring) ).
fof(c_0_642,axiom,
cancel_semigroup_add(int),
file('<stdin>',arity_Int_Oint___Groups_Ocancel__semigroup__add) ).
fof(c_0_643,axiom,
linord581940658strict(int),
file('<stdin>',arity_Int_Oint___Rings_Olinordered__ring__strict) ).
fof(c_0_644,axiom,
ring_11004092258visors(int),
file('<stdin>',arity_Int_Oint___Rings_Oring__1__no__zero__divisors) ).
fof(c_0_645,axiom,
cancel146912293up_add(int),
file('<stdin>',arity_Int_Oint___Groups_Ocancel__ab__semigroup__add) ).
fof(c_0_646,axiom,
linord219039673up_add(int),
file('<stdin>',arity_Int_Oint___Groups_Olinordered__ab__group__add) ).
fof(c_0_647,axiom,
ordere216010020id_add(int),
file('<stdin>',arity_Int_Oint___Groups_Oordered__comm__monoid__add) ).
fof(c_0_648,axiom,
ordere779506340up_add(int),
file('<stdin>',arity_Int_Oint___Groups_Oordered__ab__semigroup__add) ).
fof(c_0_649,axiom,
linord20386208strict(int),
file('<stdin>',arity_Int_Oint___Rings_Olinordered__semiring__strict) ).
fof(c_0_650,axiom,
linord893533164strict(int),
file('<stdin>',arity_Int_Oint___Rings_Olinordered__comm__semiring__strict) ).
fof(c_0_651,axiom,
ordere236663937imp_le(int),
file('<stdin>',arity_Int_Oint___Groups_Oordered__ab__semigroup__add__imp__le) ).
fof(c_0_652,axiom,
ordere223160158up_add(int),
file('<stdin>',arity_Int_Oint___Groups_Oordered__cancel__ab__semigroup__add) ).
fof(c_0_653,axiom,
semiri456707255roduct(int),
file('<stdin>',arity_Int_Oint___Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduc) ).
fof(c_0_654,axiom,
pls = zero_zero(int),
file('<stdin>',fact_73_Pls__def) ).
fof(c_0_655,axiom,
! [X31,X40] : hAPP(nat,int,power_power(int,hAPP(int,int,plus_plus(int,X31),X40)),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) = hAPP(int,int,plus_plus(int,hAPP(int,int,plus_plus(int,hAPP(nat,int,power_power(int,X31),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),number_number_of(int,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),X31)),X40))),hAPP(nat,int,power_power(int,X40),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),
c_0_0 ).
fof(c_0_656,axiom,
! [X1] :
( linordered_idom(X1)
=> ! [X5,X6] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,plus_plus(X1,hAPP(nat,X1,power_power(X1,X5),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,X1,power_power(X1,X6),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),zero_zero(X1)))
<=> ( ti(X1,X5) = zero_zero(X1)
& ti(X1,X6) = zero_zero(X1) ) ) ),
c_0_1 ).
fof(c_0_657,plain,
! [X1] :
( linordered_idom(X1)
=> ! [X10,X11] : ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,plus_plus(X1,hAPP(nat,X1,power_power(X1,X10),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,X1,power_power(X1,X11),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),zero_zero(X1))) ),
inference(fof_simplification,[status(thm)],[c_0_2]) ).
fof(c_0_658,axiom,
! [X3,X1] :
( ( order(X1)
& order(X3) )
=> ! [X46,X54,X42,X7] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X3,X1,X54,X42)),X7))
=> ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X46),X42))
=> ( ! [X47,X48] :
( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X48),X47))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X3,X1,X54,X48)),hAPP(X3,X1,X54,X47))) )
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X3,X1,X54,X46)),X7)) ) ) ) ),
c_0_3 ).
fof(c_0_659,axiom,
! [X1,X3] :
( ( order(X3)
& order(X1) )
=> ! [X54,X46,X7,X42] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X7),X42))
=> ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),hAPP(X1,X3,X54,X42)),X46))
=> ( ! [X47,X48] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X47),X48))
=> hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),hAPP(X1,X3,X54,X47)),hAPP(X1,X3,X54,X48))) )
=> hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),hAPP(X1,X3,X54,X7)),X46)) ) ) ) ),
c_0_4 ).
fof(c_0_660,axiom,
! [X3,X1] :
( ( order(X1)
& ord(X3) )
=> ! [X46,X54,X42,X7] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X3,X1,X54,X42)),X7))
=> ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X46),X42))
=> ( ! [X47,X48] :
( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X48),X47))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X3,X1,X54,X48)),hAPP(X3,X1,X54,X47))) )
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X3,X1,X54,X46)),X7)) ) ) ) ),
c_0_5 ).
fof(c_0_661,axiom,
! [X1,X3] :
( ( order(X3)
& order(X1) )
=> ! [X54,X46,X7,X42] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X7),X42))
=> ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),hAPP(X1,X3,X54,X42)),X46))
=> ( ! [X47,X48] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X47),X48))
=> hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),hAPP(X1,X3,X54,X47)),hAPP(X1,X3,X54,X48))) )
=> hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),hAPP(X1,X3,X54,X7)),X46)) ) ) ) ),
c_0_6 ).
fof(c_0_662,axiom,
! [X1,X3] :
( ( order(X3)
& order(X1) )
=> ! [X46,X7,X54,X42] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X7),hAPP(X3,X1,X54,X42)))
=> ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X42),X46))
=> ( ! [X47,X48] :
( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X47),X48))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X3,X1,X54,X47)),hAPP(X3,X1,X54,X48))) )
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X7),hAPP(X3,X1,X54,X46))) ) ) ) ),
c_0_7 ).
fof(c_0_663,axiom,
! [X1,X3] :
( ( order(X3)
& order(X1) )
=> ! [X46,X7,X54,X42] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X7),hAPP(X3,X1,X54,X42)))
=> ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X42),X46))
=> ( ! [X47,X48] :
( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X47),X48))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X3,X1,X54,X47)),hAPP(X3,X1,X54,X48))) )
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X7),hAPP(X3,X1,X54,X46))) ) ) ) ),
c_0_8 ).
fof(c_0_664,axiom,
! [X3,X1] :
( ( order(X1)
& order(X3) )
=> ! [X46,X54,X42,X7] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X42),X7))
=> ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X46),hAPP(X1,X3,X54,X42)))
=> ( ! [X47,X48] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X48),X47))
=> hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),hAPP(X1,X3,X54,X48)),hAPP(X1,X3,X54,X47))) )
=> hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X46),hAPP(X1,X3,X54,X7))) ) ) ) ),
c_0_9 ).
fof(c_0_665,axiom,
! [X3,X1] :
( ( order(X1)
& order(X3) )
=> ! [X46,X54,X42,X7] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X42),X7))
=> ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X46),hAPP(X1,X3,X54,X42)))
=> ( ! [X47,X48] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X48),X47))
=> hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),hAPP(X1,X3,X54,X48)),hAPP(X1,X3,X54,X47))) )
=> hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X46),hAPP(X1,X3,X54,X7))) ) ) ) ),
c_0_10 ).
fof(c_0_666,axiom,
! [X10,X11] : hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),hAPP(real,real,sqrt,hAPP(real,real,plus_plus(real,hAPP(nat,real,power_power(real,X10),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,real,power_power(real,X11),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))))),
c_0_11 ).
fof(c_0_667,axiom,
! [X1] :
( linordered_idom(X1)
=> ! [X5,X6] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),hAPP(X1,X1,plus_plus(X1,hAPP(nat,X1,power_power(X1,X5),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,X1,power_power(X1,X6),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))))
<=> ( ti(X1,X5) != zero_zero(X1)
| ti(X1,X6) != zero_zero(X1) ) ) ),
c_0_12 ).
fof(c_0_668,axiom,
! [X1] :
( linordered_idom(X1)
=> ! [X10,X11] : hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),hAPP(X1,X1,plus_plus(X1,hAPP(nat,X1,power_power(X1,X10),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,X1,power_power(X1,X11),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))) ),
c_0_13 ).
fof(c_0_669,axiom,
! [X1] :
( linordered_semidom(X1)
=> ! [X10,X11] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(nat,X1,power_power(X1,X10),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,X1,power_power(X1,X11),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X11))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X10),X11)) ) ) ),
c_0_14 ).
fof(c_0_670,axiom,
! [X1] :
( linordered_semidom(X1)
=> ! [X10,X11] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(nat,X1,power_power(X1,X10),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,X1,power_power(X1,X11),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X11))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X10),X11)) ) ) ),
c_0_15 ).
fof(c_0_671,plain,
! [X1] :
( linordered_ring(X1)
=> ! [X10,X11] : ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,plus_plus(X1,hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X10),X10)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X11),X11))),zero_zero(X1))) ),
inference(fof_simplification,[status(thm)],[c_0_16]) ).
fof(c_0_672,plain,
! [X1] :
( linordered_idom(X1)
=> ! [X31] : ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(nat,X1,power_power(X1,X31),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),zero_zero(X1))) ),
inference(fof_simplification,[status(thm)],[c_0_17]) ).
fof(c_0_673,axiom,
! [X1] :
( linord581940658strict(X1)
=> ! [X5,X6] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),hAPP(X1,X1,plus_plus(X1,hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X5),X5)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X6),X6))))
<=> ( ti(X1,X5) != zero_zero(X1)
| ti(X1,X6) != zero_zero(X1) ) ) ),
c_0_18 ).
fof(c_0_674,axiom,
! [X1] :
( linordered_idom(X1)
=> ! [X5,X6] :
( hAPP(X1,X1,plus_plus(X1,hAPP(nat,X1,power_power(X1,X5),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,X1,power_power(X1,X6),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) = zero_zero(X1)
<=> ( ti(X1,X5) = zero_zero(X1)
& ti(X1,X6) = zero_zero(X1) ) ) ),
c_0_19 ).
fof(c_0_675,axiom,
! [X5,X6] :
( hAPP(real,real,plus_plus(real,hAPP(nat,real,power_power(real,X5),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,real,power_power(real,X6),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) = zero_zero(real)
<=> ( X5 = zero_zero(real)
& X6 = zero_zero(real) ) ),
c_0_20 ).
fof(c_0_676,axiom,
! [X1] :
( ( number_ring(X1)
& linordered_idom(X1) )
=> ! [X15] : hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(nat,X1,semiring_1_of_nat(X1),X15)),hAPP(nat,X1,power_power(X1,number_number_of(X1,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),X15))) ),
c_0_21 ).
fof(c_0_677,axiom,
! [X15] : hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),one_one(real)),hAPP(nat,real,power_power(real,number_number_of(real,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),X15))),
c_0_22 ).
fof(c_0_678,axiom,
! [X28,X12,X54] :
( ! [X53,X43] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X53),X43))
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,X54,X53)),hAPP(nat,nat,X54,X43))) )
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,plus_plus(nat,hAPP(nat,nat,X54,X28)),X12)),hAPP(nat,nat,X54,hAPP(nat,nat,plus_plus(nat,X28),X12)))) ),
c_0_23 ).
fof(c_0_679,axiom,
! [X10] : hAPP(nat,int,power_power(int,hAPP(nat,int,power_power(int,X10),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) = hAPP(nat,int,power_power(int,X10),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),
c_0_24 ).
fof(c_0_680,axiom,
! [X1] :
( linordered_idom(X1)
=> ! [X7] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),hAPP(nat,X1,power_power(X1,X7),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))
<=> ti(X1,X7) != zero_zero(X1) ) ),
c_0_25 ).
fof(c_0_681,axiom,
! [X1] :
( linord581940658strict(X1)
=> ! [X7,X42,X46] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X46))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X46),X7)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X46),X42)))
<=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X7),X42)) ) ) ),
c_0_26 ).
fof(c_0_682,axiom,
! [X1] :
( linordered_semiring(X1)
=> ! [X31,X41,X40] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X31),X41)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X40),X41)))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X41))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X31),X40)) ) ) ),
c_0_27 ).
fof(c_0_683,axiom,
! [X1] :
( linord20386208strict(X1)
=> ! [X31,X41,X40] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X31),X41)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X40),X41)))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X41))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X31),X40)) ) ) ),
c_0_28 ).
fof(c_0_684,axiom,
! [X1] :
( linordered_semiring(X1)
=> ! [X41,X31,X40] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X41),X31)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X41),X40)))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X41))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X31),X40)) ) ) ),
c_0_29 ).
fof(c_0_685,axiom,
! [X1] :
( linord20386208strict(X1)
=> ! [X41,X31,X40] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X41),X31)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X41),X40)))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X41))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X31),X40)) ) ) ),
c_0_30 ).
fof(c_0_686,axiom,
! [X1] :
( linord20386208strict(X1)
=> ! [X31,X41,X40] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X31),X41)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X40),X41)))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X41))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X31),X40)) ) ) ),
c_0_31 ).
fof(c_0_687,axiom,
! [X1] :
( linord20386208strict(X1)
=> ! [X41,X31,X40] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X41),X31)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X41),X40)))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X41))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X31),X40)) ) ) ),
c_0_32 ).
fof(c_0_688,axiom,
! [X1] :
( linord581940658strict(X1)
=> ! [X7,X42,X46] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X46),zero_zero(X1)))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X46),X7)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X46),X42)))
<=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X42),X7)) ) ) ),
c_0_33 ).
fof(c_0_689,axiom,
! [X1] :
( linord581940658strict(X1)
=> ! [X7,X42,X46] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X46),zero_zero(X1)))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X46),X7)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X46),X42)))
<=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X42),X7)) ) ) ),
c_0_34 ).
fof(c_0_690,axiom,
! [X1] :
( linord20386208strict(X1)
=> ! [X41,X45,X31,X40] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X31),X40))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X41),X45))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X40))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X41))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X31),X41)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X40),X45))) ) ) ) ) ),
c_0_35 ).
fof(c_0_691,axiom,
! [X1] :
( linord20386208strict(X1)
=> ! [X41,X45,X31,X40] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X31),X40))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X41),X45))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X31))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X41))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X31),X41)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X40),X45))) ) ) ) ) ),
c_0_36 ).
fof(c_0_692,axiom,
! [X1] :
( linord20386208strict(X1)
=> ! [X41,X45,X31,X40] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X31),X40))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X41),X45))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X31))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X41))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X31),X41)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X40),X45))) ) ) ) ) ),
c_0_37 ).
fof(c_0_693,axiom,
! [X1] :
( linord20386208strict(X1)
=> ! [X41,X45,X31,X40] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X31),X40))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X41),X45))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X31))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X41))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X31),X41)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X40),X45))) ) ) ) ) ),
c_0_38 ).
fof(c_0_694,axiom,
! [X29] :
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,plus_plus(int,hAPP(int,int,plus_plus(int,one_one(int)),X29)),X29)),zero_zero(int)))
<=> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X29),zero_zero(int))) ),
c_0_39 ).
fof(c_0_695,axiom,
! [X1,X3] :
( ord(X3)
=> ! [X54,X57] :
( ! [X47] : hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),hAPP(X1,X3,X54,X47)),hAPP(X1,X3,X57,X47)))
=> hBOOL(hAPP(fun(X1,X3),bool,hAPP(fun(X1,X3),fun(fun(X1,X3),bool),ord_less_eq(fun(X1,X3)),X54),X57)) ) ),
c_0_40 ).
fof(c_0_696,axiom,
! [X1,X3] :
( ord(X3)
=> ! [X54,X57] :
( hBOOL(hAPP(fun(X1,X3),bool,hAPP(fun(X1,X3),fun(fun(X1,X3),bool),ord_less_eq(fun(X1,X3)),X54),X57))
<=> ! [X47] : hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),hAPP(X1,X3,X54,X47)),hAPP(X1,X3,X57,X47))) ) ),
c_0_41 ).
fof(c_0_697,axiom,
! [X1] :
( linord20386208strict(X1)
=> ! [X41,X31,X40] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X31),X40))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X41))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X31),X41)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X40),X41))) ) ) ),
c_0_42 ).
fof(c_0_698,axiom,
! [X1] :
( linord20386208strict(X1)
=> ! [X41,X31,X40] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X31),X40))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X41))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X41),X31)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X41),X40))) ) ) ),
c_0_43 ).
fof(c_0_699,axiom,
! [X1] :
( linord893533164strict(X1)
=> ! [X41,X31,X40] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X31),X40))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X41))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X41),X31)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X41),X40))) ) ) ),
c_0_44 ).
fof(c_0_700,axiom,
! [X1] :
( linord581940658strict(X1)
=> ! [X41,X40,X31] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X40),X31))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X41),zero_zero(X1)))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X31),X41)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X40),X41))) ) ) ),
c_0_45 ).
fof(c_0_701,axiom,
! [X1] :
( linord581940658strict(X1)
=> ! [X41,X40,X31] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X40),X31))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X41),zero_zero(X1)))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X41),X31)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X41),X40))) ) ) ),
c_0_46 ).
fof(c_0_702,axiom,
! [X34,X55,X54] :
( ! [X35,X56] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X35),X56))
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,X54,X35)),hAPP(nat,nat,X54,X56))) )
=> ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X34),X55))
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,X54,X34)),hAPP(nat,nat,X54,X55))) ) ),
c_0_47 ).
fof(c_0_703,axiom,
! [X1] :
( linordered_semidom(X1)
=> ! [X10,X11] :
( hAPP(nat,X1,power_power(X1,X10),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) = hAPP(nat,X1,power_power(X1,X11),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X10))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X11))
=> ti(X1,X10) = ti(X1,X11) ) ) ) ),
c_0_48 ).
fof(c_0_704,axiom,
! [X1] :
( linordered_idom(X1)
=> ! [X31] : hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),hAPP(nat,X1,power_power(X1,X31),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))) ),
c_0_49 ).
fof(c_0_705,axiom,
! [X10] : hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X10),hAPP(nat,int,power_power(int,X10),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),
c_0_50 ).
fof(c_0_706,axiom,
! [X10] :
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X10))
=> ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X10),number_number_of(int,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))
=> ( X10 = zero_zero(int)
| X10 = one_one(int) ) ) ),
c_0_51 ).
fof(c_0_707,axiom,
! [X1] :
( linord20386208strict(X1)
=> ! [X40,X31] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X31),zero_zero(X1)))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X40))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X31),X40)),zero_zero(X1))) ) ) ),
c_0_52 ).
fof(c_0_708,axiom,
! [X1] :
( linordered_semidom(X1)
=> ! [X15,X31,X40] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X31),X40))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X31))
=> ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X15))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(nat,X1,power_power(X1,X31),X15)),hAPP(nat,X1,power_power(X1,X40),X15))) ) ) ) ),
c_0_53 ).
fof(c_0_709,axiom,
! [X1] :
( linordered_semidom(X1)
=> ! [X31,X15,X32] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X15),X32))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X31))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X31),one_one(X1)))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(nat,X1,power_power(X1,X31),X32)),hAPP(nat,X1,power_power(X1,X31),X15))) ) ) ) ),
c_0_54 ).
fof(c_0_710,axiom,
! [X1] :
( linordered_semidom(X1)
=> ! [X31,X15,X32] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X15),X32))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X31))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X31),one_one(X1)))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(nat,X1,power_power(X1,X31),X32)),hAPP(nat,X1,power_power(X1,X31),X15))) ) ) ) ),
c_0_55 ).
fof(c_0_711,axiom,
! [X1] :
( linord20386208strict(X1)
=> ! [X40,X31] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X40),X31)))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X31))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X40)) ) ) ),
c_0_56 ).
fof(c_0_712,axiom,
! [X1] :
( linordered_semidom(X1)
=> ! [X31,X15,X40] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(nat,X1,power_power(X1,X31),X15)),hAPP(nat,X1,power_power(X1,X40),X15)))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X40))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X31),X40)) ) ) ),
c_0_57 ).
fof(c_0_713,axiom,
! [X1] :
( linordered_semidom(X1)
=> ! [X14,X15,X31] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),one_one(X1)),X31))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(nat,X1,power_power(X1,X31),X14)),hAPP(nat,X1,power_power(X1,X31),X15)))
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X14),X15)) ) ) ),
c_0_58 ).
fof(c_0_714,axiom,
! [X1] :
( linordered_semidom(X1)
=> ! [X5,X6,X42] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),one_one(X1)),X42))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(nat,X1,power_power(X1,X42),X5)),hAPP(nat,X1,power_power(X1,X42),X6)))
<=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X5),X6)) ) ) ),
c_0_59 ).
fof(c_0_715,axiom,
! [X1] :
( linordered_semidom(X1)
=> ! [X14,X15,X31] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),one_one(X1)),X31))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(nat,X1,power_power(X1,X31),X14)),hAPP(nat,X1,power_power(X1,X31),X15)))
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X14),X15)) ) ) ),
c_0_60 ).
fof(c_0_716,axiom,
! [X1] :
( linordered_semidom(X1)
=> ! [X5,X6,X42] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),one_one(X1)),X42))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(nat,X1,power_power(X1,X42),X5)),hAPP(nat,X1,power_power(X1,X42),X6)))
<=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X5),X6)) ) ) ),
c_0_61 ).
fof(c_0_717,axiom,
! [X1] :
( linordered_semidom(X1)
=> ! [X15,X31] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),one_one(X1)),X31))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(nat,X1,power_power(X1,X31),X15)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X31),hAPP(nat,X1,power_power(X1,X31),X15)))) ) ),
c_0_62 ).
fof(c_0_718,axiom,
! [X14,X15,X21] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X21))
=> ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,power_power(nat,X21),X14)),hAPP(nat,nat,power_power(nat,X21),X15)))
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X14),X15)) ) ),
c_0_63 ).
fof(c_0_719,axiom,
! [X1] :
( linordered_semidom(X1)
=> ! [X15,X31,X40] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X31),X40))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X31))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(nat,X1,power_power(X1,X31),X15)),hAPP(nat,X1,power_power(X1,X40),X15))) ) ) ),
c_0_64 ).
fof(c_0_720,axiom,
! [X1] :
( linord581940658strict(X1)
=> ! [X40,X31] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X31),zero_zero(X1)))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X40),zero_zero(X1)))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X31),X40))) ) ) ),
c_0_65 ).
fof(c_0_721,axiom,
! [X1] :
( ordere223160158up_add(X1)
=> ! [X41,X45,X31,X40] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X31),X40))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X41),X45))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,plus_plus(X1,X31),X41)),hAPP(X1,X1,plus_plus(X1,X40),X45))) ) ) ),
c_0_66 ).
fof(c_0_722,axiom,
! [X1] :
( ordere223160158up_add(X1)
=> ! [X41,X45,X31,X40] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X31),X40))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X41),X45))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,plus_plus(X1,X31),X41)),hAPP(X1,X1,plus_plus(X1,X40),X45))) ) ) ),
c_0_67 ).
fof(c_0_723,axiom,
! [X1] :
( ordere779506340up_add(X1)
=> ! [X41,X45,X31,X40] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X31),X40))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X41),X45))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,plus_plus(X1,X31),X41)),hAPP(X1,X1,plus_plus(X1,X40),X45))) ) ) ),
c_0_68 ).
fof(c_0_724,axiom,
! [X1] :
( ordere223160158up_add(X1)
=> ! [X41,X45,X31,X40] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X31),X40))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X41),X45))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,plus_plus(X1,X31),X41)),hAPP(X1,X1,plus_plus(X1,X40),X45))) ) ) ),
c_0_69 ).
fof(c_0_725,axiom,
! [X1] :
( linordered_semidom(X1)
=> ! [X31,X15,X32] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X15),X32))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),one_one(X1)),X31))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(nat,X1,power_power(X1,X31),X15)),hAPP(nat,X1,power_power(X1,X31),X32))) ) ) ),
c_0_70 ).
fof(c_0_726,axiom,
! [X1] :
( linordered_semidom(X1)
=> ! [X31,X15,X32] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X15),X32))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),one_one(X1)),X31))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(nat,X1,power_power(X1,X31),X15)),hAPP(nat,X1,power_power(X1,X31),X32))) ) ) ),
c_0_71 ).
fof(c_0_727,axiom,
! [X1] :
( dense_linorder(X1)
=> ! [X16,X10,X11] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X10),X11))
=> ( ! [X62] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X10),X62))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X62),X11))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X62),X16)) ) )
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X11),X16)) ) ) ),
c_0_72 ).
fof(c_0_728,axiom,
! [X20,X30,X21,X22] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X21),X22))
=> ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X20),X30))
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,plus_plus(nat,X21),X20)),hAPP(nat,nat,plus_plus(nat,X22),X30))) ) ),
c_0_73 ).
fof(c_0_729,axiom,
! [X50,X16,X51,X8] :
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X51),X8))
=> ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X50),X16))
=> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,plus_plus(int,X51),X50)),hAPP(int,int,plus_plus(int,X8),X16))) ) ),
c_0_74 ).
fof(c_0_730,axiom,
! [X20,X30,X21,X22] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X21),X22))
=> ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X20),X30))
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,plus_plus(nat,X21),X20)),hAPP(nat,nat,plus_plus(nat,X22),X30))) ) ),
c_0_75 ).
fof(c_0_731,axiom,
! [X1] :
( linordered_semidom(X1)
=> ! [X15,X31] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),one_one(X1)),X31))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),one_one(X1)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X31),hAPP(nat,X1,power_power(X1,X31),X15)))) ) ),
c_0_76 ).
fof(c_0_732,axiom,
! [X1] :
( ordere236663937imp_le(X1)
=> ! [X41,X31,X40] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,plus_plus(X1,X41),X31)),hAPP(X1,X1,plus_plus(X1,X41),X40)))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X31),X40)) ) ),
c_0_77 ).
fof(c_0_733,axiom,
! [X1] :
( ordere236663937imp_le(X1)
=> ! [X31,X41,X40] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,plus_plus(X1,X31),X41)),hAPP(X1,X1,plus_plus(X1,X40),X41)))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X31),X40)) ) ),
c_0_78 ).
fof(c_0_734,axiom,
! [X1] :
( ordere236663937imp_le(X1)
=> ! [X46,X7,X42] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,plus_plus(X1,X46),X7)),hAPP(X1,X1,plus_plus(X1,X46),X42)))
<=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X7),X42)) ) ),
c_0_79 ).
fof(c_0_735,axiom,
! [X1] :
( ordere236663937imp_le(X1)
=> ! [X7,X46,X42] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,plus_plus(X1,X7),X46)),hAPP(X1,X1,plus_plus(X1,X42),X46)))
<=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X7),X42)) ) ),
c_0_80 ).
fof(c_0_736,axiom,
! [X1] :
( ordere236663937imp_le(X1)
=> ! [X7,X46,X42] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,plus_plus(X1,X7),X46)),hAPP(X1,X1,plus_plus(X1,X42),X46)))
<=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X7),X42)) ) ),
c_0_81 ).
fof(c_0_737,axiom,
! [X1] :
( ordere236663937imp_le(X1)
=> ! [X46,X7,X42] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,plus_plus(X1,X46),X7)),hAPP(X1,X1,plus_plus(X1,X46),X42)))
<=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X7),X42)) ) ),
c_0_82 ).
fof(c_0_738,axiom,
! [X1] :
( ordere236663937imp_le(X1)
=> ! [X31,X41,X40] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,plus_plus(X1,X31),X41)),hAPP(X1,X1,plus_plus(X1,X40),X41)))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X31),X40)) ) ),
c_0_83 ).
fof(c_0_739,axiom,
! [X1] :
( ordere236663937imp_le(X1)
=> ! [X41,X31,X40] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,plus_plus(X1,X41),X31)),hAPP(X1,X1,plus_plus(X1,X41),X40)))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X31),X40)) ) ),
c_0_84 ).
fof(c_0_740,axiom,
! [X33,X12,X34] :
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X12),X34))
=> ( hBOOL(hAPP(int,bool,X33,hAPP(int,int,plus_plus(int,X12),one_one(int))))
=> ( ! [X35] :
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X12),X35))
=> ( hBOOL(hAPP(int,bool,X33,X35))
=> hBOOL(hAPP(int,bool,X33,hAPP(int,int,plus_plus(int,X35),one_one(int)))) ) )
=> hBOOL(hAPP(int,bool,X33,X34)) ) ) ),
c_0_85 ).
fof(c_0_741,axiom,
! [X20,X30] : hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,bit1,X20)),X30) = hAPP(int,int,plus_plus(int,hAPP(int,int,bit0,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),X20),X30))),X30),
c_0_86 ).
fof(c_0_742,axiom,
! [X12,X28,X17] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,plus_plus(nat,X12),X28)),hAPP(nat,nat,plus_plus(nat,X12),X17)))
<=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X28),X17)) ),
c_0_87 ).
fof(c_0_743,axiom,
! [X12,X28,X17] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,plus_plus(nat,X12),X28)),hAPP(nat,nat,plus_plus(nat,X12),X17)))
<=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X28),X17)) ),
c_0_88 ).
fof(c_0_744,axiom,
! [X33,X28,X17] :
( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X28),X17))
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X33,X17),X28)) )
=> ( ( X28 = X17
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X33,X17),X28)) )
=> ( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X17),X28))
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X33,X17),X28)) )
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X33,X17),X28)) ) ) ),
c_0_89 ).
fof(c_0_745,axiom,
! [X1] :
( ordere216010020id_add(X1)
=> ! [X40,X31] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X31),zero_zero(X1)))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X40),zero_zero(X1)))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,plus_plus(X1,X31),X40)),zero_zero(X1))) ) ) ),
c_0_90 ).
fof(c_0_746,axiom,
! [X1] :
( ordere216010020id_add(X1)
=> ! [X40,X31] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X31),zero_zero(X1)))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X40),zero_zero(X1)))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,plus_plus(X1,X31),X40)),zero_zero(X1))) ) ) ),
c_0_91 ).
fof(c_0_747,axiom,
! [X1] :
( ordere216010020id_add(X1)
=> ! [X40,X31] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X31),zero_zero(X1)))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X40),zero_zero(X1)))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,plus_plus(X1,X31),X40)),zero_zero(X1))) ) ) ),
c_0_92 ).
fof(c_0_748,axiom,
! [X1] :
( ordere216010020id_add(X1)
=> ! [X40,X31] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X31),zero_zero(X1)))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X40),zero_zero(X1)))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,plus_plus(X1,X31),X40)),zero_zero(X1))) ) ) ),
c_0_93 ).
fof(c_0_749,axiom,
! [X1] :
( linordered_semidom(X1)
=> ! [X28,X17] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(nat,X1,semiring_1_of_nat(X1),X28)),hAPP(nat,X1,semiring_1_of_nat(X1),X17)))
<=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X28),X17)) ) ),
c_0_94 ).
fof(c_0_750,axiom,
! [X1] :
( linordered_semidom(X1)
=> ! [X14,X15] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(nat,X1,semiring_1_of_nat(X1),X14)),hAPP(nat,X1,semiring_1_of_nat(X1),X15)))
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X14),X15)) ) ),
c_0_95 ).
fof(c_0_751,axiom,
! [X1] :
( linordered_semidom(X1)
=> ! [X28,X17] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(nat,X1,semiring_1_of_nat(X1),X28)),hAPP(nat,X1,semiring_1_of_nat(X1),X17)))
<=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X28),X17)) ) ),
c_0_96 ).
fof(c_0_752,axiom,
! [X28,X17] :
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(nat,int,semiring_1_of_nat(int),X28)),hAPP(nat,int,semiring_1_of_nat(int),X17)))
<=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X28),X17)) ),
c_0_97 ).
fof(c_0_753,axiom,
! [X5,X6] :
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(nat,int,semiring_1_of_nat(int),X5)),hAPP(nat,int,semiring_1_of_nat(int),X6)))
<=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X5),X6)) ),
c_0_98 ).
fof(c_0_754,axiom,
! [X28,X17] :
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(nat,int,semiring_1_of_nat(int),X28)),hAPP(nat,int,semiring_1_of_nat(int),X17)))
<=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X28),X17)) ),
c_0_99 ).
fof(c_0_755,axiom,
! [X5,X6] :
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(nat,int,semiring_1_of_nat(int),X5)),hAPP(nat,int,semiring_1_of_nat(int),X6)))
<=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X5),X6)) ),
c_0_100 ).
fof(c_0_756,axiom,
! [X18,X19] :
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,bit1,X18)),hAPP(int,int,bit0,X19)))
<=> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X18),X19)) ),
c_0_101 ).
fof(c_0_757,axiom,
! [X12,X13] :
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,bit1,X12)),hAPP(int,int,bit0,X13)))
<=> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X12),X13)) ),
c_0_102 ).
fof(c_0_758,axiom,
! [X18,X19] :
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit0,X18)),hAPP(int,int,bit1,X19)))
<=> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X18),X19)) ),
c_0_103 ).
fof(c_0_759,axiom,
! [X12,X13] :
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit0,X12)),hAPP(int,int,bit1,X13)))
<=> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X12),X13)) ),
c_0_104 ).
fof(c_0_760,axiom,
! [X18,X19] :
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,bit0,X18)),hAPP(int,int,bit1,X19)))
<=> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X18),X19)) ),
c_0_105 ).
fof(c_0_761,axiom,
! [X12,X13] :
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,bit0,X12)),hAPP(int,int,bit1,X13)))
<=> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X12),X13)) ),
c_0_106 ).
fof(c_0_762,axiom,
! [X12,X13] :
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,bit0,X12)),hAPP(int,int,bit0,X13)))
<=> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X12),X13)) ),
c_0_107 ).
fof(c_0_763,axiom,
! [X18,X19] :
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,bit0,X18)),hAPP(int,int,bit0,X19)))
<=> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X18),X19)) ),
c_0_108 ).
fof(c_0_764,axiom,
! [X12,X13] :
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,bit1,X12)),hAPP(int,int,bit1,X13)))
<=> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X12),X13)) ),
c_0_109 ).
fof(c_0_765,axiom,
! [X18,X19] :
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,bit1,X18)),hAPP(int,int,bit1,X19)))
<=> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X18),X19)) ),
c_0_110 ).
fof(c_0_766,axiom,
! [X12,X13] :
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit1,X12)),hAPP(int,int,bit0,X13)))
<=> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X12),X13)) ),
c_0_111 ).
fof(c_0_767,axiom,
! [X18,X19] :
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit1,X18)),hAPP(int,int,bit0,X19)))
<=> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X18),X19)) ),
c_0_112 ).
fof(c_0_768,axiom,
! [X12,X13] :
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit0,X12)),hAPP(int,int,bit0,X13)))
<=> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X12),X13)) ),
c_0_113 ).
fof(c_0_769,axiom,
! [X18,X19] :
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit0,X18)),hAPP(int,int,bit0,X19)))
<=> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X18),X19)) ),
c_0_114 ).
fof(c_0_770,axiom,
! [X12,X13] :
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit1,X12)),hAPP(int,int,bit1,X13)))
<=> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X12),X13)) ),
c_0_115 ).
fof(c_0_771,axiom,
! [X18,X19] :
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit1,X18)),hAPP(int,int,bit1,X19)))
<=> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X18),X19)) ),
c_0_116 ).
fof(c_0_772,axiom,
! [X1] :
( linordered_semidom(X1)
=> ! [X31,X15,X40] :
( hAPP(nat,X1,power_power(X1,X31),X15) = hAPP(nat,X1,power_power(X1,X40),X15)
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X31))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X40))
=> ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X15))
=> ti(X1,X31) = ti(X1,X40) ) ) ) ) ),
c_0_117 ).
fof(c_0_773,axiom,
! [X1,X3] :
( ord(X3)
=> ! [X5,X54,X57] :
( hBOOL(hAPP(fun(X1,X3),bool,hAPP(fun(X1,X3),fun(fun(X1,X3),bool),ord_less_eq(fun(X1,X3)),X54),X57))
=> hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),hAPP(X1,X3,X54,X5)),hAPP(X1,X3,X57,X5))) ) ),
c_0_118 ).
fof(c_0_774,axiom,
! [X1,X3] :
( ord(X3)
=> ! [X5,X54,X57] :
( hBOOL(hAPP(fun(X1,X3),bool,hAPP(fun(X1,X3),fun(fun(X1,X3),bool),ord_less_eq(fun(X1,X3)),X54),X57))
=> hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),hAPP(X1,X3,X54,X5)),hAPP(X1,X3,X57,X5))) ) ),
c_0_119 ).
fof(c_0_775,axiom,
! [X31,X15] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X15))
=> ( hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X31))
=> ? [X47] :
( hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X47))
& hAPP(nat,real,power_power(real,X47),X15) = X31
& ! [X48] :
( ( hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X48))
& hAPP(nat,real,power_power(real,X48),X15) = X31 )
=> X48 = X47 ) ) ) ),
c_0_120 ).
fof(c_0_776,axiom,
! [X1] :
( ordere216010020id_add(X1)
=> ! [X40,X31] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X31))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X40))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),hAPP(X1,X1,plus_plus(X1,X31),X40))) ) ) ),
c_0_121 ).
fof(c_0_777,axiom,
! [X1] :
( ordere216010020id_add(X1)
=> ! [X40,X31] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X31))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X40))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),hAPP(X1,X1,plus_plus(X1,X31),X40))) ) ) ),
c_0_122 ).
fof(c_0_778,axiom,
! [X1] :
( ordere216010020id_add(X1)
=> ! [X40,X31] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X31))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X40))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),hAPP(X1,X1,plus_plus(X1,X31),X40))) ) ) ),
c_0_123 ).
fof(c_0_779,axiom,
! [X1] :
( ordere216010020id_add(X1)
=> ! [X40,X31] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X31))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X40))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),hAPP(X1,X1,plus_plus(X1,X31),X40))) ) ) ),
c_0_124 ).
fof(c_0_780,axiom,
! [X1] :
( ordere216010020id_add(X1)
=> ! [X40,X41,X31] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X31))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X40),X41))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X40),hAPP(X1,X1,plus_plus(X1,X31),X41))) ) ) ),
c_0_125 ).
fof(c_0_781,axiom,
! [X1] :
( ordere216010020id_add(X1)
=> ! [X40,X41,X31] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X31))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X40),X41))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X40),hAPP(X1,X1,plus_plus(X1,X31),X41))) ) ) ),
c_0_126 ).
fof(c_0_782,axiom,
! [X1] :
( ordere216010020id_add(X1)
=> ! [X40,X31,X41] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X41))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X40),X31))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X40),hAPP(X1,X1,plus_plus(X1,X31),X41))) ) ) ),
c_0_127 ).
fof(c_0_783,axiom,
! [X1] :
( ordere216010020id_add(X1)
=> ! [X40,X41,X31] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X31))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X40),X41))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X40),hAPP(X1,X1,plus_plus(X1,X31),X41))) ) ) ),
c_0_128 ).
fof(c_0_784,axiom,
! [X1] :
( linordered_semidom(X1)
=> ! [X40,X41,X31] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X31))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X40),X41))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X40),hAPP(X1,X1,plus_plus(X1,X31),X41))) ) ) ),
c_0_129 ).
fof(c_0_785,plain,
! [X1,X3] :
( ord(X3)
=> ! [X54,X57] :
( hBOOL(hAPP(fun(X1,X3),bool,hAPP(fun(X1,X3),fun(fun(X1,X3),bool),ord_less(fun(X1,X3)),X54),X57))
<=> ( hBOOL(hAPP(fun(X1,X3),bool,hAPP(fun(X1,X3),fun(fun(X1,X3),bool),ord_less_eq(fun(X1,X3)),X54),X57))
& ~ hBOOL(hAPP(fun(X1,X3),bool,hAPP(fun(X1,X3),fun(fun(X1,X3),bool),ord_less_eq(fun(X1,X3)),X57),X54)) ) ) ),
inference(fof_simplification,[status(thm)],[c_0_130]) ).
fof(c_0_786,axiom,
! [X1] :
( linordered_semidom(X1)
=> ! [X15,X31] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),one_one(X1)),X31))
=> ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X15))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),one_one(X1)),hAPP(nat,X1,power_power(X1,X31),X15))) ) ) ),
c_0_131 ).
fof(c_0_787,axiom,
! [X11,X10] :
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X10))
=> ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X11))
=> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,plus_plus(int,X10),X11))) ) ),
c_0_132 ).
fof(c_0_788,axiom,
! [X1] :
( linord219039673up_add(X1)
=> ! [X7] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,plus_plus(X1,X7),X7)),zero_zero(X1)))
<=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X7),zero_zero(X1))) ) ),
c_0_133 ).
fof(c_0_789,axiom,
! [X1] :
( linord219039673up_add(X1)
=> ! [X7] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,plus_plus(X1,X7),X7)),zero_zero(X1)))
<=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X7),zero_zero(X1))) ) ),
c_0_134 ).
fof(c_0_790,axiom,
! [X1] :
( linordered_idom(X1)
=> ! [X7] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,plus_plus(X1,X7),X7)),zero_zero(X1)))
<=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X7),zero_zero(X1))) ) ),
c_0_135 ).
fof(c_0_791,axiom,
! [X33,X12,X34] :
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X12),X34))
=> ( hBOOL(hAPP(int,bool,X33,X12))
=> ( ! [X35] :
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X12),X35))
=> ( hBOOL(hAPP(int,bool,X33,X35))
=> hBOOL(hAPP(int,bool,X33,hAPP(int,int,plus_plus(int,X35),one_one(int)))) ) )
=> hBOOL(hAPP(int,bool,X33,X34)) ) ) ),
c_0_136 ).
fof(c_0_792,axiom,
! [X24,X29] :
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,plus_plus(int,X24),one_one(int))),X29))
<=> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X24),X29)) ),
c_0_137 ).
fof(c_0_793,axiom,
hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),number_number_of(int,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),
c_0_138 ).
fof(c_0_794,axiom,
hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),number_number_of(int,hAPP(int,int,bit1,hAPP(int,int,bit1,pls))))),
c_0_139 ).
fof(c_0_795,axiom,
hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),
c_0_140 ).
fof(c_0_796,axiom,
! [X1] :
( ordere779506340up_add(X1)
=> ! [X41,X31,X40] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X31),X40))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,plus_plus(X1,X41),X31)),hAPP(X1,X1,plus_plus(X1,X41),X40))) ) ),
c_0_141 ).
fof(c_0_797,axiom,
! [X1] :
( ordere779506340up_add(X1)
=> ! [X41,X31,X40] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X31),X40))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,plus_plus(X1,X31),X41)),hAPP(X1,X1,plus_plus(X1,X40),X41))) ) ),
c_0_142 ).
fof(c_0_798,axiom,
! [X1] :
( ordere223160158up_add(X1)
=> ! [X41,X31,X40] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X31),X40))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,plus_plus(X1,X31),X41)),hAPP(X1,X1,plus_plus(X1,X40),X41))) ) ),
c_0_143 ).
fof(c_0_799,axiom,
! [X1] :
( ordere223160158up_add(X1)
=> ! [X41,X31,X40] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X31),X40))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,plus_plus(X1,X41),X31)),hAPP(X1,X1,plus_plus(X1,X41),X40))) ) ),
c_0_144 ).
fof(c_0_800,plain,
! [X14,X20,X15] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,plus_plus(nat,X14),X20)),X15))
=> ~ ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X14),X15))
=> ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X20),X15)) ) ),
inference(fof_simplification,[status(thm)],[c_0_145]) ).
fof(c_0_801,axiom,
! [X14,X20,X15] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,plus_plus(nat,X14),X20)),X15))
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X14),X15)) ),
c_0_146 ).
fof(c_0_802,axiom,
! [X14,X20,X15] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,plus_plus(nat,X14),X20)),X15))
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X20),X15)) ),
c_0_147 ).
fof(c_0_803,axiom,
! [X21,X22,X20] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,plus_plus(nat,X21),X22)),X20))
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X21),X20)) ),
c_0_148 ).
fof(c_0_804,axiom,
! [X28,X17] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,plus_plus(nat,X28),X17)))
<=> ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X28))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X17)) ) ),
c_0_149 ).
fof(c_0_805,axiom,
! [X16,X10,X11] :
( hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X10),X11))
=> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,plus_plus(real,X16),X10)),hAPP(real,real,plus_plus(real,X16),X11))) ),
c_0_150 ).
fof(c_0_806,axiom,
! [X20,X21,X22] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X21),X22))
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,plus_plus(nat,X21),X20)),hAPP(nat,nat,plus_plus(nat,X22),X20))) ),
c_0_151 ).
fof(c_0_807,axiom,
! [X20,X21,X22] :
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X21),X22))
=> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,plus_plus(int,X20),X21)),hAPP(int,int,plus_plus(int,X20),X22))) ),
c_0_152 ).
fof(c_0_808,axiom,
! [X20,X21,X22] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X21),X22))
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,plus_plus(nat,X21),X20)),hAPP(nat,nat,plus_plus(nat,X22),X20))) ),
c_0_153 ).
fof(c_0_809,axiom,
! [X20,X21,X22] :
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X21),X22))
=> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,plus_plus(int,X21),X20)),hAPP(int,int,plus_plus(int,X22),X20))) ),
c_0_154 ).
fof(c_0_810,axiom,
! [X1] :
( ( number_ring(X1)
& linordered_idom(X1) )
=> ! [X6] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),one_one(X1)),number_number_of(X1,X6)))
<=> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,bit1,pls)),X6)) ) ),
c_0_155 ).
fof(c_0_811,axiom,
! [X1] :
( ( number_ring(X1)
& linordered_idom(X1) )
=> ! [X6] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),one_one(X1)),number_number_of(X1,X6)))
<=> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit1,pls)),X6)) ) ),
c_0_156 ).
fof(c_0_812,axiom,
! [X14,X15,X16] : hAPP(int,int,plus_plus(int,hAPP(nat,int,semiring_1_of_nat(int),X14)),hAPP(int,int,plus_plus(int,hAPP(nat,int,semiring_1_of_nat(int),X15)),X16)) = hAPP(int,int,plus_plus(int,hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,plus_plus(nat,X14),X15))),X16),
c_0_157 ).
fof(c_0_813,axiom,
! [X5] :
( hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,sqrt,X5)),one_one(real)))
<=> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X5),one_one(real))) ),
c_0_158 ).
fof(c_0_814,axiom,
! [X5] :
( hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,sqrt,X5)),zero_zero(real)))
<=> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X5),zero_zero(real))) ),
c_0_159 ).
fof(c_0_815,axiom,
! [X24] :
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit0,X24)),zero_zero(int)))
<=> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X24),zero_zero(int))) ),
c_0_160 ).
fof(c_0_816,axiom,
! [X24] :
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit1,X24)),zero_zero(int)))
<=> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X24),zero_zero(int))) ),
c_0_161 ).
fof(c_0_817,axiom,
! [X1] :
( linordered_semidom(X1)
=> ! [X14,X15] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X14),X15))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(nat,X1,semiring_1_of_nat(X1),X14)),hAPP(nat,X1,semiring_1_of_nat(X1),X15))) ) ),
c_0_162 ).
fof(c_0_818,axiom,
! [X12] :
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,bit1,X12)),pls))
<=> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X12),pls)) ),
c_0_163 ).
fof(c_0_819,axiom,
! [X12] :
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,bit0,X12)),pls))
<=> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X12),pls)) ),
c_0_164 ).
fof(c_0_820,axiom,
! [X12] :
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit0,X12)),pls))
<=> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X12),pls)) ),
c_0_165 ).
fof(c_0_821,axiom,
! [X12] :
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit1,X12)),pls))
<=> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X12),pls)) ),
c_0_166 ).
fof(c_0_822,axiom,
! [X38,X39] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),number_number_of(nat,X38)),number_number_of(nat,X39)))
<=> ( ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X38),X39))
=> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),X39)) )
& hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X38),X39)) ) ),
c_0_167 ).
fof(c_0_823,axiom,
! [X1] :
( order(X1)
=> ! [X16,X11,X10] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X11),X10))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X16),X11))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X16),X10)) ) ) ),
c_0_168 ).
fof(c_0_824,axiom,
! [X1] :
( preorder(X1)
=> ! [X16,X10,X11] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X10),X11))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X11),X16))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X10),X16)) ) ) ),
c_0_169 ).
fof(c_0_825,axiom,
! [X1] :
( order(X1)
=> ! [X16,X11,X10] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X11),X10))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X16),X11))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X16),X10)) ) ) ),
c_0_170 ).
fof(c_0_826,axiom,
! [X1] :
( preorder(X1)
=> ! [X16,X10,X11] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X10),X11))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X11),X16))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X10),X16)) ) ) ),
c_0_171 ).
fof(c_0_827,axiom,
! [X1] :
( preorder(X1)
=> ! [X16,X10,X11] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X10),X11))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X11),X16))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X10),X16)) ) ) ),
c_0_172 ).
fof(c_0_828,axiom,
! [X1] :
( order(X1)
=> ! [X16,X11,X10] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X11),X10))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X16),X11))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X16),X10)) ) ) ),
c_0_173 ).
fof(c_0_829,axiom,
! [X1] :
( preorder(X1)
=> ! [X16,X10,X11] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X10),X11))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X11),X16))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X10),X16)) ) ) ),
c_0_174 ).
fof(c_0_830,axiom,
! [X1] :
( order(X1)
=> ! [X16,X11,X10] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X11),X10))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X16),X11))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X16),X10)) ) ) ),
c_0_175 ).
fof(c_0_831,axiom,
! [X58,X59] :
( hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X59))
=> ( hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X58))
=> ? [X60] :
( hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X60))
& hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X60),X59))
& hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X60),X58)) ) ) ),
c_0_176 ).
fof(c_0_832,axiom,
! [X31,X15] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X15))
=> ( hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X31))
=> ? [X49] :
( hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X49))
& hAPP(nat,real,power_power(real,X49),X15) = X31 ) ) ),
c_0_177 ).
fof(c_0_833,axiom,
! [X20,X21,X22] :
( hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X21),X22))
=> ( hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X22),X20))
=> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X21),X20)) ) ),
c_0_178 ).
fof(c_0_834,axiom,
! [X20,X21,X22] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X21),X22))
=> ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X22),X20))
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X21),X20)) ) ),
c_0_179 ).
fof(c_0_835,axiom,
! [X20,X21,X22] :
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X21),X22))
=> ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X22),X20))
=> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X21),X20)) ) ),
c_0_180 ).
fof(c_0_836,axiom,
! [X8,X16] :
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X8),X16))
=> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,plus_plus(int,X8),one_one(int))),X16)) ),
c_0_181 ).
fof(c_0_837,axiom,
! [X15] :
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),number_number_of(int,X15)))
=> ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),number_number_of(int,hAPP(int,int,bit0,X15))))
& hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),number_number_of(int,hAPP(int,int,bit1,X15)))) ) ),
c_0_182 ).
fof(c_0_838,axiom,
! [X1] :
( linord219039673up_add(X1)
=> ! [X7] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),hAPP(X1,X1,plus_plus(X1,X7),X7)))
<=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X7)) ) ),
c_0_183 ).
fof(c_0_839,axiom,
! [X1] :
( linord219039673up_add(X1)
=> ! [X7] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),hAPP(X1,X1,plus_plus(X1,X7),X7)))
<=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X7)) ) ),
c_0_184 ).
fof(c_0_840,axiom,
! [X5,X24] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,power_power(nat,X5),number_number_of(nat,X24))))
<=> ( number_number_of(nat,X24) = zero_zero(nat)
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X5)) ) ),
c_0_185 ).
fof(c_0_841,plain,
! [X22,X21] : ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,plus_plus(nat,X22),X21)),X21)),
inference(fof_simplification,[status(thm)],[c_0_186]) ).
fof(c_0_842,plain,
! [X21,X22] : ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,plus_plus(nat,X21),X22)),X21)),
inference(fof_simplification,[status(thm)],[c_0_187]) ).
fof(c_0_843,axiom,
! [X1] :
( number_semiring(X1)
=> ! [X23,X9] :
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),X9))
=> ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),X23))
=> hAPP(X1,X1,plus_plus(X1,number_number_of(X1,X9)),number_number_of(X1,X23)) = number_number_of(X1,hAPP(int,int,plus_plus(int,X9),X23)) ) ) ),
c_0_188 ).
fof(c_0_844,plain,
! [X38,X39] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),number_number_of(nat,X38)),number_number_of(nat,X39)))
<=> ( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X38),X39))
=> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X38),pls)) ) ),
inference(fof_simplification,[status(thm)],[c_0_189]) ).
fof(c_0_845,axiom,
! [X5,X17] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,power_power(nat,X5),X17)))
<=> ( X17 = zero_zero(nat)
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X5)) ) ),
c_0_190 ).
fof(c_0_846,axiom,
! [X5,X17] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,power_power(nat,X5),X17)))
<=> ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X5))
| X17 = zero_zero(nat) ) ),
c_0_191 ).
fof(c_0_847,axiom,
! [X24,X29] :
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X24),hAPP(int,int,plus_plus(int,X29),one_one(int))))
<=> ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X24),X29))
| X24 = X29 ) ),
c_0_192 ).
fof(c_0_848,axiom,
! [X24,X29] :
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X24),hAPP(int,int,plus_plus(int,X29),one_one(int))))
<=> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X24),X29)) ),
c_0_193 ).
fof(c_0_849,plain,
! [X1] :
( preorder(X1)
=> ! [X5,X6] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X5),X6))
<=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X5),X6))
& ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X6),X5)) ) ) ),
inference(fof_simplification,[status(thm)],[c_0_194]) ).
fof(c_0_850,axiom,
! [X1] :
( linordered_semidom(X1)
=> ! [X17] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),hAPP(nat,X1,semiring_1_of_nat(X1),X17)))
<=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X17)) ) ),
c_0_195 ).
fof(c_0_851,axiom,
! [X1] :
( ( number_ring(X1)
& linordered_idom(X1) )
=> ! [X5] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),number_number_of(X1,X5)),one_one(X1)))
<=> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X5),hAPP(int,int,bit1,pls))) ) ),
c_0_196 ).
fof(c_0_852,axiom,
! [X1] :
( ( number_ring(X1)
& linordered_idom(X1) )
=> ! [X5] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),number_number_of(X1,X5)),one_one(X1)))
<=> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X5),hAPP(int,int,bit1,pls))) ) ),
c_0_197 ).
fof(c_0_853,plain,
! [X1] :
( linordered_semidom(X1)
=> ! [X14] : ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(nat,X1,semiring_1_of_nat(X1),X14)),zero_zero(X1))) ),
inference(fof_simplification,[status(thm)],[c_0_198]) ).
fof(c_0_854,axiom,
! [X52,X33,X5] :
( ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X5))
=> ( hBOOL(X33)
<=> hBOOL(X52) ) )
=> ( ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X5))
& hBOOL(X33) )
<=> ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X5))
& hBOOL(X52) ) ) ),
c_0_199 ).
fof(c_0_855,axiom,
! [X52,X33,X5] :
( ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X5))
=> ( hBOOL(X33)
<=> hBOOL(X52) ) )
=> ( ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X5))
=> hBOOL(X33) )
<=> ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X5))
=> hBOOL(X52) ) ) ),
c_0_200 ).
fof(c_0_856,axiom,
! [X17] :
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(nat,int,semiring_1_of_nat(int),X17)))
<=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X17)) ),
c_0_201 ).
fof(c_0_857,axiom,
! [X6] :
( hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),one_one(real)),hAPP(real,real,sqrt,X6)))
<=> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),one_one(real)),X6)) ),
c_0_202 ).
fof(c_0_858,axiom,
! [X6] :
( hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(real,real,sqrt,X6)))
<=> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X6)) ),
c_0_203 ).
fof(c_0_859,axiom,
! [X17] :
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(nat,int,semiring_1_of_nat(int),X17)),zero_zero(int)))
<=> X17 = zero_zero(nat) ),
c_0_204 ).
fof(c_0_860,plain,
! [X20] : ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(nat,int,semiring_1_of_nat(int),X20)),zero_zero(int))),
inference(fof_simplification,[status(thm)],[c_0_205]) ).
fof(c_0_861,axiom,
! [X1] :
( ordere216010020id_add(X1)
=> ! [X6,X5] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X5))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X6))
=> ( hAPP(X1,X1,plus_plus(X1,X5),X6) = zero_zero(X1)
<=> ( ti(X1,X5) = zero_zero(X1)
& ti(X1,X6) = zero_zero(X1) ) ) ) ) ),
c_0_206 ).
fof(c_0_862,axiom,
! [X12] :
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),hAPP(int,int,bit1,X12)))
<=> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),X12)) ),
c_0_207 ).
fof(c_0_863,axiom,
! [X12] :
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),hAPP(int,int,bit0,X12)))
<=> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),X12)) ),
c_0_208 ).
fof(c_0_864,axiom,
! [X12] :
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),hAPP(int,int,bit1,X12)))
<=> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),X12)) ),
c_0_209 ).
fof(c_0_865,axiom,
! [X12] :
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),hAPP(int,int,bit0,X12)))
<=> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),X12)) ),
c_0_210 ).
fof(c_0_866,plain,
! [X1] :
( ( number(X1)
& linorder(X1) )
=> ! [X38,X24] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),number_number_of(X1,X38)),number_number_of(X1,X24)))
<=> ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),number_number_of(X1,X24)),number_number_of(X1,X38))) ) ),
inference(fof_simplification,[status(thm)],[c_0_211]) ).
fof(c_0_867,axiom,
! [X33] :
( ! [X47] :
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X47))
=> hBOOL(hAPP(int,bool,X33,X47)) )
<=> ! [X47] : hBOOL(hAPP(int,bool,X33,hAPP(nat,int,semiring_1_of_nat(int),X47))) ),
c_0_212 ).
fof(c_0_868,axiom,
! [X1] :
( linordered_semidom(X1)
=> ! [X15,X31] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),one_one(X1)),X31))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),one_one(X1)),hAPP(nat,X1,power_power(X1,X31),X15))) ) ),
c_0_213 ).
fof(c_0_869,axiom,
! [X1] :
( linordered_semidom(X1)
=> ! [X15,X31] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X31))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),hAPP(nat,X1,power_power(X1,X31),X15))) ) ),
c_0_214 ).
fof(c_0_870,axiom,
! [X1] :
( linordered_semidom(X1)
=> ! [X15,X31] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X31))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),hAPP(nat,X1,power_power(X1,X31),X15))) ) ),
c_0_215 ).
fof(c_0_871,plain,
! [X1] :
( linorder(X1)
=> ! [X37] :
? [X61] :
! [X47] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X61),X47))
=> ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X47),X37)) ) ),
inference(fof_simplification,[status(thm)],[c_0_216]) ).
fof(c_0_872,axiom,
! [X16] :
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X16))
=> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(int,int,plus_plus(int,one_one(int)),X16))) ),
c_0_217 ).
fof(c_0_873,axiom,
! [X15,X10] :
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X10))
=> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(nat,int,power_power(int,X10),X15))) ),
c_0_218 ).
fof(c_0_874,plain,
! [X1] :
( linorder(X1)
=> ! [X37] :
? [X61] :
! [X47] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X47),X61))
=> ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X37),X47)) ) ),
inference(fof_simplification,[status(thm)],[c_0_219]) ).
fof(c_0_875,axiom,
! [X14,X21,X22] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X21),X22))
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X21),hAPP(nat,nat,plus_plus(nat,X14),X22))) ),
c_0_220 ).
fof(c_0_876,axiom,
! [X14,X21,X22] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X21),X22))
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X21),hAPP(nat,nat,plus_plus(nat,X22),X14))) ),
c_0_221 ).
fof(c_0_877,axiom,
! [X14,X21,X22] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X21),X22))
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X21),hAPP(nat,nat,plus_plus(nat,X14),X22))) ),
c_0_222 ).
fof(c_0_878,axiom,
! [X14,X21,X22] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X21),X22))
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X21),hAPP(nat,nat,plus_plus(nat,X22),X14))) ),
c_0_223 ).
fof(c_0_879,plain,
! [X1] :
( linorder(X1)
=> ! [X5,X6] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X5),X6))
=> ( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X5),X6))
<=> ti(X1,X5) = ti(X1,X6) ) ) ),
inference(fof_simplification,[status(thm)],[c_0_224]) ).
fof(c_0_880,axiom,
! [X1] :
( order(X1)
=> ! [X5,X6] :
( ti(X1,X5) = ti(X1,X6)
<=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X5),X6))
& hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X6),X5)) ) ) ),
c_0_225 ).
fof(c_0_881,axiom,
! [X1] :
( order(X1)
=> ! [X6,X5] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X6),X5))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X5),X6))
<=> ti(X1,X5) = ti(X1,X6) ) ) ),
c_0_226 ).
fof(c_0_882,axiom,
! [X1] :
( order(X1)
=> ! [X10,X11] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X10),X11))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X11),X10))
=> ti(X1,X10) = ti(X1,X11) ) ) ),
c_0_227 ).
fof(c_0_883,axiom,
! [X1] :
( order(X1)
=> ! [X11,X10] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X11),X10))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X10),X11))
=> ti(X1,X10) = ti(X1,X11) ) ) ),
c_0_228 ).
fof(c_0_884,axiom,
! [X1] :
( ring_11004092258visors(X1)
=> ! [X7] :
( hAPP(nat,X1,power_power(X1,X7),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) = zero_zero(X1)
<=> ti(X1,X7) = zero_zero(X1) ) ),
c_0_229 ).
fof(c_0_885,axiom,
! [X1] :
( preorder(X1)
=> ! [X33,X5,X6] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X5),X6))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X6),X5))
=> hBOOL(X33) ) ) ),
c_0_230 ).
fof(c_0_886,plain,
! [X1] :
( linorder(X1)
=> ! [X11,X10] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X11),X10))
=> ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X10),X11)) ) ),
inference(fof_simplification,[status(thm)],[c_0_231]) ).
fof(c_0_887,plain,
! [X1] :
( linorder(X1)
=> ! [X5,X6] :
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X5),X6))
<=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X6),X5)) ) ),
inference(fof_simplification,[status(thm)],[c_0_232]) ).
fof(c_0_888,plain,
! [X1] :
( linorder(X1)
=> ! [X5,X6] :
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X5),X6))
<=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X6),X5)) ) ),
inference(fof_simplification,[status(thm)],[c_0_233]) ).
fof(c_0_889,plain,
! [X1] :
( linorder(X1)
=> ! [X5,X6] :
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X5),X6))
<=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X6),X5))
| ti(X1,X5) = ti(X1,X6) ) ) ),
inference(fof_simplification,[status(thm)],[c_0_234]) ).
fof(c_0_890,plain,
! [X1] :
( preorder(X1)
=> ! [X10,X11] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X10),X11))
=> ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X11),X10)) ) ),
inference(fof_simplification,[status(thm)],[c_0_235]) ).
fof(c_0_891,plain,
! [X1] :
( preorder(X1)
=> ! [X10,X11] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X10),X11))
=> ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X11),X10)) ) ),
inference(fof_simplification,[status(thm)],[c_0_236]) ).
fof(c_0_892,plain,
! [X1] :
( preorder(X1)
=> ! [X31,X40] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X31),X40))
=> ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X40),X31)) ) ),
inference(fof_simplification,[status(thm)],[c_0_237]) ).
fof(c_0_893,plain,
! [X1] :
( order(X1)
=> ! [X40,X31] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X40),X31))
=> ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X31),X40)) ) ),
inference(fof_simplification,[status(thm)],[c_0_238]) ).
fof(c_0_894,plain,
! [X1] :
( preorder(X1)
=> ! [X10,X11] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X10),X11))
=> ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X11),X10)) ) ),
inference(fof_simplification,[status(thm)],[c_0_239]) ).
fof(c_0_895,axiom,
! [X10] :
( hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X10))
=> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(real,real,sqrt,X10))) ),
c_0_240 ).
fof(c_0_896,axiom,
! [X16,X8] :
( hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X16),X8))
=> ( hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X8),X16))
=> X16 = X8 ) ),
c_0_241 ).
fof(c_0_897,axiom,
! [X14,X15] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X14),X15))
=> ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X15),X14))
=> X14 = X15 ) ),
c_0_242 ).
fof(c_0_898,axiom,
! [X16,X8] :
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X16),X8))
=> ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X8),X16))
=> X16 = X8 ) ),
c_0_243 ).
fof(c_0_899,axiom,
! [X14,X15,X20,X30] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X20),X30))
=> ( hAPP(nat,nat,plus_plus(nat,X14),X30) = hAPP(nat,nat,plus_plus(nat,X20),X15)
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X14),X15)) ) ),
c_0_244 ).
fof(c_0_900,axiom,
! [X1] :
( dense_linorder(X1)
=> ! [X16,X11] :
( ! [X47] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X47),X11))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X47),X16)) )
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X11),X16)) ) ),
c_0_245 ).
fof(c_0_901,axiom,
! [X33] :
( ? [X47] :
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X47))
& hBOOL(hAPP(int,bool,X33,X47)) )
<=> ? [X47] : hBOOL(hAPP(int,bool,X33,hAPP(nat,int,semiring_1_of_nat(int),X47))) ),
c_0_246 ).
fof(c_0_902,axiom,
hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(int,int,plus_plus(int,one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),n)))),
c_0_247 ).
fof(c_0_903,axiom,
number_number_of(int,hAPP(int,int,bit1,hAPP(int,int,bit1,pls))) = hAPP(nat,int,semiring_1_of_nat(int),number_number_of(nat,hAPP(int,int,bit1,hAPP(int,int,bit1,pls)))),
c_0_248 ).
fof(c_0_904,axiom,
number_number_of(int,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))) = hAPP(nat,int,semiring_1_of_nat(int),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),
c_0_249 ).
fof(c_0_905,axiom,
hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),m1),hAPP(int,int,plus_plus(int,one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),n)))),
c_0_250 ).
fof(c_0_906,plain,
! [X17,X33] :
( ~ hBOOL(hAPP(nat,bool,X33,zero_zero(nat)))
=> ( hBOOL(hAPP(nat,bool,X33,X17))
=> ? [X44] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X44),X17))
& ! [X35] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X35),X44))
=> ~ hBOOL(hAPP(nat,bool,X33,X35)) )
& hBOOL(hAPP(nat,bool,X33,X44)) ) ) ),
inference(fof_simplification,[status(thm)],[c_0_251]) ).
fof(c_0_907,plain,
! [X17,X33] :
( ~ hBOOL(hAPP(nat,bool,X33,zero_zero(nat)))
=> ( hBOOL(hAPP(nat,bool,X33,X17))
=> ? [X44] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X44),X17))
& ! [X35] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X35),X44))
=> ~ hBOOL(hAPP(nat,bool,X33,X35)) )
& hBOOL(hAPP(nat,bool,X33,hAPP(nat,nat,plus_plus(nat,X44),one_one(nat)))) ) ) ),
inference(fof_simplification,[status(thm)],[c_0_252]) ).
fof(c_0_908,plain,
! [X5,X6,X33] :
( ( hBOOL(X33)
=> hAPP(nat,int,semiring_1_of_nat(int),X5) = hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),hAPP(bool,fun(nat,fun(nat,nat)),if(nat),X33),X5),X6)) )
& ( ~ hBOOL(X33)
=> hAPP(nat,int,semiring_1_of_nat(int),X6) = hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),hAPP(bool,fun(nat,fun(nat,nat)),if(nat),X33),X5),X6)) ) ),
inference(fof_simplification,[status(thm)],[c_0_253]) ).
fof(c_0_909,plain,
! [X23,X9] :
( ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X9),pls))
=> hAPP(nat,nat,plus_plus(nat,number_number_of(nat,X9)),number_number_of(nat,X23)) = number_number_of(nat,X23) )
& ( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X9),pls))
=> ( ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X23),pls))
=> hAPP(nat,nat,plus_plus(nat,number_number_of(nat,X9)),number_number_of(nat,X23)) = number_number_of(nat,X9) )
& ( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X23),pls))
=> hAPP(nat,nat,plus_plus(nat,number_number_of(nat,X9)),number_number_of(nat,X23)) = number_number_of(nat,hAPP(int,int,plus_plus(int,X9),X23)) ) ) ) ),
inference(fof_simplification,[status(thm)],[c_0_254]) ).
fof(c_0_910,axiom,
! [X1] :
( ( number_ring(X1)
& linordered_idom(X1) )
=> ! [X5,X6] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),number_number_of(X1,X5)),number_number_of(X1,X6)))
<=> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X5),X6)) ) ),
c_0_255 ).
fof(c_0_911,axiom,
! [X1] :
( ( number_ring(X1)
& linordered_idom(X1) )
=> ! [X5,X6] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),number_number_of(X1,X5)),number_number_of(X1,X6)))
<=> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X5),X6)) ) ),
c_0_256 ).
fof(c_0_912,axiom,
! [X1] :
( linorder(X1)
=> ! [X37] :
? [X61] :
! [X47] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X61),X47))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X37),X47)) ) ),
c_0_257 ).
fof(c_0_913,axiom,
! [X1] :
( ( number_ring(X1)
& linordered_idom(X1) )
=> ! [X5] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),number_number_of(X1,X5)),zero_zero(X1)))
<=> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X5),pls)) ) ),
c_0_258 ).
fof(c_0_914,axiom,
! [X1] :
( ( number_ring(X1)
& linordered_idom(X1) )
=> ! [X5] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),number_number_of(X1,X5)),zero_zero(X1)))
<=> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X5),pls)) ) ),
c_0_259 ).
fof(c_0_915,axiom,
! [X12,X13] :
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),number_number_of(int,X12)),number_number_of(int,X13)))
<=> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X12),X13)) ),
c_0_260 ).
fof(c_0_916,axiom,
! [X12,X13] :
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),number_number_of(int,X12)),number_number_of(int,X13)))
<=> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X12),X13)) ),
c_0_261 ).
fof(c_0_917,axiom,
! [X1] :
( ( number_ring(X1)
& linordered_idom(X1) )
=> ! [X6] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),number_number_of(X1,X6)))
<=> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),X6)) ) ),
c_0_262 ).
fof(c_0_918,axiom,
! [X1] :
( ( number_ring(X1)
& linordered_idom(X1) )
=> ! [X6] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),number_number_of(X1,X6)))
<=> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),X6)) ) ),
c_0_263 ).
fof(c_0_919,axiom,
! [X1] :
( linorder(X1)
=> ! [X37] :
? [X61] :
! [X47] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X47),X61))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X47),X37)) ) ),
c_0_264 ).
fof(c_0_920,plain,
! [X1] :
( linorder(X1)
=> ! [X6,X5] :
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X6),X5))
=> ( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X5),X6))
<=> ti(X1,X5) = ti(X1,X6) ) ) ),
inference(fof_simplification,[status(thm)],[c_0_265]) ).
fof(c_0_921,axiom,
! [X1] :
( order(X1)
=> ! [X41,X31,X40] :
( ti(X1,X31) = ti(X1,X40)
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X41),X40))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X41),X31)) ) ) ),
c_0_266 ).
fof(c_0_922,axiom,
! [X1] :
( order(X1)
=> ! [X41,X40,X31] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X40),X31))
=> ( ti(X1,X40) = ti(X1,X41)
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X41),X31)) ) ) ),
c_0_267 ).
fof(c_0_923,axiom,
! [X1] :
( order(X1)
=> ! [X41,X31,X40] :
( ti(X1,X31) = ti(X1,X40)
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X41),X40))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X41),X31)) ) ) ),
c_0_268 ).
fof(c_0_924,axiom,
! [X1] :
( order(X1)
=> ! [X41,X40,X31] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X40),X31))
=> ( ti(X1,X40) = ti(X1,X41)
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X41),X31)) ) ) ),
c_0_269 ).
fof(c_0_925,axiom,
! [X1] :
( order(X1)
=> ! [X40,X31] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X40),X31))
=> ( ti(X1,X31) != ti(X1,X40)
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X40),X31)) ) ) ),
c_0_270 ).
fof(c_0_926,axiom,
! [X1] :
( order(X1)
=> ! [X31,X40] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X31),X40))
=> ( ti(X1,X31) != ti(X1,X40)
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X31),X40)) ) ) ),
c_0_271 ).
fof(c_0_927,axiom,
! [X1] :
( order(X1)
=> ! [X10,X11] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X10),X11))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X10),X11))
| ti(X1,X10) = ti(X1,X11) ) ) ),
c_0_272 ).
fof(c_0_928,axiom,
! [X1] :
( order(X1)
=> ! [X31,X40] :
( ti(X1,X31) != ti(X1,X40)
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X40),X31))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X40),X31)) ) ) ),
c_0_273 ).
fof(c_0_929,axiom,
! [X1] :
( order(X1)
=> ! [X31,X40] :
( ti(X1,X31) != ti(X1,X40)
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X31),X40))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X31),X40)) ) ) ),
c_0_274 ).
fof(c_0_930,plain,
! [X1] :
( linorder(X1)
=> ! [X5,X6] :
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X5),X6))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X5),X6))
<=> ti(X1,X5) = ti(X1,X6) ) ) ),
inference(fof_simplification,[status(thm)],[c_0_275]) ).
fof(c_0_931,axiom,
! [X1] :
( order(X1)
=> ! [X5,X6] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X5),X6))
<=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X5),X6))
| ti(X1,X5) = ti(X1,X6) ) ) ),
c_0_276 ).
fof(c_0_932,axiom,
! [X1] :
( order(X1)
=> ! [X5,X6] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X5),X6))
<=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X5),X6))
& ti(X1,X5) != ti(X1,X6) ) ) ),
c_0_277 ).
fof(c_0_933,axiom,
! [X1] :
( ord(X1)
=> ! [X41,X31,X40] :
( X31 = X40
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X40),X41))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X31),X41)) ) ) ),
c_0_278 ).
fof(c_0_934,axiom,
! [X1] :
( ord(X1)
=> ! [X41,X31,X40] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X31),X40))
=> ( X40 = X41
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X31),X41)) ) ) ),
c_0_279 ).
fof(c_0_935,axiom,
! [X1] :
( ord(X1)
=> ! [X41,X31,X40] :
( X31 = X40
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X40),X41))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X31),X41)) ) ) ),
c_0_280 ).
fof(c_0_936,axiom,
! [X1] :
( ord(X1)
=> ! [X41,X31,X40] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X31),X40))
=> ( X40 = X41
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X31),X41)) ) ) ),
c_0_281 ).
fof(c_0_937,axiom,
! [X1] :
( preorder(X1)
=> ! [X10,X11] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X10),X11))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X10),X11)) ) ),
c_0_282 ).
fof(c_0_938,axiom,
! [X38] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),number_number_of(nat,X38)))
<=> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),X38)) ),
c_0_283 ).
fof(c_0_939,axiom,
! [X21,X22] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X21),X22))
=> ? [X44] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X44))
& hAPP(nat,nat,plus_plus(nat,X21),X44) = X22 ) ),
c_0_284 ).
fof(c_0_940,axiom,
! [X20] :
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),X20))
=> ? [X43] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X43))
& X20 = hAPP(nat,int,semiring_1_of_nat(int),X43) ) ),
c_0_285 ).
fof(c_0_941,axiom,
! [X29] :
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),one_one(int)),X29))
<=> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),X29)) ),
c_0_286 ).
fof(c_0_942,axiom,
! [X5,X6] :
( hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X5),X6))
<=> ( hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X5),X6))
& X5 != X6 ) ),
c_0_287 ).
fof(c_0_943,axiom,
! [X5,X6] :
( hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X5),X6))
<=> ( hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X5),X6))
| X5 = X6 ) ),
c_0_288 ).
fof(c_0_944,axiom,
! [X28,X17] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X28),X17))
<=> ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X28),X17))
& X28 != X17 ) ),
c_0_289 ).
fof(c_0_945,axiom,
! [X28,X17] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X28),X17))
<=> ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X28),X17))
| X28 = X17 ) ),
c_0_290 ).
fof(c_0_946,axiom,
! [X14,X15] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X14),X15))
=> ( X14 != X15
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X14),X15)) ) ),
c_0_291 ).
fof(c_0_947,axiom,
! [X29,X24] :
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X29),X24))
<=> ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X29),X24))
& X29 != X24 ) ),
c_0_292 ).
fof(c_0_948,axiom,
! [X14,X15] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X14),X15))
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X14),X15)) ),
c_0_293 ).
fof(c_0_949,axiom,
! [X14,X15] :
( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X14),X15))
| X14 = X15 )
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X14),X15)) ),
c_0_294 ).
fof(c_0_950,axiom,
! [X1] :
( comm_semiring_1(X1)
=> ! [X31,X40,X41,X45] : hAPP(X1,X1,plus_plus(X1,hAPP(X1,X1,plus_plus(X1,X31),X40)),hAPP(X1,X1,plus_plus(X1,X41),X45)) = hAPP(X1,X1,plus_plus(X1,hAPP(X1,X1,plus_plus(X1,X31),X41)),hAPP(X1,X1,plus_plus(X1,X40),X45)) ),
c_0_295 ).
fof(c_0_951,axiom,
! [X20,X30] : hAPP(int,int,plus_plus(int,hAPP(int,int,bit1,X20)),hAPP(int,int,bit1,X30)) = hAPP(int,int,bit0,hAPP(int,int,plus_plus(int,X20),hAPP(int,int,succ,X30))),
c_0_296 ).
fof(c_0_952,axiom,
! [X1] :
( number_ring(X1)
=> ! [X9,X8,X16] : hAPP(X1,X1,plus_plus(X1,number_number_of(X1,X9)),hAPP(X1,X1,plus_plus(X1,number_number_of(X1,X8)),X16)) = hAPP(X1,X1,plus_plus(X1,number_number_of(X1,hAPP(int,int,plus_plus(int,X9),X8))),X16) ),
c_0_297 ).
fof(c_0_953,axiom,
! [X1] :
( linordered_semidom(X1)
=> ! [X28,X17,X7] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),one_one(X1)),X7))
=> ( hAPP(nat,X1,power_power(X1,X7),X28) = hAPP(nat,X1,power_power(X1,X7),X17)
<=> X28 = X17 ) ) ),
c_0_298 ).
fof(c_0_954,axiom,
! [X1] :
( number_semiring(X1)
=> ! [X9] :
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),X9))
=> hAPP(X1,X1,plus_plus(X1,number_number_of(X1,X9)),one_one(X1)) = number_number_of(X1,hAPP(int,int,succ,X9)) ) ),
c_0_299 ).
fof(c_0_955,axiom,
! [X24,X29] :
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X24),X29))
<=> ? [X43] : X29 = hAPP(int,int,plus_plus(int,X24),hAPP(nat,int,semiring_1_of_nat(int),X43)) ),
c_0_300 ).
fof(c_0_956,axiom,
! [X1] :
( number_semiring(X1)
=> ! [X9] :
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),X9))
=> hAPP(X1,X1,plus_plus(X1,one_one(X1)),number_number_of(X1,X9)) = number_number_of(X1,hAPP(int,int,succ,X9)) ) ),
c_0_301 ).
fof(c_0_957,axiom,
! [X1] :
( linorder(X1)
=> ! [X5,X6] :
( ti(X1,X5) != ti(X1,X6)
<=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X5),X6))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X6),X5)) ) ) ),
c_0_302 ).
fof(c_0_958,axiom,
! [X1] :
( linorder(X1)
=> ! [X10,X11] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X10),X11))
| ti(X1,X10) = ti(X1,X11)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X11),X10)) ) ),
c_0_303 ).
fof(c_0_959,plain,
! [X1] :
( linorder(X1)
=> ! [X10,X11] :
( ti(X1,X10) != ti(X1,X11)
=> ( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X10),X11))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X11),X10)) ) ) ),
inference(fof_simplification,[status(thm)],[c_0_304]) ).
fof(c_0_960,plain,
! [X1] :
( linorder(X1)
=> ! [X10,X11] :
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X10),X11))
=> ( ti(X1,X10) != ti(X1,X11)
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X11),X10)) ) ) ),
inference(fof_simplification,[status(thm)],[c_0_305]) ).
fof(c_0_961,plain,
! [X1] :
( linordered_idom(X1)
=> ! [X10,X11] :
( ti(X1,X10) != ti(X1,X11)
=> ( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X10),X11))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X11),X10)) ) ) ),
inference(fof_simplification,[status(thm)],[c_0_306]) ).
fof(c_0_962,axiom,
! [X1] :
( semiring_1(X1)
=> hAPP(nat,X1,power_power(X1,zero_zero(X1)),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) = zero_zero(X1) ),
c_0_307 ).
fof(c_0_963,axiom,
! [X1] :
( semiring_1(X1)
=> hAPP(nat,X1,power_power(X1,one_one(X1)),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) = one_one(X1) ),
c_0_308 ).
fof(c_0_964,plain,
! [X1] :
( linorder(X1)
=> ! [X11,X10] :
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X11),X10))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X10),X11)) ) ),
inference(fof_simplification,[status(thm)],[c_0_309]) ).
fof(c_0_965,plain,
! [X1] :
( linorder(X1)
=> ! [X10,X11] :
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X10),X11))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X11),X10)) ) ),
inference(fof_simplification,[status(thm)],[c_0_310]) ).
fof(c_0_966,axiom,
! [X1] :
( linorder(X1)
=> ! [X10,X11] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X10),X11))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X11),X10)) ) ),
c_0_311 ).
fof(c_0_967,axiom,
! [X1] :
( linorder(X1)
=> ! [X10,X11] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X10),X11))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X11),X10)) ) ),
c_0_312 ).
fof(c_0_968,plain,
! [X1] :
( linorder(X1)
=> ! [X10,X11] :
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X10),X11))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X11),X10)) ) ),
inference(fof_simplification,[status(thm)],[c_0_313]) ).
fof(c_0_969,plain,
! [X10,X11] :
( X10 != X11
=> ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X10),X11))
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X11),X10)) ) ),
inference(fof_simplification,[status(thm)],[c_0_314]) ).
fof(c_0_970,axiom,
! [X28,X17] :
( X28 != X17
<=> ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X28),X17))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X17),X28)) ) ),
c_0_315 ).
fof(c_0_971,axiom,
! [X10,X11] :
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X10),X11))
| X10 = X11
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X11),X10)) ),
c_0_316 ).
fof(c_0_972,axiom,
! [X16,X8] :
( hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X16),X8))
| hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X8),X16)) ),
c_0_317 ).
fof(c_0_973,axiom,
! [X14,X15] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X14),X15))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X15),X14)) ),
c_0_318 ).
fof(c_0_974,axiom,
! [X16,X8] :
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X16),X8))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X8),X16)) ),
c_0_319 ).
fof(c_0_975,axiom,
! [X10] :
( hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X10))
=> hAPP(real,real,sqrt,X10) != zero_zero(real) ),
c_0_320 ).
fof(c_0_976,plain,
! [X1] :
( number_ring(X1)
=> ! [X9] :
( ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),number_number_of(int,X9)))
=> hAPP(nat,X1,semiring_1_of_nat(X1),number_number_of(nat,X9)) = number_number_of(X1,X9) )
& ( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),number_number_of(int,X9)))
=> hAPP(nat,X1,semiring_1_of_nat(X1),number_number_of(nat,X9)) = zero_zero(X1) ) ) ),
inference(fof_simplification,[status(thm)],[c_0_321]) ).
fof(c_0_977,axiom,
! [X1] :
( linordered_semidom(X1)
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),hAPP(X1,X1,plus_plus(X1,one_one(X1)),one_one(X1)))) ),
c_0_322 ).
fof(c_0_978,axiom,
! [X1] :
( number_ring(X1)
=> ! [X8] : hAPP(X1,X1,plus_plus(X1,one_one(X1)),number_number_of(X1,X8)) = number_number_of(X1,hAPP(int,int,plus_plus(int,hAPP(int,int,bit1,pls)),X8)) ),
c_0_323 ).
fof(c_0_979,plain,
! [X9] :
( ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X9),pls))
=> hAPP(nat,nat,plus_plus(nat,number_number_of(nat,X9)),one_one(nat)) = one_one(nat) )
& ( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X9),pls))
=> hAPP(nat,nat,plus_plus(nat,number_number_of(nat,X9)),one_one(nat)) = number_number_of(nat,hAPP(int,int,succ,X9)) ) ),
inference(fof_simplification,[status(thm)],[c_0_324]) ).
fof(c_0_980,axiom,
! [X28,X17] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X28),X17))
<=> ? [X44] : X17 = hAPP(nat,nat,plus_plus(nat,X28),X44) ),
c_0_325 ).
fof(c_0_981,plain,
! [X9] :
( ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X9),pls))
=> hAPP(nat,nat,plus_plus(nat,one_one(nat)),number_number_of(nat,X9)) = one_one(nat) )
& ( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X9),pls))
=> hAPP(nat,nat,plus_plus(nat,one_one(nat)),number_number_of(nat,X9)) = number_number_of(nat,hAPP(int,int,succ,X9)) ) ),
inference(fof_simplification,[status(thm)],[c_0_326]) ).
fof(c_0_982,axiom,
! [X1] :
( comm_semiring_1(X1)
=> ! [X31,X40,X41] : hAPP(X1,X1,plus_plus(X1,hAPP(X1,X1,plus_plus(X1,X31),X40)),X41) = hAPP(X1,X1,plus_plus(X1,hAPP(X1,X1,plus_plus(X1,X31),X41)),X40) ),
c_0_327 ).
fof(c_0_983,axiom,
! [X16] :
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X16))
=> ~ ! [X53] : X16 != hAPP(nat,int,semiring_1_of_nat(int),X53) ),
c_0_328 ).
fof(c_0_984,axiom,
! [X20] :
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X20))
=> ~ ! [X43] : X20 != hAPP(nat,int,semiring_1_of_nat(int),X43) ),
c_0_329 ).
fof(c_0_985,axiom,
! [X20] :
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X20))
=> ? [X43] : X20 = hAPP(nat,int,semiring_1_of_nat(int),X43) ),
c_0_330 ).
fof(c_0_986,axiom,
! [X1] :
( linordered_semidom(X1)
=> ! [X31] : hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X31),hAPP(X1,X1,plus_plus(X1,X31),one_one(X1)))) ),
c_0_331 ).
fof(c_0_987,axiom,
! [X1] :
( linordered_semidom(X1)
=> ! [X15] : hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),hAPP(nat,X1,semiring_1_of_nat(X1),X15))) ),
c_0_332 ).
fof(c_0_988,axiom,
! [X1] :
( linordered_semidom(X1)
=> ! [X14] : hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),hAPP(nat,X1,semiring_1_of_nat(X1),X14))) ),
c_0_333 ).
fof(c_0_989,axiom,
! [X15,X14] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X15),hAPP(nat,nat,plus_plus(nat,X15),X14))),
c_0_334 ).
fof(c_0_990,axiom,
! [X15,X14] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X15),hAPP(nat,nat,plus_plus(nat,X14),X15))),
c_0_335 ).
fof(c_0_991,plain,
! [X1] :
( linordered_semidom(X1)
=> ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),one_one(X1)),zero_zero(X1))) ),
inference(fof_simplification,[status(thm)],[c_0_336]) ).
fof(c_0_992,plain,
! [X1] :
( linordered_semidom(X1)
=> ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),one_one(X1)),zero_zero(X1))) ),
inference(fof_simplification,[status(thm)],[c_0_337]) ).
fof(c_0_993,axiom,
! [X1] :
( semiring_1(X1)
=> ! [X14,X15] : hAPP(nat,X1,semiring_1_of_nat(X1),hAPP(nat,nat,plus_plus(nat,X14),X15)) = hAPP(X1,X1,plus_plus(X1,hAPP(nat,X1,semiring_1_of_nat(X1),X14)),hAPP(nat,X1,semiring_1_of_nat(X1),X15)) ),
c_0_338 ).
fof(c_0_994,axiom,
! [X15] : hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(nat,int,semiring_1_of_nat(int),X15))),
c_0_339 ).
fof(c_0_995,axiom,
! [X16] : hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(nat,int,semiring_1_of_nat(int),X16))),
c_0_340 ).
fof(c_0_996,axiom,
! [X1] :
( order(X1)
=> ! [X10,X11] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X10),X11))
=> ti(X1,X10) != ti(X1,X11) ) ),
c_0_341 ).
fof(c_0_997,axiom,
! [X1] :
( order(X1)
=> ! [X10,X11] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X10),X11))
=> ti(X1,X10) != ti(X1,X11) ) ),
c_0_342 ).
fof(c_0_998,axiom,
! [X1] :
( order(X1)
=> ! [X10,X11] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X10),X11))
=> ti(X1,X11) != ti(X1,X10) ) ),
c_0_343 ).
fof(c_0_999,axiom,
! [X10,X11] : hAPP(int,int,plus_plus(int,hAPP(nat,int,semiring_1_of_nat(int),X10)),hAPP(nat,int,semiring_1_of_nat(int),X11)) = hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,plus_plus(nat,X10),X11)),
c_0_344 ).
fof(c_0_1000,axiom,
! [X14,X15] : hAPP(int,int,plus_plus(int,hAPP(nat,int,semiring_1_of_nat(int),X14)),hAPP(nat,int,semiring_1_of_nat(int),X15)) = hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,plus_plus(nat,X14),X15)),
c_0_345 ).
fof(c_0_1001,plain,
! [X1] :
( preorder(X1)
=> ! [X10] : ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X10),X10)) ),
inference(fof_simplification,[status(thm)],[c_0_346]) ).
fof(c_0_1002,axiom,
! [X20,X30] : hAPP(int,int,plus_plus(int,hAPP(int,int,bit0,X20)),hAPP(int,int,bit1,X30)) = hAPP(int,int,bit1,hAPP(int,int,plus_plus(int,X20),X30)),
c_0_347 ).
fof(c_0_1003,axiom,
! [X20,X30] : hAPP(int,int,plus_plus(int,hAPP(int,int,bit1,X20)),hAPP(int,int,bit0,X30)) = hAPP(int,int,bit1,hAPP(int,int,plus_plus(int,X20),X30)),
c_0_348 ).
fof(c_0_1004,axiom,
! [X20,X30] : hAPP(int,int,plus_plus(int,hAPP(int,int,bit0,X20)),hAPP(int,int,bit0,X30)) = hAPP(int,int,bit0,hAPP(int,int,plus_plus(int,X20),X30)),
c_0_349 ).
fof(c_0_1005,axiom,
! [X17] :
( X17 != zero_zero(nat)
<=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X17)) ),
c_0_350 ).
fof(c_0_1006,axiom,
! [X17] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X17),zero_zero(nat)))
<=> X17 = zero_zero(nat) ),
c_0_351 ).
fof(c_0_1007,axiom,
! [X38] :
( number_number_of(nat,X38) = zero_zero(nat)
<=> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X38),pls)) ),
c_0_352 ).
fof(c_0_1008,axiom,
! [X38] :
( zero_zero(nat) = number_number_of(nat,X38)
<=> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X38),pls)) ),
c_0_353 ).
fof(c_0_1009,plain,
! [X15] : ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X15),zero_zero(nat))),
inference(fof_simplification,[status(thm)],[c_0_354]) ).
fof(c_0_1010,plain,
! [X15] : ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X15),zero_zero(nat))),
inference(fof_simplification,[status(thm)],[c_0_355]) ).
fof(c_0_1011,plain,
! [X15] : ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X15),zero_zero(nat))),
inference(fof_simplification,[status(thm)],[c_0_356]) ).
fof(c_0_1012,axiom,
! [X14,X15] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X14),X15))
=> X15 != zero_zero(nat) ),
c_0_357 ).
fof(c_0_1013,axiom,
! [X36,X37] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X36),X37))
=> X36 != X37 ),
c_0_358 ).
fof(c_0_1014,axiom,
! [X15,X14] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X15),X14))
=> X14 != X15 ),
c_0_359 ).
fof(c_0_1015,plain,
! [X15] : ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X15),X15)),
inference(fof_simplification,[status(thm)],[c_0_360]) ).
fof(c_0_1016,plain,
! [X15] : ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X15),X15)),
inference(fof_simplification,[status(thm)],[c_0_361]) ).
fof(c_0_1017,plain,
~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),zero_zero(int))),
inference(fof_simplification,[status(thm)],[c_0_362]) ).
fof(c_0_1018,plain,
~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),pls)),
inference(fof_simplification,[status(thm)],[c_0_363]) ).
fof(c_0_1019,axiom,
! [X1] :
( comm_semiring_1(X1)
=> ! [X31,X41,X45] : hAPP(X1,X1,plus_plus(X1,X31),hAPP(X1,X1,plus_plus(X1,X41),X45)) = hAPP(X1,X1,plus_plus(X1,hAPP(X1,X1,plus_plus(X1,X31),X41)),X45) ),
c_0_364 ).
fof(c_0_1020,axiom,
! [X1] :
( comm_semiring_1(X1)
=> ! [X31,X40,X41] : hAPP(X1,X1,plus_plus(X1,hAPP(X1,X1,plus_plus(X1,X31),X40)),X41) = hAPP(X1,X1,plus_plus(X1,X31),hAPP(X1,X1,plus_plus(X1,X40),X41)) ),
c_0_365 ).
fof(c_0_1021,axiom,
! [X1] :
( ab_semigroup_add(X1)
=> ! [X31,X40,X41] : hAPP(X1,X1,plus_plus(X1,hAPP(X1,X1,plus_plus(X1,X31),X40)),X41) = hAPP(X1,X1,plus_plus(X1,X31),hAPP(X1,X1,plus_plus(X1,X40),X41)) ),
c_0_366 ).
fof(c_0_1022,axiom,
! [X16] : hAPP(int,int,plus_plus(int,hAPP(int,int,plus_plus(int,one_one(int)),X16)),X16) != zero_zero(int),
c_0_367 ).
fof(c_0_1023,axiom,
! [X14,X15,X20] : hAPP(nat,nat,plus_plus(nat,hAPP(nat,nat,plus_plus(nat,X14),X15)),X20) = hAPP(nat,nat,plus_plus(nat,X14),hAPP(nat,nat,plus_plus(nat,X15),X20)),
c_0_368 ).
fof(c_0_1024,axiom,
! [X25,X26,X27] : hAPP(int,int,plus_plus(int,hAPP(int,int,plus_plus(int,X25),X26)),X27) = hAPP(int,int,plus_plus(int,X25),hAPP(int,int,plus_plus(int,X26),X27)),
c_0_369 ).
fof(c_0_1025,axiom,
! [X1,X10,X11] : hAPP(X1,X1,hAPP(X1,fun(X1,X1),hAPP(bool,fun(X1,fun(X1,X1)),if(X1),fFalse),X10),X11) = ti(X1,X11),
c_0_370 ).
fof(c_0_1026,axiom,
! [X1,X10,X11] : hAPP(X1,X1,hAPP(X1,fun(X1,X1),hAPP(bool,fun(X1,fun(X1,X1)),if(X1),fTrue),X10),X11) = ti(X1,X10),
c_0_371 ).
fof(c_0_1027,axiom,
! [X1] :
( semiring_1(X1)
=> ! [X14,X15] : hAPP(nat,X1,semiring_1_of_nat(X1),hAPP(nat,nat,power_power(nat,X14),X15)) = hAPP(nat,X1,power_power(X1,hAPP(nat,X1,semiring_1_of_nat(X1),X14)),X15) ),
c_0_372 ).
fof(c_0_1028,axiom,
! [X1] :
( number_ring(X1)
=> ! [X8] : number_number_of(X1,hAPP(int,int,bit1,X8)) = hAPP(X1,X1,plus_plus(X1,hAPP(X1,X1,plus_plus(X1,one_one(X1)),number_number_of(X1,X8))),number_number_of(X1,X8)) ),
c_0_373 ).
fof(c_0_1029,axiom,
! [X1] :
( number_ring(X1)
=> ! [X8] : number_number_of(X1,hAPP(int,int,bit0,X8)) = hAPP(X1,X1,plus_plus(X1,hAPP(X1,X1,plus_plus(X1,zero_zero(X1)),number_number_of(X1,X8))),number_number_of(X1,X8)) ),
c_0_374 ).
fof(c_0_1030,axiom,
! [X10,X15] : hAPP(nat,int,power_power(int,hAPP(nat,int,semiring_1_of_nat(int),X10)),X15) = hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,power_power(nat,X10),X15)),
c_0_375 ).
fof(c_0_1031,axiom,
! [X14,X15] : hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,power_power(nat,X14),X15)) = hAPP(nat,int,power_power(int,hAPP(nat,int,semiring_1_of_nat(int),X14)),X15),
c_0_376 ).
fof(c_0_1032,axiom,
! [X14,X15] : hAPP(nat,int,power_power(int,hAPP(nat,int,semiring_1_of_nat(int),X14)),X15) = hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,power_power(nat,X14),X15)),
c_0_377 ).
fof(c_0_1033,axiom,
! [X1] :
( number_ring(X1)
=> ! [X9] : hAPP(X1,X1,plus_plus(X1,number_number_of(X1,X9)),one_one(X1)) = number_number_of(X1,hAPP(int,int,plus_plus(int,X9),hAPP(int,int,bit1,pls))) ),
c_0_378 ).
fof(c_0_1034,axiom,
! [X1] :
( number_semiring(X1)
=> hAPP(X1,X1,plus_plus(X1,one_one(X1)),one_one(X1)) = number_number_of(X1,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))) ),
c_0_379 ).
fof(c_0_1035,axiom,
! [X1] :
( number_ring(X1)
=> hAPP(X1,X1,plus_plus(X1,one_one(X1)),one_one(X1)) = number_number_of(X1,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))) ),
c_0_380 ).
fof(c_0_1036,axiom,
hAPP(nat,nat,plus_plus(nat,one_one(nat)),one_one(nat)) = number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))),
c_0_381 ).
fof(c_0_1037,axiom,
! [X1] :
( comm_semiring_1(X1)
=> ! [X31,X41,X45] : hAPP(X1,X1,plus_plus(X1,X31),hAPP(X1,X1,plus_plus(X1,X41),X45)) = hAPP(X1,X1,plus_plus(X1,X41),hAPP(X1,X1,plus_plus(X1,X31),X45)) ),
c_0_382 ).
fof(c_0_1038,axiom,
! [X1] :
( linordered_semidom(X1)
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),one_one(X1))) ),
c_0_383 ).
fof(c_0_1039,axiom,
! [X1] :
( linordered_semidom(X1)
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),one_one(X1))) ),
c_0_384 ).
fof(c_0_1040,axiom,
hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),number_number_of(int,pls))),
c_0_385 ).
fof(c_0_1041,axiom,
! [X1] :
( preorder(X1)
=> ! [X10,X11] :
( X10 = X11
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X10),X11)) ) ),
c_0_386 ).
fof(c_0_1042,axiom,
! [X1] :
( preorder(X1)
=> ! [X10] : hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X10),X10)) ),
c_0_387 ).
fof(c_0_1043,axiom,
! [X10,X11,X16] : hAPP(nat,nat,plus_plus(nat,X10),hAPP(nat,nat,plus_plus(nat,X11),X16)) = hAPP(nat,nat,plus_plus(nat,X11),hAPP(nat,nat,plus_plus(nat,X10),X16)),
c_0_388 ).
fof(c_0_1044,axiom,
! [X20] : hAPP(int,int,bit1,X20) = hAPP(int,int,plus_plus(int,hAPP(int,int,plus_plus(int,one_one(int)),X20)),X20),
c_0_389 ).
fof(c_0_1045,axiom,
! [X10,X11,X16] : hAPP(int,int,plus_plus(int,X10),hAPP(int,int,plus_plus(int,X11),X16)) = hAPP(int,int,plus_plus(int,X11),hAPP(int,int,plus_plus(int,X10),X16)),
c_0_390 ).
fof(c_0_1046,axiom,
hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),one_one(int))),
c_0_391 ).
fof(c_0_1047,axiom,
hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),zero_zero(int))),
c_0_392 ).
fof(c_0_1048,axiom,
hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),one_one(int))),
c_0_393 ).
fof(c_0_1049,axiom,
! [X15] :
( X15 != zero_zero(nat)
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X15)) ),
c_0_394 ).
fof(c_0_1050,axiom,
! [X15] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),zero_zero(nat)),X15)),
c_0_395 ).
fof(c_0_1051,axiom,
! [X15] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),zero_zero(nat)),X15)),
c_0_396 ).
fof(c_0_1052,axiom,
hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),one_one(int)),t)),
c_0_397 ).
fof(c_0_1053,axiom,
hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),tn)),
c_0_398 ).
fof(c_0_1054,axiom,
hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),n)),
c_0_399 ).
fof(c_0_1055,axiom,
hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),t)),
c_0_400 ).
fof(c_0_1056,axiom,
! [X14,X15] :
( X14 = X15
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X14),X15)) ),
c_0_401 ).
fof(c_0_1057,axiom,
! [X8] : hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X8),X8)),
c_0_402 ).
fof(c_0_1058,axiom,
! [X15] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X15),X15)),
c_0_403 ).
fof(c_0_1059,axiom,
! [X8] : hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X8),X8)),
c_0_404 ).
fof(c_0_1060,axiom,
hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),pls)),
c_0_405 ).
fof(c_0_1061,axiom,
! [X20] : hAPP(int,int,succ,hAPP(int,int,bit1,X20)) = hAPP(int,int,bit0,hAPP(int,int,succ,X20)),
c_0_406 ).
fof(c_0_1062,axiom,
! [X1,X2,X4] : ti(fun(X1,fun(X1,X1)),hAPP(bool,fun(X1,fun(X1,X1)),X2,X4)) = hAPP(bool,fun(X1,fun(X1,X1)),X2,X4),
c_0_407 ).
fof(c_0_1063,axiom,
! [X1,X2,X4] : hAPP(bool,fun(X1,fun(X1,X1)),ti(fun(bool,fun(X1,fun(X1,X1))),X2),X4) = hAPP(bool,fun(X1,fun(X1,X1)),X2,X4),
c_0_408 ).
fof(c_0_1064,axiom,
! [X20] : hAPP(int,int,succ,hAPP(int,int,bit0,X20)) = hAPP(int,int,bit1,X20),
c_0_409 ).
fof(c_0_1065,axiom,
! [X1] :
( number_ring(X1)
=> ! [X9,X8] : number_number_of(X1,hAPP(int,int,plus_plus(int,X9),X8)) = hAPP(X1,X1,plus_plus(X1,number_number_of(X1,X9)),number_number_of(X1,X8)) ),
c_0_410 ).
fof(c_0_1066,axiom,
! [X1] :
( number_ring(X1)
=> ! [X9,X8] : hAPP(X1,X1,plus_plus(X1,number_number_of(X1,X9)),number_number_of(X1,X8)) = number_number_of(X1,hAPP(int,int,plus_plus(int,X9),X8)) ),
c_0_411 ).
fof(c_0_1067,axiom,
! [X1] :
( cancel_semigroup_add(X1)
=> ! [X7,X42,X46] :
( hAPP(X1,X1,plus_plus(X1,X7),X42) = hAPP(X1,X1,plus_plus(X1,X7),X46)
<=> ti(X1,X42) = ti(X1,X46) ) ),
c_0_412 ).
fof(c_0_1068,axiom,
! [X1] :
( cancel_semigroup_add(X1)
=> ! [X42,X7,X46] :
( hAPP(X1,X1,plus_plus(X1,X42),X7) = hAPP(X1,X1,plus_plus(X1,X46),X7)
<=> ti(X1,X42) = ti(X1,X46) ) ),
c_0_413 ).
fof(c_0_1069,axiom,
! [X1] :
( cancel_semigroup_add(X1)
=> ! [X31,X40,X41] :
( hAPP(X1,X1,plus_plus(X1,X31),X40) = hAPP(X1,X1,plus_plus(X1,X31),X41)
=> ti(X1,X40) = ti(X1,X41) ) ),
c_0_414 ).
fof(c_0_1070,axiom,
! [X1] :
( cancel146912293up_add(X1)
=> ! [X31,X40,X41] :
( hAPP(X1,X1,plus_plus(X1,X31),X40) = hAPP(X1,X1,plus_plus(X1,X31),X41)
=> ti(X1,X40) = ti(X1,X41) ) ),
c_0_415 ).
fof(c_0_1071,axiom,
! [X1] :
( cancel_semigroup_add(X1)
=> ! [X40,X31,X41] :
( hAPP(X1,X1,plus_plus(X1,X40),X31) = hAPP(X1,X1,plus_plus(X1,X41),X31)
=> ti(X1,X40) = ti(X1,X41) ) ),
c_0_416 ).
fof(c_0_1072,axiom,
! [X9,X8] : hAPP(int,int,plus_plus(int,number_number_of(int,X9)),number_number_of(int,X8)) = number_number_of(int,hAPP(int,int,plus_plus(int,X9),X8)),
c_0_417 ).
fof(c_0_1073,axiom,
! [X1,X2,X4] : ti(fun(X1,X1),hAPP(X1,fun(X1,X1),X2,X4)) = hAPP(X1,fun(X1,X1),X2,X4),
c_0_418 ).
fof(c_0_1074,axiom,
! [X28,X12,X17] :
( hAPP(nat,nat,plus_plus(nat,X28),X12) = hAPP(nat,nat,plus_plus(nat,X17),X12)
<=> X28 = X17 ),
c_0_419 ).
fof(c_0_1075,axiom,
! [X12,X28,X17] :
( hAPP(nat,nat,plus_plus(nat,X12),X28) = hAPP(nat,nat,plus_plus(nat,X12),X17)
<=> X28 = X17 ),
c_0_420 ).
fof(c_0_1076,axiom,
! [X1] :
( number_ring(X1)
=> ! [X20] : number_number_of(X1,hAPP(int,int,succ,X20)) = hAPP(X1,X1,plus_plus(X1,one_one(X1)),number_number_of(X1,X20)) ),
c_0_421 ).
fof(c_0_1077,axiom,
! [X1] :
( semiring_char_0(X1)
=> ! [X28,X17] :
( hAPP(nat,X1,semiring_1_of_nat(X1),X28) = hAPP(nat,X1,semiring_1_of_nat(X1),X17)
<=> X28 = X17 ) ),
c_0_422 ).
fof(c_0_1078,axiom,
! [X5,X6] :
( hAPP(nat,int,semiring_1_of_nat(int),X5) = hAPP(nat,int,semiring_1_of_nat(int),X6)
<=> X5 = X6 ),
c_0_423 ).
fof(c_0_1079,axiom,
! [X28,X17] :
( hAPP(nat,int,semiring_1_of_nat(int),X28) = hAPP(nat,int,semiring_1_of_nat(int),X17)
<=> X28 = X17 ),
c_0_424 ).
fof(c_0_1080,axiom,
! [X1] :
( number_semiring(X1)
=> ! [X15] : number_number_of(X1,hAPP(nat,int,semiring_1_of_nat(int),X15)) = hAPP(nat,X1,semiring_1_of_nat(X1),X15) ),
c_0_425 ).
fof(c_0_1081,axiom,
! [X12,X13] :
( hAPP(int,int,bit0,X12) = hAPP(int,int,bit0,X13)
<=> X12 = X13 ),
c_0_426 ).
fof(c_0_1082,axiom,
! [X12,X13] :
( hAPP(int,int,bit1,X12) = hAPP(int,int,bit1,X13)
<=> X12 = X13 ),
c_0_427 ).
fof(c_0_1083,axiom,
! [X20,X30] : hAPP(int,int,bit0,X20) != hAPP(int,int,bit1,X30),
c_0_428 ).
fof(c_0_1084,axiom,
! [X20,X30] : hAPP(int,int,bit1,X20) != hAPP(int,int,bit0,X30),
c_0_429 ).
fof(c_0_1085,axiom,
! [X1,X2,X4,X3] :
( ord(X3)
=> ti(X3,hAPP(X1,X3,X2,X4)) = hAPP(X1,X3,X2,X4) ),
c_0_430 ).
fof(c_0_1086,axiom,
! [X2,X4,X1] :
( power(X1)
=> ti(X1,hAPP(nat,X1,X2,X4)) = hAPP(nat,X1,X2,X4) ),
c_0_431 ).
fof(c_0_1087,axiom,
! [X1,X2,X4] : ti(X1,hAPP(X1,X1,X2,X4)) = hAPP(X1,X1,X2,X4),
c_0_432 ).
fof(c_0_1088,axiom,
! [X1,X2,X4] : hAPP(X1,fun(X1,X1),ti(fun(X1,fun(X1,X1)),X2),X4) = hAPP(X1,fun(X1,X1),X2,X4),
c_0_433 ).
fof(c_0_1089,axiom,
! [X1,X2,X4] : hAPP(bool,fun(X1,fun(X1,X1)),X2,ti(bool,X4)) = hAPP(bool,fun(X1,fun(X1,X1)),X2,X4),
c_0_434 ).
fof(c_0_1090,axiom,
! [X1,X2,X4,X3] :
( ord(X3)
=> hAPP(X1,X3,ti(fun(X1,X3),X2),X4) = hAPP(X1,X3,X2,X4) ),
c_0_435 ).
fof(c_0_1091,axiom,
! [X1,X2,X4] : hAPP(X1,X1,ti(fun(X1,X1),X2),X4) = hAPP(X1,X1,X2,X4),
c_0_436 ).
fof(c_0_1092,axiom,
! [X1,X2,X4] : hAPP(X1,fun(X1,X1),X2,ti(X1,X4)) = hAPP(X1,fun(X1,X1),X2,X4),
c_0_437 ).
fof(c_0_1093,axiom,
! [X2,X4,X1] :
( power(X1)
=> hAPP(nat,X1,ti(fun(nat,X1),X2),X4) = hAPP(nat,X1,X2,X4) ),
c_0_438 ).
fof(c_0_1094,axiom,
! [X1] :
( comm_semiring_1(X1)
=> ! [X31,X41] : hAPP(X1,X1,plus_plus(X1,X31),X41) = hAPP(X1,X1,plus_plus(X1,X41),X31) ),
c_0_439 ).
fof(c_0_1095,axiom,
! [X14,X15] : hAPP(nat,nat,plus_plus(nat,X14),X15) = hAPP(nat,nat,plus_plus(nat,X15),X14),
c_0_440 ).
fof(c_0_1096,axiom,
! [X16,X8] : hAPP(int,int,plus_plus(int,X16),X8) = hAPP(int,int,plus_plus(int,X8),X16),
c_0_441 ).
fof(c_0_1097,axiom,
! [X1,X2,X4,X3] :
( ord(X3)
=> hAPP(X1,X3,X2,ti(X1,X4)) = hAPP(X1,X3,X2,X4) ),
c_0_442 ).
fof(c_0_1098,axiom,
! [X1] :
( ( power(X1)
& mult_zero(X1)
& no_zero_divisors(X1)
& zero_neq_one(X1) )
=> ! [X7,X24] :
( hAPP(nat,X1,power_power(X1,X7),number_number_of(nat,X24)) = zero_zero(X1)
<=> ( ti(X1,X7) = zero_zero(X1)
& number_number_of(nat,X24) != zero_zero(nat) ) ) ),
c_0_443 ).
fof(c_0_1099,axiom,
! [X2,X4,X1] :
( power(X1)
=> hAPP(nat,X1,X2,ti(nat,X4)) = hAPP(nat,X1,X2,X4) ),
c_0_444 ).
fof(c_0_1100,axiom,
! [X1,X2,X4] : hAPP(X1,X1,X2,ti(X1,X4)) = hAPP(X1,X1,X2,X4),
c_0_445 ).
fof(c_0_1101,axiom,
! [X20] : hAPP(int,int,succ,X20) = hAPP(int,int,plus_plus(int,X20),one_one(int)),
c_0_446 ).
fof(c_0_1102,axiom,
! [X20] : hAPP(int,int,bit0,X20) = hAPP(int,int,plus_plus(int,X20),X20),
c_0_447 ).
fof(c_0_1103,axiom,
! [X1] :
( number_semiring(X1)
=> number_number_of(X1,hAPP(int,int,bit1,pls)) = one_one(X1) ),
c_0_448 ).
fof(c_0_1104,axiom,
! [X1] :
( number_ring(X1)
=> number_number_of(X1,hAPP(int,int,bit1,pls)) = one_one(X1) ),
c_0_449 ).
fof(c_0_1105,axiom,
! [X1] :
( number_ring(X1)
=> one_one(X1) = number_number_of(X1,hAPP(int,int,bit1,pls)) ),
c_0_450 ).
fof(c_0_1106,axiom,
one_one(nat) = number_number_of(nat,hAPP(int,int,bit1,pls)),
c_0_451 ).
fof(c_0_1107,axiom,
number_number_of(nat,hAPP(int,int,bit1,pls)) = one_one(nat),
c_0_452 ).
fof(c_0_1108,axiom,
one_one(int) = number_number_of(int,hAPP(int,int,bit1,pls)),
c_0_453 ).
fof(c_0_1109,axiom,
hAPP(int,int,succ,pls) = hAPP(int,int,bit1,pls),
c_0_454 ).
fof(c_0_1110,axiom,
! [X1] :
( ( power(X1)
& mult_zero(X1)
& no_zero_divisors(X1)
& zero_neq_one(X1) )
=> ! [X7,X17] :
( hAPP(nat,X1,power_power(X1,X7),X17) = zero_zero(X1)
<=> ( ti(X1,X7) = zero_zero(X1)
& X17 != zero_zero(nat) ) ) ),
c_0_455 ).
fof(c_0_1111,axiom,
! [X1] :
( semiri456707255roduct(X1)
=> ! [X42,X7] :
( ti(X1,X42) = hAPP(X1,X1,plus_plus(X1,X42),X7)
<=> ti(X1,X7) = zero_zero(X1) ) ),
c_0_456 ).
fof(c_0_1112,axiom,
! [X1] :
( linord219039673up_add(X1)
=> ! [X7] :
( zero_zero(X1) = hAPP(X1,X1,plus_plus(X1,X7),X7)
<=> ti(X1,X7) = zero_zero(X1) ) ),
c_0_457 ).
fof(c_0_1113,axiom,
! [X1] :
( linord219039673up_add(X1)
=> ! [X7] :
( hAPP(X1,X1,plus_plus(X1,X7),X7) = zero_zero(X1)
<=> ti(X1,X7) = zero_zero(X1) ) ),
c_0_458 ).
fof(c_0_1114,axiom,
! [X1] :
( ring_11004092258visors(X1)
=> ! [X15,X31] :
( ti(X1,X31) != zero_zero(X1)
=> hAPP(nat,X1,power_power(X1,X31),X15) != zero_zero(X1) ) ),
c_0_459 ).
fof(c_0_1115,axiom,
! [X5,X17] :
( hAPP(nat,nat,power_power(nat,X5),X17) = one_one(nat)
<=> ( X5 = one_one(nat)
| X17 = zero_zero(nat) ) ),
c_0_460 ).
fof(c_0_1116,axiom,
! [X28,X17] :
( hAPP(nat,nat,power_power(nat,X28),X17) = zero_zero(nat)
<=> ( X17 != zero_zero(nat)
& X28 = zero_zero(nat) ) ),
c_0_461 ).
fof(c_0_1117,axiom,
! [X28,X17] :
( hAPP(nat,nat,plus_plus(nat,X28),X17) = zero_zero(nat)
<=> ( X28 = zero_zero(nat)
& X17 = zero_zero(nat) ) ),
c_0_462 ).
fof(c_0_1118,axiom,
! [X14,X15] :
( hAPP(nat,nat,plus_plus(nat,X14),X15) = X14
=> X15 = zero_zero(nat) ),
c_0_463 ).
fof(c_0_1119,axiom,
! [X17] :
( hAPP(nat,int,semiring_1_of_nat(int),X17) = zero_zero(int)
<=> X17 = zero_zero(nat) ),
c_0_464 ).
fof(c_0_1120,axiom,
! [X13] :
( pls = hAPP(int,int,bit0,X13)
<=> pls = X13 ),
c_0_465 ).
fof(c_0_1121,axiom,
! [X12] :
( hAPP(int,int,bit0,X12) = pls
<=> X12 = pls ),
c_0_466 ).
fof(c_0_1122,axiom,
! [X30] : pls != hAPP(int,int,bit1,X30),
c_0_467 ).
fof(c_0_1123,axiom,
! [X20] : hAPP(int,int,bit1,X20) != pls,
c_0_468 ).
fof(c_0_1124,axiom,
! [X1] :
( ( power(X1)
& semiring_0(X1) )
=> ! [X8] :
( ( number_number_of(nat,X8) = zero_zero(nat)
=> hAPP(nat,X1,power_power(X1,zero_zero(X1)),number_number_of(nat,X8)) = one_one(X1) )
& ( number_number_of(nat,X8) != zero_zero(nat)
=> hAPP(nat,X1,power_power(X1,zero_zero(X1)),number_number_of(nat,X8)) = zero_zero(X1) ) ) ),
c_0_469 ).
fof(c_0_1125,axiom,
! [X1] :
( number_ring(X1)
=> ! [X31] : hAPP(X1,X1,plus_plus(X1,number_number_of(X1,pls)),X31) = ti(X1,X31) ),
c_0_470 ).
fof(c_0_1126,axiom,
! [X1] :
( number_ring(X1)
=> ! [X31] : hAPP(X1,X1,plus_plus(X1,X31),number_number_of(X1,pls)) = ti(X1,X31) ),
c_0_471 ).
fof(c_0_1127,axiom,
! [X1] :
( ( power(X1)
& semiring_0(X1) )
=> ! [X15] :
( ( X15 = zero_zero(nat)
=> hAPP(nat,X1,power_power(X1,zero_zero(X1)),X15) = one_one(X1) )
& ( X15 != zero_zero(nat)
=> hAPP(nat,X1,power_power(X1,zero_zero(X1)),X15) = zero_zero(X1) ) ) ),
c_0_472 ).
fof(c_0_1128,axiom,
! [X1] :
( monoid_add(X1)
=> ! [X31] : hAPP(X1,X1,plus_plus(X1,zero_zero(X1)),X31) = ti(X1,X31) ),
c_0_473 ).
fof(c_0_1129,axiom,
! [X1] :
( comm_semiring_1(X1)
=> ! [X31] : hAPP(X1,X1,plus_plus(X1,zero_zero(X1)),X31) = ti(X1,X31) ),
c_0_474 ).
fof(c_0_1130,axiom,
! [X1] :
( comm_monoid_add(X1)
=> ! [X31] : hAPP(X1,X1,plus_plus(X1,zero_zero(X1)),X31) = ti(X1,X31) ),
c_0_475 ).
fof(c_0_1131,axiom,
! [X1] :
( monoid_add(X1)
=> ! [X31] : hAPP(X1,X1,plus_plus(X1,X31),zero_zero(X1)) = ti(X1,X31) ),
c_0_476 ).
fof(c_0_1132,axiom,
! [X1] :
( comm_semiring_1(X1)
=> ! [X31] : hAPP(X1,X1,plus_plus(X1,X31),zero_zero(X1)) = ti(X1,X31) ),
c_0_477 ).
fof(c_0_1133,axiom,
! [X1] :
( comm_monoid_add(X1)
=> ! [X31] : hAPP(X1,X1,plus_plus(X1,X31),zero_zero(X1)) = ti(X1,X31) ),
c_0_478 ).
fof(c_0_1134,axiom,
! [X1] :
( comm_semiring_1(X1)
=> ! [X10] : hAPP(nat,X1,power_power(X1,X10),one_one(nat)) = ti(X1,X10) ),
c_0_479 ).
fof(c_0_1135,axiom,
! [X1] :
( monoid_mult(X1)
=> ! [X31] : hAPP(nat,X1,power_power(X1,X31),one_one(nat)) = ti(X1,X31) ),
c_0_480 ).
fof(c_0_1136,axiom,
! [X1] :
( monoid_mult(X1)
=> ! [X15] : hAPP(nat,X1,power_power(X1,one_one(X1)),X15) = one_one(X1) ),
c_0_481 ).
fof(c_0_1137,axiom,
! [X1] :
( comm_semiring_1(X1)
=> ! [X10] : hAPP(nat,X1,power_power(X1,X10),zero_zero(nat)) = one_one(X1) ),
c_0_482 ).
fof(c_0_1138,axiom,
! [X1] :
( power(X1)
=> ! [X31] : hAPP(nat,X1,power_power(X1,X31),zero_zero(nat)) = one_one(X1) ),
c_0_483 ).
fof(c_0_1139,axiom,
! [X15] : hAPP(nat,nat,plus_plus(nat,zero_zero(nat)),X15) = X15,
c_0_484 ).
fof(c_0_1140,axiom,
! [X16] : hAPP(int,int,plus_plus(int,zero_zero(int)),X16) = X16,
c_0_485 ).
fof(c_0_1141,axiom,
! [X14] : hAPP(nat,nat,plus_plus(nat,X14),zero_zero(nat)) = X14,
c_0_486 ).
fof(c_0_1142,axiom,
! [X16] : hAPP(int,int,plus_plus(int,X16),zero_zero(int)) = X16,
c_0_487 ).
fof(c_0_1143,axiom,
! [X20] : hAPP(int,int,plus_plus(int,X20),pls) = X20,
c_0_488 ).
fof(c_0_1144,axiom,
! [X1] :
( semiring_1(X1)
=> hAPP(nat,X1,semiring_1_of_nat(X1),zero_zero(nat)) = zero_zero(X1) ),
c_0_489 ).
fof(c_0_1145,axiom,
! [X1] :
( semiring_1(X1)
=> hAPP(nat,X1,semiring_1_of_nat(X1),one_one(nat)) = one_one(X1) ),
c_0_490 ).
fof(c_0_1146,axiom,
! [X20] : hAPP(int,int,plus_plus(int,pls),X20) = X20,
c_0_491 ).
fof(c_0_1147,axiom,
zero_zero(int) = hAPP(nat,int,semiring_1_of_nat(int),zero_zero(nat)),
c_0_492 ).
fof(c_0_1148,axiom,
one_one(int) = hAPP(nat,int,semiring_1_of_nat(int),one_one(nat)),
c_0_493 ).
fof(c_0_1149,axiom,
hAPP(nat,int,semiring_1_of_nat(int),zero_zero(nat)) = zero_zero(int),
c_0_494 ).
fof(c_0_1150,axiom,
hAPP(nat,int,semiring_1_of_nat(int),one_one(nat)) = one_one(int),
c_0_495 ).
fof(c_0_1151,axiom,
hAPP(int,int,bit0,pls) = pls,
c_0_496 ).
fof(c_0_1152,axiom,
! [X1] : ti(fun(bool,fun(X1,fun(X1,X1))),if(X1)) = if(X1),
c_0_497 ).
fof(c_0_1153,axiom,
! [X1] :
( linordered_semiring(X1)
=> ti(fun(X1,fun(X1,X1)),times_times(X1)) = times_times(X1) ),
c_0_498 ).
fof(c_0_1154,axiom,
! [X3] :
( ord(X3)
=> ti(fun(X3,fun(X3,bool)),ord_less_eq(X3)) = ord_less_eq(X3) ),
c_0_499 ).
fof(c_0_1155,axiom,
! [X1] :
( ord(X1)
=> ti(fun(X1,fun(X1,bool)),ord_less(X1)) = ord_less(X1) ),
c_0_500 ).
fof(c_0_1156,axiom,
! [X2,X1] :
( cancel_semigroup_add(X1)
=> ti(fun(X1,X1),plus_plus(X1,X2)) = plus_plus(X1,X2) ),
c_0_501 ).
fof(c_0_1157,axiom,
! [X2,X1] :
( ab_semigroup_add(X1)
=> ti(fun(X1,X1),plus_plus(X1,X2)) = plus_plus(X1,X2) ),
c_0_502 ).
fof(c_0_1158,axiom,
! [X2,X1] :
( monoid_add(X1)
=> ti(fun(X1,X1),plus_plus(X1,X2)) = plus_plus(X1,X2) ),
c_0_503 ).
fof(c_0_1159,axiom,
! [X2,X1] :
( power(X1)
=> ti(fun(nat,X1),power_power(X1,X2)) = power_power(X1,X2) ),
c_0_504 ).
fof(c_0_1160,axiom,
! [X1] :
( number(X1)
=> ! [X24,X5] :
( number_number_of(X1,X24) = ti(X1,X5)
<=> ti(X1,X5) = number_number_of(X1,X24) ) ),
c_0_505 ).
fof(c_0_1161,axiom,
! [X2,X1] :
( power(X1)
=> power_power(X1,ti(X1,X2)) = power_power(X1,X2) ),
c_0_506 ).
fof(c_0_1162,axiom,
! [X2,X1] :
( number(X1)
=> ti(X1,number_number_of(X1,X2)) = number_number_of(X1,X2) ),
c_0_507 ).
fof(c_0_1163,axiom,
! [X2,X1] :
( cancel_semigroup_add(X1)
=> plus_plus(X1,ti(X1,X2)) = plus_plus(X1,X2) ),
c_0_508 ).
fof(c_0_1164,axiom,
! [X2,X1] :
( ab_semigroup_add(X1)
=> plus_plus(X1,ti(X1,X2)) = plus_plus(X1,X2) ),
c_0_509 ).
fof(c_0_1165,axiom,
! [X2,X1] :
( monoid_add(X1)
=> plus_plus(X1,ti(X1,X2)) = plus_plus(X1,X2) ),
c_0_510 ).
fof(c_0_1166,axiom,
! [X1] :
( ( number_ring(X1)
& ring_char_0(X1) )
=> ! [X5,X6] :
( number_number_of(X1,X5) = number_number_of(X1,X6)
<=> X5 = X6 ) ),
c_0_511 ).
fof(c_0_1167,axiom,
! [X2,X1] :
( number(X1)
=> number_number_of(X1,ti(int,X2)) = number_number_of(X1,X2) ),
c_0_512 ).
fof(c_0_1168,axiom,
! [X1] :
( semiring_1(X1)
=> ti(fun(nat,X1),semiring_1_of_nat(X1)) = semiring_1_of_nat(X1) ),
c_0_513 ).
fof(c_0_1169,axiom,
! [X1] :
( one(X1)
=> ! [X5] :
( one_one(X1) = ti(X1,X5)
<=> ti(X1,X5) = one_one(X1) ) ),
c_0_514 ).
fof(c_0_1170,axiom,
! [X1] :
( zero(X1)
=> ! [X5] :
( zero_zero(X1) = ti(X1,X5)
<=> ti(X1,X5) = zero_zero(X1) ) ),
c_0_515 ).
fof(c_0_1171,axiom,
! [X65,X66] : ti(X65,ti(X65,X66)) = ti(X65,X66),
c_0_516 ).
fof(c_0_1172,axiom,
! [X2] :
( hBOOL(ti(bool,X2))
<=> hBOOL(X2) ),
c_0_517 ).
fof(c_0_1173,axiom,
! [X63,X64] :
( ord(X64)
=> ord(fun(X63,X64)) ),
c_0_518 ).
fof(c_0_1174,axiom,
! [X63,X64] :
( order(X64)
=> order(fun(X63,X64)) ),
c_0_519 ).
fof(c_0_1175,axiom,
! [X63,X64] :
( preorder(X64)
=> preorder(fun(X63,X64)) ),
c_0_520 ).
fof(c_0_1176,axiom,
ti(fun(real,real),sqrt) = sqrt,
c_0_521 ).
fof(c_0_1177,axiom,
ti(fun(int,int),succ) = succ,
c_0_522 ).
fof(c_0_1178,axiom,
! [X1] :
( zero(X1)
=> ti(X1,zero_zero(X1)) = zero_zero(X1) ),
c_0_523 ).
fof(c_0_1179,axiom,
! [X1] :
( one(X1)
=> ti(X1,one_one(X1)) = one_one(X1) ),
c_0_524 ).
fof(c_0_1180,axiom,
! [X67] :
( ti(bool,X67) = fTrue
| ti(bool,X67) = fFalse ),
c_0_525 ).
fof(c_0_1181,axiom,
! [X1] : ti(X1,undefined(X1)) = undefined(X1),
c_0_526 ).
fof(c_0_1182,axiom,
! [X1] :
( number_ring(X1)
=> zero_zero(X1) = number_number_of(X1,pls) ),
c_0_527 ).
fof(c_0_1183,axiom,
! [X1] :
( number_ring(X1)
=> number_number_of(X1,pls) = zero_zero(X1) ),
c_0_528 ).
fof(c_0_1184,axiom,
! [X1] :
( number_semiring(X1)
=> number_number_of(X1,pls) = zero_zero(X1) ),
c_0_529 ).
fof(c_0_1185,axiom,
! [X1] :
( zero_neq_one(X1)
=> zero_zero(X1) != one_one(X1) ),
c_0_530 ).
fof(c_0_1186,axiom,
! [X1] :
( zero_neq_one(X1)
=> one_one(X1) != zero_zero(X1) ),
c_0_531 ).
fof(c_0_1187,axiom,
! [X20] : number_number_of(int,X20) = X20,
c_0_532 ).
fof(c_0_1188,axiom,
zero_zero(nat) = number_number_of(nat,pls),
c_0_533 ).
fof(c_0_1189,axiom,
number_number_of(nat,pls) = zero_zero(nat),
c_0_534 ).
fof(c_0_1190,axiom,
zero_zero(int) = number_number_of(int,pls),
c_0_535 ).
fof(c_0_1191,axiom,
ti(nat,tn) = tn,
c_0_536 ).
fof(c_0_1192,axiom,
ti(int,t) = t,
c_0_537 ).
fof(c_0_1193,axiom,
ti(int,m1) = m1,
c_0_538 ).
fof(c_0_1194,axiom,
ti(bool,fTrue) = fTrue,
c_0_539 ).
fof(c_0_1195,axiom,
ti(bool,fFalse) = fFalse,
c_0_540 ).
fof(c_0_1196,axiom,
zero_zero(real) != one_one(real),
c_0_541 ).
fof(c_0_1197,axiom,
zero_zero(int) != one_one(int),
c_0_542 ).
fof(c_0_1198,axiom,
one(real),
c_0_543 ).
fof(c_0_1199,axiom,
number(real),
c_0_544 ).
fof(c_0_1200,axiom,
zero(real),
c_0_545 ).
fof(c_0_1201,axiom,
power(real),
c_0_546 ).
fof(c_0_1202,axiom,
ord(real),
c_0_547 ).
fof(c_0_1203,axiom,
number_ring(real),
c_0_548 ).
fof(c_0_1204,axiom,
ring_char_0(real),
c_0_549 ).
fof(c_0_1205,axiom,
order(real),
c_0_550 ).
fof(c_0_1206,axiom,
mult_zero(real),
c_0_551 ).
fof(c_0_1207,axiom,
semiring_0(real),
c_0_552 ).
fof(c_0_1208,axiom,
semiring_1(real),
c_0_553 ).
fof(c_0_1209,axiom,
monoid_add(real),
c_0_554 ).
fof(c_0_1210,axiom,
monoid_mult(real),
c_0_555 ).
fof(c_0_1211,axiom,
linorder(real),
c_0_556 ).
fof(c_0_1212,axiom,
preorder(real),
c_0_557 ).
fof(c_0_1213,axiom,
zero_neq_one(real),
c_0_558 ).
fof(c_0_1214,axiom,
number_semiring(real),
c_0_559 ).
fof(c_0_1215,axiom,
semiring_char_0(real),
c_0_560 ).
fof(c_0_1216,axiom,
comm_semiring_1(real),
c_0_561 ).
fof(c_0_1217,axiom,
linordered_idom(real),
c_0_562 ).
fof(c_0_1218,axiom,
linordered_ring(real),
c_0_563 ).
fof(c_0_1219,axiom,
comm_monoid_add(real),
c_0_564 ).
fof(c_0_1220,axiom,
no_zero_divisors(real),
c_0_565 ).
fof(c_0_1221,axiom,
ab_semigroup_add(real),
c_0_566 ).
fof(c_0_1222,axiom,
dense_linorder(real),
c_0_567 ).
fof(c_0_1223,axiom,
linordered_semidom(real),
c_0_568 ).
fof(c_0_1224,axiom,
linordered_semiring(real),
c_0_569 ).
fof(c_0_1225,axiom,
cancel_semigroup_add(real),
c_0_570 ).
fof(c_0_1226,axiom,
linord581940658strict(real),
c_0_571 ).
fof(c_0_1227,axiom,
ring_11004092258visors(real),
c_0_572 ).
fof(c_0_1228,axiom,
cancel146912293up_add(real),
c_0_573 ).
fof(c_0_1229,axiom,
linord219039673up_add(real),
c_0_574 ).
fof(c_0_1230,axiom,
ordere216010020id_add(real),
c_0_575 ).
fof(c_0_1231,axiom,
ordere779506340up_add(real),
c_0_576 ).
fof(c_0_1232,axiom,
linord20386208strict(real),
c_0_577 ).
fof(c_0_1233,axiom,
linord893533164strict(real),
c_0_578 ).
fof(c_0_1234,axiom,
ordere236663937imp_le(real),
c_0_579 ).
fof(c_0_1235,axiom,
ordere223160158up_add(real),
c_0_580 ).
fof(c_0_1236,axiom,
semiri456707255roduct(real),
c_0_581 ).
fof(c_0_1237,axiom,
ord(bool),
c_0_582 ).
fof(c_0_1238,axiom,
order(bool),
c_0_583 ).
fof(c_0_1239,axiom,
preorder(bool),
c_0_584 ).
fof(c_0_1240,axiom,
one(nat),
c_0_585 ).
fof(c_0_1241,axiom,
number(nat),
c_0_586 ).
fof(c_0_1242,axiom,
zero(nat),
c_0_587 ).
fof(c_0_1243,axiom,
power(nat),
c_0_588 ).
fof(c_0_1244,axiom,
ord(nat),
c_0_589 ).
fof(c_0_1245,axiom,
order(nat),
c_0_590 ).
fof(c_0_1246,axiom,
mult_zero(nat),
c_0_591 ).
fof(c_0_1247,axiom,
semiring_0(nat),
c_0_592 ).
fof(c_0_1248,axiom,
semiring_1(nat),
c_0_593 ).
fof(c_0_1249,axiom,
monoid_add(nat),
c_0_594 ).
fof(c_0_1250,axiom,
monoid_mult(nat),
c_0_595 ).
fof(c_0_1251,axiom,
linorder(nat),
c_0_596 ).
fof(c_0_1252,axiom,
preorder(nat),
c_0_597 ).
fof(c_0_1253,axiom,
zero_neq_one(nat),
c_0_598 ).
fof(c_0_1254,axiom,
number_semiring(nat),
c_0_599 ).
fof(c_0_1255,axiom,
semiring_char_0(nat),
c_0_600 ).
fof(c_0_1256,axiom,
comm_semiring_1(nat),
c_0_601 ).
fof(c_0_1257,axiom,
comm_monoid_add(nat),
c_0_602 ).
fof(c_0_1258,axiom,
no_zero_divisors(nat),
c_0_603 ).
fof(c_0_1259,axiom,
ab_semigroup_add(nat),
c_0_604 ).
fof(c_0_1260,axiom,
linordered_semidom(nat),
c_0_605 ).
fof(c_0_1261,axiom,
linordered_semiring(nat),
c_0_606 ).
fof(c_0_1262,axiom,
cancel_semigroup_add(nat),
c_0_607 ).
fof(c_0_1263,axiom,
cancel146912293up_add(nat),
c_0_608 ).
fof(c_0_1264,axiom,
ordere216010020id_add(nat),
c_0_609 ).
fof(c_0_1265,axiom,
ordere779506340up_add(nat),
c_0_610 ).
fof(c_0_1266,axiom,
linord20386208strict(nat),
c_0_611 ).
fof(c_0_1267,axiom,
linord893533164strict(nat),
c_0_612 ).
fof(c_0_1268,axiom,
ordere236663937imp_le(nat),
c_0_613 ).
fof(c_0_1269,axiom,
ordere223160158up_add(nat),
c_0_614 ).
fof(c_0_1270,axiom,
semiri456707255roduct(nat),
c_0_615 ).
fof(c_0_1271,axiom,
one(int),
c_0_616 ).
fof(c_0_1272,axiom,
number(int),
c_0_617 ).
fof(c_0_1273,axiom,
zero(int),
c_0_618 ).
fof(c_0_1274,axiom,
power(int),
c_0_619 ).
fof(c_0_1275,axiom,
ord(int),
c_0_620 ).
fof(c_0_1276,axiom,
number_ring(int),
c_0_621 ).
fof(c_0_1277,axiom,
ring_char_0(int),
c_0_622 ).
fof(c_0_1278,axiom,
order(int),
c_0_623 ).
fof(c_0_1279,axiom,
mult_zero(int),
c_0_624 ).
fof(c_0_1280,axiom,
semiring_0(int),
c_0_625 ).
fof(c_0_1281,axiom,
semiring_1(int),
c_0_626 ).
fof(c_0_1282,axiom,
monoid_add(int),
c_0_627 ).
fof(c_0_1283,axiom,
monoid_mult(int),
c_0_628 ).
fof(c_0_1284,axiom,
linorder(int),
c_0_629 ).
fof(c_0_1285,axiom,
preorder(int),
c_0_630 ).
fof(c_0_1286,axiom,
zero_neq_one(int),
c_0_631 ).
fof(c_0_1287,axiom,
number_semiring(int),
c_0_632 ).
fof(c_0_1288,axiom,
semiring_char_0(int),
c_0_633 ).
fof(c_0_1289,axiom,
comm_semiring_1(int),
c_0_634 ).
fof(c_0_1290,axiom,
linordered_idom(int),
c_0_635 ).
fof(c_0_1291,axiom,
linordered_ring(int),
c_0_636 ).
fof(c_0_1292,axiom,
comm_monoid_add(int),
c_0_637 ).
fof(c_0_1293,axiom,
no_zero_divisors(int),
c_0_638 ).
fof(c_0_1294,axiom,
ab_semigroup_add(int),
c_0_639 ).
fof(c_0_1295,axiom,
linordered_semidom(int),
c_0_640 ).
fof(c_0_1296,axiom,
linordered_semiring(int),
c_0_641 ).
fof(c_0_1297,axiom,
cancel_semigroup_add(int),
c_0_642 ).
fof(c_0_1298,axiom,
linord581940658strict(int),
c_0_643 ).
fof(c_0_1299,axiom,
ring_11004092258visors(int),
c_0_644 ).
fof(c_0_1300,axiom,
cancel146912293up_add(int),
c_0_645 ).
fof(c_0_1301,axiom,
linord219039673up_add(int),
c_0_646 ).
fof(c_0_1302,axiom,
ordere216010020id_add(int),
c_0_647 ).
fof(c_0_1303,axiom,
ordere779506340up_add(int),
c_0_648 ).
fof(c_0_1304,axiom,
linord20386208strict(int),
c_0_649 ).
fof(c_0_1305,axiom,
linord893533164strict(int),
c_0_650 ).
fof(c_0_1306,axiom,
ordere236663937imp_le(int),
c_0_651 ).
fof(c_0_1307,axiom,
ordere223160158up_add(int),
c_0_652 ).
fof(c_0_1308,axiom,
semiri456707255roduct(int),
c_0_653 ).
fof(c_0_1309,axiom,
pls = zero_zero(int),
c_0_654 ).
fof(c_0_1310,plain,
! [X41,X42] : hAPP(nat,int,power_power(int,hAPP(int,int,plus_plus(int,X41),X42)),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) = hAPP(int,int,plus_plus(int,hAPP(int,int,plus_plus(int,hAPP(nat,int,power_power(int,X41),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),number_number_of(int,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),X41)),X42))),hAPP(nat,int,power_power(int,X42),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),
inference(variable_rename,[status(thm)],[c_0_655]) ).
fof(c_0_1311,plain,
! [X7,X8,X9,X10,X11] :
( ( ti(X7,X8) = zero_zero(X7)
| ~ hBOOL(hAPP(X7,bool,hAPP(X7,fun(X7,bool),ord_less_eq(X7),hAPP(X7,X7,plus_plus(X7,hAPP(nat,X7,power_power(X7,X8),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,X7,power_power(X7,X9),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),zero_zero(X7)))
| ~ linordered_idom(X7) )
& ( ti(X7,X9) = zero_zero(X7)
| ~ hBOOL(hAPP(X7,bool,hAPP(X7,fun(X7,bool),ord_less_eq(X7),hAPP(X7,X7,plus_plus(X7,hAPP(nat,X7,power_power(X7,X8),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,X7,power_power(X7,X9),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),zero_zero(X7)))
| ~ linordered_idom(X7) )
& ( ti(X7,X10) != zero_zero(X7)
| ti(X7,X11) != zero_zero(X7)
| hBOOL(hAPP(X7,bool,hAPP(X7,fun(X7,bool),ord_less_eq(X7),hAPP(X7,X7,plus_plus(X7,hAPP(nat,X7,power_power(X7,X10),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,X7,power_power(X7,X11),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),zero_zero(X7)))
| ~ linordered_idom(X7) ) ),
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_656])])])])]) ).
fof(c_0_1312,plain,
! [X12,X13,X14] :
( ~ linordered_idom(X12)
| ~ hBOOL(hAPP(X12,bool,hAPP(X12,fun(X12,bool),ord_less(X12),hAPP(X12,X12,plus_plus(X12,hAPP(nat,X12,power_power(X12,X13),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,X12,power_power(X12,X14),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),zero_zero(X12))) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_657])])]) ).
fof(c_0_1313,plain,
! [X55,X56,X57,X58,X59,X60] :
( ( hBOOL(hAPP(X55,bool,hAPP(X55,fun(X55,bool),ord_less_eq(X55),esk44_6(X55,X56,X57,X58,X59,X60)),esk43_6(X55,X56,X57,X58,X59,X60)))
| hBOOL(hAPP(X56,bool,hAPP(X56,fun(X56,bool),ord_less(X56),hAPP(X55,X56,X58,X57)),X60))
| ~ hBOOL(hAPP(X55,bool,hAPP(X55,fun(X55,bool),ord_less_eq(X55),X57),X59))
| ~ hBOOL(hAPP(X56,bool,hAPP(X56,fun(X56,bool),ord_less(X56),hAPP(X55,X56,X58,X59)),X60))
| ~ order(X56)
| ~ order(X55) )
& ( ~ hBOOL(hAPP(X56,bool,hAPP(X56,fun(X56,bool),ord_less_eq(X56),hAPP(X55,X56,X58,esk44_6(X55,X56,X57,X58,X59,X60))),hAPP(X55,X56,X58,esk43_6(X55,X56,X57,X58,X59,X60))))
| hBOOL(hAPP(X56,bool,hAPP(X56,fun(X56,bool),ord_less(X56),hAPP(X55,X56,X58,X57)),X60))
| ~ hBOOL(hAPP(X55,bool,hAPP(X55,fun(X55,bool),ord_less_eq(X55),X57),X59))
| ~ hBOOL(hAPP(X56,bool,hAPP(X56,fun(X56,bool),ord_less(X56),hAPP(X55,X56,X58,X59)),X60))
| ~ order(X56)
| ~ order(X55) ) ),
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_658])])])])]) ).
fof(c_0_1314,plain,
! [X55,X56,X57,X58,X59,X60] :
( ( hBOOL(hAPP(X55,bool,hAPP(X55,fun(X55,bool),ord_less_eq(X55),esk39_6(X55,X56,X57,X58,X59,X60)),esk40_6(X55,X56,X57,X58,X59,X60)))
| hBOOL(hAPP(X56,bool,hAPP(X56,fun(X56,bool),ord_less(X56),hAPP(X55,X56,X57,X59)),X58))
| ~ hBOOL(hAPP(X56,bool,hAPP(X56,fun(X56,bool),ord_less(X56),hAPP(X55,X56,X57,X60)),X58))
| ~ hBOOL(hAPP(X55,bool,hAPP(X55,fun(X55,bool),ord_less_eq(X55),X59),X60))
| ~ order(X56)
| ~ order(X55) )
& ( ~ hBOOL(hAPP(X56,bool,hAPP(X56,fun(X56,bool),ord_less_eq(X56),hAPP(X55,X56,X57,esk39_6(X55,X56,X57,X58,X59,X60))),hAPP(X55,X56,X57,esk40_6(X55,X56,X57,X58,X59,X60))))
| hBOOL(hAPP(X56,bool,hAPP(X56,fun(X56,bool),ord_less(X56),hAPP(X55,X56,X57,X59)),X58))
| ~ hBOOL(hAPP(X56,bool,hAPP(X56,fun(X56,bool),ord_less(X56),hAPP(X55,X56,X57,X60)),X58))
| ~ hBOOL(hAPP(X55,bool,hAPP(X55,fun(X55,bool),ord_less_eq(X55),X59),X60))
| ~ order(X56)
| ~ order(X55) ) ),
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_659])])])])]) ).
fof(c_0_1315,plain,
! [X55,X56,X57,X58,X59,X60] :
( ( hBOOL(hAPP(X55,bool,hAPP(X55,fun(X55,bool),ord_less(X55),esk38_6(X55,X56,X57,X58,X59,X60)),esk37_6(X55,X56,X57,X58,X59,X60)))
| hBOOL(hAPP(X56,bool,hAPP(X56,fun(X56,bool),ord_less(X56),hAPP(X55,X56,X58,X57)),X60))
| ~ hBOOL(hAPP(X55,bool,hAPP(X55,fun(X55,bool),ord_less(X55),X57),X59))
| ~ hBOOL(hAPP(X56,bool,hAPP(X56,fun(X56,bool),ord_less_eq(X56),hAPP(X55,X56,X58,X59)),X60))
| ~ order(X56)
| ~ ord(X55) )
& ( ~ hBOOL(hAPP(X56,bool,hAPP(X56,fun(X56,bool),ord_less(X56),hAPP(X55,X56,X58,esk38_6(X55,X56,X57,X58,X59,X60))),hAPP(X55,X56,X58,esk37_6(X55,X56,X57,X58,X59,X60))))
| hBOOL(hAPP(X56,bool,hAPP(X56,fun(X56,bool),ord_less(X56),hAPP(X55,X56,X58,X57)),X60))
| ~ hBOOL(hAPP(X55,bool,hAPP(X55,fun(X55,bool),ord_less(X55),X57),X59))
| ~ hBOOL(hAPP(X56,bool,hAPP(X56,fun(X56,bool),ord_less_eq(X56),hAPP(X55,X56,X58,X59)),X60))
| ~ order(X56)
| ~ ord(X55) ) ),
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_660])])])])]) ).
fof(c_0_1316,plain,
! [X55,X56,X57,X58,X59,X60] :
( ( hBOOL(hAPP(X55,bool,hAPP(X55,fun(X55,bool),ord_less(X55),esk34_6(X55,X56,X57,X58,X59,X60)),esk35_6(X55,X56,X57,X58,X59,X60)))
| hBOOL(hAPP(X56,bool,hAPP(X56,fun(X56,bool),ord_less(X56),hAPP(X55,X56,X57,X59)),X58))
| ~ hBOOL(hAPP(X56,bool,hAPP(X56,fun(X56,bool),ord_less_eq(X56),hAPP(X55,X56,X57,X60)),X58))
| ~ hBOOL(hAPP(X55,bool,hAPP(X55,fun(X55,bool),ord_less(X55),X59),X60))
| ~ order(X56)
| ~ order(X55) )
& ( ~ hBOOL(hAPP(X56,bool,hAPP(X56,fun(X56,bool),ord_less(X56),hAPP(X55,X56,X57,esk34_6(X55,X56,X57,X58,X59,X60))),hAPP(X55,X56,X57,esk35_6(X55,X56,X57,X58,X59,X60))))
| hBOOL(hAPP(X56,bool,hAPP(X56,fun(X56,bool),ord_less(X56),hAPP(X55,X56,X57,X59)),X58))
| ~ hBOOL(hAPP(X56,bool,hAPP(X56,fun(X56,bool),ord_less_eq(X56),hAPP(X55,X56,X57,X60)),X58))
| ~ hBOOL(hAPP(X55,bool,hAPP(X55,fun(X55,bool),ord_less(X55),X59),X60))
| ~ order(X56)
| ~ order(X55) ) ),
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_661])])])])]) ).
fof(c_0_1317,plain,
! [X55,X56,X57,X58,X59,X60] :
( ( hBOOL(hAPP(X56,bool,hAPP(X56,fun(X56,bool),ord_less(X56),esk45_6(X55,X56,X57,X58,X59,X60)),esk46_6(X55,X56,X57,X58,X59,X60)))
| hBOOL(hAPP(X55,bool,hAPP(X55,fun(X55,bool),ord_less(X55),X58),hAPP(X56,X55,X59,X57)))
| ~ hBOOL(hAPP(X56,bool,hAPP(X56,fun(X56,bool),ord_less(X56),X60),X57))
| ~ hBOOL(hAPP(X55,bool,hAPP(X55,fun(X55,bool),ord_less_eq(X55),X58),hAPP(X56,X55,X59,X60)))
| ~ order(X56)
| ~ order(X55) )
& ( ~ hBOOL(hAPP(X55,bool,hAPP(X55,fun(X55,bool),ord_less(X55),hAPP(X56,X55,X59,esk45_6(X55,X56,X57,X58,X59,X60))),hAPP(X56,X55,X59,esk46_6(X55,X56,X57,X58,X59,X60))))
| hBOOL(hAPP(X55,bool,hAPP(X55,fun(X55,bool),ord_less(X55),X58),hAPP(X56,X55,X59,X57)))
| ~ hBOOL(hAPP(X56,bool,hAPP(X56,fun(X56,bool),ord_less(X56),X60),X57))
| ~ hBOOL(hAPP(X55,bool,hAPP(X55,fun(X55,bool),ord_less_eq(X55),X58),hAPP(X56,X55,X59,X60)))
| ~ order(X56)
| ~ order(X55) ) ),
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_662])])])])]) ).
fof(c_0_1318,plain,
! [X55,X56,X57,X58,X59,X60] :
( ( hBOOL(hAPP(X56,bool,hAPP(X56,fun(X56,bool),ord_less_eq(X56),esk41_6(X55,X56,X57,X58,X59,X60)),esk42_6(X55,X56,X57,X58,X59,X60)))
| hBOOL(hAPP(X55,bool,hAPP(X55,fun(X55,bool),ord_less(X55),X58),hAPP(X56,X55,X59,X57)))
| ~ hBOOL(hAPP(X56,bool,hAPP(X56,fun(X56,bool),ord_less_eq(X56),X60),X57))
| ~ hBOOL(hAPP(X55,bool,hAPP(X55,fun(X55,bool),ord_less(X55),X58),hAPP(X56,X55,X59,X60)))
| ~ order(X56)
| ~ order(X55) )
& ( ~ hBOOL(hAPP(X55,bool,hAPP(X55,fun(X55,bool),ord_less_eq(X55),hAPP(X56,X55,X59,esk41_6(X55,X56,X57,X58,X59,X60))),hAPP(X56,X55,X59,esk42_6(X55,X56,X57,X58,X59,X60))))
| hBOOL(hAPP(X55,bool,hAPP(X55,fun(X55,bool),ord_less(X55),X58),hAPP(X56,X55,X59,X57)))
| ~ hBOOL(hAPP(X56,bool,hAPP(X56,fun(X56,bool),ord_less_eq(X56),X60),X57))
| ~ hBOOL(hAPP(X55,bool,hAPP(X55,fun(X55,bool),ord_less(X55),X58),hAPP(X56,X55,X59,X60)))
| ~ order(X56)
| ~ order(X55) ) ),
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_663])])])])]) ).
fof(c_0_1319,plain,
! [X55,X56,X57,X58,X59,X60] :
( ( hBOOL(hAPP(X56,bool,hAPP(X56,fun(X56,bool),ord_less_eq(X56),esk33_6(X55,X56,X57,X58,X59,X60)),esk32_6(X55,X56,X57,X58,X59,X60)))
| hBOOL(hAPP(X55,bool,hAPP(X55,fun(X55,bool),ord_less(X55),X57),hAPP(X56,X55,X58,X60)))
| ~ hBOOL(hAPP(X55,bool,hAPP(X55,fun(X55,bool),ord_less(X55),X57),hAPP(X56,X55,X58,X59)))
| ~ hBOOL(hAPP(X56,bool,hAPP(X56,fun(X56,bool),ord_less_eq(X56),X59),X60))
| ~ order(X56)
| ~ order(X55) )
& ( ~ hBOOL(hAPP(X55,bool,hAPP(X55,fun(X55,bool),ord_less_eq(X55),hAPP(X56,X55,X58,esk33_6(X55,X56,X57,X58,X59,X60))),hAPP(X56,X55,X58,esk32_6(X55,X56,X57,X58,X59,X60))))
| hBOOL(hAPP(X55,bool,hAPP(X55,fun(X55,bool),ord_less(X55),X57),hAPP(X56,X55,X58,X60)))
| ~ hBOOL(hAPP(X55,bool,hAPP(X55,fun(X55,bool),ord_less(X55),X57),hAPP(X56,X55,X58,X59)))
| ~ hBOOL(hAPP(X56,bool,hAPP(X56,fun(X56,bool),ord_less_eq(X56),X59),X60))
| ~ order(X56)
| ~ order(X55) ) ),
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_664])])])])]) ).
fof(c_0_1320,plain,
! [X55,X56,X57,X58,X59,X60] :
( ( hBOOL(hAPP(X56,bool,hAPP(X56,fun(X56,bool),ord_less(X56),esk29_6(X55,X56,X57,X58,X59,X60)),esk28_6(X55,X56,X57,X58,X59,X60)))
| hBOOL(hAPP(X55,bool,hAPP(X55,fun(X55,bool),ord_less(X55),X57),hAPP(X56,X55,X58,X60)))
| ~ hBOOL(hAPP(X55,bool,hAPP(X55,fun(X55,bool),ord_less_eq(X55),X57),hAPP(X56,X55,X58,X59)))
| ~ hBOOL(hAPP(X56,bool,hAPP(X56,fun(X56,bool),ord_less(X56),X59),X60))
| ~ order(X56)
| ~ order(X55) )
& ( ~ hBOOL(hAPP(X55,bool,hAPP(X55,fun(X55,bool),ord_less(X55),hAPP(X56,X55,X58,esk29_6(X55,X56,X57,X58,X59,X60))),hAPP(X56,X55,X58,esk28_6(X55,X56,X57,X58,X59,X60))))
| hBOOL(hAPP(X55,bool,hAPP(X55,fun(X55,bool),ord_less(X55),X57),hAPP(X56,X55,X58,X60)))
| ~ hBOOL(hAPP(X55,bool,hAPP(X55,fun(X55,bool),ord_less_eq(X55),X57),hAPP(X56,X55,X58,X59)))
| ~ hBOOL(hAPP(X56,bool,hAPP(X56,fun(X56,bool),ord_less(X56),X59),X60))
| ~ order(X56)
| ~ order(X55) ) ),
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_665])])])])]) ).
fof(c_0_1321,plain,
! [X12,X13] : hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),hAPP(real,real,sqrt,hAPP(real,real,plus_plus(real,hAPP(nat,real,power_power(real,X12),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,real,power_power(real,X13),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))))),
inference(variable_rename,[status(thm)],[c_0_666]) ).
fof(c_0_1322,plain,
! [X7,X8,X9,X10,X11] :
( ( ~ hBOOL(hAPP(X7,bool,hAPP(X7,fun(X7,bool),ord_less(X7),zero_zero(X7)),hAPP(X7,X7,plus_plus(X7,hAPP(nat,X7,power_power(X7,X8),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,X7,power_power(X7,X9),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))))
| ti(X7,X8) != zero_zero(X7)
| ti(X7,X9) != zero_zero(X7)
| ~ linordered_idom(X7) )
& ( ti(X7,X10) = zero_zero(X7)
| hBOOL(hAPP(X7,bool,hAPP(X7,fun(X7,bool),ord_less(X7),zero_zero(X7)),hAPP(X7,X7,plus_plus(X7,hAPP(nat,X7,power_power(X7,X10),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,X7,power_power(X7,X11),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))))
| ~ linordered_idom(X7) )
& ( ti(X7,X11) = zero_zero(X7)
| hBOOL(hAPP(X7,bool,hAPP(X7,fun(X7,bool),ord_less(X7),zero_zero(X7)),hAPP(X7,X7,plus_plus(X7,hAPP(nat,X7,power_power(X7,X10),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,X7,power_power(X7,X11),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))))
| ~ linordered_idom(X7) ) ),
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_667])])])])]) ).
fof(c_0_1323,plain,
! [X12,X13,X14] :
( ~ linordered_idom(X12)
| hBOOL(hAPP(X12,bool,hAPP(X12,fun(X12,bool),ord_less_eq(X12),zero_zero(X12)),hAPP(X12,X12,plus_plus(X12,hAPP(nat,X12,power_power(X12,X13),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,X12,power_power(X12,X14),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_668])])]) ).
fof(c_0_1324,plain,
! [X12,X13,X14] :
( ~ linordered_semidom(X12)
| ~ hBOOL(hAPP(X12,bool,hAPP(X12,fun(X12,bool),ord_less(X12),hAPP(nat,X12,power_power(X12,X13),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,X12,power_power(X12,X14),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))
| ~ hBOOL(hAPP(X12,bool,hAPP(X12,fun(X12,bool),ord_less_eq(X12),zero_zero(X12)),X14))
| hBOOL(hAPP(X12,bool,hAPP(X12,fun(X12,bool),ord_less(X12),X13),X14)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_669])])]) ).
fof(c_0_1325,plain,
! [X12,X13,X14] :
( ~ linordered_semidom(X12)
| ~ hBOOL(hAPP(X12,bool,hAPP(X12,fun(X12,bool),ord_less_eq(X12),hAPP(nat,X12,power_power(X12,X13),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,X12,power_power(X12,X14),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))
| ~ hBOOL(hAPP(X12,bool,hAPP(X12,fun(X12,bool),ord_less_eq(X12),zero_zero(X12)),X14))
| hBOOL(hAPP(X12,bool,hAPP(X12,fun(X12,bool),ord_less_eq(X12),X13),X14)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_670])])]) ).
fof(c_0_1326,plain,
! [X12,X13,X14] :
( ~ linordered_ring(X12)
| ~ hBOOL(hAPP(X12,bool,hAPP(X12,fun(X12,bool),ord_less(X12),hAPP(X12,X12,plus_plus(X12,hAPP(X12,X12,hAPP(X12,fun(X12,X12),times_times(X12),X13),X13)),hAPP(X12,X12,hAPP(X12,fun(X12,X12),times_times(X12),X14),X14))),zero_zero(X12))) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_671])])]) ).
fof(c_0_1327,plain,
! [X32,X33] :
( ~ linordered_idom(X32)
| ~ hBOOL(hAPP(X32,bool,hAPP(X32,fun(X32,bool),ord_less(X32),hAPP(nat,X32,power_power(X32,X33),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),zero_zero(X32))) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_672])])]) ).
fof(c_0_1328,plain,
! [X7,X8,X9,X10,X11] :
( ( ~ hBOOL(hAPP(X7,bool,hAPP(X7,fun(X7,bool),ord_less(X7),zero_zero(X7)),hAPP(X7,X7,plus_plus(X7,hAPP(X7,X7,hAPP(X7,fun(X7,X7),times_times(X7),X8),X8)),hAPP(X7,X7,hAPP(X7,fun(X7,X7),times_times(X7),X9),X9))))
| ti(X7,X8) != zero_zero(X7)
| ti(X7,X9) != zero_zero(X7)
| ~ linord581940658strict(X7) )
& ( ti(X7,X10) = zero_zero(X7)
| hBOOL(hAPP(X7,bool,hAPP(X7,fun(X7,bool),ord_less(X7),zero_zero(X7)),hAPP(X7,X7,plus_plus(X7,hAPP(X7,X7,hAPP(X7,fun(X7,X7),times_times(X7),X10),X10)),hAPP(X7,X7,hAPP(X7,fun(X7,X7),times_times(X7),X11),X11))))
| ~ linord581940658strict(X7) )
& ( ti(X7,X11) = zero_zero(X7)
| hBOOL(hAPP(X7,bool,hAPP(X7,fun(X7,bool),ord_less(X7),zero_zero(X7)),hAPP(X7,X7,plus_plus(X7,hAPP(X7,X7,hAPP(X7,fun(X7,X7),times_times(X7),X10),X10)),hAPP(X7,X7,hAPP(X7,fun(X7,X7),times_times(X7),X11),X11))))
| ~ linord581940658strict(X7) ) ),
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_673])])])])]) ).
fof(c_0_1329,plain,
! [X7,X8,X9,X10,X11] :
( ( ti(X7,X8) = zero_zero(X7)
| hAPP(X7,X7,plus_plus(X7,hAPP(nat,X7,power_power(X7,X8),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,X7,power_power(X7,X9),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) != zero_zero(X7)
| ~ linordered_idom(X7) )
& ( ti(X7,X9) = zero_zero(X7)
| hAPP(X7,X7,plus_plus(X7,hAPP(nat,X7,power_power(X7,X8),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,X7,power_power(X7,X9),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) != zero_zero(X7)
| ~ linordered_idom(X7) )
& ( ti(X7,X10) != zero_zero(X7)
| ti(X7,X11) != zero_zero(X7)
| hAPP(X7,X7,plus_plus(X7,hAPP(nat,X7,power_power(X7,X10),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,X7,power_power(X7,X11),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) = zero_zero(X7)
| ~ linordered_idom(X7) ) ),
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_674])])])])]) ).
fof(c_0_1330,plain,
! [X7,X8,X9,X10] :
( ( X7 = zero_zero(real)
| hAPP(real,real,plus_plus(real,hAPP(nat,real,power_power(real,X7),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,real,power_power(real,X8),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) != zero_zero(real) )
& ( X8 = zero_zero(real)
| hAPP(real,real,plus_plus(real,hAPP(nat,real,power_power(real,X7),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,real,power_power(real,X8),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) != zero_zero(real) )
& ( X9 != zero_zero(real)
| X10 != zero_zero(real)
| hAPP(real,real,plus_plus(real,hAPP(nat,real,power_power(real,X9),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,real,power_power(real,X10),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,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_675])])])])]) ).
fof(c_0_1331,plain,
! [X16,X17] :
( ~ number_ring(X16)
| ~ linordered_idom(X16)
| hBOOL(hAPP(X16,bool,hAPP(X16,fun(X16,bool),ord_less(X16),hAPP(nat,X16,semiring_1_of_nat(X16),X17)),hAPP(nat,X16,power_power(X16,number_number_of(X16,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),X17))) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_676])])]) ).
fof(c_0_1332,plain,
! [X16] : hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),one_one(real)),hAPP(nat,real,power_power(real,number_number_of(real,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),X16))),
inference(variable_rename,[status(thm)],[c_0_677]) ).
fof(c_0_1333,plain,
! [X55,X56,X57] :
( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),esk16_3(X55,X56,X57)),esk17_3(X55,X56,X57)))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,plus_plus(nat,hAPP(nat,nat,X57,X55)),X56)),hAPP(nat,nat,X57,hAPP(nat,nat,plus_plus(nat,X55),X56)))) )
& ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,X57,esk16_3(X55,X56,X57))),hAPP(nat,nat,X57,esk17_3(X55,X56,X57))))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,plus_plus(nat,hAPP(nat,nat,X57,X55)),X56)),hAPP(nat,nat,X57,hAPP(nat,nat,plus_plus(nat,X55),X56)))) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_678])])])]) ).
fof(c_0_1334,plain,
! [X11] : hAPP(nat,int,power_power(int,hAPP(nat,int,power_power(int,X11),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) = hAPP(nat,int,power_power(int,X11),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),
inference(variable_rename,[status(thm)],[c_0_679]) ).
fof(c_0_1335,plain,
! [X8,X9,X10] :
( ( ~ hBOOL(hAPP(X8,bool,hAPP(X8,fun(X8,bool),ord_less(X8),zero_zero(X8)),hAPP(nat,X8,power_power(X8,X9),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))
| ti(X8,X9) != zero_zero(X8)
| ~ linordered_idom(X8) )
& ( ti(X8,X10) = zero_zero(X8)
| hBOOL(hAPP(X8,bool,hAPP(X8,fun(X8,bool),ord_less(X8),zero_zero(X8)),hAPP(nat,X8,power_power(X8,X10),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))
| ~ linordered_idom(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_680])])])])]) ).
fof(c_0_1336,plain,
! [X47,X48,X49,X50] :
( ( ~ hBOOL(hAPP(X47,bool,hAPP(X47,fun(X47,bool),ord_less_eq(X47),hAPP(X47,X47,hAPP(X47,fun(X47,X47),times_times(X47),X50),X48)),hAPP(X47,X47,hAPP(X47,fun(X47,X47),times_times(X47),X50),X49)))
| hBOOL(hAPP(X47,bool,hAPP(X47,fun(X47,bool),ord_less_eq(X47),X48),X49))
| ~ hBOOL(hAPP(X47,bool,hAPP(X47,fun(X47,bool),ord_less(X47),zero_zero(X47)),X50))
| ~ linord581940658strict(X47) )
& ( ~ hBOOL(hAPP(X47,bool,hAPP(X47,fun(X47,bool),ord_less_eq(X47),X48),X49))
| hBOOL(hAPP(X47,bool,hAPP(X47,fun(X47,bool),ord_less_eq(X47),hAPP(X47,X47,hAPP(X47,fun(X47,X47),times_times(X47),X50),X48)),hAPP(X47,X47,hAPP(X47,fun(X47,X47),times_times(X47),X50),X49)))
| ~ hBOOL(hAPP(X47,bool,hAPP(X47,fun(X47,bool),ord_less(X47),zero_zero(X47)),X50))
| ~ linord581940658strict(X47) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_681])])])]) ).
fof(c_0_1337,plain,
! [X42,X43,X44,X45] :
( ~ linordered_semiring(X42)
| ~ hBOOL(hAPP(X42,bool,hAPP(X42,fun(X42,bool),ord_less(X42),hAPP(X42,X42,hAPP(X42,fun(X42,X42),times_times(X42),X43),X44)),hAPP(X42,X42,hAPP(X42,fun(X42,X42),times_times(X42),X45),X44)))
| ~ hBOOL(hAPP(X42,bool,hAPP(X42,fun(X42,bool),ord_less_eq(X42),zero_zero(X42)),X44))
| hBOOL(hAPP(X42,bool,hAPP(X42,fun(X42,bool),ord_less(X42),X43),X45)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_682])])]) ).
fof(c_0_1338,plain,
! [X42,X43,X44,X45] :
( ~ linord20386208strict(X42)
| ~ hBOOL(hAPP(X42,bool,hAPP(X42,fun(X42,bool),ord_less(X42),hAPP(X42,X42,hAPP(X42,fun(X42,X42),times_times(X42),X43),X44)),hAPP(X42,X42,hAPP(X42,fun(X42,X42),times_times(X42),X45),X44)))
| ~ hBOOL(hAPP(X42,bool,hAPP(X42,fun(X42,bool),ord_less_eq(X42),zero_zero(X42)),X44))
| hBOOL(hAPP(X42,bool,hAPP(X42,fun(X42,bool),ord_less(X42),X43),X45)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_683])])]) ).
fof(c_0_1339,plain,
! [X42,X43,X44,X45] :
( ~ linordered_semiring(X42)
| ~ hBOOL(hAPP(X42,bool,hAPP(X42,fun(X42,bool),ord_less(X42),hAPP(X42,X42,hAPP(X42,fun(X42,X42),times_times(X42),X43),X44)),hAPP(X42,X42,hAPP(X42,fun(X42,X42),times_times(X42),X43),X45)))
| ~ hBOOL(hAPP(X42,bool,hAPP(X42,fun(X42,bool),ord_less_eq(X42),zero_zero(X42)),X43))
| hBOOL(hAPP(X42,bool,hAPP(X42,fun(X42,bool),ord_less(X42),X44),X45)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_684])])]) ).
fof(c_0_1340,plain,
! [X42,X43,X44,X45] :
( ~ linord20386208strict(X42)
| ~ hBOOL(hAPP(X42,bool,hAPP(X42,fun(X42,bool),ord_less(X42),hAPP(X42,X42,hAPP(X42,fun(X42,X42),times_times(X42),X43),X44)),hAPP(X42,X42,hAPP(X42,fun(X42,X42),times_times(X42),X43),X45)))
| ~ hBOOL(hAPP(X42,bool,hAPP(X42,fun(X42,bool),ord_less_eq(X42),zero_zero(X42)),X43))
| hBOOL(hAPP(X42,bool,hAPP(X42,fun(X42,bool),ord_less(X42),X44),X45)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_685])])]) ).
fof(c_0_1341,plain,
! [X42,X43,X44,X45] :
( ~ linord20386208strict(X42)
| ~ hBOOL(hAPP(X42,bool,hAPP(X42,fun(X42,bool),ord_less_eq(X42),hAPP(X42,X42,hAPP(X42,fun(X42,X42),times_times(X42),X43),X44)),hAPP(X42,X42,hAPP(X42,fun(X42,X42),times_times(X42),X45),X44)))
| ~ hBOOL(hAPP(X42,bool,hAPP(X42,fun(X42,bool),ord_less(X42),zero_zero(X42)),X44))
| hBOOL(hAPP(X42,bool,hAPP(X42,fun(X42,bool),ord_less_eq(X42),X43),X45)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_686])])]) ).
fof(c_0_1342,plain,
! [X42,X43,X44,X45] :
( ~ linord20386208strict(X42)
| ~ hBOOL(hAPP(X42,bool,hAPP(X42,fun(X42,bool),ord_less_eq(X42),hAPP(X42,X42,hAPP(X42,fun(X42,X42),times_times(X42),X43),X44)),hAPP(X42,X42,hAPP(X42,fun(X42,X42),times_times(X42),X43),X45)))
| ~ hBOOL(hAPP(X42,bool,hAPP(X42,fun(X42,bool),ord_less(X42),zero_zero(X42)),X43))
| hBOOL(hAPP(X42,bool,hAPP(X42,fun(X42,bool),ord_less_eq(X42),X44),X45)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_687])])]) ).
fof(c_0_1343,plain,
! [X47,X48,X49,X50] :
( ( ~ hBOOL(hAPP(X47,bool,hAPP(X47,fun(X47,bool),ord_less(X47),hAPP(X47,X47,hAPP(X47,fun(X47,X47),times_times(X47),X50),X48)),hAPP(X47,X47,hAPP(X47,fun(X47,X47),times_times(X47),X50),X49)))
| hBOOL(hAPP(X47,bool,hAPP(X47,fun(X47,bool),ord_less(X47),X49),X48))
| ~ hBOOL(hAPP(X47,bool,hAPP(X47,fun(X47,bool),ord_less(X47),X50),zero_zero(X47)))
| ~ linord581940658strict(X47) )
& ( ~ hBOOL(hAPP(X47,bool,hAPP(X47,fun(X47,bool),ord_less(X47),X49),X48))
| hBOOL(hAPP(X47,bool,hAPP(X47,fun(X47,bool),ord_less(X47),hAPP(X47,X47,hAPP(X47,fun(X47,X47),times_times(X47),X50),X48)),hAPP(X47,X47,hAPP(X47,fun(X47,X47),times_times(X47),X50),X49)))
| ~ hBOOL(hAPP(X47,bool,hAPP(X47,fun(X47,bool),ord_less(X47),X50),zero_zero(X47)))
| ~ linord581940658strict(X47) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_688])])])]) ).
fof(c_0_1344,plain,
! [X47,X48,X49,X50] :
( ( ~ hBOOL(hAPP(X47,bool,hAPP(X47,fun(X47,bool),ord_less_eq(X47),hAPP(X47,X47,hAPP(X47,fun(X47,X47),times_times(X47),X50),X48)),hAPP(X47,X47,hAPP(X47,fun(X47,X47),times_times(X47),X50),X49)))
| hBOOL(hAPP(X47,bool,hAPP(X47,fun(X47,bool),ord_less_eq(X47),X49),X48))
| ~ hBOOL(hAPP(X47,bool,hAPP(X47,fun(X47,bool),ord_less(X47),X50),zero_zero(X47)))
| ~ linord581940658strict(X47) )
& ( ~ hBOOL(hAPP(X47,bool,hAPP(X47,fun(X47,bool),ord_less_eq(X47),X49),X48))
| hBOOL(hAPP(X47,bool,hAPP(X47,fun(X47,bool),ord_less_eq(X47),hAPP(X47,X47,hAPP(X47,fun(X47,X47),times_times(X47),X50),X48)),hAPP(X47,X47,hAPP(X47,fun(X47,X47),times_times(X47),X50),X49)))
| ~ hBOOL(hAPP(X47,bool,hAPP(X47,fun(X47,bool),ord_less(X47),X50),zero_zero(X47)))
| ~ linord581940658strict(X47) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_689])])])]) ).
fof(c_0_1345,plain,
! [X46,X47,X48,X49,X50] :
( ~ linord20386208strict(X46)
| ~ hBOOL(hAPP(X46,bool,hAPP(X46,fun(X46,bool),ord_less(X46),X49),X50))
| ~ hBOOL(hAPP(X46,bool,hAPP(X46,fun(X46,bool),ord_less(X46),X47),X48))
| ~ hBOOL(hAPP(X46,bool,hAPP(X46,fun(X46,bool),ord_less(X46),zero_zero(X46)),X50))
| ~ hBOOL(hAPP(X46,bool,hAPP(X46,fun(X46,bool),ord_less_eq(X46),zero_zero(X46)),X47))
| hBOOL(hAPP(X46,bool,hAPP(X46,fun(X46,bool),ord_less(X46),hAPP(X46,X46,hAPP(X46,fun(X46,X46),times_times(X46),X49),X47)),hAPP(X46,X46,hAPP(X46,fun(X46,X46),times_times(X46),X50),X48))) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_690])])]) ).
fof(c_0_1346,plain,
! [X46,X47,X48,X49,X50] :
( ~ linord20386208strict(X46)
| ~ hBOOL(hAPP(X46,bool,hAPP(X46,fun(X46,bool),ord_less(X46),X49),X50))
| ~ hBOOL(hAPP(X46,bool,hAPP(X46,fun(X46,bool),ord_less(X46),X47),X48))
| ~ hBOOL(hAPP(X46,bool,hAPP(X46,fun(X46,bool),ord_less_eq(X46),zero_zero(X46)),X49))
| ~ hBOOL(hAPP(X46,bool,hAPP(X46,fun(X46,bool),ord_less_eq(X46),zero_zero(X46)),X47))
| hBOOL(hAPP(X46,bool,hAPP(X46,fun(X46,bool),ord_less(X46),hAPP(X46,X46,hAPP(X46,fun(X46,X46),times_times(X46),X49),X47)),hAPP(X46,X46,hAPP(X46,fun(X46,X46),times_times(X46),X50),X48))) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_691])])]) ).
fof(c_0_1347,plain,
! [X46,X47,X48,X49,X50] :
( ~ linord20386208strict(X46)
| ~ hBOOL(hAPP(X46,bool,hAPP(X46,fun(X46,bool),ord_less(X46),X49),X50))
| ~ hBOOL(hAPP(X46,bool,hAPP(X46,fun(X46,bool),ord_less_eq(X46),X47),X48))
| ~ hBOOL(hAPP(X46,bool,hAPP(X46,fun(X46,bool),ord_less_eq(X46),zero_zero(X46)),X49))
| ~ hBOOL(hAPP(X46,bool,hAPP(X46,fun(X46,bool),ord_less(X46),zero_zero(X46)),X47))
| hBOOL(hAPP(X46,bool,hAPP(X46,fun(X46,bool),ord_less(X46),hAPP(X46,X46,hAPP(X46,fun(X46,X46),times_times(X46),X49),X47)),hAPP(X46,X46,hAPP(X46,fun(X46,X46),times_times(X46),X50),X48))) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_692])])]) ).
fof(c_0_1348,plain,
! [X46,X47,X48,X49,X50] :
( ~ linord20386208strict(X46)
| ~ hBOOL(hAPP(X46,bool,hAPP(X46,fun(X46,bool),ord_less_eq(X46),X49),X50))
| ~ hBOOL(hAPP(X46,bool,hAPP(X46,fun(X46,bool),ord_less(X46),X47),X48))
| ~ hBOOL(hAPP(X46,bool,hAPP(X46,fun(X46,bool),ord_less(X46),zero_zero(X46)),X49))
| ~ hBOOL(hAPP(X46,bool,hAPP(X46,fun(X46,bool),ord_less_eq(X46),zero_zero(X46)),X47))
| hBOOL(hAPP(X46,bool,hAPP(X46,fun(X46,bool),ord_less(X46),hAPP(X46,X46,hAPP(X46,fun(X46,X46),times_times(X46),X49),X47)),hAPP(X46,X46,hAPP(X46,fun(X46,X46),times_times(X46),X50),X48))) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_693])])]) ).
fof(c_0_1349,plain,
! [X30,X31] :
( ( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,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(int,fun(int,bool),ord_less(int),X30),zero_zero(int))) )
& ( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X31),zero_zero(int)))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,plus_plus(int,hAPP(int,int,plus_plus(int,one_one(int)),X31)),X31)),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_694])])])]) ).
fof(c_0_1350,plain,
! [X58,X59,X60,X61] :
( ~ ord(X59)
| ~ hBOOL(hAPP(X59,bool,hAPP(X59,fun(X59,bool),ord_less_eq(X59),hAPP(X58,X59,X60,esk25_4(X58,X59,X60,X61))),hAPP(X58,X59,X61,esk25_4(X58,X59,X60,X61))))
| hBOOL(hAPP(fun(X58,X59),bool,hAPP(fun(X58,X59),fun(fun(X58,X59),bool),ord_less_eq(fun(X58,X59)),X60),X61)) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_695])])])]) ).
fof(c_0_1351,plain,
! [X58,X59,X60,X61,X62,X63,X64] :
( ( ~ hBOOL(hAPP(fun(X58,X59),bool,hAPP(fun(X58,X59),fun(fun(X58,X59),bool),ord_less_eq(fun(X58,X59)),X60),X61))
| hBOOL(hAPP(X59,bool,hAPP(X59,fun(X59,bool),ord_less_eq(X59),hAPP(X58,X59,X60,X62)),hAPP(X58,X59,X61,X62)))
| ~ ord(X59) )
& ( ~ hBOOL(hAPP(X59,bool,hAPP(X59,fun(X59,bool),ord_less_eq(X59),hAPP(X58,X59,X63,esk22_4(X58,X59,X63,X64))),hAPP(X58,X59,X64,esk22_4(X58,X59,X63,X64))))
| hBOOL(hAPP(fun(X58,X59),bool,hAPP(fun(X58,X59),fun(fun(X58,X59),bool),ord_less_eq(fun(X58,X59)),X63),X64))
| ~ ord(X59) ) ),
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_696])])])])])]) ).
fof(c_0_1352,plain,
! [X42,X43,X44,X45] :
( ~ linord20386208strict(X42)
| ~ hBOOL(hAPP(X42,bool,hAPP(X42,fun(X42,bool),ord_less(X42),X44),X45))
| ~ hBOOL(hAPP(X42,bool,hAPP(X42,fun(X42,bool),ord_less(X42),zero_zero(X42)),X43))
| hBOOL(hAPP(X42,bool,hAPP(X42,fun(X42,bool),ord_less(X42),hAPP(X42,X42,hAPP(X42,fun(X42,X42),times_times(X42),X44),X43)),hAPP(X42,X42,hAPP(X42,fun(X42,X42),times_times(X42),X45),X43))) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_697])])]) ).
fof(c_0_1353,plain,
! [X42,X43,X44,X45] :
( ~ linord20386208strict(X42)
| ~ hBOOL(hAPP(X42,bool,hAPP(X42,fun(X42,bool),ord_less(X42),X44),X45))
| ~ hBOOL(hAPP(X42,bool,hAPP(X42,fun(X42,bool),ord_less(X42),zero_zero(X42)),X43))
| hBOOL(hAPP(X42,bool,hAPP(X42,fun(X42,bool),ord_less(X42),hAPP(X42,X42,hAPP(X42,fun(X42,X42),times_times(X42),X43),X44)),hAPP(X42,X42,hAPP(X42,fun(X42,X42),times_times(X42),X43),X45))) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_698])])]) ).
fof(c_0_1354,plain,
! [X42,X43,X44,X45] :
( ~ linord893533164strict(X42)
| ~ hBOOL(hAPP(X42,bool,hAPP(X42,fun(X42,bool),ord_less(X42),X44),X45))
| ~ hBOOL(hAPP(X42,bool,hAPP(X42,fun(X42,bool),ord_less(X42),zero_zero(X42)),X43))
| hBOOL(hAPP(X42,bool,hAPP(X42,fun(X42,bool),ord_less(X42),hAPP(X42,X42,hAPP(X42,fun(X42,X42),times_times(X42),X43),X44)),hAPP(X42,X42,hAPP(X42,fun(X42,X42),times_times(X42),X43),X45))) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_699])])]) ).
fof(c_0_1355,plain,
! [X42,X43,X44,X45] :
( ~ linord581940658strict(X42)
| ~ hBOOL(hAPP(X42,bool,hAPP(X42,fun(X42,bool),ord_less(X42),X44),X45))
| ~ hBOOL(hAPP(X42,bool,hAPP(X42,fun(X42,bool),ord_less(X42),X43),zero_zero(X42)))
| hBOOL(hAPP(X42,bool,hAPP(X42,fun(X42,bool),ord_less(X42),hAPP(X42,X42,hAPP(X42,fun(X42,X42),times_times(X42),X45),X43)),hAPP(X42,X42,hAPP(X42,fun(X42,X42),times_times(X42),X44),X43))) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_700])])]) ).
fof(c_0_1356,plain,
! [X42,X43,X44,X45] :
( ~ linord581940658strict(X42)
| ~ hBOOL(hAPP(X42,bool,hAPP(X42,fun(X42,bool),ord_less(X42),X44),X45))
| ~ hBOOL(hAPP(X42,bool,hAPP(X42,fun(X42,bool),ord_less(X42),X43),zero_zero(X42)))
| hBOOL(hAPP(X42,bool,hAPP(X42,fun(X42,bool),ord_less(X42),hAPP(X42,X42,hAPP(X42,fun(X42,X42),times_times(X42),X43),X45)),hAPP(X42,X42,hAPP(X42,fun(X42,X42),times_times(X42),X43),X44))) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_701])])]) ).
fof(c_0_1357,plain,
! [X57,X58,X59] :
( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),esk20_3(X57,X58,X59)),esk21_3(X57,X58,X59)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X57),X58))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,X59,X57)),hAPP(nat,nat,X59,X58))) )
& ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,X59,esk20_3(X57,X58,X59))),hAPP(nat,nat,X59,esk21_3(X57,X58,X59))))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X57),X58))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,X59,X57)),hAPP(nat,nat,X59,X58))) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_702])])])]) ).
fof(c_0_1358,plain,
! [X12,X13,X14] :
( ~ linordered_semidom(X12)
| hAPP(nat,X12,power_power(X12,X13),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) != hAPP(nat,X12,power_power(X12,X14),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))
| ~ hBOOL(hAPP(X12,bool,hAPP(X12,fun(X12,bool),ord_less_eq(X12),zero_zero(X12)),X13))
| ~ hBOOL(hAPP(X12,bool,hAPP(X12,fun(X12,bool),ord_less_eq(X12),zero_zero(X12)),X14))
| ti(X12,X13) = ti(X12,X14) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_703])])]) ).
fof(c_0_1359,plain,
! [X32,X33] :
( ~ linordered_idom(X32)
| hBOOL(hAPP(X32,bool,hAPP(X32,fun(X32,bool),ord_less_eq(X32),zero_zero(X32)),hAPP(nat,X32,power_power(X32,X33),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_704])])]) ).
fof(c_0_1360,plain,
! [X11] : hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X11),hAPP(nat,int,power_power(int,X11),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),
inference(variable_rename,[status(thm)],[c_0_705]) ).
fof(c_0_1361,plain,
! [X11] :
( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X11))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X11),number_number_of(int,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))
| X11 = zero_zero(int)
| X11 = one_one(int) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_706])]) ).
fof(c_0_1362,plain,
! [X41,X42,X43] :
( ~ linord20386208strict(X41)
| ~ hBOOL(hAPP(X41,bool,hAPP(X41,fun(X41,bool),ord_less(X41),X43),zero_zero(X41)))
| ~ hBOOL(hAPP(X41,bool,hAPP(X41,fun(X41,bool),ord_less(X41),zero_zero(X41)),X42))
| hBOOL(hAPP(X41,bool,hAPP(X41,fun(X41,bool),ord_less(X41),hAPP(X41,X41,hAPP(X41,fun(X41,X41),times_times(X41),X43),X42)),zero_zero(X41))) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_707])])]) ).
fof(c_0_1363,plain,
! [X41,X42,X43,X44] :
( ~ linordered_semidom(X41)
| ~ hBOOL(hAPP(X41,bool,hAPP(X41,fun(X41,bool),ord_less(X41),X43),X44))
| ~ hBOOL(hAPP(X41,bool,hAPP(X41,fun(X41,bool),ord_less_eq(X41),zero_zero(X41)),X43))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X42))
| hBOOL(hAPP(X41,bool,hAPP(X41,fun(X41,bool),ord_less(X41),hAPP(nat,X41,power_power(X41,X43),X42)),hAPP(nat,X41,power_power(X41,X44),X42))) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_708])])]) ).
fof(c_0_1364,plain,
! [X33,X34,X35,X36] :
( ~ linordered_semidom(X33)
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X35),X36))
| ~ hBOOL(hAPP(X33,bool,hAPP(X33,fun(X33,bool),ord_less_eq(X33),zero_zero(X33)),X34))
| ~ hBOOL(hAPP(X33,bool,hAPP(X33,fun(X33,bool),ord_less_eq(X33),X34),one_one(X33)))
| hBOOL(hAPP(X33,bool,hAPP(X33,fun(X33,bool),ord_less_eq(X33),hAPP(nat,X33,power_power(X33,X34),X36)),hAPP(nat,X33,power_power(X33,X34),X35))) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_709])])]) ).
fof(c_0_1365,plain,
! [X33,X34,X35,X36] :
( ~ linordered_semidom(X33)
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X35),X36))
| ~ hBOOL(hAPP(X33,bool,hAPP(X33,fun(X33,bool),ord_less(X33),zero_zero(X33)),X34))
| ~ hBOOL(hAPP(X33,bool,hAPP(X33,fun(X33,bool),ord_less(X33),X34),one_one(X33)))
| hBOOL(hAPP(X33,bool,hAPP(X33,fun(X33,bool),ord_less(X33),hAPP(nat,X33,power_power(X33,X34),X36)),hAPP(nat,X33,power_power(X33,X34),X35))) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_710])])]) ).
fof(c_0_1366,plain,
! [X41,X42,X43] :
( ~ linord20386208strict(X41)
| ~ hBOOL(hAPP(X41,bool,hAPP(X41,fun(X41,bool),ord_less(X41),zero_zero(X41)),hAPP(X41,X41,hAPP(X41,fun(X41,X41),times_times(X41),X42),X43)))
| ~ hBOOL(hAPP(X41,bool,hAPP(X41,fun(X41,bool),ord_less(X41),zero_zero(X41)),X43))
| hBOOL(hAPP(X41,bool,hAPP(X41,fun(X41,bool),ord_less(X41),zero_zero(X41)),X42)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_711])])]) ).
fof(c_0_1367,plain,
! [X41,X42,X43,X44] :
( ~ linordered_semidom(X41)
| ~ hBOOL(hAPP(X41,bool,hAPP(X41,fun(X41,bool),ord_less(X41),hAPP(nat,X41,power_power(X41,X42),X43)),hAPP(nat,X41,power_power(X41,X44),X43)))
| ~ hBOOL(hAPP(X41,bool,hAPP(X41,fun(X41,bool),ord_less_eq(X41),zero_zero(X41)),X44))
| hBOOL(hAPP(X41,bool,hAPP(X41,fun(X41,bool),ord_less(X41),X42),X44)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_712])])]) ).
fof(c_0_1368,plain,
! [X32,X33,X34,X35] :
( ~ linordered_semidom(X32)
| ~ hBOOL(hAPP(X32,bool,hAPP(X32,fun(X32,bool),ord_less(X32),one_one(X32)),X35))
| ~ hBOOL(hAPP(X32,bool,hAPP(X32,fun(X32,bool),ord_less_eq(X32),hAPP(nat,X32,power_power(X32,X35),X33)),hAPP(nat,X32,power_power(X32,X35),X34)))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X33),X34)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_713])])]) ).
fof(c_0_1369,plain,
! [X43,X44,X45,X46] :
( ( ~ hBOOL(hAPP(X43,bool,hAPP(X43,fun(X43,bool),ord_less_eq(X43),hAPP(nat,X43,power_power(X43,X46),X44)),hAPP(nat,X43,power_power(X43,X46),X45)))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X44),X45))
| ~ hBOOL(hAPP(X43,bool,hAPP(X43,fun(X43,bool),ord_less(X43),one_one(X43)),X46))
| ~ linordered_semidom(X43) )
& ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X44),X45))
| hBOOL(hAPP(X43,bool,hAPP(X43,fun(X43,bool),ord_less_eq(X43),hAPP(nat,X43,power_power(X43,X46),X44)),hAPP(nat,X43,power_power(X43,X46),X45)))
| ~ hBOOL(hAPP(X43,bool,hAPP(X43,fun(X43,bool),ord_less(X43),one_one(X43)),X46))
| ~ linordered_semidom(X43) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_714])])])]) ).
fof(c_0_1370,plain,
! [X32,X33,X34,X35] :
( ~ linordered_semidom(X32)
| ~ hBOOL(hAPP(X32,bool,hAPP(X32,fun(X32,bool),ord_less(X32),one_one(X32)),X35))
| ~ hBOOL(hAPP(X32,bool,hAPP(X32,fun(X32,bool),ord_less(X32),hAPP(nat,X32,power_power(X32,X35),X33)),hAPP(nat,X32,power_power(X32,X35),X34)))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X33),X34)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_715])])]) ).
fof(c_0_1371,plain,
! [X43,X44,X45,X46] :
( ( ~ hBOOL(hAPP(X43,bool,hAPP(X43,fun(X43,bool),ord_less(X43),hAPP(nat,X43,power_power(X43,X46),X44)),hAPP(nat,X43,power_power(X43,X46),X45)))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X44),X45))
| ~ hBOOL(hAPP(X43,bool,hAPP(X43,fun(X43,bool),ord_less(X43),one_one(X43)),X46))
| ~ linordered_semidom(X43) )
& ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X44),X45))
| hBOOL(hAPP(X43,bool,hAPP(X43,fun(X43,bool),ord_less(X43),hAPP(nat,X43,power_power(X43,X46),X44)),hAPP(nat,X43,power_power(X43,X46),X45)))
| ~ hBOOL(hAPP(X43,bool,hAPP(X43,fun(X43,bool),ord_less(X43),one_one(X43)),X46))
| ~ linordered_semidom(X43) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_716])])])]) ).
fof(c_0_1372,plain,
! [X32,X33,X34] :
( ~ linordered_semidom(X32)
| ~ hBOOL(hAPP(X32,bool,hAPP(X32,fun(X32,bool),ord_less(X32),one_one(X32)),X34))
| hBOOL(hAPP(X32,bool,hAPP(X32,fun(X32,bool),ord_less(X32),hAPP(nat,X32,power_power(X32,X34),X33)),hAPP(X32,X32,hAPP(X32,fun(X32,X32),times_times(X32),X34),hAPP(nat,X32,power_power(X32,X34),X33)))) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_717])])]) ).
fof(c_0_1373,plain,
! [X22,X23,X24] :
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X24))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,power_power(nat,X24),X22)),hAPP(nat,nat,power_power(nat,X24),X23)))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X22),X23)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_718])]) ).
fof(c_0_1374,plain,
! [X41,X42,X43,X44] :
( ~ linordered_semidom(X41)
| ~ hBOOL(hAPP(X41,bool,hAPP(X41,fun(X41,bool),ord_less_eq(X41),X43),X44))
| ~ hBOOL(hAPP(X41,bool,hAPP(X41,fun(X41,bool),ord_less_eq(X41),zero_zero(X41)),X43))
| hBOOL(hAPP(X41,bool,hAPP(X41,fun(X41,bool),ord_less_eq(X41),hAPP(nat,X41,power_power(X41,X43),X42)),hAPP(nat,X41,power_power(X41,X44),X42))) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_719])])]) ).
fof(c_0_1375,plain,
! [X41,X42,X43] :
( ~ linord581940658strict(X41)
| ~ hBOOL(hAPP(X41,bool,hAPP(X41,fun(X41,bool),ord_less(X41),X43),zero_zero(X41)))
| ~ hBOOL(hAPP(X41,bool,hAPP(X41,fun(X41,bool),ord_less(X41),X42),zero_zero(X41)))
| hBOOL(hAPP(X41,bool,hAPP(X41,fun(X41,bool),ord_less(X41),zero_zero(X41)),hAPP(X41,X41,hAPP(X41,fun(X41,X41),times_times(X41),X43),X42))) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_720])])]) ).
fof(c_0_1376,plain,
! [X46,X47,X48,X49,X50] :
( ~ ordere223160158up_add(X46)
| ~ hBOOL(hAPP(X46,bool,hAPP(X46,fun(X46,bool),ord_less_eq(X46),X49),X50))
| ~ hBOOL(hAPP(X46,bool,hAPP(X46,fun(X46,bool),ord_less(X46),X47),X48))
| hBOOL(hAPP(X46,bool,hAPP(X46,fun(X46,bool),ord_less(X46),hAPP(X46,X46,plus_plus(X46,X49),X47)),hAPP(X46,X46,plus_plus(X46,X50),X48))) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_721])])]) ).
fof(c_0_1377,plain,
! [X46,X47,X48,X49,X50] :
( ~ ordere223160158up_add(X46)
| ~ hBOOL(hAPP(X46,bool,hAPP(X46,fun(X46,bool),ord_less(X46),X49),X50))
| ~ hBOOL(hAPP(X46,bool,hAPP(X46,fun(X46,bool),ord_less_eq(X46),X47),X48))
| hBOOL(hAPP(X46,bool,hAPP(X46,fun(X46,bool),ord_less(X46),hAPP(X46,X46,plus_plus(X46,X49),X47)),hAPP(X46,X46,plus_plus(X46,X50),X48))) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_722])])]) ).
fof(c_0_1378,plain,
! [X46,X47,X48,X49,X50] :
( ~ ordere779506340up_add(X46)
| ~ hBOOL(hAPP(X46,bool,hAPP(X46,fun(X46,bool),ord_less_eq(X46),X49),X50))
| ~ hBOOL(hAPP(X46,bool,hAPP(X46,fun(X46,bool),ord_less_eq(X46),X47),X48))
| hBOOL(hAPP(X46,bool,hAPP(X46,fun(X46,bool),ord_less_eq(X46),hAPP(X46,X46,plus_plus(X46,X49),X47)),hAPP(X46,X46,plus_plus(X46,X50),X48))) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_723])])]) ).
fof(c_0_1379,plain,
! [X46,X47,X48,X49,X50] :
( ~ ordere223160158up_add(X46)
| ~ hBOOL(hAPP(X46,bool,hAPP(X46,fun(X46,bool),ord_less(X46),X49),X50))
| ~ hBOOL(hAPP(X46,bool,hAPP(X46,fun(X46,bool),ord_less(X46),X47),X48))
| hBOOL(hAPP(X46,bool,hAPP(X46,fun(X46,bool),ord_less(X46),hAPP(X46,X46,plus_plus(X46,X49),X47)),hAPP(X46,X46,plus_plus(X46,X50),X48))) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_724])])]) ).
fof(c_0_1380,plain,
! [X33,X34,X35,X36] :
( ~ linordered_semidom(X33)
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X35),X36))
| ~ hBOOL(hAPP(X33,bool,hAPP(X33,fun(X33,bool),ord_less_eq(X33),one_one(X33)),X34))
| hBOOL(hAPP(X33,bool,hAPP(X33,fun(X33,bool),ord_less_eq(X33),hAPP(nat,X33,power_power(X33,X34),X35)),hAPP(nat,X33,power_power(X33,X34),X36))) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_725])])]) ).
fof(c_0_1381,plain,
! [X33,X34,X35,X36] :
( ~ linordered_semidom(X33)
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X35),X36))
| ~ hBOOL(hAPP(X33,bool,hAPP(X33,fun(X33,bool),ord_less(X33),one_one(X33)),X34))
| hBOOL(hAPP(X33,bool,hAPP(X33,fun(X33,bool),ord_less(X33),hAPP(nat,X33,power_power(X33,X34),X35)),hAPP(nat,X33,power_power(X33,X34),X36))) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_726])])]) ).
fof(c_0_1382,plain,
! [X63,X64,X65,X66] :
( ( hBOOL(hAPP(X63,bool,hAPP(X63,fun(X63,bool),ord_less(X63),X65),esk27_4(X63,X64,X65,X66)))
| hBOOL(hAPP(X63,bool,hAPP(X63,fun(X63,bool),ord_less_eq(X63),X66),X64))
| ~ hBOOL(hAPP(X63,bool,hAPP(X63,fun(X63,bool),ord_less(X63),X65),X66))
| ~ dense_linorder(X63) )
& ( hBOOL(hAPP(X63,bool,hAPP(X63,fun(X63,bool),ord_less(X63),esk27_4(X63,X64,X65,X66)),X66))
| hBOOL(hAPP(X63,bool,hAPP(X63,fun(X63,bool),ord_less_eq(X63),X66),X64))
| ~ hBOOL(hAPP(X63,bool,hAPP(X63,fun(X63,bool),ord_less(X63),X65),X66))
| ~ dense_linorder(X63) )
& ( ~ hBOOL(hAPP(X63,bool,hAPP(X63,fun(X63,bool),ord_less_eq(X63),esk27_4(X63,X64,X65,X66)),X64))
| hBOOL(hAPP(X63,bool,hAPP(X63,fun(X63,bool),ord_less_eq(X63),X66),X64))
| ~ hBOOL(hAPP(X63,bool,hAPP(X63,fun(X63,bool),ord_less(X63),X65),X66))
| ~ dense_linorder(X63) ) ),
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_727])])])])]) ).
fof(c_0_1383,plain,
! [X31,X32,X33,X34] :
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X33),X34))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X31),X32))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,plus_plus(nat,X33),X31)),hAPP(nat,nat,plus_plus(nat,X34),X32))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_728])]) ).
fof(c_0_1384,plain,
! [X52,X53,X54,X55] :
( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X54),X55))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X52),X53))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,plus_plus(int,X54),X52)),hAPP(int,int,plus_plus(int,X55),X53))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_729])]) ).
fof(c_0_1385,plain,
! [X31,X32,X33,X34] :
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X33),X34))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X31),X32))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,plus_plus(nat,X33),X31)),hAPP(nat,nat,plus_plus(nat,X34),X32))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_730])]) ).
fof(c_0_1386,plain,
! [X32,X33,X34] :
( ~ linordered_semidom(X32)
| ~ hBOOL(hAPP(X32,bool,hAPP(X32,fun(X32,bool),ord_less(X32),one_one(X32)),X34))
| hBOOL(hAPP(X32,bool,hAPP(X32,fun(X32,bool),ord_less(X32),one_one(X32)),hAPP(X32,X32,hAPP(X32,fun(X32,X32),times_times(X32),X34),hAPP(nat,X32,power_power(X32,X34),X33)))) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_731])])]) ).
fof(c_0_1387,plain,
! [X42,X43,X44,X45] :
( ~ ordere236663937imp_le(X42)
| ~ hBOOL(hAPP(X42,bool,hAPP(X42,fun(X42,bool),ord_less_eq(X42),hAPP(X42,X42,plus_plus(X42,X43),X44)),hAPP(X42,X42,plus_plus(X42,X43),X45)))
| hBOOL(hAPP(X42,bool,hAPP(X42,fun(X42,bool),ord_less_eq(X42),X44),X45)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_732])])]) ).
fof(c_0_1388,plain,
! [X42,X43,X44,X45] :
( ~ ordere236663937imp_le(X42)
| ~ hBOOL(hAPP(X42,bool,hAPP(X42,fun(X42,bool),ord_less_eq(X42),hAPP(X42,X42,plus_plus(X42,X43),X44)),hAPP(X42,X42,plus_plus(X42,X45),X44)))
| hBOOL(hAPP(X42,bool,hAPP(X42,fun(X42,bool),ord_less_eq(X42),X43),X45)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_733])])]) ).
fof(c_0_1389,plain,
! [X47,X48,X49,X50,X51,X52,X53] :
( ( ~ hBOOL(hAPP(X47,bool,hAPP(X47,fun(X47,bool),ord_less_eq(X47),hAPP(X47,X47,plus_plus(X47,X48),X49)),hAPP(X47,X47,plus_plus(X47,X48),X50)))
| hBOOL(hAPP(X47,bool,hAPP(X47,fun(X47,bool),ord_less_eq(X47),X49),X50))
| ~ ordere236663937imp_le(X47) )
& ( ~ hBOOL(hAPP(X47,bool,hAPP(X47,fun(X47,bool),ord_less_eq(X47),X52),X53))
| hBOOL(hAPP(X47,bool,hAPP(X47,fun(X47,bool),ord_less_eq(X47),hAPP(X47,X47,plus_plus(X47,X51),X52)),hAPP(X47,X47,plus_plus(X47,X51),X53)))
| ~ ordere236663937imp_le(X47) ) ),
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_734])])])])]) ).
fof(c_0_1390,plain,
! [X47,X48,X49,X50,X51,X52,X53] :
( ( ~ hBOOL(hAPP(X47,bool,hAPP(X47,fun(X47,bool),ord_less_eq(X47),hAPP(X47,X47,plus_plus(X47,X48),X49)),hAPP(X47,X47,plus_plus(X47,X50),X49)))
| hBOOL(hAPP(X47,bool,hAPP(X47,fun(X47,bool),ord_less_eq(X47),X48),X50))
| ~ ordere236663937imp_le(X47) )
& ( ~ hBOOL(hAPP(X47,bool,hAPP(X47,fun(X47,bool),ord_less_eq(X47),X51),X53))
| hBOOL(hAPP(X47,bool,hAPP(X47,fun(X47,bool),ord_less_eq(X47),hAPP(X47,X47,plus_plus(X47,X51),X52)),hAPP(X47,X47,plus_plus(X47,X53),X52)))
| ~ ordere236663937imp_le(X47) ) ),
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_735])])])])]) ).
fof(c_0_1391,plain,
! [X47,X48,X49,X50,X51,X52,X53] :
( ( ~ hBOOL(hAPP(X47,bool,hAPP(X47,fun(X47,bool),ord_less(X47),hAPP(X47,X47,plus_plus(X47,X48),X49)),hAPP(X47,X47,plus_plus(X47,X50),X49)))
| hBOOL(hAPP(X47,bool,hAPP(X47,fun(X47,bool),ord_less(X47),X48),X50))
| ~ ordere236663937imp_le(X47) )
& ( ~ hBOOL(hAPP(X47,bool,hAPP(X47,fun(X47,bool),ord_less(X47),X51),X53))
| hBOOL(hAPP(X47,bool,hAPP(X47,fun(X47,bool),ord_less(X47),hAPP(X47,X47,plus_plus(X47,X51),X52)),hAPP(X47,X47,plus_plus(X47,X53),X52)))
| ~ ordere236663937imp_le(X47) ) ),
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_736])])])])]) ).
fof(c_0_1392,plain,
! [X47,X48,X49,X50,X51,X52,X53] :
( ( ~ hBOOL(hAPP(X47,bool,hAPP(X47,fun(X47,bool),ord_less(X47),hAPP(X47,X47,plus_plus(X47,X48),X49)),hAPP(X47,X47,plus_plus(X47,X48),X50)))
| hBOOL(hAPP(X47,bool,hAPP(X47,fun(X47,bool),ord_less(X47),X49),X50))
| ~ ordere236663937imp_le(X47) )
& ( ~ hBOOL(hAPP(X47,bool,hAPP(X47,fun(X47,bool),ord_less(X47),X52),X53))
| hBOOL(hAPP(X47,bool,hAPP(X47,fun(X47,bool),ord_less(X47),hAPP(X47,X47,plus_plus(X47,X51),X52)),hAPP(X47,X47,plus_plus(X47,X51),X53)))
| ~ ordere236663937imp_le(X47) ) ),
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_737])])])])]) ).
fof(c_0_1393,plain,
! [X42,X43,X44,X45] :
( ~ ordere236663937imp_le(X42)
| ~ hBOOL(hAPP(X42,bool,hAPP(X42,fun(X42,bool),ord_less(X42),hAPP(X42,X42,plus_plus(X42,X43),X44)),hAPP(X42,X42,plus_plus(X42,X45),X44)))
| hBOOL(hAPP(X42,bool,hAPP(X42,fun(X42,bool),ord_less(X42),X43),X45)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_738])])]) ).
fof(c_0_1394,plain,
! [X42,X43,X44,X45] :
( ~ ordere236663937imp_le(X42)
| ~ hBOOL(hAPP(X42,bool,hAPP(X42,fun(X42,bool),ord_less(X42),hAPP(X42,X42,plus_plus(X42,X43),X44)),hAPP(X42,X42,plus_plus(X42,X43),X45)))
| hBOOL(hAPP(X42,bool,hAPP(X42,fun(X42,bool),ord_less(X42),X44),X45)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_739])])]) ).
fof(c_0_1395,plain,
! [X36,X37,X38] :
( ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X37),esk1_3(X36,X37,X38)))
| hBOOL(hAPP(int,bool,X36,X38))
| ~ hBOOL(hAPP(int,bool,X36,hAPP(int,int,plus_plus(int,X37),one_one(int))))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X37),X38)) )
& ( hBOOL(hAPP(int,bool,X36,esk1_3(X36,X37,X38)))
| hBOOL(hAPP(int,bool,X36,X38))
| ~ hBOOL(hAPP(int,bool,X36,hAPP(int,int,plus_plus(int,X37),one_one(int))))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X37),X38)) )
& ( ~ hBOOL(hAPP(int,bool,X36,hAPP(int,int,plus_plus(int,esk1_3(X36,X37,X38)),one_one(int))))
| hBOOL(hAPP(int,bool,X36,X38))
| ~ hBOOL(hAPP(int,bool,X36,hAPP(int,int,plus_plus(int,X37),one_one(int))))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X37),X38)) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_740])])])]) ).
fof(c_0_1396,plain,
! [X31,X32] : hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,bit1,X31)),X32) = hAPP(int,int,plus_plus(int,hAPP(int,int,bit0,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),X31),X32))),X32),
inference(variable_rename,[status(thm)],[c_0_741]) ).
fof(c_0_1397,plain,
! [X29,X30,X31,X32,X33,X34] :
( ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,plus_plus(nat,X29),X30)),hAPP(nat,nat,plus_plus(nat,X29),X31)))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X30),X31)) )
& ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X33),X34))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,plus_plus(nat,X32),X33)),hAPP(nat,nat,plus_plus(nat,X32),X34))) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_742])])])]) ).
fof(c_0_1398,plain,
! [X29,X30,X31,X32,X33,X34] :
( ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,plus_plus(nat,X29),X30)),hAPP(nat,nat,plus_plus(nat,X29),X31)))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X30),X31)) )
& ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X33),X34))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,plus_plus(nat,X32),X33)),hAPP(nat,nat,plus_plus(nat,X32),X34))) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_743])])])]) ).
fof(c_0_1399,plain,
! [X34,X35,X36] :
( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X36),X35))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X34,X36),X35))
| X35 = X36
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X35),X36)) )
& ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X34,X36),X35))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X34,X36),X35))
| X35 = X36
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X35),X36)) )
& ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X36),X35))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X34,X36),X35))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X34,X36),X35))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X35),X36)) )
& ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X34,X36),X35))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X34,X36),X35))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X34,X36),X35))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X35),X36)) )
& ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X36),X35))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X34,X36),X35))
| X35 = X36
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X34,X36),X35)) )
& ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X34,X36),X35))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X34,X36),X35))
| X35 = X36
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X34,X36),X35)) )
& ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X36),X35))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X34,X36),X35))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X34,X36),X35))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X34,X36),X35)) )
& ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X34,X36),X35))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X34,X36),X35))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X34,X36),X35))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X34,X36),X35)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_744])])]) ).
fof(c_0_1400,plain,
! [X41,X42,X43] :
( ~ ordere216010020id_add(X41)
| ~ hBOOL(hAPP(X41,bool,hAPP(X41,fun(X41,bool),ord_less_eq(X41),X43),zero_zero(X41)))
| ~ hBOOL(hAPP(X41,bool,hAPP(X41,fun(X41,bool),ord_less(X41),X42),zero_zero(X41)))
| hBOOL(hAPP(X41,bool,hAPP(X41,fun(X41,bool),ord_less(X41),hAPP(X41,X41,plus_plus(X41,X43),X42)),zero_zero(X41))) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_745])])]) ).
fof(c_0_1401,plain,
! [X41,X42,X43] :
( ~ ordere216010020id_add(X41)
| ~ hBOOL(hAPP(X41,bool,hAPP(X41,fun(X41,bool),ord_less(X41),X43),zero_zero(X41)))
| ~ hBOOL(hAPP(X41,bool,hAPP(X41,fun(X41,bool),ord_less_eq(X41),X42),zero_zero(X41)))
| hBOOL(hAPP(X41,bool,hAPP(X41,fun(X41,bool),ord_less(X41),hAPP(X41,X41,plus_plus(X41,X43),X42)),zero_zero(X41))) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_746])])]) ).
fof(c_0_1402,plain,
! [X41,X42,X43] :
( ~ ordere216010020id_add(X41)
| ~ hBOOL(hAPP(X41,bool,hAPP(X41,fun(X41,bool),ord_less_eq(X41),X43),zero_zero(X41)))
| ~ hBOOL(hAPP(X41,bool,hAPP(X41,fun(X41,bool),ord_less_eq(X41),X42),zero_zero(X41)))
| hBOOL(hAPP(X41,bool,hAPP(X41,fun(X41,bool),ord_less_eq(X41),hAPP(X41,X41,plus_plus(X41,X43),X42)),zero_zero(X41))) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_747])])]) ).
fof(c_0_1403,plain,
! [X41,X42,X43] :
( ~ ordere216010020id_add(X41)
| ~ hBOOL(hAPP(X41,bool,hAPP(X41,fun(X41,bool),ord_less(X41),X43),zero_zero(X41)))
| ~ hBOOL(hAPP(X41,bool,hAPP(X41,fun(X41,bool),ord_less(X41),X42),zero_zero(X41)))
| hBOOL(hAPP(X41,bool,hAPP(X41,fun(X41,bool),ord_less(X41),hAPP(X41,X41,plus_plus(X41,X43),X42)),zero_zero(X41))) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_748])])]) ).
fof(c_0_1404,plain,
! [X29,X30,X31,X32,X33] :
( ( ~ hBOOL(hAPP(X29,bool,hAPP(X29,fun(X29,bool),ord_less_eq(X29),hAPP(nat,X29,semiring_1_of_nat(X29),X30)),hAPP(nat,X29,semiring_1_of_nat(X29),X31)))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X30),X31))
| ~ linordered_semidom(X29) )
& ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X32),X33))
| hBOOL(hAPP(X29,bool,hAPP(X29,fun(X29,bool),ord_less_eq(X29),hAPP(nat,X29,semiring_1_of_nat(X29),X32)),hAPP(nat,X29,semiring_1_of_nat(X29),X33)))
| ~ linordered_semidom(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_749])])])])]) ).
fof(c_0_1405,plain,
! [X16,X17,X18] :
( ~ linordered_semidom(X16)
| ~ hBOOL(hAPP(X16,bool,hAPP(X16,fun(X16,bool),ord_less(X16),hAPP(nat,X16,semiring_1_of_nat(X16),X17)),hAPP(nat,X16,semiring_1_of_nat(X16),X18)))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X17),X18)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_750])])]) ).
fof(c_0_1406,plain,
! [X29,X30,X31,X32,X33] :
( ( ~ hBOOL(hAPP(X29,bool,hAPP(X29,fun(X29,bool),ord_less(X29),hAPP(nat,X29,semiring_1_of_nat(X29),X30)),hAPP(nat,X29,semiring_1_of_nat(X29),X31)))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X30),X31))
| ~ linordered_semidom(X29) )
& ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X32),X33))
| hBOOL(hAPP(X29,bool,hAPP(X29,fun(X29,bool),ord_less(X29),hAPP(nat,X29,semiring_1_of_nat(X29),X32)),hAPP(nat,X29,semiring_1_of_nat(X29),X33)))
| ~ linordered_semidom(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_751])])])])]) ).
fof(c_0_1407,plain,
! [X29,X30,X31,X32] :
( ( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(nat,int,semiring_1_of_nat(int),X29)),hAPP(nat,int,semiring_1_of_nat(int),X30)))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X29),X30)) )
& ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X31),X32))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(nat,int,semiring_1_of_nat(int),X31)),hAPP(nat,int,semiring_1_of_nat(int),X32))) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_752])])])]) ).
fof(c_0_1408,plain,
! [X7,X8,X9,X10] :
( ( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(nat,int,semiring_1_of_nat(int),X7)),hAPP(nat,int,semiring_1_of_nat(int),X8)))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X7),X8)) )
& ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X9),X10))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(nat,int,semiring_1_of_nat(int),X9)),hAPP(nat,int,semiring_1_of_nat(int),X10))) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_753])])])]) ).
fof(c_0_1409,plain,
! [X29,X30,X31,X32] :
( ( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(nat,int,semiring_1_of_nat(int),X29)),hAPP(nat,int,semiring_1_of_nat(int),X30)))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X29),X30)) )
& ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X31),X32))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(nat,int,semiring_1_of_nat(int),X31)),hAPP(nat,int,semiring_1_of_nat(int),X32))) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_754])])])]) ).
fof(c_0_1410,plain,
! [X7,X8,X9,X10] :
( ( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(nat,int,semiring_1_of_nat(int),X7)),hAPP(nat,int,semiring_1_of_nat(int),X8)))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X7),X8)) )
& ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X9),X10))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(nat,int,semiring_1_of_nat(int),X9)),hAPP(nat,int,semiring_1_of_nat(int),X10))) ) ),
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_1411,plain,
! [X20,X21,X22,X23] :
( ( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,bit1,X20)),hAPP(int,int,bit0,X21)))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X20),X21)) )
& ( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X22),X23))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,bit1,X22)),hAPP(int,int,bit0,X23))) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_756])])])]) ).
fof(c_0_1412,plain,
! [X14,X15,X16,X17] :
( ( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,bit1,X14)),hAPP(int,int,bit0,X15)))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X14),X15)) )
& ( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X16),X17))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,bit1,X16)),hAPP(int,int,bit0,X17))) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_757])])])]) ).
fof(c_0_1413,plain,
! [X20,X21,X22,X23] :
( ( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit0,X20)),hAPP(int,int,bit1,X21)))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X20),X21)) )
& ( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X22),X23))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit0,X22)),hAPP(int,int,bit1,X23))) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_758])])])]) ).
fof(c_0_1414,plain,
! [X14,X15,X16,X17] :
( ( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit0,X14)),hAPP(int,int,bit1,X15)))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X14),X15)) )
& ( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X16),X17))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit0,X16)),hAPP(int,int,bit1,X17))) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_759])])])]) ).
fof(c_0_1415,plain,
! [X20,X21,X22,X23] :
( ( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,bit0,X20)),hAPP(int,int,bit1,X21)))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X20),X21)) )
& ( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X22),X23))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,bit0,X22)),hAPP(int,int,bit1,X23))) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_760])])])]) ).
fof(c_0_1416,plain,
! [X14,X15,X16,X17] :
( ( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,bit0,X14)),hAPP(int,int,bit1,X15)))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X14),X15)) )
& ( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X16),X17))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,bit0,X16)),hAPP(int,int,bit1,X17))) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_761])])])]) ).
fof(c_0_1417,plain,
! [X14,X15,X16,X17] :
( ( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,bit0,X14)),hAPP(int,int,bit0,X15)))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X14),X15)) )
& ( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X16),X17))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,bit0,X16)),hAPP(int,int,bit0,X17))) ) ),
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_1418,plain,
! [X20,X21,X22,X23] :
( ( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,bit0,X20)),hAPP(int,int,bit0,X21)))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X20),X21)) )
& ( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X22),X23))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,bit0,X22)),hAPP(int,int,bit0,X23))) ) ),
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_1419,plain,
! [X14,X15,X16,X17] :
( ( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,bit1,X14)),hAPP(int,int,bit1,X15)))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X14),X15)) )
& ( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X16),X17))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,bit1,X16)),hAPP(int,int,bit1,X17))) ) ),
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_1420,plain,
! [X20,X21,X22,X23] :
( ( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,bit1,X20)),hAPP(int,int,bit1,X21)))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X20),X21)) )
& ( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X22),X23))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,bit1,X22)),hAPP(int,int,bit1,X23))) ) ),
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_1421,plain,
! [X14,X15,X16,X17] :
( ( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit1,X14)),hAPP(int,int,bit0,X15)))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X14),X15)) )
& ( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X16),X17))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit1,X16)),hAPP(int,int,bit0,X17))) ) ),
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_1422,plain,
! [X20,X21,X22,X23] :
( ( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit1,X20)),hAPP(int,int,bit0,X21)))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X20),X21)) )
& ( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X22),X23))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit1,X22)),hAPP(int,int,bit0,X23))) ) ),
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_1423,plain,
! [X14,X15,X16,X17] :
( ( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit0,X14)),hAPP(int,int,bit0,X15)))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X14),X15)) )
& ( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X16),X17))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit0,X16)),hAPP(int,int,bit0,X17))) ) ),
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_1424,plain,
! [X20,X21,X22,X23] :
( ( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit0,X20)),hAPP(int,int,bit0,X21)))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X20),X21)) )
& ( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X22),X23))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit0,X22)),hAPP(int,int,bit0,X23))) ) ),
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_1425,plain,
! [X14,X15,X16,X17] :
( ( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit1,X14)),hAPP(int,int,bit1,X15)))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X14),X15)) )
& ( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X16),X17))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit1,X16)),hAPP(int,int,bit1,X17))) ) ),
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_1426,plain,
! [X20,X21,X22,X23] :
( ( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit1,X20)),hAPP(int,int,bit1,X21)))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X20),X21)) )
& ( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X22),X23))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit1,X22)),hAPP(int,int,bit1,X23))) ) ),
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_1427,plain,
! [X41,X42,X43,X44] :
( ~ linordered_semidom(X41)
| hAPP(nat,X41,power_power(X41,X42),X43) != hAPP(nat,X41,power_power(X41,X44),X43)
| ~ hBOOL(hAPP(X41,bool,hAPP(X41,fun(X41,bool),ord_less_eq(X41),zero_zero(X41)),X42))
| ~ hBOOL(hAPP(X41,bool,hAPP(X41,fun(X41,bool),ord_less_eq(X41),zero_zero(X41)),X44))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X43))
| ti(X41,X42) = ti(X41,X44) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_772])])]) ).
fof(c_0_1428,plain,
! [X58,X59,X60,X61,X62] :
( ~ ord(X59)
| ~ hBOOL(hAPP(fun(X58,X59),bool,hAPP(fun(X58,X59),fun(fun(X58,X59),bool),ord_less_eq(fun(X58,X59)),X61),X62))
| hBOOL(hAPP(X59,bool,hAPP(X59,fun(X59,bool),ord_less_eq(X59),hAPP(X58,X59,X61,X60)),hAPP(X58,X59,X62,X60))) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_773])])]) ).
fof(c_0_1429,plain,
! [X58,X59,X60,X61,X62] :
( ~ ord(X59)
| ~ hBOOL(hAPP(fun(X58,X59),bool,hAPP(fun(X58,X59),fun(fun(X58,X59),bool),ord_less_eq(fun(X58,X59)),X61),X62))
| hBOOL(hAPP(X59,bool,hAPP(X59,fun(X59,bool),ord_less_eq(X59),hAPP(X58,X59,X61,X60)),hAPP(X58,X59,X62,X60))) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_774])])]) ).
fof(c_0_1430,plain,
! [X49,X50,X52] :
( ( hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),esk4_2(X49,X50)))
| ~ hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X49))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X50)) )
& ( hAPP(nat,real,power_power(real,esk4_2(X49,X50)),X50) = X49
| ~ hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X49))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X50)) )
& ( ~ hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X52))
| hAPP(nat,real,power_power(real,X52),X50) != X49
| X52 = esk4_2(X49,X50)
| ~ hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X49))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X50)) ) ),
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_775])])])])]) ).
fof(c_0_1431,plain,
! [X41,X42,X43] :
( ~ ordere216010020id_add(X41)
| ~ hBOOL(hAPP(X41,bool,hAPP(X41,fun(X41,bool),ord_less_eq(X41),zero_zero(X41)),X43))
| ~ hBOOL(hAPP(X41,bool,hAPP(X41,fun(X41,bool),ord_less(X41),zero_zero(X41)),X42))
| hBOOL(hAPP(X41,bool,hAPP(X41,fun(X41,bool),ord_less(X41),zero_zero(X41)),hAPP(X41,X41,plus_plus(X41,X43),X42))) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_776])])]) ).
fof(c_0_1432,plain,
! [X41,X42,X43] :
( ~ ordere216010020id_add(X41)
| ~ hBOOL(hAPP(X41,bool,hAPP(X41,fun(X41,bool),ord_less(X41),zero_zero(X41)),X43))
| ~ hBOOL(hAPP(X41,bool,hAPP(X41,fun(X41,bool),ord_less_eq(X41),zero_zero(X41)),X42))
| hBOOL(hAPP(X41,bool,hAPP(X41,fun(X41,bool),ord_less(X41),zero_zero(X41)),hAPP(X41,X41,plus_plus(X41,X43),X42))) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_777])])]) ).
fof(c_0_1433,plain,
! [X41,X42,X43] :
( ~ ordere216010020id_add(X41)
| ~ hBOOL(hAPP(X41,bool,hAPP(X41,fun(X41,bool),ord_less_eq(X41),zero_zero(X41)),X43))
| ~ hBOOL(hAPP(X41,bool,hAPP(X41,fun(X41,bool),ord_less_eq(X41),zero_zero(X41)),X42))
| hBOOL(hAPP(X41,bool,hAPP(X41,fun(X41,bool),ord_less_eq(X41),zero_zero(X41)),hAPP(X41,X41,plus_plus(X41,X43),X42))) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_778])])]) ).
fof(c_0_1434,plain,
! [X41,X42,X43] :
( ~ ordere216010020id_add(X41)
| ~ hBOOL(hAPP(X41,bool,hAPP(X41,fun(X41,bool),ord_less(X41),zero_zero(X41)),X43))
| ~ hBOOL(hAPP(X41,bool,hAPP(X41,fun(X41,bool),ord_less(X41),zero_zero(X41)),X42))
| hBOOL(hAPP(X41,bool,hAPP(X41,fun(X41,bool),ord_less(X41),zero_zero(X41)),hAPP(X41,X41,plus_plus(X41,X43),X42))) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_779])])]) ).
fof(c_0_1435,plain,
! [X42,X43,X44,X45] :
( ~ ordere216010020id_add(X42)
| ~ hBOOL(hAPP(X42,bool,hAPP(X42,fun(X42,bool),ord_less_eq(X42),zero_zero(X42)),X45))
| ~ hBOOL(hAPP(X42,bool,hAPP(X42,fun(X42,bool),ord_less(X42),X43),X44))
| hBOOL(hAPP(X42,bool,hAPP(X42,fun(X42,bool),ord_less(X42),X43),hAPP(X42,X42,plus_plus(X42,X45),X44))) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_780])])]) ).
fof(c_0_1436,plain,
! [X42,X43,X44,X45] :
( ~ ordere216010020id_add(X42)
| ~ hBOOL(hAPP(X42,bool,hAPP(X42,fun(X42,bool),ord_less(X42),zero_zero(X42)),X45))
| ~ hBOOL(hAPP(X42,bool,hAPP(X42,fun(X42,bool),ord_less_eq(X42),X43),X44))
| hBOOL(hAPP(X42,bool,hAPP(X42,fun(X42,bool),ord_less(X42),X43),hAPP(X42,X42,plus_plus(X42,X45),X44))) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_781])])]) ).
fof(c_0_1437,plain,
! [X42,X43,X44,X45] :
( ~ ordere216010020id_add(X42)
| ~ hBOOL(hAPP(X42,bool,hAPP(X42,fun(X42,bool),ord_less_eq(X42),zero_zero(X42)),X45))
| ~ hBOOL(hAPP(X42,bool,hAPP(X42,fun(X42,bool),ord_less_eq(X42),X43),X44))
| hBOOL(hAPP(X42,bool,hAPP(X42,fun(X42,bool),ord_less_eq(X42),X43),hAPP(X42,X42,plus_plus(X42,X44),X45))) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_782])])]) ).
fof(c_0_1438,plain,
! [X42,X43,X44,X45] :
( ~ ordere216010020id_add(X42)
| ~ hBOOL(hAPP(X42,bool,hAPP(X42,fun(X42,bool),ord_less_eq(X42),zero_zero(X42)),X45))
| ~ hBOOL(hAPP(X42,bool,hAPP(X42,fun(X42,bool),ord_less_eq(X42),X43),X44))
| hBOOL(hAPP(X42,bool,hAPP(X42,fun(X42,bool),ord_less_eq(X42),X43),hAPP(X42,X42,plus_plus(X42,X45),X44))) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_783])])]) ).
fof(c_0_1439,plain,
! [X42,X43,X44,X45] :
( ~ linordered_semidom(X42)
| ~ hBOOL(hAPP(X42,bool,hAPP(X42,fun(X42,bool),ord_less(X42),zero_zero(X42)),X45))
| ~ hBOOL(hAPP(X42,bool,hAPP(X42,fun(X42,bool),ord_less(X42),X43),X44))
| hBOOL(hAPP(X42,bool,hAPP(X42,fun(X42,bool),ord_less(X42),X43),hAPP(X42,X42,plus_plus(X42,X45),X44))) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_784])])]) ).
fof(c_0_1440,plain,
! [X58,X59,X60,X61,X62,X63] :
( ( hBOOL(hAPP(fun(X58,X59),bool,hAPP(fun(X58,X59),fun(fun(X58,X59),bool),ord_less_eq(fun(X58,X59)),X60),X61))
| ~ hBOOL(hAPP(fun(X58,X59),bool,hAPP(fun(X58,X59),fun(fun(X58,X59),bool),ord_less(fun(X58,X59)),X60),X61))
| ~ ord(X59) )
& ( ~ hBOOL(hAPP(fun(X58,X59),bool,hAPP(fun(X58,X59),fun(fun(X58,X59),bool),ord_less_eq(fun(X58,X59)),X61),X60))
| ~ hBOOL(hAPP(fun(X58,X59),bool,hAPP(fun(X58,X59),fun(fun(X58,X59),bool),ord_less(fun(X58,X59)),X60),X61))
| ~ ord(X59) )
& ( ~ hBOOL(hAPP(fun(X58,X59),bool,hAPP(fun(X58,X59),fun(fun(X58,X59),bool),ord_less_eq(fun(X58,X59)),X62),X63))
| hBOOL(hAPP(fun(X58,X59),bool,hAPP(fun(X58,X59),fun(fun(X58,X59),bool),ord_less_eq(fun(X58,X59)),X63),X62))
| hBOOL(hAPP(fun(X58,X59),bool,hAPP(fun(X58,X59),fun(fun(X58,X59),bool),ord_less(fun(X58,X59)),X62),X63))
| ~ ord(X59) ) ),
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_785])])])])]) ).
fof(c_0_1441,plain,
! [X32,X33,X34] :
( ~ linordered_semidom(X32)
| ~ hBOOL(hAPP(X32,bool,hAPP(X32,fun(X32,bool),ord_less(X32),one_one(X32)),X34))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X33))
| hBOOL(hAPP(X32,bool,hAPP(X32,fun(X32,bool),ord_less(X32),one_one(X32)),hAPP(nat,X32,power_power(X32,X34),X33))) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_786])])]) ).
fof(c_0_1442,plain,
! [X12,X13] :
( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X13))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X12))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,plus_plus(int,X13),X12))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_787])]) ).
fof(c_0_1443,plain,
! [X8,X9,X10] :
( ( ~ hBOOL(hAPP(X8,bool,hAPP(X8,fun(X8,bool),ord_less_eq(X8),hAPP(X8,X8,plus_plus(X8,X9),X9)),zero_zero(X8)))
| hBOOL(hAPP(X8,bool,hAPP(X8,fun(X8,bool),ord_less_eq(X8),X9),zero_zero(X8)))
| ~ linord219039673up_add(X8) )
& ( ~ hBOOL(hAPP(X8,bool,hAPP(X8,fun(X8,bool),ord_less_eq(X8),X10),zero_zero(X8)))
| hBOOL(hAPP(X8,bool,hAPP(X8,fun(X8,bool),ord_less_eq(X8),hAPP(X8,X8,plus_plus(X8,X10),X10)),zero_zero(X8)))
| ~ linord219039673up_add(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_788])])])])]) ).
fof(c_0_1444,plain,
! [X8,X9,X10] :
( ( ~ hBOOL(hAPP(X8,bool,hAPP(X8,fun(X8,bool),ord_less(X8),hAPP(X8,X8,plus_plus(X8,X9),X9)),zero_zero(X8)))
| hBOOL(hAPP(X8,bool,hAPP(X8,fun(X8,bool),ord_less(X8),X9),zero_zero(X8)))
| ~ linord219039673up_add(X8) )
& ( ~ hBOOL(hAPP(X8,bool,hAPP(X8,fun(X8,bool),ord_less(X8),X10),zero_zero(X8)))
| hBOOL(hAPP(X8,bool,hAPP(X8,fun(X8,bool),ord_less(X8),hAPP(X8,X8,plus_plus(X8,X10),X10)),zero_zero(X8)))
| ~ linord219039673up_add(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_789])])])])]) ).
fof(c_0_1445,plain,
! [X8,X9,X10] :
( ( ~ hBOOL(hAPP(X8,bool,hAPP(X8,fun(X8,bool),ord_less(X8),hAPP(X8,X8,plus_plus(X8,X9),X9)),zero_zero(X8)))
| hBOOL(hAPP(X8,bool,hAPP(X8,fun(X8,bool),ord_less(X8),X9),zero_zero(X8)))
| ~ linordered_idom(X8) )
& ( ~ hBOOL(hAPP(X8,bool,hAPP(X8,fun(X8,bool),ord_less(X8),X10),zero_zero(X8)))
| hBOOL(hAPP(X8,bool,hAPP(X8,fun(X8,bool),ord_less(X8),hAPP(X8,X8,plus_plus(X8,X10),X10)),zero_zero(X8)))
| ~ linordered_idom(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_790])])])])]) ).
fof(c_0_1446,plain,
! [X36,X37,X38] :
( ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X37),esk18_3(X36,X37,X38)))
| hBOOL(hAPP(int,bool,X36,X38))
| ~ hBOOL(hAPP(int,bool,X36,X37))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X37),X38)) )
& ( hBOOL(hAPP(int,bool,X36,esk18_3(X36,X37,X38)))
| hBOOL(hAPP(int,bool,X36,X38))
| ~ hBOOL(hAPP(int,bool,X36,X37))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X37),X38)) )
& ( ~ hBOOL(hAPP(int,bool,X36,hAPP(int,int,plus_plus(int,esk18_3(X36,X37,X38)),one_one(int))))
| hBOOL(hAPP(int,bool,X36,X38))
| ~ hBOOL(hAPP(int,bool,X36,X37))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X37),X38)) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_791])])])]) ).
fof(c_0_1447,plain,
! [X30,X31,X32,X33] :
( ( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,plus_plus(int,X30),one_one(int))),X31))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X30),X31)) )
& ( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X32),X33))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,plus_plus(int,X32),one_one(int))),X33)) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_792])])])]) ).
fof(c_0_1448,axiom,
hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),number_number_of(int,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),
c_0_793 ).
fof(c_0_1449,axiom,
hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),number_number_of(int,hAPP(int,int,bit1,hAPP(int,int,bit1,pls))))),
c_0_794 ).
fof(c_0_1450,axiom,
hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),
c_0_795 ).
fof(c_0_1451,plain,
! [X42,X43,X44,X45] :
( ~ ordere779506340up_add(X42)
| ~ hBOOL(hAPP(X42,bool,hAPP(X42,fun(X42,bool),ord_less_eq(X42),X44),X45))
| hBOOL(hAPP(X42,bool,hAPP(X42,fun(X42,bool),ord_less_eq(X42),hAPP(X42,X42,plus_plus(X42,X43),X44)),hAPP(X42,X42,plus_plus(X42,X43),X45))) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_796])])]) ).
fof(c_0_1452,plain,
! [X42,X43,X44,X45] :
( ~ ordere779506340up_add(X42)
| ~ hBOOL(hAPP(X42,bool,hAPP(X42,fun(X42,bool),ord_less_eq(X42),X44),X45))
| hBOOL(hAPP(X42,bool,hAPP(X42,fun(X42,bool),ord_less_eq(X42),hAPP(X42,X42,plus_plus(X42,X44),X43)),hAPP(X42,X42,plus_plus(X42,X45),X43))) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_797])])]) ).
fof(c_0_1453,plain,
! [X42,X43,X44,X45] :
( ~ ordere223160158up_add(X42)
| ~ hBOOL(hAPP(X42,bool,hAPP(X42,fun(X42,bool),ord_less(X42),X44),X45))
| hBOOL(hAPP(X42,bool,hAPP(X42,fun(X42,bool),ord_less(X42),hAPP(X42,X42,plus_plus(X42,X44),X43)),hAPP(X42,X42,plus_plus(X42,X45),X43))) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_798])])]) ).
fof(c_0_1454,plain,
! [X42,X43,X44,X45] :
( ~ ordere223160158up_add(X42)
| ~ hBOOL(hAPP(X42,bool,hAPP(X42,fun(X42,bool),ord_less(X42),X44),X45))
| hBOOL(hAPP(X42,bool,hAPP(X42,fun(X42,bool),ord_less(X42),hAPP(X42,X42,plus_plus(X42,X43),X44)),hAPP(X42,X42,plus_plus(X42,X43),X45))) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_799])])]) ).
fof(c_0_1455,plain,
! [X21,X22,X23] :
( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X21),X23))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,plus_plus(nat,X21),X22)),X23)) )
& ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X22),X23))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,plus_plus(nat,X21),X22)),X23)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_800])])]) ).
fof(c_0_1456,plain,
! [X21,X22,X23] :
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,plus_plus(nat,X21),X22)),X23))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X21),X23)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_801])]) ).
fof(c_0_1457,plain,
! [X21,X22,X23] :
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,plus_plus(nat,X21),X22)),X23))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X22),X23)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_802])]) ).
fof(c_0_1458,plain,
! [X23,X24,X25] :
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,plus_plus(nat,X23),X24)),X25))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X23),X25)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_803])]) ).
fof(c_0_1459,plain,
! [X29,X30,X31,X32] :
( ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,plus_plus(nat,X29),X30)))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X29))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X30)) )
& ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X31))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,plus_plus(nat,X31),X32))) )
& ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X32))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,plus_plus(nat,X31),X32))) ) ),
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_804])])])])]) ).
fof(c_0_1460,plain,
! [X17,X18,X19] :
( ~ hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X18),X19))
| hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,plus_plus(real,X17),X18)),hAPP(real,real,plus_plus(real,X17),X19))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_805])]) ).
fof(c_0_1461,plain,
! [X23,X24,X25] :
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X24),X25))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,plus_plus(nat,X24),X23)),hAPP(nat,nat,plus_plus(nat,X25),X23))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_806])]) ).
fof(c_0_1462,plain,
! [X23,X24,X25] :
( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X24),X25))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,plus_plus(int,X23),X24)),hAPP(int,int,plus_plus(int,X23),X25))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_807])]) ).
fof(c_0_1463,plain,
! [X23,X24,X25] :
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X24),X25))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,plus_plus(nat,X24),X23)),hAPP(nat,nat,plus_plus(nat,X25),X23))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_808])]) ).
fof(c_0_1464,plain,
! [X23,X24,X25] :
( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X24),X25))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,plus_plus(int,X24),X23)),hAPP(int,int,plus_plus(int,X25),X23))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_809])]) ).
fof(c_0_1465,plain,
! [X7,X8,X9] :
( ( ~ hBOOL(hAPP(X7,bool,hAPP(X7,fun(X7,bool),ord_less_eq(X7),one_one(X7)),number_number_of(X7,X8)))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,bit1,pls)),X8))
| ~ number_ring(X7)
| ~ linordered_idom(X7) )
& ( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,bit1,pls)),X9))
| hBOOL(hAPP(X7,bool,hAPP(X7,fun(X7,bool),ord_less_eq(X7),one_one(X7)),number_number_of(X7,X9)))
| ~ number_ring(X7)
| ~ linordered_idom(X7) ) ),
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_810])])])])]) ).
fof(c_0_1466,plain,
! [X7,X8,X9] :
( ( ~ hBOOL(hAPP(X7,bool,hAPP(X7,fun(X7,bool),ord_less(X7),one_one(X7)),number_number_of(X7,X8)))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit1,pls)),X8))
| ~ number_ring(X7)
| ~ linordered_idom(X7) )
& ( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit1,pls)),X9))
| hBOOL(hAPP(X7,bool,hAPP(X7,fun(X7,bool),ord_less(X7),one_one(X7)),number_number_of(X7,X9)))
| ~ number_ring(X7)
| ~ linordered_idom(X7) ) ),
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_811])])])])]) ).
fof(c_0_1467,plain,
! [X17,X18,X19] : hAPP(int,int,plus_plus(int,hAPP(nat,int,semiring_1_of_nat(int),X17)),hAPP(int,int,plus_plus(int,hAPP(nat,int,semiring_1_of_nat(int),X18)),X19)) = hAPP(int,int,plus_plus(int,hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,plus_plus(nat,X17),X18))),X19),
inference(variable_rename,[status(thm)],[c_0_812]) ).
fof(c_0_1468,plain,
! [X6,X7] :
( ( ~ hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,sqrt,X6)),one_one(real)))
| hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X6),one_one(real))) )
& ( ~ hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X7),one_one(real)))
| hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,sqrt,X7)),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_813])])])]) ).
fof(c_0_1469,plain,
! [X6,X7] :
( ( ~ hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,sqrt,X6)),zero_zero(real)))
| hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X6),zero_zero(real))) )
& ( ~ hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X7),zero_zero(real)))
| hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,sqrt,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_814])])])]) ).
fof(c_0_1470,plain,
! [X25,X26] :
( ( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit0,X25)),zero_zero(int)))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X25),zero_zero(int))) )
& ( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X26),zero_zero(int)))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit0,X26)),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_815])])])]) ).
fof(c_0_1471,plain,
! [X25,X26] :
( ( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit1,X25)),zero_zero(int)))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X25),zero_zero(int))) )
& ( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X26),zero_zero(int)))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit1,X26)),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_816])])])]) ).
fof(c_0_1472,plain,
! [X16,X17,X18] :
( ~ linordered_semidom(X16)
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X17),X18))
| hBOOL(hAPP(X16,bool,hAPP(X16,fun(X16,bool),ord_less(X16),hAPP(nat,X16,semiring_1_of_nat(X16),X17)),hAPP(nat,X16,semiring_1_of_nat(X16),X18))) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_817])])]) ).
fof(c_0_1473,plain,
! [X13,X14] :
( ( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,bit1,X13)),pls))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X13),pls)) )
& ( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X14),pls))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,bit1,X14)),pls)) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_818])])])]) ).
fof(c_0_1474,plain,
! [X13,X14] :
( ( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,bit0,X13)),pls))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X13),pls)) )
& ( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X14),pls))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,bit0,X14)),pls)) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_819])])])]) ).
fof(c_0_1475,plain,
! [X13,X14] :
( ( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit0,X13)),pls))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X13),pls)) )
& ( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X14),pls))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit0,X14)),pls)) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_820])])])]) ).
fof(c_0_1476,plain,
! [X13,X14] :
( ( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit1,X13)),pls))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X13),pls)) )
& ( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X14),pls))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit1,X14)),pls)) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_821])])])]) ).
fof(c_0_1477,plain,
! [X40,X41,X42,X43] :
( ( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X40),X41))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),X41))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),number_number_of(nat,X40)),number_number_of(nat,X41))) )
& ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X40),X41))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),number_number_of(nat,X40)),number_number_of(nat,X41))) )
& ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X42),X43))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X42),X43))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),number_number_of(nat,X42)),number_number_of(nat,X43))) )
& ( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),X43))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X42),X43))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),number_number_of(nat,X42)),number_number_of(nat,X43))) ) ),
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_822])])])])]) ).
fof(c_0_1478,plain,
! [X17,X18,X19,X20] :
( ~ order(X17)
| ~ hBOOL(hAPP(X17,bool,hAPP(X17,fun(X17,bool),ord_less_eq(X17),X19),X20))
| ~ hBOOL(hAPP(X17,bool,hAPP(X17,fun(X17,bool),ord_less(X17),X18),X19))
| hBOOL(hAPP(X17,bool,hAPP(X17,fun(X17,bool),ord_less(X17),X18),X20)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_823])])]) ).
fof(c_0_1479,plain,
! [X17,X18,X19,X20] :
( ~ preorder(X17)
| ~ hBOOL(hAPP(X17,bool,hAPP(X17,fun(X17,bool),ord_less_eq(X17),X19),X20))
| ~ hBOOL(hAPP(X17,bool,hAPP(X17,fun(X17,bool),ord_less(X17),X20),X18))
| hBOOL(hAPP(X17,bool,hAPP(X17,fun(X17,bool),ord_less(X17),X19),X18)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_824])])]) ).
fof(c_0_1480,plain,
! [X17,X18,X19,X20] :
( ~ order(X17)
| ~ hBOOL(hAPP(X17,bool,hAPP(X17,fun(X17,bool),ord_less(X17),X19),X20))
| ~ hBOOL(hAPP(X17,bool,hAPP(X17,fun(X17,bool),ord_less_eq(X17),X18),X19))
| hBOOL(hAPP(X17,bool,hAPP(X17,fun(X17,bool),ord_less(X17),X18),X20)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_825])])]) ).
fof(c_0_1481,plain,
! [X17,X18,X19,X20] :
( ~ preorder(X17)
| ~ hBOOL(hAPP(X17,bool,hAPP(X17,fun(X17,bool),ord_less(X17),X19),X20))
| ~ hBOOL(hAPP(X17,bool,hAPP(X17,fun(X17,bool),ord_less_eq(X17),X20),X18))
| hBOOL(hAPP(X17,bool,hAPP(X17,fun(X17,bool),ord_less(X17),X19),X18)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_826])])]) ).
fof(c_0_1482,plain,
! [X17,X18,X19,X20] :
( ~ preorder(X17)
| ~ hBOOL(hAPP(X17,bool,hAPP(X17,fun(X17,bool),ord_less(X17),X19),X20))
| ~ hBOOL(hAPP(X17,bool,hAPP(X17,fun(X17,bool),ord_less(X17),X20),X18))
| hBOOL(hAPP(X17,bool,hAPP(X17,fun(X17,bool),ord_less(X17),X19),X18)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_827])])]) ).
fof(c_0_1483,plain,
! [X17,X18,X19,X20] :
( ~ order(X17)
| ~ hBOOL(hAPP(X17,bool,hAPP(X17,fun(X17,bool),ord_less(X17),X19),X20))
| ~ hBOOL(hAPP(X17,bool,hAPP(X17,fun(X17,bool),ord_less(X17),X18),X19))
| hBOOL(hAPP(X17,bool,hAPP(X17,fun(X17,bool),ord_less(X17),X18),X20)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_828])])]) ).
fof(c_0_1484,plain,
! [X17,X18,X19,X20] :
( ~ preorder(X17)
| ~ hBOOL(hAPP(X17,bool,hAPP(X17,fun(X17,bool),ord_less_eq(X17),X19),X20))
| ~ hBOOL(hAPP(X17,bool,hAPP(X17,fun(X17,bool),ord_less_eq(X17),X20),X18))
| hBOOL(hAPP(X17,bool,hAPP(X17,fun(X17,bool),ord_less_eq(X17),X19),X18)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_829])])]) ).
fof(c_0_1485,plain,
! [X17,X18,X19,X20] :
( ~ order(X17)
| ~ hBOOL(hAPP(X17,bool,hAPP(X17,fun(X17,bool),ord_less_eq(X17),X19),X20))
| ~ hBOOL(hAPP(X17,bool,hAPP(X17,fun(X17,bool),ord_less_eq(X17),X18),X19))
| hBOOL(hAPP(X17,bool,hAPP(X17,fun(X17,bool),ord_less_eq(X17),X18),X20)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_830])])]) ).
fof(c_0_1486,plain,
! [X61,X62] :
( ( hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),esk23_2(X61,X62)))
| ~ hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X61))
| ~ hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X62)) )
& ( hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),esk23_2(X61,X62)),X62))
| ~ hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X61))
| ~ hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X62)) )
& ( hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),esk23_2(X61,X62)),X61))
| ~ hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X61))
| ~ hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X62)) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_831])])])]) ).
fof(c_0_1487,plain,
! [X50,X51] :
( ( hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),esk5_2(X50,X51)))
| ~ hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X50))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X51)) )
& ( hAPP(nat,real,power_power(real,esk5_2(X50,X51)),X51) = X50
| ~ hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X50))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X51)) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_832])])])]) ).
fof(c_0_1488,plain,
! [X23,X24,X25] :
( ~ hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X24),X25))
| ~ hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X25),X23))
| hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X24),X23)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_833])]) ).
fof(c_0_1489,plain,
! [X23,X24,X25] :
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X24),X25))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X25),X23))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X24),X23)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_834])]) ).
fof(c_0_1490,plain,
! [X23,X24,X25] :
( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X24),X25))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X25),X23))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X24),X23)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_835])]) ).
fof(c_0_1491,plain,
! [X17,X18] :
( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X17),X18))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,plus_plus(int,X17),one_one(int))),X18)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_836])]) ).
fof(c_0_1492,plain,
! [X16] :
( ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),number_number_of(int,hAPP(int,int,bit0,X16))))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),number_number_of(int,X16))) )
& ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),number_number_of(int,hAPP(int,int,bit1,X16))))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),number_number_of(int,X16))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_837])])]) ).
fof(c_0_1493,plain,
! [X8,X9,X10] :
( ( ~ hBOOL(hAPP(X8,bool,hAPP(X8,fun(X8,bool),ord_less_eq(X8),zero_zero(X8)),hAPP(X8,X8,plus_plus(X8,X9),X9)))
| hBOOL(hAPP(X8,bool,hAPP(X8,fun(X8,bool),ord_less_eq(X8),zero_zero(X8)),X9))
| ~ linord219039673up_add(X8) )
& ( ~ hBOOL(hAPP(X8,bool,hAPP(X8,fun(X8,bool),ord_less_eq(X8),zero_zero(X8)),X10))
| hBOOL(hAPP(X8,bool,hAPP(X8,fun(X8,bool),ord_less_eq(X8),zero_zero(X8)),hAPP(X8,X8,plus_plus(X8,X10),X10)))
| ~ linord219039673up_add(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_838])])])])]) ).
fof(c_0_1494,plain,
! [X8,X9,X10] :
( ( ~ hBOOL(hAPP(X8,bool,hAPP(X8,fun(X8,bool),ord_less(X8),zero_zero(X8)),hAPP(X8,X8,plus_plus(X8,X9),X9)))
| hBOOL(hAPP(X8,bool,hAPP(X8,fun(X8,bool),ord_less(X8),zero_zero(X8)),X9))
| ~ linord219039673up_add(X8) )
& ( ~ hBOOL(hAPP(X8,bool,hAPP(X8,fun(X8,bool),ord_less(X8),zero_zero(X8)),X10))
| hBOOL(hAPP(X8,bool,hAPP(X8,fun(X8,bool),ord_less(X8),zero_zero(X8)),hAPP(X8,X8,plus_plus(X8,X10),X10)))
| ~ linord219039673up_add(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_839])])])])]) ).
fof(c_0_1495,plain,
! [X25,X26,X27,X28] :
( ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,power_power(nat,X25),number_number_of(nat,X26))))
| number_number_of(nat,X26) = zero_zero(nat)
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X25)) )
& ( number_number_of(nat,X28) != zero_zero(nat)
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,power_power(nat,X27),number_number_of(nat,X28)))) )
& ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X27))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,power_power(nat,X27),number_number_of(nat,X28)))) ) ),
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_840])])])])]) ).
fof(c_0_1496,plain,
! [X23,X24] : ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,plus_plus(nat,X23),X24)),X24)),
inference(variable_rename,[status(thm)],[c_0_841]) ).
fof(c_0_1497,plain,
! [X23,X24] : ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,plus_plus(nat,X23),X24)),X23)),
inference(variable_rename,[status(thm)],[c_0_842]) ).
fof(c_0_1498,plain,
! [X24,X25,X26] :
( ~ number_semiring(X24)
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),X26))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),X25))
| hAPP(X24,X24,plus_plus(X24,number_number_of(X24,X26)),number_number_of(X24,X25)) = number_number_of(X24,hAPP(int,int,plus_plus(int,X26),X25)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_843])])]) ).
fof(c_0_1499,plain,
! [X40,X41,X42,X43] :
( ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),number_number_of(nat,X40)),number_number_of(nat,X41)))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X40),X41))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X40),pls)) )
& ( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X42),X43))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),number_number_of(nat,X42)),number_number_of(nat,X43))) )
& ( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X42),pls))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),number_number_of(nat,X42)),number_number_of(nat,X43))) ) ),
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_844])])])])]) ).
fof(c_0_1500,plain,
! [X18,X19,X20,X21] :
( ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,power_power(nat,X18),X19)))
| X19 = zero_zero(nat)
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X18)) )
& ( X21 != zero_zero(nat)
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,power_power(nat,X20),X21))) )
& ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X20))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,power_power(nat,X20),X21))) ) ),
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_845])])])])]) ).
fof(c_0_1501,plain,
! [X18,X19,X20,X21] :
( ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,power_power(nat,X18),X19)))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X18))
| X19 = zero_zero(nat) )
& ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X20))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,power_power(nat,X20),X21))) )
& ( X21 != zero_zero(nat)
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,power_power(nat,X20),X21))) ) ),
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_846])])])])]) ).
fof(c_0_1502,plain,
! [X30,X31,X32,X33] :
( ( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X30),hAPP(int,int,plus_plus(int,X31),one_one(int))))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X30),X31))
| X30 = X31 )
& ( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X32),X33))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X32),hAPP(int,int,plus_plus(int,X33),one_one(int)))) )
& ( X32 != X33
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X32),hAPP(int,int,plus_plus(int,X33),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_847])])])])]) ).
fof(c_0_1503,plain,
! [X30,X31,X32,X33] :
( ( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X30),hAPP(int,int,plus_plus(int,X31),one_one(int))))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X30),X31)) )
& ( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X32),X33))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X32),hAPP(int,int,plus_plus(int,X33),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_848])])])]) ).
fof(c_0_1504,plain,
! [X7,X8,X9,X10,X11] :
( ( hBOOL(hAPP(X7,bool,hAPP(X7,fun(X7,bool),ord_less_eq(X7),X8),X9))
| ~ hBOOL(hAPP(X7,bool,hAPP(X7,fun(X7,bool),ord_less(X7),X8),X9))
| ~ preorder(X7) )
& ( ~ hBOOL(hAPP(X7,bool,hAPP(X7,fun(X7,bool),ord_less_eq(X7),X9),X8))
| ~ hBOOL(hAPP(X7,bool,hAPP(X7,fun(X7,bool),ord_less(X7),X8),X9))
| ~ preorder(X7) )
& ( ~ hBOOL(hAPP(X7,bool,hAPP(X7,fun(X7,bool),ord_less_eq(X7),X10),X11))
| hBOOL(hAPP(X7,bool,hAPP(X7,fun(X7,bool),ord_less_eq(X7),X11),X10))
| hBOOL(hAPP(X7,bool,hAPP(X7,fun(X7,bool),ord_less(X7),X10),X11))
| ~ preorder(X7) ) ),
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_849])])])])]) ).
fof(c_0_1505,plain,
! [X18,X19,X20] :
( ( ~ hBOOL(hAPP(X18,bool,hAPP(X18,fun(X18,bool),ord_less(X18),zero_zero(X18)),hAPP(nat,X18,semiring_1_of_nat(X18),X19)))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X19))
| ~ linordered_semidom(X18) )
& ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X20))
| hBOOL(hAPP(X18,bool,hAPP(X18,fun(X18,bool),ord_less(X18),zero_zero(X18)),hAPP(nat,X18,semiring_1_of_nat(X18),X20)))
| ~ linordered_semidom(X18) ) ),
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_850])])])])]) ).
fof(c_0_1506,plain,
! [X6,X7,X8] :
( ( ~ hBOOL(hAPP(X6,bool,hAPP(X6,fun(X6,bool),ord_less_eq(X6),number_number_of(X6,X7)),one_one(X6)))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X7),hAPP(int,int,bit1,pls)))
| ~ number_ring(X6)
| ~ linordered_idom(X6) )
& ( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X8),hAPP(int,int,bit1,pls)))
| hBOOL(hAPP(X6,bool,hAPP(X6,fun(X6,bool),ord_less_eq(X6),number_number_of(X6,X8)),one_one(X6)))
| ~ number_ring(X6)
| ~ linordered_idom(X6) ) ),
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_851])])])])]) ).
fof(c_0_1507,plain,
! [X6,X7,X8] :
( ( ~ hBOOL(hAPP(X6,bool,hAPP(X6,fun(X6,bool),ord_less(X6),number_number_of(X6,X7)),one_one(X6)))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X7),hAPP(int,int,bit1,pls)))
| ~ number_ring(X6)
| ~ linordered_idom(X6) )
& ( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X8),hAPP(int,int,bit1,pls)))
| hBOOL(hAPP(X6,bool,hAPP(X6,fun(X6,bool),ord_less(X6),number_number_of(X6,X8)),one_one(X6)))
| ~ number_ring(X6)
| ~ linordered_idom(X6) ) ),
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_852])])])])]) ).
fof(c_0_1508,plain,
! [X15,X16] :
( ~ linordered_semidom(X15)
| ~ hBOOL(hAPP(X15,bool,hAPP(X15,fun(X15,bool),ord_less(X15),hAPP(nat,X15,semiring_1_of_nat(X15),X16)),zero_zero(X15))) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_853])])]) ).
fof(c_0_1509,plain,
! [X53,X54,X55] :
( ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X55))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X55))
| ~ hBOOL(X54)
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X55)) )
& ( hBOOL(X53)
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X55))
| ~ hBOOL(X54)
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X55)) )
& ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X55))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X55))
| ~ hBOOL(X53)
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X55)) )
& ( hBOOL(X54)
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X55))
| ~ hBOOL(X53)
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X55)) )
& ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X55))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X55))
| ~ hBOOL(X54)
| ~ hBOOL(X54)
| ~ hBOOL(X53) )
& ( hBOOL(X53)
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X55))
| ~ hBOOL(X54)
| ~ hBOOL(X54)
| ~ hBOOL(X53) )
& ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X55))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X55))
| ~ hBOOL(X53)
| ~ hBOOL(X54)
| ~ hBOOL(X53) )
& ( hBOOL(X54)
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X55))
| ~ hBOOL(X53)
| ~ hBOOL(X54)
| ~ hBOOL(X53) )
& ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X55))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X55))
| ~ hBOOL(X54)
| hBOOL(X54)
| hBOOL(X53) )
& ( hBOOL(X53)
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X55))
| ~ hBOOL(X54)
| hBOOL(X54)
| hBOOL(X53) )
& ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X55))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X55))
| ~ hBOOL(X53)
| hBOOL(X54)
| hBOOL(X53) )
& ( hBOOL(X54)
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X55))
| ~ hBOOL(X53)
| hBOOL(X54)
| hBOOL(X53) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_854])])]) ).
fof(c_0_1510,plain,
! [X53,X54,X55] :
( ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X55))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X55))
| hBOOL(X53)
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X55)) )
& ( ~ hBOOL(X54)
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X55))
| hBOOL(X53)
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X55)) )
& ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X55))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X55))
| hBOOL(X54)
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X55)) )
& ( ~ hBOOL(X53)
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X55))
| hBOOL(X54)
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X55)) )
& ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X55))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X55))
| hBOOL(X53)
| ~ hBOOL(X54)
| ~ hBOOL(X53) )
& ( ~ hBOOL(X54)
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X55))
| hBOOL(X53)
| ~ hBOOL(X54)
| ~ hBOOL(X53) )
& ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X55))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X55))
| hBOOL(X54)
| ~ hBOOL(X54)
| ~ hBOOL(X53) )
& ( ~ hBOOL(X53)
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X55))
| hBOOL(X54)
| ~ hBOOL(X54)
| ~ hBOOL(X53) )
& ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X55))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X55))
| hBOOL(X53)
| hBOOL(X54)
| hBOOL(X53) )
& ( ~ hBOOL(X54)
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X55))
| hBOOL(X53)
| hBOOL(X54)
| hBOOL(X53) )
& ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X55))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X55))
| hBOOL(X54)
| hBOOL(X54)
| hBOOL(X53) )
& ( ~ hBOOL(X53)
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X55))
| hBOOL(X54)
| hBOOL(X54)
| hBOOL(X53) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_855])])]) ).
fof(c_0_1511,plain,
! [X18,X19] :
( ( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(nat,int,semiring_1_of_nat(int),X18)))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X18)) )
& ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X19))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(nat,int,semiring_1_of_nat(int),X19))) ) ),
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_1512,plain,
! [X7,X8] :
( ( ~ hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),one_one(real)),hAPP(real,real,sqrt,X7)))
| hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),one_one(real)),X7)) )
& ( ~ hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),one_one(real)),X8))
| hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),one_one(real)),hAPP(real,real,sqrt,X8))) ) ),
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_1513,plain,
! [X7,X8] :
( ( ~ hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(real,real,sqrt,X7)))
| hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X7)) )
& ( ~ hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X8))
| hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(real,real,sqrt,X8))) ) ),
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_1514,plain,
! [X18,X19] :
( ( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(nat,int,semiring_1_of_nat(int),X18)),zero_zero(int)))
| X18 = zero_zero(nat) )
& ( X19 != zero_zero(nat)
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(nat,int,semiring_1_of_nat(int),X19)),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_859])])])]) ).
fof(c_0_1515,plain,
! [X21] : ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(nat,int,semiring_1_of_nat(int),X21)),zero_zero(int))),
inference(variable_rename,[status(thm)],[c_0_860]) ).
fof(c_0_1516,plain,
! [X7,X8,X9] :
( ( ti(X7,X9) = zero_zero(X7)
| hAPP(X7,X7,plus_plus(X7,X9),X8) != zero_zero(X7)
| ~ hBOOL(hAPP(X7,bool,hAPP(X7,fun(X7,bool),ord_less_eq(X7),zero_zero(X7)),X8))
| ~ hBOOL(hAPP(X7,bool,hAPP(X7,fun(X7,bool),ord_less_eq(X7),zero_zero(X7)),X9))
| ~ ordere216010020id_add(X7) )
& ( ti(X7,X8) = zero_zero(X7)
| hAPP(X7,X7,plus_plus(X7,X9),X8) != zero_zero(X7)
| ~ hBOOL(hAPP(X7,bool,hAPP(X7,fun(X7,bool),ord_less_eq(X7),zero_zero(X7)),X8))
| ~ hBOOL(hAPP(X7,bool,hAPP(X7,fun(X7,bool),ord_less_eq(X7),zero_zero(X7)),X9))
| ~ ordere216010020id_add(X7) )
& ( ti(X7,X9) != zero_zero(X7)
| ti(X7,X8) != zero_zero(X7)
| hAPP(X7,X7,plus_plus(X7,X9),X8) = zero_zero(X7)
| ~ hBOOL(hAPP(X7,bool,hAPP(X7,fun(X7,bool),ord_less_eq(X7),zero_zero(X7)),X8))
| ~ hBOOL(hAPP(X7,bool,hAPP(X7,fun(X7,bool),ord_less_eq(X7),zero_zero(X7)),X9))
| ~ ordere216010020id_add(X7) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_861])])])]) ).
fof(c_0_1517,plain,
! [X13,X14] :
( ( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),hAPP(int,int,bit1,X13)))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),X13)) )
& ( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),X14))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),hAPP(int,int,bit1,X14))) ) ),
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_1518,plain,
! [X13,X14] :
( ( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),hAPP(int,int,bit0,X13)))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),X13)) )
& ( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),X14))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),hAPP(int,int,bit0,X14))) ) ),
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_1519,plain,
! [X13,X14] :
( ( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),hAPP(int,int,bit1,X13)))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),X13)) )
& ( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),X14))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),hAPP(int,int,bit1,X14))) ) ),
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_1520,plain,
! [X13,X14] :
( ( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),hAPP(int,int,bit0,X13)))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),X13)) )
& ( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),X14))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),hAPP(int,int,bit0,X14))) ) ),
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_1521,plain,
! [X39,X40,X41,X42,X43] :
( ( ~ hBOOL(hAPP(X39,bool,hAPP(X39,fun(X39,bool),ord_less_eq(X39),number_number_of(X39,X40)),number_number_of(X39,X41)))
| ~ hBOOL(hAPP(X39,bool,hAPP(X39,fun(X39,bool),ord_less(X39),number_number_of(X39,X41)),number_number_of(X39,X40)))
| ~ number(X39)
| ~ linorder(X39) )
& ( hBOOL(hAPP(X39,bool,hAPP(X39,fun(X39,bool),ord_less(X39),number_number_of(X39,X43)),number_number_of(X39,X42)))
| hBOOL(hAPP(X39,bool,hAPP(X39,fun(X39,bool),ord_less_eq(X39),number_number_of(X39,X42)),number_number_of(X39,X43)))
| ~ number(X39)
| ~ linorder(X39) ) ),
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_866])])])])]) ).
fof(c_0_1522,plain,
! [X48,X50,X51,X53] :
( ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),esk8_1(X48)))
| hBOOL(hAPP(int,bool,X48,hAPP(nat,int,semiring_1_of_nat(int),X50))) )
& ( ~ hBOOL(hAPP(int,bool,X48,esk8_1(X48)))
| hBOOL(hAPP(int,bool,X48,hAPP(nat,int,semiring_1_of_nat(int),X50))) )
& ( ~ hBOOL(hAPP(int,bool,X51,hAPP(nat,int,semiring_1_of_nat(int),esk9_1(X51))))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X53))
| hBOOL(hAPP(int,bool,X51,X53)) ) ),
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_867])])])])])]) ).
fof(c_0_1523,plain,
! [X32,X33,X34] :
( ~ linordered_semidom(X32)
| ~ hBOOL(hAPP(X32,bool,hAPP(X32,fun(X32,bool),ord_less_eq(X32),one_one(X32)),X34))
| hBOOL(hAPP(X32,bool,hAPP(X32,fun(X32,bool),ord_less_eq(X32),one_one(X32)),hAPP(nat,X32,power_power(X32,X34),X33))) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_868])])]) ).
fof(c_0_1524,plain,
! [X32,X33,X34] :
( ~ linordered_semidom(X32)
| ~ hBOOL(hAPP(X32,bool,hAPP(X32,fun(X32,bool),ord_less_eq(X32),zero_zero(X32)),X34))
| hBOOL(hAPP(X32,bool,hAPP(X32,fun(X32,bool),ord_less_eq(X32),zero_zero(X32)),hAPP(nat,X32,power_power(X32,X34),X33))) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_869])])]) ).
fof(c_0_1525,plain,
! [X32,X33,X34] :
( ~ linordered_semidom(X32)
| ~ hBOOL(hAPP(X32,bool,hAPP(X32,fun(X32,bool),ord_less(X32),zero_zero(X32)),X34))
| hBOOL(hAPP(X32,bool,hAPP(X32,fun(X32,bool),ord_less(X32),zero_zero(X32)),hAPP(nat,X32,power_power(X32,X34),X33))) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_870])])]) ).
fof(c_0_1526,plain,
! [X62,X63,X65] :
( ~ linorder(X62)
| ~ hBOOL(hAPP(X62,bool,hAPP(X62,fun(X62,bool),ord_less(X62),esk26_2(X62,X63)),X65))
| ~ hBOOL(hAPP(X62,bool,hAPP(X62,fun(X62,bool),ord_less_eq(X62),X65),X63)) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_871])])])]) ).
fof(c_0_1527,plain,
! [X17] :
( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X17))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(int,int,plus_plus(int,one_one(int)),X17))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_872])]) ).
fof(c_0_1528,plain,
! [X16,X17] :
( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X17))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(nat,int,power_power(int,X17),X16))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_873])]) ).
fof(c_0_1529,plain,
! [X62,X63,X65] :
( ~ linorder(X62)
| ~ hBOOL(hAPP(X62,bool,hAPP(X62,fun(X62,bool),ord_less(X62),X65),esk36_2(X62,X63)))
| ~ hBOOL(hAPP(X62,bool,hAPP(X62,fun(X62,bool),ord_less_eq(X62),X63),X65)) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_874])])])]) ).
fof(c_0_1530,plain,
! [X23,X24,X25] :
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X24),X25))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X24),hAPP(nat,nat,plus_plus(nat,X23),X25))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_875])]) ).
fof(c_0_1531,plain,
! [X23,X24,X25] :
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X24),X25))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X24),hAPP(nat,nat,plus_plus(nat,X25),X23))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_876])]) ).
fof(c_0_1532,plain,
! [X23,X24,X25] :
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X24),X25))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X24),hAPP(nat,nat,plus_plus(nat,X23),X25))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_877])]) ).
fof(c_0_1533,plain,
! [X23,X24,X25] :
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X24),X25))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X24),hAPP(nat,nat,plus_plus(nat,X25),X23))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_878])]) ).
fof(c_0_1534,plain,
! [X7,X8,X9] :
( ( hBOOL(hAPP(X7,bool,hAPP(X7,fun(X7,bool),ord_less(X7),X8),X9))
| ti(X7,X8) = ti(X7,X9)
| ~ hBOOL(hAPP(X7,bool,hAPP(X7,fun(X7,bool),ord_less_eq(X7),X8),X9))
| ~ linorder(X7) )
& ( ti(X7,X8) != ti(X7,X9)
| ~ hBOOL(hAPP(X7,bool,hAPP(X7,fun(X7,bool),ord_less(X7),X8),X9))
| ~ hBOOL(hAPP(X7,bool,hAPP(X7,fun(X7,bool),ord_less_eq(X7),X8),X9))
| ~ linorder(X7) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_879])])])]) ).
fof(c_0_1535,plain,
! [X7,X8,X9,X10,X11] :
( ( hBOOL(hAPP(X7,bool,hAPP(X7,fun(X7,bool),ord_less_eq(X7),X8),X9))
| ti(X7,X8) != ti(X7,X9)
| ~ order(X7) )
& ( hBOOL(hAPP(X7,bool,hAPP(X7,fun(X7,bool),ord_less_eq(X7),X9),X8))
| ti(X7,X8) != ti(X7,X9)
| ~ order(X7) )
& ( ~ hBOOL(hAPP(X7,bool,hAPP(X7,fun(X7,bool),ord_less_eq(X7),X10),X11))
| ~ hBOOL(hAPP(X7,bool,hAPP(X7,fun(X7,bool),ord_less_eq(X7),X11),X10))
| ti(X7,X10) = ti(X7,X11)
| ~ order(X7) ) ),
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_880])])])])]) ).
fof(c_0_1536,plain,
! [X7,X8,X9] :
( ( ~ hBOOL(hAPP(X7,bool,hAPP(X7,fun(X7,bool),ord_less_eq(X7),X9),X8))
| ti(X7,X9) = ti(X7,X8)
| ~ hBOOL(hAPP(X7,bool,hAPP(X7,fun(X7,bool),ord_less_eq(X7),X8),X9))
| ~ order(X7) )
& ( ti(X7,X9) != ti(X7,X8)
| hBOOL(hAPP(X7,bool,hAPP(X7,fun(X7,bool),ord_less_eq(X7),X9),X8))
| ~ hBOOL(hAPP(X7,bool,hAPP(X7,fun(X7,bool),ord_less_eq(X7),X8),X9))
| ~ order(X7) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_881])])])]) ).
fof(c_0_1537,plain,
! [X12,X13,X14] :
( ~ order(X12)
| ~ hBOOL(hAPP(X12,bool,hAPP(X12,fun(X12,bool),ord_less_eq(X12),X13),X14))
| ~ hBOOL(hAPP(X12,bool,hAPP(X12,fun(X12,bool),ord_less_eq(X12),X14),X13))
| ti(X12,X13) = ti(X12,X14) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_882])])]) ).
fof(c_0_1538,plain,
! [X12,X13,X14] :
( ~ order(X12)
| ~ hBOOL(hAPP(X12,bool,hAPP(X12,fun(X12,bool),ord_less_eq(X12),X13),X14))
| ~ hBOOL(hAPP(X12,bool,hAPP(X12,fun(X12,bool),ord_less_eq(X12),X14),X13))
| ti(X12,X14) = ti(X12,X13) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_883])])]) ).
fof(c_0_1539,plain,
! [X8,X9,X10] :
( ( hAPP(nat,X8,power_power(X8,X9),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) != zero_zero(X8)
| ti(X8,X9) = zero_zero(X8)
| ~ ring_11004092258visors(X8) )
& ( ti(X8,X10) != zero_zero(X8)
| hAPP(nat,X8,power_power(X8,X10),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) = zero_zero(X8)
| ~ ring_11004092258visors(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_884])])])])]) ).
fof(c_0_1540,plain,
! [X34,X35,X36,X37] :
( ~ preorder(X34)
| ~ hBOOL(hAPP(X34,bool,hAPP(X34,fun(X34,bool),ord_less(X34),X36),X37))
| ~ hBOOL(hAPP(X34,bool,hAPP(X34,fun(X34,bool),ord_less(X34),X37),X36))
| hBOOL(X35) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_885])])]) ).
fof(c_0_1541,plain,
! [X12,X13,X14] :
( ~ linorder(X12)
| ~ hBOOL(hAPP(X12,bool,hAPP(X12,fun(X12,bool),ord_less_eq(X12),X13),X14))
| ~ hBOOL(hAPP(X12,bool,hAPP(X12,fun(X12,bool),ord_less(X12),X14),X13)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_886])])]) ).
fof(c_0_1542,plain,
! [X7,X8,X9,X10,X11] :
( ( hBOOL(hAPP(X7,bool,hAPP(X7,fun(X7,bool),ord_less_eq(X7),X8),X9))
| hBOOL(hAPP(X7,bool,hAPP(X7,fun(X7,bool),ord_less(X7),X9),X8))
| ~ linorder(X7) )
& ( ~ hBOOL(hAPP(X7,bool,hAPP(X7,fun(X7,bool),ord_less(X7),X11),X10))
| ~ hBOOL(hAPP(X7,bool,hAPP(X7,fun(X7,bool),ord_less_eq(X7),X10),X11))
| ~ linorder(X7) ) ),
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_887])])])])]) ).
fof(c_0_1543,plain,
! [X7,X8,X9,X10,X11] :
( ( hBOOL(hAPP(X7,bool,hAPP(X7,fun(X7,bool),ord_less(X7),X8),X9))
| hBOOL(hAPP(X7,bool,hAPP(X7,fun(X7,bool),ord_less_eq(X7),X9),X8))
| ~ linorder(X7) )
& ( ~ hBOOL(hAPP(X7,bool,hAPP(X7,fun(X7,bool),ord_less_eq(X7),X11),X10))
| ~ hBOOL(hAPP(X7,bool,hAPP(X7,fun(X7,bool),ord_less(X7),X10),X11))
| ~ linorder(X7) ) ),
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_888])])])])]) ).
fof(c_0_1544,plain,
! [X7,X8,X9,X10,X11] :
( ( hBOOL(hAPP(X7,bool,hAPP(X7,fun(X7,bool),ord_less(X7),X8),X9))
| hBOOL(hAPP(X7,bool,hAPP(X7,fun(X7,bool),ord_less(X7),X9),X8))
| ti(X7,X8) = ti(X7,X9)
| ~ linorder(X7) )
& ( ~ hBOOL(hAPP(X7,bool,hAPP(X7,fun(X7,bool),ord_less(X7),X11),X10))
| ~ hBOOL(hAPP(X7,bool,hAPP(X7,fun(X7,bool),ord_less(X7),X10),X11))
| ~ linorder(X7) )
& ( ti(X7,X10) != ti(X7,X11)
| ~ hBOOL(hAPP(X7,bool,hAPP(X7,fun(X7,bool),ord_less(X7),X10),X11))
| ~ linorder(X7) ) ),
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_889])])])])]) ).
fof(c_0_1545,plain,
! [X12,X13,X14] :
( ~ preorder(X12)
| ~ hBOOL(hAPP(X12,bool,hAPP(X12,fun(X12,bool),ord_less(X12),X13),X14))
| ~ hBOOL(hAPP(X12,bool,hAPP(X12,fun(X12,bool),ord_less(X12),X14),X13)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_890])])]) ).
fof(c_0_1546,plain,
! [X12,X13,X14] :
( ~ preorder(X12)
| ~ hBOOL(hAPP(X12,bool,hAPP(X12,fun(X12,bool),ord_less(X12),X13),X14))
| ~ hBOOL(hAPP(X12,bool,hAPP(X12,fun(X12,bool),ord_less(X12),X14),X13)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_891])])]) ).
fof(c_0_1547,plain,
! [X41,X42,X43] :
( ~ preorder(X41)
| ~ hBOOL(hAPP(X41,bool,hAPP(X41,fun(X41,bool),ord_less(X41),X42),X43))
| ~ hBOOL(hAPP(X41,bool,hAPP(X41,fun(X41,bool),ord_less(X41),X43),X42)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_892])])]) ).
fof(c_0_1548,plain,
! [X41,X42,X43] :
( ~ order(X41)
| ~ hBOOL(hAPP(X41,bool,hAPP(X41,fun(X41,bool),ord_less(X41),X42),X43))
| ~ hBOOL(hAPP(X41,bool,hAPP(X41,fun(X41,bool),ord_less(X41),X43),X42)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_893])])]) ).
fof(c_0_1549,plain,
! [X12,X13,X14] :
( ~ preorder(X12)
| ~ hBOOL(hAPP(X12,bool,hAPP(X12,fun(X12,bool),ord_less(X12),X13),X14))
| ~ hBOOL(hAPP(X12,bool,hAPP(X12,fun(X12,bool),ord_less(X12),X14),X13)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_894])])]) ).
fof(c_0_1550,plain,
! [X11] :
( ~ hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X11))
| hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(real,real,sqrt,X11))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_895])]) ).
fof(c_0_1551,plain,
! [X17,X18] :
( ~ hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X17),X18))
| ~ hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X18),X17))
| X17 = X18 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_896])]) ).
fof(c_0_1552,plain,
! [X16,X17] :
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X16),X17))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X17),X16))
| X16 = X17 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_897])]) ).
fof(c_0_1553,plain,
! [X17,X18] :
( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X17),X18))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X18),X17))
| X17 = X18 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_898])]) ).
fof(c_0_1554,plain,
! [X31,X32,X33,X34] :
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X33),X34))
| hAPP(nat,nat,plus_plus(nat,X31),X34) != hAPP(nat,nat,plus_plus(nat,X33),X32)
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X31),X32)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_899])]) ).
fof(c_0_1555,plain,
! [X48,X49,X50] :
( ( hBOOL(hAPP(X48,bool,hAPP(X48,fun(X48,bool),ord_less(X48),esk24_3(X48,X49,X50)),X50))
| hBOOL(hAPP(X48,bool,hAPP(X48,fun(X48,bool),ord_less_eq(X48),X50),X49))
| ~ dense_linorder(X48) )
& ( ~ hBOOL(hAPP(X48,bool,hAPP(X48,fun(X48,bool),ord_less_eq(X48),esk24_3(X48,X49,X50)),X49))
| hBOOL(hAPP(X48,bool,hAPP(X48,fun(X48,bool),ord_less_eq(X48),X50),X49))
| ~ dense_linorder(X48) ) ),
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_900])])])])]) ).
fof(c_0_1556,plain,
! [X48,X49,X51,X52] :
( ( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X49))
| ~ hBOOL(hAPP(int,bool,X48,X49))
| hBOOL(hAPP(int,bool,X48,hAPP(nat,int,semiring_1_of_nat(int),esk6_1(X48)))) )
& ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),esk7_1(X51)))
| ~ hBOOL(hAPP(int,bool,X51,hAPP(nat,int,semiring_1_of_nat(int),X52))) )
& ( hBOOL(hAPP(int,bool,X51,esk7_1(X51)))
| ~ hBOOL(hAPP(int,bool,X51,hAPP(nat,int,semiring_1_of_nat(int),X52))) ) ),
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_901])])])])])]) ).
fof(c_0_1557,axiom,
hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(int,int,plus_plus(int,one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),n)))),
c_0_902 ).
fof(c_0_1558,axiom,
number_number_of(int,hAPP(int,int,bit1,hAPP(int,int,bit1,pls))) = hAPP(nat,int,semiring_1_of_nat(int),number_number_of(nat,hAPP(int,int,bit1,hAPP(int,int,bit1,pls)))),
c_0_903 ).
fof(c_0_1559,axiom,
number_number_of(int,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))) = hAPP(nat,int,semiring_1_of_nat(int),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),
c_0_904 ).
fof(c_0_1560,axiom,
hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),m1),hAPP(int,int,plus_plus(int,one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),n)))),
c_0_905 ).
fof(c_0_1561,plain,
! [X45,X46,X48] :
( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),esk19_2(X45,X46)),X45))
| ~ hBOOL(hAPP(nat,bool,X46,X45))
| hBOOL(hAPP(nat,bool,X46,zero_zero(nat))) )
& ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X48),esk19_2(X45,X46)))
| ~ hBOOL(hAPP(nat,bool,X46,X48))
| ~ hBOOL(hAPP(nat,bool,X46,X45))
| hBOOL(hAPP(nat,bool,X46,zero_zero(nat))) )
& ( hBOOL(hAPP(nat,bool,X46,esk19_2(X45,X46)))
| ~ hBOOL(hAPP(nat,bool,X46,X45))
| hBOOL(hAPP(nat,bool,X46,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_906])])])])]) ).
fof(c_0_1562,plain,
! [X45,X46,X48] :
( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),esk14_2(X45,X46)),X45))
| ~ hBOOL(hAPP(nat,bool,X46,X45))
| hBOOL(hAPP(nat,bool,X46,zero_zero(nat))) )
& ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X48),esk14_2(X45,X46)))
| ~ hBOOL(hAPP(nat,bool,X46,X48))
| ~ hBOOL(hAPP(nat,bool,X46,X45))
| hBOOL(hAPP(nat,bool,X46,zero_zero(nat))) )
& ( hBOOL(hAPP(nat,bool,X46,hAPP(nat,nat,plus_plus(nat,esk14_2(X45,X46)),one_one(nat))))
| ~ hBOOL(hAPP(nat,bool,X46,X45))
| hBOOL(hAPP(nat,bool,X46,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_907])])])])]) ).
fof(c_0_1563,plain,
! [X34,X35,X36,X37,X38,X39] :
( ( ~ hBOOL(X36)
| hAPP(nat,int,semiring_1_of_nat(int),X34) = hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),hAPP(bool,fun(nat,fun(nat,nat)),if(nat),X36),X34),X35)) )
& ( hBOOL(X39)
| hAPP(nat,int,semiring_1_of_nat(int),X38) = hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),hAPP(bool,fun(nat,fun(nat,nat)),if(nat),X39),X37),X38)) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_908])])])]) ).
fof(c_0_1564,plain,
! [X24,X25,X26,X27] :
( ( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X25),pls))
| hAPP(nat,nat,plus_plus(nat,number_number_of(nat,X25)),number_number_of(nat,X24)) = number_number_of(nat,X24) )
& ( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X26),pls))
| hAPP(nat,nat,plus_plus(nat,number_number_of(nat,X27)),number_number_of(nat,X26)) = number_number_of(nat,X27)
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X27),pls)) )
& ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X26),pls))
| hAPP(nat,nat,plus_plus(nat,number_number_of(nat,X27)),number_number_of(nat,X26)) = number_number_of(nat,hAPP(int,int,plus_plus(int,X27),X26))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X27),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_909])])])])]) ).
fof(c_0_1565,plain,
! [X7,X8,X9,X10,X11] :
( ( ~ hBOOL(hAPP(X7,bool,hAPP(X7,fun(X7,bool),ord_less_eq(X7),number_number_of(X7,X8)),number_number_of(X7,X9)))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X8),X9))
| ~ number_ring(X7)
| ~ linordered_idom(X7) )
& ( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X10),X11))
| hBOOL(hAPP(X7,bool,hAPP(X7,fun(X7,bool),ord_less_eq(X7),number_number_of(X7,X10)),number_number_of(X7,X11)))
| ~ number_ring(X7)
| ~ linordered_idom(X7) ) ),
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_910])])])])]) ).
fof(c_0_1566,plain,
! [X7,X8,X9,X10,X11] :
( ( ~ hBOOL(hAPP(X7,bool,hAPP(X7,fun(X7,bool),ord_less(X7),number_number_of(X7,X8)),number_number_of(X7,X9)))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X8),X9))
| ~ number_ring(X7)
| ~ linordered_idom(X7) )
& ( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X10),X11))
| hBOOL(hAPP(X7,bool,hAPP(X7,fun(X7,bool),ord_less(X7),number_number_of(X7,X10)),number_number_of(X7,X11)))
| ~ number_ring(X7)
| ~ linordered_idom(X7) ) ),
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_911])])])])]) ).
fof(c_0_1567,plain,
! [X62,X63,X65] :
( ~ linorder(X62)
| ~ hBOOL(hAPP(X62,bool,hAPP(X62,fun(X62,bool),ord_less(X62),esk31_2(X62,X63)),X65))
| hBOOL(hAPP(X62,bool,hAPP(X62,fun(X62,bool),ord_less_eq(X62),X63),X65)) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_912])])])]) ).
fof(c_0_1568,plain,
! [X6,X7,X8] :
( ( ~ hBOOL(hAPP(X6,bool,hAPP(X6,fun(X6,bool),ord_less_eq(X6),number_number_of(X6,X7)),zero_zero(X6)))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X7),pls))
| ~ number_ring(X6)
| ~ linordered_idom(X6) )
& ( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X8),pls))
| hBOOL(hAPP(X6,bool,hAPP(X6,fun(X6,bool),ord_less_eq(X6),number_number_of(X6,X8)),zero_zero(X6)))
| ~ number_ring(X6)
| ~ linordered_idom(X6) ) ),
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_913])])])])]) ).
fof(c_0_1569,plain,
! [X6,X7,X8] :
( ( ~ hBOOL(hAPP(X6,bool,hAPP(X6,fun(X6,bool),ord_less(X6),number_number_of(X6,X7)),zero_zero(X6)))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X7),pls))
| ~ number_ring(X6)
| ~ linordered_idom(X6) )
& ( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X8),pls))
| hBOOL(hAPP(X6,bool,hAPP(X6,fun(X6,bool),ord_less(X6),number_number_of(X6,X8)),zero_zero(X6)))
| ~ number_ring(X6)
| ~ linordered_idom(X6) ) ),
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_914])])])])]) ).
fof(c_0_1570,plain,
! [X14,X15,X16,X17] :
( ( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),number_number_of(int,X14)),number_number_of(int,X15)))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X14),X15)) )
& ( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X16),X17))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),number_number_of(int,X16)),number_number_of(int,X17))) ) ),
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_1571,plain,
! [X14,X15,X16,X17] :
( ( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),number_number_of(int,X14)),number_number_of(int,X15)))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X14),X15)) )
& ( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X16),X17))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),number_number_of(int,X16)),number_number_of(int,X17))) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_916])])])]) ).
fof(c_0_1572,plain,
! [X7,X8,X9] :
( ( ~ hBOOL(hAPP(X7,bool,hAPP(X7,fun(X7,bool),ord_less_eq(X7),zero_zero(X7)),number_number_of(X7,X8)))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),X8))
| ~ number_ring(X7)
| ~ linordered_idom(X7) )
& ( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),X9))
| hBOOL(hAPP(X7,bool,hAPP(X7,fun(X7,bool),ord_less_eq(X7),zero_zero(X7)),number_number_of(X7,X9)))
| ~ number_ring(X7)
| ~ linordered_idom(X7) ) ),
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_917])])])])]) ).
fof(c_0_1573,plain,
! [X7,X8,X9] :
( ( ~ hBOOL(hAPP(X7,bool,hAPP(X7,fun(X7,bool),ord_less(X7),zero_zero(X7)),number_number_of(X7,X8)))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),X8))
| ~ number_ring(X7)
| ~ linordered_idom(X7) )
& ( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),X9))
| hBOOL(hAPP(X7,bool,hAPP(X7,fun(X7,bool),ord_less(X7),zero_zero(X7)),number_number_of(X7,X9)))
| ~ number_ring(X7)
| ~ linordered_idom(X7) ) ),
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_918])])])])]) ).
fof(c_0_1574,plain,
! [X62,X63,X65] :
( ~ linorder(X62)
| ~ hBOOL(hAPP(X62,bool,hAPP(X62,fun(X62,bool),ord_less(X62),X65),esk30_2(X62,X63)))
| hBOOL(hAPP(X62,bool,hAPP(X62,fun(X62,bool),ord_less_eq(X62),X65),X63)) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_919])])])]) ).
fof(c_0_1575,plain,
! [X7,X8,X9] :
( ( hBOOL(hAPP(X7,bool,hAPP(X7,fun(X7,bool),ord_less(X7),X9),X8))
| ti(X7,X9) = ti(X7,X8)
| hBOOL(hAPP(X7,bool,hAPP(X7,fun(X7,bool),ord_less(X7),X8),X9))
| ~ linorder(X7) )
& ( ti(X7,X9) != ti(X7,X8)
| ~ hBOOL(hAPP(X7,bool,hAPP(X7,fun(X7,bool),ord_less(X7),X9),X8))
| hBOOL(hAPP(X7,bool,hAPP(X7,fun(X7,bool),ord_less(X7),X8),X9))
| ~ linorder(X7) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_920])])])]) ).
fof(c_0_1576,plain,
! [X42,X43,X44,X45] :
( ~ order(X42)
| ti(X42,X44) != ti(X42,X45)
| ~ hBOOL(hAPP(X42,bool,hAPP(X42,fun(X42,bool),ord_less(X42),X43),X45))
| hBOOL(hAPP(X42,bool,hAPP(X42,fun(X42,bool),ord_less(X42),X43),X44)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_921])])]) ).
fof(c_0_1577,plain,
! [X42,X43,X44,X45] :
( ~ order(X42)
| ~ hBOOL(hAPP(X42,bool,hAPP(X42,fun(X42,bool),ord_less(X42),X44),X45))
| ti(X42,X44) != ti(X42,X43)
| hBOOL(hAPP(X42,bool,hAPP(X42,fun(X42,bool),ord_less(X42),X43),X45)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_922])])]) ).
fof(c_0_1578,plain,
! [X42,X43,X44,X45] :
( ~ order(X42)
| ti(X42,X44) != ti(X42,X45)
| ~ hBOOL(hAPP(X42,bool,hAPP(X42,fun(X42,bool),ord_less_eq(X42),X43),X45))
| hBOOL(hAPP(X42,bool,hAPP(X42,fun(X42,bool),ord_less_eq(X42),X43),X44)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_923])])]) ).
fof(c_0_1579,plain,
! [X42,X43,X44,X45] :
( ~ order(X42)
| ~ hBOOL(hAPP(X42,bool,hAPP(X42,fun(X42,bool),ord_less_eq(X42),X44),X45))
| ti(X42,X44) != ti(X42,X43)
| hBOOL(hAPP(X42,bool,hAPP(X42,fun(X42,bool),ord_less_eq(X42),X43),X45)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_924])])]) ).
fof(c_0_1580,plain,
! [X41,X42,X43] :
( ~ order(X41)
| ~ hBOOL(hAPP(X41,bool,hAPP(X41,fun(X41,bool),ord_less_eq(X41),X42),X43))
| ti(X41,X43) = ti(X41,X42)
| hBOOL(hAPP(X41,bool,hAPP(X41,fun(X41,bool),ord_less(X41),X42),X43)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_925])])]) ).
fof(c_0_1581,plain,
! [X41,X42,X43] :
( ~ order(X41)
| ~ hBOOL(hAPP(X41,bool,hAPP(X41,fun(X41,bool),ord_less_eq(X41),X42),X43))
| ti(X41,X42) = ti(X41,X43)
| hBOOL(hAPP(X41,bool,hAPP(X41,fun(X41,bool),ord_less(X41),X42),X43)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_926])])]) ).
fof(c_0_1582,plain,
! [X12,X13,X14] :
( ~ order(X12)
| ~ hBOOL(hAPP(X12,bool,hAPP(X12,fun(X12,bool),ord_less_eq(X12),X13),X14))
| hBOOL(hAPP(X12,bool,hAPP(X12,fun(X12,bool),ord_less(X12),X13),X14))
| ti(X12,X13) = ti(X12,X14) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_927])])]) ).
fof(c_0_1583,plain,
! [X41,X42,X43] :
( ~ order(X41)
| ti(X41,X42) = ti(X41,X43)
| ~ hBOOL(hAPP(X41,bool,hAPP(X41,fun(X41,bool),ord_less_eq(X41),X43),X42))
| hBOOL(hAPP(X41,bool,hAPP(X41,fun(X41,bool),ord_less(X41),X43),X42)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_928])])]) ).
fof(c_0_1584,plain,
! [X41,X42,X43] :
( ~ order(X41)
| ti(X41,X42) = ti(X41,X43)
| ~ hBOOL(hAPP(X41,bool,hAPP(X41,fun(X41,bool),ord_less_eq(X41),X42),X43))
| hBOOL(hAPP(X41,bool,hAPP(X41,fun(X41,bool),ord_less(X41),X42),X43)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_929])])]) ).
fof(c_0_1585,plain,
! [X7,X8,X9] :
( ( ~ hBOOL(hAPP(X7,bool,hAPP(X7,fun(X7,bool),ord_less_eq(X7),X8),X9))
| ti(X7,X8) = ti(X7,X9)
| hBOOL(hAPP(X7,bool,hAPP(X7,fun(X7,bool),ord_less(X7),X8),X9))
| ~ linorder(X7) )
& ( ti(X7,X8) != ti(X7,X9)
| hBOOL(hAPP(X7,bool,hAPP(X7,fun(X7,bool),ord_less_eq(X7),X8),X9))
| hBOOL(hAPP(X7,bool,hAPP(X7,fun(X7,bool),ord_less(X7),X8),X9))
| ~ linorder(X7) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_930])])])]) ).
fof(c_0_1586,plain,
! [X7,X8,X9,X10,X11] :
( ( ~ hBOOL(hAPP(X7,bool,hAPP(X7,fun(X7,bool),ord_less_eq(X7),X8),X9))
| hBOOL(hAPP(X7,bool,hAPP(X7,fun(X7,bool),ord_less(X7),X8),X9))
| ti(X7,X8) = ti(X7,X9)
| ~ order(X7) )
& ( ~ hBOOL(hAPP(X7,bool,hAPP(X7,fun(X7,bool),ord_less(X7),X10),X11))
| hBOOL(hAPP(X7,bool,hAPP(X7,fun(X7,bool),ord_less_eq(X7),X10),X11))
| ~ order(X7) )
& ( ti(X7,X10) != ti(X7,X11)
| hBOOL(hAPP(X7,bool,hAPP(X7,fun(X7,bool),ord_less_eq(X7),X10),X11))
| ~ order(X7) ) ),
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_931])])])])]) ).
fof(c_0_1587,plain,
! [X7,X8,X9,X10,X11] :
( ( hBOOL(hAPP(X7,bool,hAPP(X7,fun(X7,bool),ord_less_eq(X7),X8),X9))
| ~ hBOOL(hAPP(X7,bool,hAPP(X7,fun(X7,bool),ord_less(X7),X8),X9))
| ~ order(X7) )
& ( ti(X7,X8) != ti(X7,X9)
| ~ hBOOL(hAPP(X7,bool,hAPP(X7,fun(X7,bool),ord_less(X7),X8),X9))
| ~ order(X7) )
& ( ~ hBOOL(hAPP(X7,bool,hAPP(X7,fun(X7,bool),ord_less_eq(X7),X10),X11))
| ti(X7,X10) = ti(X7,X11)
| hBOOL(hAPP(X7,bool,hAPP(X7,fun(X7,bool),ord_less(X7),X10),X11))
| ~ order(X7) ) ),
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_932])])])])]) ).
fof(c_0_1588,plain,
! [X42,X43,X44,X45] :
( ~ ord(X42)
| X44 != X45
| ~ hBOOL(hAPP(X42,bool,hAPP(X42,fun(X42,bool),ord_less(X42),X45),X43))
| hBOOL(hAPP(X42,bool,hAPP(X42,fun(X42,bool),ord_less(X42),X44),X43)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_933])])]) ).
fof(c_0_1589,plain,
! [X42,X43,X44,X45] :
( ~ ord(X42)
| ~ hBOOL(hAPP(X42,bool,hAPP(X42,fun(X42,bool),ord_less(X42),X44),X45))
| X45 != X43
| hBOOL(hAPP(X42,bool,hAPP(X42,fun(X42,bool),ord_less(X42),X44),X43)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_934])])]) ).
fof(c_0_1590,plain,
! [X42,X43,X44,X45] :
( ~ ord(X42)
| X44 != X45
| ~ hBOOL(hAPP(X42,bool,hAPP(X42,fun(X42,bool),ord_less_eq(X42),X45),X43))
| hBOOL(hAPP(X42,bool,hAPP(X42,fun(X42,bool),ord_less_eq(X42),X44),X43)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_935])])]) ).
fof(c_0_1591,plain,
! [X42,X43,X44,X45] :
( ~ ord(X42)
| ~ hBOOL(hAPP(X42,bool,hAPP(X42,fun(X42,bool),ord_less_eq(X42),X44),X45))
| X45 != X43
| hBOOL(hAPP(X42,bool,hAPP(X42,fun(X42,bool),ord_less_eq(X42),X44),X43)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_936])])]) ).
fof(c_0_1592,plain,
! [X12,X13,X14] :
( ~ preorder(X12)
| ~ hBOOL(hAPP(X12,bool,hAPP(X12,fun(X12,bool),ord_less(X12),X13),X14))
| hBOOL(hAPP(X12,bool,hAPP(X12,fun(X12,bool),ord_less_eq(X12),X13),X14)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_937])])]) ).
fof(c_0_1593,plain,
! [X39,X40] :
( ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),number_number_of(nat,X39)))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),X39)) )
& ( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),X40))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),number_number_of(nat,X40))) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_938])])])]) ).
fof(c_0_1594,plain,
! [X45,X46] :
( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),esk3_2(X45,X46)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X45),X46)) )
& ( hAPP(nat,nat,plus_plus(nat,X45),esk3_2(X45,X46)) = X46
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X45),X46)) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_939])])])]) ).
fof(c_0_1595,plain,
! [X44] :
( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),esk2_1(X44)))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),X44)) )
& ( X44 = hAPP(nat,int,semiring_1_of_nat(int),esk2_1(X44))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),X44)) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_940])])])]) ).
fof(c_0_1596,plain,
! [X30,X31] :
( ( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),one_one(int)),X30))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),X30)) )
& ( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),X31))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),one_one(int)),X31)) ) ),
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_1597,plain,
! [X7,X8,X9,X10] :
( ( hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X7),X8))
| ~ hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X7),X8)) )
& ( X7 != X8
| ~ hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X7),X8)) )
& ( ~ hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X9),X10))
| X9 = X10
| hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X9),X10)) ) ),
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_942])])])])]) ).
fof(c_0_1598,plain,
! [X7,X8,X9,X10] :
( ( ~ hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X7),X8))
| hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X7),X8))
| X7 = X8 )
& ( ~ hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X9),X10))
| hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X9),X10)) )
& ( X9 != X10
| hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X9),X10)) ) ),
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_943])])])])]) ).
fof(c_0_1599,plain,
! [X29,X30,X31,X32] :
( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X29),X30))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X29),X30)) )
& ( X29 != X30
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X29),X30)) )
& ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X31),X32))
| X31 = X32
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X31),X32)) ) ),
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_944])])])])]) ).
fof(c_0_1600,plain,
! [X29,X30,X31,X32] :
( ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X29),X30))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X29),X30))
| X29 = X30 )
& ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X31),X32))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X31),X32)) )
& ( X31 != X32
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X31),X32)) ) ),
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_945])])])])]) ).
fof(c_0_1601,plain,
! [X16,X17] :
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X16),X17))
| X16 = X17
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X16),X17)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_946])]) ).
fof(c_0_1602,plain,
! [X30,X31,X32,X33] :
( ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X30),X31))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X30),X31)) )
& ( X30 != X31
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X30),X31)) )
& ( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X32),X33))
| X32 = X33
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),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_947])])])])]) ).
fof(c_0_1603,plain,
! [X16,X17] :
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X16),X17))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X16),X17)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_948])]) ).
fof(c_0_1604,plain,
! [X16,X17] :
( ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X16),X17))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X16),X17)) )
& ( X16 != X17
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X16),X17)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_949])])]) ).
fof(c_0_1605,plain,
! [X46,X47,X48,X49,X50] :
( ~ comm_semiring_1(X46)
| hAPP(X46,X46,plus_plus(X46,hAPP(X46,X46,plus_plus(X46,X47),X48)),hAPP(X46,X46,plus_plus(X46,X49),X50)) = hAPP(X46,X46,plus_plus(X46,hAPP(X46,X46,plus_plus(X46,X47),X49)),hAPP(X46,X46,plus_plus(X46,X48),X50)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_950])])]) ).
fof(c_0_1606,plain,
! [X31,X32] : hAPP(int,int,plus_plus(int,hAPP(int,int,bit1,X31)),hAPP(int,int,bit1,X32)) = hAPP(int,int,bit0,hAPP(int,int,plus_plus(int,X31),hAPP(int,int,succ,X32))),
inference(variable_rename,[status(thm)],[c_0_951]) ).
fof(c_0_1607,plain,
! [X17,X18,X19,X20] :
( ~ number_ring(X17)
| hAPP(X17,X17,plus_plus(X17,number_number_of(X17,X18)),hAPP(X17,X17,plus_plus(X17,number_number_of(X17,X19)),X20)) = hAPP(X17,X17,plus_plus(X17,number_number_of(X17,hAPP(int,int,plus_plus(int,X18),X19))),X20) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_952])])]) ).
fof(c_0_1608,plain,
! [X29,X30,X31,X32] :
( ( hAPP(nat,X29,power_power(X29,X32),X30) != hAPP(nat,X29,power_power(X29,X32),X31)
| X30 = X31
| ~ hBOOL(hAPP(X29,bool,hAPP(X29,fun(X29,bool),ord_less(X29),one_one(X29)),X32))
| ~ linordered_semidom(X29) )
& ( X30 != X31
| hAPP(nat,X29,power_power(X29,X32),X30) = hAPP(nat,X29,power_power(X29,X32),X31)
| ~ hBOOL(hAPP(X29,bool,hAPP(X29,fun(X29,bool),ord_less(X29),one_one(X29)),X32))
| ~ linordered_semidom(X29) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_953])])])]) ).
fof(c_0_1609,plain,
! [X10,X11] :
( ~ number_semiring(X10)
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),X11))
| hAPP(X10,X10,plus_plus(X10,number_number_of(X10,X11)),one_one(X10)) = number_number_of(X10,hAPP(int,int,succ,X11)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_954])])]) ).
fof(c_0_1610,plain,
! [X44,X45,X47,X48,X49] :
( ( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X44),X45))
| X45 = hAPP(int,int,plus_plus(int,X44),hAPP(nat,int,semiring_1_of_nat(int),esk10_2(X44,X45))) )
& ( X48 != hAPP(int,int,plus_plus(int,X47),hAPP(nat,int,semiring_1_of_nat(int),X49))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X47),X48)) ) ),
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_955])])])])]) ).
fof(c_0_1611,plain,
! [X10,X11] :
( ~ number_semiring(X10)
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),X11))
| hAPP(X10,X10,plus_plus(X10,one_one(X10)),number_number_of(X10,X11)) = number_number_of(X10,hAPP(int,int,succ,X11)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_956])])]) ).
fof(c_0_1612,plain,
! [X7,X8,X9,X10,X11] :
( ( ti(X7,X8) = ti(X7,X9)
| hBOOL(hAPP(X7,bool,hAPP(X7,fun(X7,bool),ord_less(X7),X8),X9))
| hBOOL(hAPP(X7,bool,hAPP(X7,fun(X7,bool),ord_less(X7),X9),X8))
| ~ linorder(X7) )
& ( ~ hBOOL(hAPP(X7,bool,hAPP(X7,fun(X7,bool),ord_less(X7),X10),X11))
| ti(X7,X10) != ti(X7,X11)
| ~ linorder(X7) )
& ( ~ hBOOL(hAPP(X7,bool,hAPP(X7,fun(X7,bool),ord_less(X7),X11),X10))
| ti(X7,X10) != ti(X7,X11)
| ~ linorder(X7) ) ),
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_957])])])])]) ).
fof(c_0_1613,plain,
! [X12,X13,X14] :
( ~ linorder(X12)
| hBOOL(hAPP(X12,bool,hAPP(X12,fun(X12,bool),ord_less(X12),X13),X14))
| ti(X12,X13) = ti(X12,X14)
| hBOOL(hAPP(X12,bool,hAPP(X12,fun(X12,bool),ord_less(X12),X14),X13)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_958])])]) ).
fof(c_0_1614,plain,
! [X12,X13,X14] :
( ~ linorder(X12)
| ti(X12,X13) = ti(X12,X14)
| hBOOL(hAPP(X12,bool,hAPP(X12,fun(X12,bool),ord_less(X12),X13),X14))
| hBOOL(hAPP(X12,bool,hAPP(X12,fun(X12,bool),ord_less(X12),X14),X13)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_959])])]) ).
fof(c_0_1615,plain,
! [X12,X13,X14] :
( ~ linorder(X12)
| hBOOL(hAPP(X12,bool,hAPP(X12,fun(X12,bool),ord_less(X12),X13),X14))
| ti(X12,X13) = ti(X12,X14)
| hBOOL(hAPP(X12,bool,hAPP(X12,fun(X12,bool),ord_less(X12),X14),X13)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_960])])]) ).
fof(c_0_1616,plain,
! [X12,X13,X14] :
( ~ linordered_idom(X12)
| ti(X12,X13) = ti(X12,X14)
| hBOOL(hAPP(X12,bool,hAPP(X12,fun(X12,bool),ord_less(X12),X13),X14))
| hBOOL(hAPP(X12,bool,hAPP(X12,fun(X12,bool),ord_less(X12),X14),X13)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_961])])]) ).
fof(c_0_1617,plain,
! [X2] :
( ~ semiring_1(X2)
| hAPP(nat,X2,power_power(X2,zero_zero(X2)),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) = zero_zero(X2) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_962])]) ).
fof(c_0_1618,plain,
! [X2] :
( ~ semiring_1(X2)
| hAPP(nat,X2,power_power(X2,one_one(X2)),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) = one_one(X2) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_963])]) ).
fof(c_0_1619,plain,
! [X12,X13,X14] :
( ~ linorder(X12)
| hBOOL(hAPP(X12,bool,hAPP(X12,fun(X12,bool),ord_less_eq(X12),X13),X14))
| hBOOL(hAPP(X12,bool,hAPP(X12,fun(X12,bool),ord_less(X12),X14),X13)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_964])])]) ).
fof(c_0_1620,plain,
! [X12,X13,X14] :
( ~ linorder(X12)
| hBOOL(hAPP(X12,bool,hAPP(X12,fun(X12,bool),ord_less(X12),X13),X14))
| hBOOL(hAPP(X12,bool,hAPP(X12,fun(X12,bool),ord_less_eq(X12),X14),X13)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_965])])]) ).
fof(c_0_1621,plain,
! [X12,X13,X14] :
( ~ linorder(X12)
| hBOOL(hAPP(X12,bool,hAPP(X12,fun(X12,bool),ord_less_eq(X12),X13),X14))
| hBOOL(hAPP(X12,bool,hAPP(X12,fun(X12,bool),ord_less(X12),X14),X13)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_966])])]) ).
fof(c_0_1622,plain,
! [X12,X13,X14] :
( ~ linorder(X12)
| hBOOL(hAPP(X12,bool,hAPP(X12,fun(X12,bool),ord_less_eq(X12),X13),X14))
| hBOOL(hAPP(X12,bool,hAPP(X12,fun(X12,bool),ord_less_eq(X12),X14),X13)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_967])])]) ).
fof(c_0_1623,plain,
! [X12,X13,X14] :
( ~ linorder(X12)
| hBOOL(hAPP(X12,bool,hAPP(X12,fun(X12,bool),ord_less_eq(X12),X13),X14))
| hBOOL(hAPP(X12,bool,hAPP(X12,fun(X12,bool),ord_less_eq(X12),X14),X13)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_968])])]) ).
fof(c_0_1624,plain,
! [X12,X13] :
( X12 = X13
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X12),X13))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X13),X12)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_969])]) ).
fof(c_0_1625,plain,
! [X29,X30,X31,X32] :
( ( X29 = X30
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X29),X30))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X30),X29)) )
& ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X31),X32))
| X31 != X32 )
& ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X32),X31))
| X31 != X32 ) ),
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_970])])])])]) ).
fof(c_0_1626,plain,
! [X12,X13] :
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X12),X13))
| X12 = X13
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X13),X12)) ),
inference(variable_rename,[status(thm)],[c_0_971]) ).
fof(c_0_1627,plain,
! [X17,X18] :
( hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X17),X18))
| hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X18),X17)) ),
inference(variable_rename,[status(thm)],[c_0_972]) ).
fof(c_0_1628,plain,
! [X16,X17] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X16),X17))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X17),X16)) ),
inference(variable_rename,[status(thm)],[c_0_973]) ).
fof(c_0_1629,plain,
! [X17,X18] :
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X17),X18))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X18),X17)) ),
inference(variable_rename,[status(thm)],[c_0_974]) ).
fof(c_0_1630,plain,
! [X11] :
( ~ hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X11))
| hAPP(real,real,sqrt,X11) != zero_zero(real) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_975])]) ).
fof(c_0_1631,plain,
! [X10,X11,X12] :
( ( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),number_number_of(int,X11)))
| hAPP(nat,X10,semiring_1_of_nat(X10),number_number_of(nat,X11)) = number_number_of(X10,X11)
| ~ number_ring(X10) )
& ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),number_number_of(int,X12)))
| hAPP(nat,X10,semiring_1_of_nat(X10),number_number_of(nat,X12)) = zero_zero(X10)
| ~ number_ring(X10) ) ),
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_976])])])])]) ).
fof(c_0_1632,plain,
! [X2] :
( ~ linordered_semidom(X2)
| hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),zero_zero(X2)),hAPP(X2,X2,plus_plus(X2,one_one(X2)),one_one(X2)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_977])]) ).
fof(c_0_1633,plain,
! [X9,X10] :
( ~ number_ring(X9)
| hAPP(X9,X9,plus_plus(X9,one_one(X9)),number_number_of(X9,X10)) = number_number_of(X9,hAPP(int,int,plus_plus(int,hAPP(int,int,bit1,pls)),X10)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_978])])]) ).
fof(c_0_1634,plain,
! [X10,X11] :
( ( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X10),pls))
| hAPP(nat,nat,plus_plus(nat,number_number_of(nat,X10)),one_one(nat)) = one_one(nat) )
& ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X11),pls))
| hAPP(nat,nat,plus_plus(nat,number_number_of(nat,X11)),one_one(nat)) = number_number_of(nat,hAPP(int,int,succ,X11)) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_979])])])]) ).
fof(c_0_1635,plain,
! [X45,X46,X48,X49,X50] :
( ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X45),X46))
| X46 = hAPP(nat,nat,plus_plus(nat,X45),esk13_2(X45,X46)) )
& ( X49 != hAPP(nat,nat,plus_plus(nat,X48),X50)
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X48),X49)) ) ),
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_980])])])])]) ).
fof(c_0_1636,plain,
! [X10,X11] :
( ( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X10),pls))
| hAPP(nat,nat,plus_plus(nat,one_one(nat)),number_number_of(nat,X10)) = one_one(nat) )
& ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X11),pls))
| hAPP(nat,nat,plus_plus(nat,one_one(nat)),number_number_of(nat,X11)) = number_number_of(nat,hAPP(int,int,succ,X11)) ) ),
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_1637,plain,
! [X42,X43,X44,X45] :
( ~ comm_semiring_1(X42)
| hAPP(X42,X42,plus_plus(X42,hAPP(X42,X42,plus_plus(X42,X43),X44)),X45) = hAPP(X42,X42,plus_plus(X42,hAPP(X42,X42,plus_plus(X42,X43),X45)),X44) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_982])])]) ).
fof(c_0_1638,plain,
! [X54] :
( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X54))
| X54 = hAPP(nat,int,semiring_1_of_nat(int),esk15_1(X54)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_983])])]) ).
fof(c_0_1639,plain,
! [X44] :
( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X44))
| X44 = hAPP(nat,int,semiring_1_of_nat(int),esk12_1(X44)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_984])])]) ).
fof(c_0_1640,plain,
! [X44] :
( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X44))
| X44 = hAPP(nat,int,semiring_1_of_nat(int),esk11_1(X44)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_985])])]) ).
fof(c_0_1641,plain,
! [X32,X33] :
( ~ linordered_semidom(X32)
| hBOOL(hAPP(X32,bool,hAPP(X32,fun(X32,bool),ord_less(X32),X33),hAPP(X32,X32,plus_plus(X32,X33),one_one(X32)))) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_986])])]) ).
fof(c_0_1642,plain,
! [X16,X17] :
( ~ linordered_semidom(X16)
| hBOOL(hAPP(X16,bool,hAPP(X16,fun(X16,bool),ord_less_eq(X16),zero_zero(X16)),hAPP(nat,X16,semiring_1_of_nat(X16),X17))) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_987])])]) ).
fof(c_0_1643,plain,
! [X15,X16] :
( ~ linordered_semidom(X15)
| hBOOL(hAPP(X15,bool,hAPP(X15,fun(X15,bool),ord_less_eq(X15),zero_zero(X15)),hAPP(nat,X15,semiring_1_of_nat(X15),X16))) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_988])])]) ).
fof(c_0_1644,plain,
! [X16,X17] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X16),hAPP(nat,nat,plus_plus(nat,X16),X17))),
inference(variable_rename,[status(thm)],[c_0_989]) ).
fof(c_0_1645,plain,
! [X16,X17] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X16),hAPP(nat,nat,plus_plus(nat,X17),X16))),
inference(variable_rename,[status(thm)],[c_0_990]) ).
fof(c_0_1646,plain,
! [X2] :
( ~ linordered_semidom(X2)
| ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less_eq(X2),one_one(X2)),zero_zero(X2))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_991])]) ).
fof(c_0_1647,plain,
! [X2] :
( ~ linordered_semidom(X2)
| ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),one_one(X2)),zero_zero(X2))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_992])]) ).
fof(c_0_1648,plain,
! [X16,X17,X18] :
( ~ semiring_1(X16)
| hAPP(nat,X16,semiring_1_of_nat(X16),hAPP(nat,nat,plus_plus(nat,X17),X18)) = hAPP(X16,X16,plus_plus(X16,hAPP(nat,X16,semiring_1_of_nat(X16),X17)),hAPP(nat,X16,semiring_1_of_nat(X16),X18)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_993])])]) ).
fof(c_0_1649,plain,
! [X16] : hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(nat,int,semiring_1_of_nat(int),X16))),
inference(variable_rename,[status(thm)],[c_0_994]) ).
fof(c_0_1650,plain,
! [X17] : hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(nat,int,semiring_1_of_nat(int),X17))),
inference(variable_rename,[status(thm)],[c_0_995]) ).
fof(c_0_1651,plain,
! [X12,X13,X14] :
( ~ order(X12)
| ~ hBOOL(hAPP(X12,bool,hAPP(X12,fun(X12,bool),ord_less(X12),X13),X14))
| ti(X12,X13) != ti(X12,X14) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_996])])]) ).
fof(c_0_1652,plain,
! [X12,X13,X14] :
( ~ order(X12)
| ~ hBOOL(hAPP(X12,bool,hAPP(X12,fun(X12,bool),ord_less(X12),X13),X14))
| ti(X12,X13) != ti(X12,X14) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_997])])]) ).
fof(c_0_1653,plain,
! [X12,X13,X14] :
( ~ order(X12)
| ~ hBOOL(hAPP(X12,bool,hAPP(X12,fun(X12,bool),ord_less(X12),X13),X14))
| ti(X12,X14) != ti(X12,X13) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_998])])]) ).
fof(c_0_1654,plain,
! [X12,X13] : hAPP(int,int,plus_plus(int,hAPP(nat,int,semiring_1_of_nat(int),X12)),hAPP(nat,int,semiring_1_of_nat(int),X13)) = hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,plus_plus(nat,X12),X13)),
inference(variable_rename,[status(thm)],[c_0_999]) ).
fof(c_0_1655,plain,
! [X16,X17] : hAPP(int,int,plus_plus(int,hAPP(nat,int,semiring_1_of_nat(int),X16)),hAPP(nat,int,semiring_1_of_nat(int),X17)) = hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,plus_plus(nat,X16),X17)),
inference(variable_rename,[status(thm)],[c_0_1000]) ).
fof(c_0_1656,plain,
! [X11,X12] :
( ~ preorder(X11)
| ~ hBOOL(hAPP(X11,bool,hAPP(X11,fun(X11,bool),ord_less(X11),X12),X12)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1001])])]) ).
fof(c_0_1657,plain,
! [X31,X32] : hAPP(int,int,plus_plus(int,hAPP(int,int,bit0,X31)),hAPP(int,int,bit1,X32)) = hAPP(int,int,bit1,hAPP(int,int,plus_plus(int,X31),X32)),
inference(variable_rename,[status(thm)],[c_0_1002]) ).
fof(c_0_1658,plain,
! [X31,X32] : hAPP(int,int,plus_plus(int,hAPP(int,int,bit1,X31)),hAPP(int,int,bit0,X32)) = hAPP(int,int,bit1,hAPP(int,int,plus_plus(int,X31),X32)),
inference(variable_rename,[status(thm)],[c_0_1003]) ).
fof(c_0_1659,plain,
! [X31,X32] : hAPP(int,int,plus_plus(int,hAPP(int,int,bit0,X31)),hAPP(int,int,bit0,X32)) = hAPP(int,int,bit0,hAPP(int,int,plus_plus(int,X31),X32)),
inference(variable_rename,[status(thm)],[c_0_1004]) ).
fof(c_0_1660,plain,
! [X18,X19] :
( ( X18 = zero_zero(nat)
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X18)) )
& ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X19))
| X19 != 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_1005])])])]) ).
fof(c_0_1661,plain,
! [X18,X19] :
( ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X18),zero_zero(nat)))
| X18 = zero_zero(nat) )
& ( X19 != zero_zero(nat)
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X19),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_1006])])])]) ).
fof(c_0_1662,plain,
! [X39,X40] :
( ( number_number_of(nat,X39) != zero_zero(nat)
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X39),pls)) )
& ( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X40),pls))
| number_number_of(nat,X40) = 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_1007])])])]) ).
fof(c_0_1663,plain,
! [X39,X40] :
( ( zero_zero(nat) != number_number_of(nat,X39)
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X39),pls)) )
& ( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X40),pls))
| zero_zero(nat) = number_number_of(nat,X40) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1008])])])]) ).
fof(c_0_1664,plain,
! [X16] : ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X16),zero_zero(nat))),
inference(variable_rename,[status(thm)],[c_0_1009]) ).
fof(c_0_1665,plain,
! [X16] : ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X16),zero_zero(nat))),
inference(variable_rename,[status(thm)],[c_0_1010]) ).
fof(c_0_1666,plain,
! [X16] : ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X16),zero_zero(nat))),
inference(variable_rename,[status(thm)],[c_0_1011]) ).
fof(c_0_1667,plain,
! [X16,X17] :
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X16),X17))
| X17 != zero_zero(nat) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1012])]) ).
fof(c_0_1668,plain,
! [X38,X39] :
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X38),X39))
| X38 != X39 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1013])]) ).
fof(c_0_1669,plain,
! [X16,X17] :
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X16),X17))
| X17 != X16 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1014])]) ).
fof(c_0_1670,plain,
! [X16] : ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X16),X16)),
inference(variable_rename,[status(thm)],[c_0_1015]) ).
fof(c_0_1671,plain,
! [X16] : ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X16),X16)),
inference(variable_rename,[status(thm)],[c_0_1016]) ).
fof(c_0_1672,plain,
~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),zero_zero(int))),
c_0_1017 ).
fof(c_0_1673,plain,
~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),pls)),
c_0_1018 ).
fof(c_0_1674,plain,
! [X46,X47,X48,X49] :
( ~ comm_semiring_1(X46)
| hAPP(X46,X46,plus_plus(X46,X47),hAPP(X46,X46,plus_plus(X46,X48),X49)) = hAPP(X46,X46,plus_plus(X46,hAPP(X46,X46,plus_plus(X46,X47),X48)),X49) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1019])])]) ).
fof(c_0_1675,plain,
! [X42,X43,X44,X45] :
( ~ comm_semiring_1(X42)
| hAPP(X42,X42,plus_plus(X42,hAPP(X42,X42,plus_plus(X42,X43),X44)),X45) = hAPP(X42,X42,plus_plus(X42,X43),hAPP(X42,X42,plus_plus(X42,X44),X45)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1020])])]) ).
fof(c_0_1676,plain,
! [X42,X43,X44,X45] :
( ~ ab_semigroup_add(X42)
| hAPP(X42,X42,plus_plus(X42,hAPP(X42,X42,plus_plus(X42,X43),X44)),X45) = hAPP(X42,X42,plus_plus(X42,X43),hAPP(X42,X42,plus_plus(X42,X44),X45)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1021])])]) ).
fof(c_0_1677,plain,
! [X17] : hAPP(int,int,plus_plus(int,hAPP(int,int,plus_plus(int,one_one(int)),X17)),X17) != zero_zero(int),
inference(variable_rename,[status(thm)],[c_0_1022]) ).
fof(c_0_1678,plain,
! [X21,X22,X23] : hAPP(nat,nat,plus_plus(nat,hAPP(nat,nat,plus_plus(nat,X21),X22)),X23) = hAPP(nat,nat,plus_plus(nat,X21),hAPP(nat,nat,plus_plus(nat,X22),X23)),
inference(variable_rename,[status(thm)],[c_0_1023]) ).
fof(c_0_1679,plain,
! [X28,X29,X30] : hAPP(int,int,plus_plus(int,hAPP(int,int,plus_plus(int,X28),X29)),X30) = hAPP(int,int,plus_plus(int,X28),hAPP(int,int,plus_plus(int,X29),X30)),
inference(variable_rename,[status(thm)],[c_0_1024]) ).
fof(c_0_1680,plain,
! [X12,X13,X14] : hAPP(X12,X12,hAPP(X12,fun(X12,X12),hAPP(bool,fun(X12,fun(X12,X12)),if(X12),fFalse),X13),X14) = ti(X12,X14),
inference(variable_rename,[status(thm)],[c_0_1025]) ).
fof(c_0_1681,plain,
! [X12,X13,X14] : hAPP(X12,X12,hAPP(X12,fun(X12,X12),hAPP(bool,fun(X12,fun(X12,X12)),if(X12),fTrue),X13),X14) = ti(X12,X13),
inference(variable_rename,[status(thm)],[c_0_1026]) ).
fof(c_0_1682,plain,
! [X16,X17,X18] :
( ~ semiring_1(X16)
| hAPP(nat,X16,semiring_1_of_nat(X16),hAPP(nat,nat,power_power(nat,X17),X18)) = hAPP(nat,X16,power_power(X16,hAPP(nat,X16,semiring_1_of_nat(X16),X17)),X18) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1027])])]) ).
fof(c_0_1683,plain,
! [X9,X10] :
( ~ number_ring(X9)
| number_number_of(X9,hAPP(int,int,bit1,X10)) = hAPP(X9,X9,plus_plus(X9,hAPP(X9,X9,plus_plus(X9,one_one(X9)),number_number_of(X9,X10))),number_number_of(X9,X10)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1028])])]) ).
fof(c_0_1684,plain,
! [X9,X10] :
( ~ number_ring(X9)
| number_number_of(X9,hAPP(int,int,bit0,X10)) = hAPP(X9,X9,plus_plus(X9,hAPP(X9,X9,plus_plus(X9,zero_zero(X9)),number_number_of(X9,X10))),number_number_of(X9,X10)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1029])])]) ).
fof(c_0_1685,plain,
! [X16,X17] : hAPP(nat,int,power_power(int,hAPP(nat,int,semiring_1_of_nat(int),X16)),X17) = hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,power_power(nat,X16),X17)),
inference(variable_rename,[status(thm)],[c_0_1030]) ).
fof(c_0_1686,plain,
! [X16,X17] : hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,power_power(nat,X16),X17)) = hAPP(nat,int,power_power(int,hAPP(nat,int,semiring_1_of_nat(int),X16)),X17),
inference(variable_rename,[status(thm)],[c_0_1031]) ).
fof(c_0_1687,plain,
! [X16,X17] : hAPP(nat,int,power_power(int,hAPP(nat,int,semiring_1_of_nat(int),X16)),X17) = hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,power_power(nat,X16),X17)),
inference(variable_rename,[status(thm)],[c_0_1032]) ).
fof(c_0_1688,plain,
! [X10,X11] :
( ~ number_ring(X10)
| hAPP(X10,X10,plus_plus(X10,number_number_of(X10,X11)),one_one(X10)) = number_number_of(X10,hAPP(int,int,plus_plus(int,X11),hAPP(int,int,bit1,pls))) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1033])])]) ).
fof(c_0_1689,plain,
! [X2] :
( ~ number_semiring(X2)
| hAPP(X2,X2,plus_plus(X2,one_one(X2)),one_one(X2)) = number_number_of(X2,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1034])]) ).
fof(c_0_1690,plain,
! [X2] :
( ~ number_ring(X2)
| hAPP(X2,X2,plus_plus(X2,one_one(X2)),one_one(X2)) = number_number_of(X2,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1035])]) ).
fof(c_0_1691,axiom,
hAPP(nat,nat,plus_plus(nat,one_one(nat)),one_one(nat)) = number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))),
c_0_1036 ).
fof(c_0_1692,plain,
! [X46,X47,X48,X49] :
( ~ comm_semiring_1(X46)
| hAPP(X46,X46,plus_plus(X46,X47),hAPP(X46,X46,plus_plus(X46,X48),X49)) = hAPP(X46,X46,plus_plus(X46,X48),hAPP(X46,X46,plus_plus(X46,X47),X49)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1037])])]) ).
fof(c_0_1693,plain,
! [X2] :
( ~ linordered_semidom(X2)
| hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less_eq(X2),zero_zero(X2)),one_one(X2))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1038])]) ).
fof(c_0_1694,plain,
! [X2] :
( ~ linordered_semidom(X2)
| hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),zero_zero(X2)),one_one(X2))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1039])]) ).
fof(c_0_1695,axiom,
hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),number_number_of(int,pls))),
c_0_1040 ).
fof(c_0_1696,plain,
! [X12,X13,X14] :
( ~ preorder(X12)
| X13 != X14
| hBOOL(hAPP(X12,bool,hAPP(X12,fun(X12,bool),ord_less_eq(X12),X13),X14)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1041])])]) ).
fof(c_0_1697,plain,
! [X11,X12] :
( ~ preorder(X11)
| hBOOL(hAPP(X11,bool,hAPP(X11,fun(X11,bool),ord_less_eq(X11),X12),X12)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1042])])]) ).
fof(c_0_1698,plain,
! [X17,X18,X19] : hAPP(nat,nat,plus_plus(nat,X17),hAPP(nat,nat,plus_plus(nat,X18),X19)) = hAPP(nat,nat,plus_plus(nat,X18),hAPP(nat,nat,plus_plus(nat,X17),X19)),
inference(variable_rename,[status(thm)],[c_0_1043]) ).
fof(c_0_1699,plain,
! [X21] : hAPP(int,int,bit1,X21) = hAPP(int,int,plus_plus(int,hAPP(int,int,plus_plus(int,one_one(int)),X21)),X21),
inference(variable_rename,[status(thm)],[c_0_1044]) ).
fof(c_0_1700,plain,
! [X17,X18,X19] : hAPP(int,int,plus_plus(int,X17),hAPP(int,int,plus_plus(int,X18),X19)) = hAPP(int,int,plus_plus(int,X18),hAPP(int,int,plus_plus(int,X17),X19)),
inference(variable_rename,[status(thm)],[c_0_1045]) ).
fof(c_0_1701,axiom,
hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),one_one(int))),
c_0_1046 ).
fof(c_0_1702,axiom,
hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),zero_zero(int))),
c_0_1047 ).
fof(c_0_1703,axiom,
hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),one_one(int))),
c_0_1048 ).
fof(c_0_1704,plain,
! [X16] :
( X16 = zero_zero(nat)
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X16)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1049])]) ).
fof(c_0_1705,plain,
! [X16] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),zero_zero(nat)),X16)),
inference(variable_rename,[status(thm)],[c_0_1050]) ).
fof(c_0_1706,plain,
! [X16] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),zero_zero(nat)),X16)),
inference(variable_rename,[status(thm)],[c_0_1051]) ).
fof(c_0_1707,axiom,
hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),one_one(int)),t)),
c_0_1052 ).
fof(c_0_1708,axiom,
hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),tn)),
c_0_1053 ).
fof(c_0_1709,axiom,
hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),n)),
c_0_1054 ).
fof(c_0_1710,axiom,
hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),t)),
c_0_1055 ).
fof(c_0_1711,plain,
! [X16,X17] :
( X16 != X17
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X16),X17)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1056])]) ).
fof(c_0_1712,plain,
! [X9] : hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X9),X9)),
inference(variable_rename,[status(thm)],[c_0_1057]) ).
fof(c_0_1713,plain,
! [X16] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X16),X16)),
inference(variable_rename,[status(thm)],[c_0_1058]) ).
fof(c_0_1714,plain,
! [X9] : hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X9),X9)),
inference(variable_rename,[status(thm)],[c_0_1059]) ).
fof(c_0_1715,axiom,
hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),pls)),
c_0_1060 ).
fof(c_0_1716,plain,
! [X21] : hAPP(int,int,succ,hAPP(int,int,bit1,X21)) = hAPP(int,int,bit0,hAPP(int,int,succ,X21)),
inference(variable_rename,[status(thm)],[c_0_1061]) ).
fof(c_0_1717,plain,
! [X5,X6,X7] : ti(fun(X5,fun(X5,X5)),hAPP(bool,fun(X5,fun(X5,X5)),X6,X7)) = hAPP(bool,fun(X5,fun(X5,X5)),X6,X7),
inference(variable_rename,[status(thm)],[c_0_1062]) ).
fof(c_0_1718,plain,
! [X5,X6,X7] : hAPP(bool,fun(X5,fun(X5,X5)),ti(fun(bool,fun(X5,fun(X5,X5))),X6),X7) = hAPP(bool,fun(X5,fun(X5,X5)),X6,X7),
inference(variable_rename,[status(thm)],[c_0_1063]) ).
fof(c_0_1719,plain,
! [X21] : hAPP(int,int,succ,hAPP(int,int,bit0,X21)) = hAPP(int,int,bit1,X21),
inference(variable_rename,[status(thm)],[c_0_1064]) ).
fof(c_0_1720,plain,
! [X10,X11,X12] :
( ~ number_ring(X10)
| number_number_of(X10,hAPP(int,int,plus_plus(int,X11),X12)) = hAPP(X10,X10,plus_plus(X10,number_number_of(X10,X11)),number_number_of(X10,X12)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1065])])]) ).
fof(c_0_1721,plain,
! [X10,X11,X12] :
( ~ number_ring(X10)
| hAPP(X10,X10,plus_plus(X10,number_number_of(X10,X11)),number_number_of(X10,X12)) = number_number_of(X10,hAPP(int,int,plus_plus(int,X11),X12)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1066])])]) ).
fof(c_0_1722,plain,
! [X47,X48,X49,X50,X51,X52,X53] :
( ( hAPP(X47,X47,plus_plus(X47,X48),X49) != hAPP(X47,X47,plus_plus(X47,X48),X50)
| ti(X47,X49) = ti(X47,X50)
| ~ cancel_semigroup_add(X47) )
& ( ti(X47,X52) != ti(X47,X53)
| hAPP(X47,X47,plus_plus(X47,X51),X52) = hAPP(X47,X47,plus_plus(X47,X51),X53)
| ~ cancel_semigroup_add(X47) ) ),
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_1067])])])])]) ).
fof(c_0_1723,plain,
! [X47,X48,X49,X50,X51,X52,X53] :
( ( hAPP(X47,X47,plus_plus(X47,X48),X49) != hAPP(X47,X47,plus_plus(X47,X50),X49)
| ti(X47,X48) = ti(X47,X50)
| ~ cancel_semigroup_add(X47) )
& ( ti(X47,X51) != ti(X47,X53)
| hAPP(X47,X47,plus_plus(X47,X51),X52) = hAPP(X47,X47,plus_plus(X47,X53),X52)
| ~ cancel_semigroup_add(X47) ) ),
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_1724,plain,
! [X42,X43,X44,X45] :
( ~ cancel_semigroup_add(X42)
| hAPP(X42,X42,plus_plus(X42,X43),X44) != hAPP(X42,X42,plus_plus(X42,X43),X45)
| ti(X42,X44) = ti(X42,X45) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1069])])]) ).
fof(c_0_1725,plain,
! [X42,X43,X44,X45] :
( ~ cancel146912293up_add(X42)
| hAPP(X42,X42,plus_plus(X42,X43),X44) != hAPP(X42,X42,plus_plus(X42,X43),X45)
| ti(X42,X44) = ti(X42,X45) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1070])])]) ).
fof(c_0_1726,plain,
! [X42,X43,X44,X45] :
( ~ cancel_semigroup_add(X42)
| hAPP(X42,X42,plus_plus(X42,X43),X44) != hAPP(X42,X42,plus_plus(X42,X45),X44)
| ti(X42,X43) = ti(X42,X45) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1071])])]) ).
fof(c_0_1727,plain,
! [X10,X11] : hAPP(int,int,plus_plus(int,number_number_of(int,X10)),number_number_of(int,X11)) = number_number_of(int,hAPP(int,int,plus_plus(int,X10),X11)),
inference(variable_rename,[status(thm)],[c_0_1072]) ).
fof(c_0_1728,plain,
! [X5,X6,X7] : ti(fun(X5,X5),hAPP(X5,fun(X5,X5),X6,X7)) = hAPP(X5,fun(X5,X5),X6,X7),
inference(variable_rename,[status(thm)],[c_0_1073]) ).
fof(c_0_1729,plain,
! [X29,X30,X31,X32,X33,X34] :
( ( hAPP(nat,nat,plus_plus(nat,X29),X30) != hAPP(nat,nat,plus_plus(nat,X31),X30)
| X29 = X31 )
& ( X32 != X34
| hAPP(nat,nat,plus_plus(nat,X32),X33) = hAPP(nat,nat,plus_plus(nat,X34),X33) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1074])])])]) ).
fof(c_0_1730,plain,
! [X29,X30,X31,X32,X33,X34] :
( ( hAPP(nat,nat,plus_plus(nat,X29),X30) != hAPP(nat,nat,plus_plus(nat,X29),X31)
| X30 = X31 )
& ( X33 != X34
| hAPP(nat,nat,plus_plus(nat,X32),X33) = hAPP(nat,nat,plus_plus(nat,X32),X34) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1075])])])]) ).
fof(c_0_1731,plain,
! [X21,X22] :
( ~ number_ring(X21)
| number_number_of(X21,hAPP(int,int,succ,X22)) = hAPP(X21,X21,plus_plus(X21,one_one(X21)),number_number_of(X21,X22)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1076])])]) ).
fof(c_0_1732,plain,
! [X29,X30,X31,X32,X33] :
( ( hAPP(nat,X29,semiring_1_of_nat(X29),X30) != hAPP(nat,X29,semiring_1_of_nat(X29),X31)
| X30 = X31
| ~ semiring_char_0(X29) )
& ( X32 != X33
| hAPP(nat,X29,semiring_1_of_nat(X29),X32) = hAPP(nat,X29,semiring_1_of_nat(X29),X33)
| ~ semiring_char_0(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_1077])])])])]) ).
fof(c_0_1733,plain,
! [X7,X8,X9,X10] :
( ( hAPP(nat,int,semiring_1_of_nat(int),X7) != hAPP(nat,int,semiring_1_of_nat(int),X8)
| X7 = X8 )
& ( X9 != X10
| hAPP(nat,int,semiring_1_of_nat(int),X9) = hAPP(nat,int,semiring_1_of_nat(int),X10) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1078])])])]) ).
fof(c_0_1734,plain,
! [X29,X30,X31,X32] :
( ( hAPP(nat,int,semiring_1_of_nat(int),X29) != hAPP(nat,int,semiring_1_of_nat(int),X30)
| X29 = X30 )
& ( X31 != X32
| hAPP(nat,int,semiring_1_of_nat(int),X31) = hAPP(nat,int,semiring_1_of_nat(int),X32) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1079])])])]) ).
fof(c_0_1735,plain,
! [X16,X17] :
( ~ number_semiring(X16)
| number_number_of(X16,hAPP(nat,int,semiring_1_of_nat(int),X17)) = hAPP(nat,X16,semiring_1_of_nat(X16),X17) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1080])])]) ).
fof(c_0_1736,plain,
! [X14,X15,X16,X17] :
( ( hAPP(int,int,bit0,X14) != hAPP(int,int,bit0,X15)
| X14 = X15 )
& ( X16 != X17
| hAPP(int,int,bit0,X16) = hAPP(int,int,bit0,X17) ) ),
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_1737,plain,
! [X14,X15,X16,X17] :
( ( hAPP(int,int,bit1,X14) != hAPP(int,int,bit1,X15)
| X14 = X15 )
& ( X16 != X17
| hAPP(int,int,bit1,X16) = hAPP(int,int,bit1,X17) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1082])])])]) ).
fof(c_0_1738,plain,
! [X31,X32] : hAPP(int,int,bit0,X31) != hAPP(int,int,bit1,X32),
inference(variable_rename,[status(thm)],[c_0_1083]) ).
fof(c_0_1739,plain,
! [X31,X32] : hAPP(int,int,bit1,X31) != hAPP(int,int,bit0,X32),
inference(variable_rename,[status(thm)],[c_0_1084]) ).
fof(c_0_1740,plain,
! [X5,X6,X7,X8] :
( ~ ord(X8)
| ti(X8,hAPP(X5,X8,X6,X7)) = hAPP(X5,X8,X6,X7) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1085])]) ).
fof(c_0_1741,plain,
! [X5,X6,X7] :
( ~ power(X7)
| ti(X7,hAPP(nat,X7,X5,X6)) = hAPP(nat,X7,X5,X6) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1086])]) ).
fof(c_0_1742,plain,
! [X5,X6,X7] : ti(X5,hAPP(X5,X5,X6,X7)) = hAPP(X5,X5,X6,X7),
inference(variable_rename,[status(thm)],[c_0_1087]) ).
fof(c_0_1743,plain,
! [X5,X6,X7] : hAPP(X5,fun(X5,X5),ti(fun(X5,fun(X5,X5)),X6),X7) = hAPP(X5,fun(X5,X5),X6,X7),
inference(variable_rename,[status(thm)],[c_0_1088]) ).
fof(c_0_1744,plain,
! [X5,X6,X7] : hAPP(bool,fun(X5,fun(X5,X5)),X6,ti(bool,X7)) = hAPP(bool,fun(X5,fun(X5,X5)),X6,X7),
inference(variable_rename,[status(thm)],[c_0_1089]) ).
fof(c_0_1745,plain,
! [X5,X6,X7,X8] :
( ~ ord(X8)
| hAPP(X5,X8,ti(fun(X5,X8),X6),X7) = hAPP(X5,X8,X6,X7) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1090])]) ).
fof(c_0_1746,plain,
! [X5,X6,X7] : hAPP(X5,X5,ti(fun(X5,X5),X6),X7) = hAPP(X5,X5,X6,X7),
inference(variable_rename,[status(thm)],[c_0_1091]) ).
fof(c_0_1747,plain,
! [X5,X6,X7] : hAPP(X5,fun(X5,X5),X6,ti(X5,X7)) = hAPP(X5,fun(X5,X5),X6,X7),
inference(variable_rename,[status(thm)],[c_0_1092]) ).
fof(c_0_1748,plain,
! [X5,X6,X7] :
( ~ power(X7)
| hAPP(nat,X7,ti(fun(nat,X7),X5),X6) = hAPP(nat,X7,X5,X6) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1093])]) ).
fof(c_0_1749,plain,
! [X42,X43,X44] :
( ~ comm_semiring_1(X42)
| hAPP(X42,X42,plus_plus(X42,X43),X44) = hAPP(X42,X42,plus_plus(X42,X44),X43) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1094])])]) ).
fof(c_0_1750,plain,
! [X16,X17] : hAPP(nat,nat,plus_plus(nat,X16),X17) = hAPP(nat,nat,plus_plus(nat,X17),X16),
inference(variable_rename,[status(thm)],[c_0_1095]) ).
fof(c_0_1751,plain,
! [X17,X18] : hAPP(int,int,plus_plus(int,X17),X18) = hAPP(int,int,plus_plus(int,X18),X17),
inference(variable_rename,[status(thm)],[c_0_1096]) ).
fof(c_0_1752,plain,
! [X5,X6,X7,X8] :
( ~ ord(X8)
| hAPP(X5,X8,X6,ti(X5,X7)) = hAPP(X5,X8,X6,X7) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1097])]) ).
fof(c_0_1753,plain,
! [X25,X26,X27,X28,X29] :
( ( ti(X25,X26) = zero_zero(X25)
| hAPP(nat,X25,power_power(X25,X26),number_number_of(nat,X27)) != zero_zero(X25)
| ~ power(X25)
| ~ mult_zero(X25)
| ~ no_zero_divisors(X25)
| ~ zero_neq_one(X25) )
& ( number_number_of(nat,X27) != zero_zero(nat)
| hAPP(nat,X25,power_power(X25,X26),number_number_of(nat,X27)) != zero_zero(X25)
| ~ power(X25)
| ~ mult_zero(X25)
| ~ no_zero_divisors(X25)
| ~ zero_neq_one(X25) )
& ( ti(X25,X28) != zero_zero(X25)
| number_number_of(nat,X29) = zero_zero(nat)
| hAPP(nat,X25,power_power(X25,X28),number_number_of(nat,X29)) = zero_zero(X25)
| ~ power(X25)
| ~ mult_zero(X25)
| ~ no_zero_divisors(X25)
| ~ zero_neq_one(X25) ) ),
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_1098])])])])]) ).
fof(c_0_1754,plain,
! [X5,X6,X7] :
( ~ power(X7)
| hAPP(nat,X7,X5,ti(nat,X6)) = hAPP(nat,X7,X5,X6) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1099])]) ).
fof(c_0_1755,plain,
! [X5,X6,X7] : hAPP(X5,X5,X6,ti(X5,X7)) = hAPP(X5,X5,X6,X7),
inference(variable_rename,[status(thm)],[c_0_1100]) ).
fof(c_0_1756,plain,
! [X21] : hAPP(int,int,succ,X21) = hAPP(int,int,plus_plus(int,X21),one_one(int)),
inference(variable_rename,[status(thm)],[c_0_1101]) ).
fof(c_0_1757,plain,
! [X21] : hAPP(int,int,bit0,X21) = hAPP(int,int,plus_plus(int,X21),X21),
inference(variable_rename,[status(thm)],[c_0_1102]) ).
fof(c_0_1758,plain,
! [X2] :
( ~ number_semiring(X2)
| number_number_of(X2,hAPP(int,int,bit1,pls)) = one_one(X2) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1103])]) ).
fof(c_0_1759,plain,
! [X2] :
( ~ number_ring(X2)
| number_number_of(X2,hAPP(int,int,bit1,pls)) = one_one(X2) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1104])]) ).
fof(c_0_1760,plain,
! [X2] :
( ~ number_ring(X2)
| one_one(X2) = number_number_of(X2,hAPP(int,int,bit1,pls)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1105])]) ).
fof(c_0_1761,axiom,
one_one(nat) = number_number_of(nat,hAPP(int,int,bit1,pls)),
c_0_1106 ).
fof(c_0_1762,axiom,
number_number_of(nat,hAPP(int,int,bit1,pls)) = one_one(nat),
c_0_1107 ).
fof(c_0_1763,axiom,
one_one(int) = number_number_of(int,hAPP(int,int,bit1,pls)),
c_0_1108 ).
fof(c_0_1764,axiom,
hAPP(int,int,succ,pls) = hAPP(int,int,bit1,pls),
c_0_1109 ).
fof(c_0_1765,plain,
! [X18,X19,X20,X21,X22] :
( ( ti(X18,X19) = zero_zero(X18)
| hAPP(nat,X18,power_power(X18,X19),X20) != zero_zero(X18)
| ~ power(X18)
| ~ mult_zero(X18)
| ~ no_zero_divisors(X18)
| ~ zero_neq_one(X18) )
& ( X20 != zero_zero(nat)
| hAPP(nat,X18,power_power(X18,X19),X20) != zero_zero(X18)
| ~ power(X18)
| ~ mult_zero(X18)
| ~ no_zero_divisors(X18)
| ~ zero_neq_one(X18) )
& ( ti(X18,X21) != zero_zero(X18)
| X22 = zero_zero(nat)
| hAPP(nat,X18,power_power(X18,X21),X22) = zero_zero(X18)
| ~ power(X18)
| ~ mult_zero(X18)
| ~ no_zero_divisors(X18)
| ~ zero_neq_one(X18) ) ),
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_1110])])])])]) ).
fof(c_0_1766,plain,
! [X43,X44,X45,X46,X47] :
( ( ti(X43,X44) != hAPP(X43,X43,plus_plus(X43,X44),X45)
| ti(X43,X45) = zero_zero(X43)
| ~ semiri456707255roduct(X43) )
& ( ti(X43,X47) != zero_zero(X43)
| ti(X43,X46) = hAPP(X43,X43,plus_plus(X43,X46),X47)
| ~ semiri456707255roduct(X43) ) ),
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_1111])])])])]) ).
fof(c_0_1767,plain,
! [X8,X9,X10] :
( ( zero_zero(X8) != hAPP(X8,X8,plus_plus(X8,X9),X9)
| ti(X8,X9) = zero_zero(X8)
| ~ linord219039673up_add(X8) )
& ( ti(X8,X10) != zero_zero(X8)
| zero_zero(X8) = hAPP(X8,X8,plus_plus(X8,X10),X10)
| ~ linord219039673up_add(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_1112])])])])]) ).
fof(c_0_1768,plain,
! [X8,X9,X10] :
( ( hAPP(X8,X8,plus_plus(X8,X9),X9) != zero_zero(X8)
| ti(X8,X9) = zero_zero(X8)
| ~ linord219039673up_add(X8) )
& ( ti(X8,X10) != zero_zero(X8)
| hAPP(X8,X8,plus_plus(X8,X10),X10) = zero_zero(X8)
| ~ linord219039673up_add(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_1113])])])])]) ).
fof(c_0_1769,plain,
! [X32,X33,X34] :
( ~ ring_11004092258visors(X32)
| ti(X32,X34) = zero_zero(X32)
| hAPP(nat,X32,power_power(X32,X34),X33) != zero_zero(X32) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1114])])]) ).
fof(c_0_1770,plain,
! [X18,X19,X20,X21] :
( ( hAPP(nat,nat,power_power(nat,X18),X19) != one_one(nat)
| X18 = one_one(nat)
| X19 = zero_zero(nat) )
& ( X20 != one_one(nat)
| hAPP(nat,nat,power_power(nat,X20),X21) = one_one(nat) )
& ( X21 != zero_zero(nat)
| hAPP(nat,nat,power_power(nat,X20),X21) = 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_1115])])])])]) ).
fof(c_0_1771,plain,
! [X29,X30,X31,X32] :
( ( X30 != zero_zero(nat)
| hAPP(nat,nat,power_power(nat,X29),X30) != zero_zero(nat) )
& ( X29 = zero_zero(nat)
| hAPP(nat,nat,power_power(nat,X29),X30) != zero_zero(nat) )
& ( X32 = zero_zero(nat)
| X31 != zero_zero(nat)
| hAPP(nat,nat,power_power(nat,X31),X32) = 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_1116])])])])]) ).
fof(c_0_1772,plain,
! [X29,X30,X31,X32] :
( ( X29 = zero_zero(nat)
| hAPP(nat,nat,plus_plus(nat,X29),X30) != zero_zero(nat) )
& ( X30 = zero_zero(nat)
| hAPP(nat,nat,plus_plus(nat,X29),X30) != zero_zero(nat) )
& ( X31 != zero_zero(nat)
| X32 != zero_zero(nat)
| hAPP(nat,nat,plus_plus(nat,X31),X32) = 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_1117])])])])]) ).
fof(c_0_1773,plain,
! [X16,X17] :
( hAPP(nat,nat,plus_plus(nat,X16),X17) != X16
| X17 = zero_zero(nat) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1118])]) ).
fof(c_0_1774,plain,
! [X18,X19] :
( ( hAPP(nat,int,semiring_1_of_nat(int),X18) != zero_zero(int)
| X18 = zero_zero(nat) )
& ( X19 != zero_zero(nat)
| hAPP(nat,int,semiring_1_of_nat(int),X19) = 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_1119])])])]) ).
fof(c_0_1775,plain,
! [X14,X15] :
( ( pls != hAPP(int,int,bit0,X14)
| pls = X14 )
& ( pls != X15
| pls = hAPP(int,int,bit0,X15) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1120])])])]) ).
fof(c_0_1776,plain,
! [X13,X14] :
( ( hAPP(int,int,bit0,X13) != pls
| X13 = pls )
& ( X14 != pls
| hAPP(int,int,bit0,X14) = pls ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1121])])])]) ).
fof(c_0_1777,plain,
! [X31] : pls != hAPP(int,int,bit1,X31),
inference(variable_rename,[status(thm)],[c_0_1122]) ).
fof(c_0_1778,plain,
! [X21] : hAPP(int,int,bit1,X21) != pls,
inference(variable_rename,[status(thm)],[c_0_1123]) ).
fof(c_0_1779,plain,
! [X9,X10,X11] :
( ( number_number_of(nat,X10) != zero_zero(nat)
| hAPP(nat,X9,power_power(X9,zero_zero(X9)),number_number_of(nat,X10)) = one_one(X9)
| ~ power(X9)
| ~ semiring_0(X9) )
& ( number_number_of(nat,X11) = zero_zero(nat)
| hAPP(nat,X9,power_power(X9,zero_zero(X9)),number_number_of(nat,X11)) = zero_zero(X9)
| ~ power(X9)
| ~ semiring_0(X9) ) ),
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_1124])])])])]) ).
fof(c_0_1780,plain,
! [X32,X33] :
( ~ number_ring(X32)
| hAPP(X32,X32,plus_plus(X32,number_number_of(X32,pls)),X33) = ti(X32,X33) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1125])])]) ).
fof(c_0_1781,plain,
! [X32,X33] :
( ~ number_ring(X32)
| hAPP(X32,X32,plus_plus(X32,X33),number_number_of(X32,pls)) = ti(X32,X33) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1126])])]) ).
fof(c_0_1782,plain,
! [X16,X17,X18] :
( ( X17 != zero_zero(nat)
| hAPP(nat,X16,power_power(X16,zero_zero(X16)),X17) = one_one(X16)
| ~ power(X16)
| ~ semiring_0(X16) )
& ( X18 = zero_zero(nat)
| hAPP(nat,X16,power_power(X16,zero_zero(X16)),X18) = zero_zero(X16)
| ~ power(X16)
| ~ semiring_0(X16) ) ),
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_1127])])])])]) ).
fof(c_0_1783,plain,
! [X32,X33] :
( ~ monoid_add(X32)
| hAPP(X32,X32,plus_plus(X32,zero_zero(X32)),X33) = ti(X32,X33) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1128])])]) ).
fof(c_0_1784,plain,
! [X32,X33] :
( ~ comm_semiring_1(X32)
| hAPP(X32,X32,plus_plus(X32,zero_zero(X32)),X33) = ti(X32,X33) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1129])])]) ).
fof(c_0_1785,plain,
! [X32,X33] :
( ~ comm_monoid_add(X32)
| hAPP(X32,X32,plus_plus(X32,zero_zero(X32)),X33) = ti(X32,X33) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1130])])]) ).
fof(c_0_1786,plain,
! [X32,X33] :
( ~ monoid_add(X32)
| hAPP(X32,X32,plus_plus(X32,X33),zero_zero(X32)) = ti(X32,X33) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1131])])]) ).
fof(c_0_1787,plain,
! [X32,X33] :
( ~ comm_semiring_1(X32)
| hAPP(X32,X32,plus_plus(X32,X33),zero_zero(X32)) = ti(X32,X33) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1132])])]) ).
fof(c_0_1788,plain,
! [X32,X33] :
( ~ comm_monoid_add(X32)
| hAPP(X32,X32,plus_plus(X32,X33),zero_zero(X32)) = ti(X32,X33) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1133])])]) ).
fof(c_0_1789,plain,
! [X11,X12] :
( ~ comm_semiring_1(X11)
| hAPP(nat,X11,power_power(X11,X12),one_one(nat)) = ti(X11,X12) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1134])])]) ).
fof(c_0_1790,plain,
! [X32,X33] :
( ~ monoid_mult(X32)
| hAPP(nat,X32,power_power(X32,X33),one_one(nat)) = ti(X32,X33) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1135])])]) ).
fof(c_0_1791,plain,
! [X16,X17] :
( ~ monoid_mult(X16)
| hAPP(nat,X16,power_power(X16,one_one(X16)),X17) = one_one(X16) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1136])])]) ).
fof(c_0_1792,plain,
! [X11,X12] :
( ~ comm_semiring_1(X11)
| hAPP(nat,X11,power_power(X11,X12),zero_zero(nat)) = one_one(X11) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1137])])]) ).
fof(c_0_1793,plain,
! [X32,X33] :
( ~ power(X32)
| hAPP(nat,X32,power_power(X32,X33),zero_zero(nat)) = one_one(X32) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1138])])]) ).
fof(c_0_1794,plain,
! [X16] : hAPP(nat,nat,plus_plus(nat,zero_zero(nat)),X16) = X16,
inference(variable_rename,[status(thm)],[c_0_1139]) ).
fof(c_0_1795,plain,
! [X17] : hAPP(int,int,plus_plus(int,zero_zero(int)),X17) = X17,
inference(variable_rename,[status(thm)],[c_0_1140]) ).
fof(c_0_1796,plain,
! [X15] : hAPP(nat,nat,plus_plus(nat,X15),zero_zero(nat)) = X15,
inference(variable_rename,[status(thm)],[c_0_1141]) ).
fof(c_0_1797,plain,
! [X17] : hAPP(int,int,plus_plus(int,X17),zero_zero(int)) = X17,
inference(variable_rename,[status(thm)],[c_0_1142]) ).
fof(c_0_1798,plain,
! [X21] : hAPP(int,int,plus_plus(int,X21),pls) = X21,
inference(variable_rename,[status(thm)],[c_0_1143]) ).
fof(c_0_1799,plain,
! [X2] :
( ~ semiring_1(X2)
| hAPP(nat,X2,semiring_1_of_nat(X2),zero_zero(nat)) = zero_zero(X2) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1144])]) ).
fof(c_0_1800,plain,
! [X2] :
( ~ semiring_1(X2)
| hAPP(nat,X2,semiring_1_of_nat(X2),one_one(nat)) = one_one(X2) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1145])]) ).
fof(c_0_1801,plain,
! [X21] : hAPP(int,int,plus_plus(int,pls),X21) = X21,
inference(variable_rename,[status(thm)],[c_0_1146]) ).
fof(c_0_1802,axiom,
zero_zero(int) = hAPP(nat,int,semiring_1_of_nat(int),zero_zero(nat)),
c_0_1147 ).
fof(c_0_1803,axiom,
one_one(int) = hAPP(nat,int,semiring_1_of_nat(int),one_one(nat)),
c_0_1148 ).
fof(c_0_1804,axiom,
hAPP(nat,int,semiring_1_of_nat(int),zero_zero(nat)) = zero_zero(int),
c_0_1149 ).
fof(c_0_1805,axiom,
hAPP(nat,int,semiring_1_of_nat(int),one_one(nat)) = one_one(int),
c_0_1150 ).
fof(c_0_1806,axiom,
hAPP(int,int,bit0,pls) = pls,
c_0_1151 ).
fof(c_0_1807,plain,
! [X2] : ti(fun(bool,fun(X2,fun(X2,X2))),if(X2)) = if(X2),
inference(variable_rename,[status(thm)],[c_0_1152]) ).
fof(c_0_1808,plain,
! [X2] :
( ~ linordered_semiring(X2)
| ti(fun(X2,fun(X2,X2)),times_times(X2)) = times_times(X2) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1153])]) ).
fof(c_0_1809,plain,
! [X4] :
( ~ ord(X4)
| ti(fun(X4,fun(X4,bool)),ord_less_eq(X4)) = ord_less_eq(X4) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1154])]) ).
fof(c_0_1810,plain,
! [X2] :
( ~ ord(X2)
| ti(fun(X2,fun(X2,bool)),ord_less(X2)) = ord_less(X2) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1155])]) ).
fof(c_0_1811,plain,
! [X3,X4] :
( ~ cancel_semigroup_add(X4)
| ti(fun(X4,X4),plus_plus(X4,X3)) = plus_plus(X4,X3) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1156])]) ).
fof(c_0_1812,plain,
! [X3,X4] :
( ~ ab_semigroup_add(X4)
| ti(fun(X4,X4),plus_plus(X4,X3)) = plus_plus(X4,X3) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1157])]) ).
fof(c_0_1813,plain,
! [X3,X4] :
( ~ monoid_add(X4)
| ti(fun(X4,X4),plus_plus(X4,X3)) = plus_plus(X4,X3) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1158])]) ).
fof(c_0_1814,plain,
! [X3,X4] :
( ~ power(X4)
| ti(fun(nat,X4),power_power(X4,X3)) = power_power(X4,X3) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1159])]) ).
fof(c_0_1815,plain,
! [X25,X26,X27,X28,X29] :
( ( number_number_of(X25,X26) != ti(X25,X27)
| ti(X25,X27) = number_number_of(X25,X26)
| ~ number(X25) )
& ( ti(X25,X29) != number_number_of(X25,X28)
| number_number_of(X25,X28) = ti(X25,X29)
| ~ number(X25) ) ),
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_1160])])])])]) ).
fof(c_0_1816,plain,
! [X3,X4] :
( ~ power(X4)
| power_power(X4,ti(X4,X3)) = power_power(X4,X3) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1161])]) ).
fof(c_0_1817,plain,
! [X3,X4] :
( ~ number(X4)
| ti(X4,number_number_of(X4,X3)) = number_number_of(X4,X3) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1162])]) ).
fof(c_0_1818,plain,
! [X3,X4] :
( ~ cancel_semigroup_add(X4)
| plus_plus(X4,ti(X4,X3)) = plus_plus(X4,X3) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1163])]) ).
fof(c_0_1819,plain,
! [X3,X4] :
( ~ ab_semigroup_add(X4)
| plus_plus(X4,ti(X4,X3)) = plus_plus(X4,X3) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1164])]) ).
fof(c_0_1820,plain,
! [X3,X4] :
( ~ monoid_add(X4)
| plus_plus(X4,ti(X4,X3)) = plus_plus(X4,X3) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1165])]) ).
fof(c_0_1821,plain,
! [X7,X8,X9,X10,X11] :
( ( number_number_of(X7,X8) != number_number_of(X7,X9)
| X8 = X9
| ~ number_ring(X7)
| ~ ring_char_0(X7) )
& ( X10 != X11
| number_number_of(X7,X10) = number_number_of(X7,X11)
| ~ number_ring(X7)
| ~ ring_char_0(X7) ) ),
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_1166])])])])]) ).
fof(c_0_1822,plain,
! [X3,X4] :
( ~ number(X4)
| number_number_of(X4,ti(int,X3)) = number_number_of(X4,X3) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1167])]) ).
fof(c_0_1823,plain,
! [X2] :
( ~ semiring_1(X2)
| ti(fun(nat,X2),semiring_1_of_nat(X2)) = semiring_1_of_nat(X2) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1168])]) ).
fof(c_0_1824,plain,
! [X6,X7,X8] :
( ( one_one(X6) != ti(X6,X7)
| ti(X6,X7) = one_one(X6)
| ~ one(X6) )
& ( ti(X6,X8) != one_one(X6)
| one_one(X6) = ti(X6,X8)
| ~ one(X6) ) ),
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_1169])])])])]) ).
fof(c_0_1825,plain,
! [X6,X7,X8] :
( ( zero_zero(X6) != ti(X6,X7)
| ti(X6,X7) = zero_zero(X6)
| ~ zero(X6) )
& ( ti(X6,X8) != zero_zero(X6)
| zero_zero(X6) = ti(X6,X8)
| ~ zero(X6) ) ),
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_1170])])])])]) ).
fof(c_0_1826,plain,
! [X67,X68] : ti(X67,ti(X67,X68)) = ti(X67,X68),
inference(variable_rename,[status(thm)],[c_0_1171]) ).
fof(c_0_1827,plain,
! [X3,X4] :
( ( ~ hBOOL(ti(bool,X3))
| hBOOL(X3) )
& ( ~ hBOOL(X4)
| hBOOL(ti(bool,X4)) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1172])])])]) ).
fof(c_0_1828,plain,
! [X65,X66] :
( ~ ord(X66)
| ord(fun(X65,X66)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1173])]) ).
fof(c_0_1829,plain,
! [X65,X66] :
( ~ order(X66)
| order(fun(X65,X66)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1174])]) ).
fof(c_0_1830,plain,
! [X65,X66] :
( ~ preorder(X66)
| preorder(fun(X65,X66)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1175])]) ).
fof(c_0_1831,axiom,
ti(fun(real,real),sqrt) = sqrt,
c_0_1176 ).
fof(c_0_1832,axiom,
ti(fun(int,int),succ) = succ,
c_0_1177 ).
fof(c_0_1833,plain,
! [X2] :
( ~ zero(X2)
| ti(X2,zero_zero(X2)) = zero_zero(X2) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1178])]) ).
fof(c_0_1834,plain,
! [X2] :
( ~ one(X2)
| ti(X2,one_one(X2)) = one_one(X2) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1179])]) ).
fof(c_0_1835,plain,
! [X68] :
( ti(bool,X68) = fTrue
| ti(bool,X68) = fFalse ),
inference(variable_rename,[status(thm)],[c_0_1180]) ).
fof(c_0_1836,plain,
! [X2] : ti(X2,undefined(X2)) = undefined(X2),
inference(variable_rename,[status(thm)],[c_0_1181]) ).
fof(c_0_1837,plain,
! [X2] :
( ~ number_ring(X2)
| zero_zero(X2) = number_number_of(X2,pls) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1182])]) ).
fof(c_0_1838,plain,
! [X2] :
( ~ number_ring(X2)
| number_number_of(X2,pls) = zero_zero(X2) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1183])]) ).
fof(c_0_1839,plain,
! [X2] :
( ~ number_semiring(X2)
| number_number_of(X2,pls) = zero_zero(X2) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1184])]) ).
fof(c_0_1840,plain,
! [X2] :
( ~ zero_neq_one(X2)
| zero_zero(X2) != one_one(X2) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1185])]) ).
fof(c_0_1841,plain,
! [X2] :
( ~ zero_neq_one(X2)
| one_one(X2) != zero_zero(X2) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1186])]) ).
fof(c_0_1842,plain,
! [X21] : number_number_of(int,X21) = X21,
inference(variable_rename,[status(thm)],[c_0_1187]) ).
fof(c_0_1843,axiom,
zero_zero(nat) = number_number_of(nat,pls),
c_0_1188 ).
fof(c_0_1844,axiom,
number_number_of(nat,pls) = zero_zero(nat),
c_0_1189 ).
fof(c_0_1845,axiom,
zero_zero(int) = number_number_of(int,pls),
c_0_1190 ).
fof(c_0_1846,axiom,
ti(nat,tn) = tn,
c_0_1191 ).
fof(c_0_1847,axiom,
ti(int,t) = t,
c_0_1192 ).
fof(c_0_1848,axiom,
ti(int,m1) = m1,
c_0_1193 ).
fof(c_0_1849,axiom,
ti(bool,fTrue) = fTrue,
c_0_1194 ).
fof(c_0_1850,axiom,
ti(bool,fFalse) = fFalse,
c_0_1195 ).
fof(c_0_1851,axiom,
zero_zero(real) != one_one(real),
c_0_1196 ).
fof(c_0_1852,axiom,
zero_zero(int) != one_one(int),
c_0_1197 ).
fof(c_0_1853,axiom,
one(real),
c_0_1198 ).
fof(c_0_1854,axiom,
number(real),
c_0_1199 ).
fof(c_0_1855,axiom,
zero(real),
c_0_1200 ).
fof(c_0_1856,axiom,
power(real),
c_0_1201 ).
fof(c_0_1857,axiom,
ord(real),
c_0_1202 ).
fof(c_0_1858,axiom,
number_ring(real),
c_0_1203 ).
fof(c_0_1859,axiom,
ring_char_0(real),
c_0_1204 ).
fof(c_0_1860,axiom,
order(real),
c_0_1205 ).
fof(c_0_1861,axiom,
mult_zero(real),
c_0_1206 ).
fof(c_0_1862,axiom,
semiring_0(real),
c_0_1207 ).
fof(c_0_1863,axiom,
semiring_1(real),
c_0_1208 ).
fof(c_0_1864,axiom,
monoid_add(real),
c_0_1209 ).
fof(c_0_1865,axiom,
monoid_mult(real),
c_0_1210 ).
fof(c_0_1866,axiom,
linorder(real),
c_0_1211 ).
fof(c_0_1867,axiom,
preorder(real),
c_0_1212 ).
fof(c_0_1868,axiom,
zero_neq_one(real),
c_0_1213 ).
fof(c_0_1869,axiom,
number_semiring(real),
c_0_1214 ).
fof(c_0_1870,axiom,
semiring_char_0(real),
c_0_1215 ).
fof(c_0_1871,axiom,
comm_semiring_1(real),
c_0_1216 ).
fof(c_0_1872,axiom,
linordered_idom(real),
c_0_1217 ).
fof(c_0_1873,axiom,
linordered_ring(real),
c_0_1218 ).
fof(c_0_1874,axiom,
comm_monoid_add(real),
c_0_1219 ).
fof(c_0_1875,axiom,
no_zero_divisors(real),
c_0_1220 ).
fof(c_0_1876,axiom,
ab_semigroup_add(real),
c_0_1221 ).
fof(c_0_1877,axiom,
dense_linorder(real),
c_0_1222 ).
fof(c_0_1878,axiom,
linordered_semidom(real),
c_0_1223 ).
fof(c_0_1879,axiom,
linordered_semiring(real),
c_0_1224 ).
fof(c_0_1880,axiom,
cancel_semigroup_add(real),
c_0_1225 ).
fof(c_0_1881,axiom,
linord581940658strict(real),
c_0_1226 ).
fof(c_0_1882,axiom,
ring_11004092258visors(real),
c_0_1227 ).
fof(c_0_1883,axiom,
cancel146912293up_add(real),
c_0_1228 ).
fof(c_0_1884,axiom,
linord219039673up_add(real),
c_0_1229 ).
fof(c_0_1885,axiom,
ordere216010020id_add(real),
c_0_1230 ).
fof(c_0_1886,axiom,
ordere779506340up_add(real),
c_0_1231 ).
fof(c_0_1887,axiom,
linord20386208strict(real),
c_0_1232 ).
fof(c_0_1888,axiom,
linord893533164strict(real),
c_0_1233 ).
fof(c_0_1889,axiom,
ordere236663937imp_le(real),
c_0_1234 ).
fof(c_0_1890,axiom,
ordere223160158up_add(real),
c_0_1235 ).
fof(c_0_1891,axiom,
semiri456707255roduct(real),
c_0_1236 ).
fof(c_0_1892,axiom,
ord(bool),
c_0_1237 ).
fof(c_0_1893,axiom,
order(bool),
c_0_1238 ).
fof(c_0_1894,axiom,
preorder(bool),
c_0_1239 ).
fof(c_0_1895,axiom,
one(nat),
c_0_1240 ).
fof(c_0_1896,axiom,
number(nat),
c_0_1241 ).
fof(c_0_1897,axiom,
zero(nat),
c_0_1242 ).
fof(c_0_1898,axiom,
power(nat),
c_0_1243 ).
fof(c_0_1899,axiom,
ord(nat),
c_0_1244 ).
fof(c_0_1900,axiom,
order(nat),
c_0_1245 ).
fof(c_0_1901,axiom,
mult_zero(nat),
c_0_1246 ).
fof(c_0_1902,axiom,
semiring_0(nat),
c_0_1247 ).
fof(c_0_1903,axiom,
semiring_1(nat),
c_0_1248 ).
fof(c_0_1904,axiom,
monoid_add(nat),
c_0_1249 ).
fof(c_0_1905,axiom,
monoid_mult(nat),
c_0_1250 ).
fof(c_0_1906,axiom,
linorder(nat),
c_0_1251 ).
fof(c_0_1907,axiom,
preorder(nat),
c_0_1252 ).
fof(c_0_1908,axiom,
zero_neq_one(nat),
c_0_1253 ).
fof(c_0_1909,axiom,
number_semiring(nat),
c_0_1254 ).
fof(c_0_1910,axiom,
semiring_char_0(nat),
c_0_1255 ).
fof(c_0_1911,axiom,
comm_semiring_1(nat),
c_0_1256 ).
fof(c_0_1912,axiom,
comm_monoid_add(nat),
c_0_1257 ).
fof(c_0_1913,axiom,
no_zero_divisors(nat),
c_0_1258 ).
fof(c_0_1914,axiom,
ab_semigroup_add(nat),
c_0_1259 ).
fof(c_0_1915,axiom,
linordered_semidom(nat),
c_0_1260 ).
fof(c_0_1916,axiom,
linordered_semiring(nat),
c_0_1261 ).
fof(c_0_1917,axiom,
cancel_semigroup_add(nat),
c_0_1262 ).
fof(c_0_1918,axiom,
cancel146912293up_add(nat),
c_0_1263 ).
fof(c_0_1919,axiom,
ordere216010020id_add(nat),
c_0_1264 ).
fof(c_0_1920,axiom,
ordere779506340up_add(nat),
c_0_1265 ).
fof(c_0_1921,axiom,
linord20386208strict(nat),
c_0_1266 ).
fof(c_0_1922,axiom,
linord893533164strict(nat),
c_0_1267 ).
fof(c_0_1923,axiom,
ordere236663937imp_le(nat),
c_0_1268 ).
fof(c_0_1924,axiom,
ordere223160158up_add(nat),
c_0_1269 ).
fof(c_0_1925,axiom,
semiri456707255roduct(nat),
c_0_1270 ).
fof(c_0_1926,axiom,
one(int),
c_0_1271 ).
fof(c_0_1927,axiom,
number(int),
c_0_1272 ).
fof(c_0_1928,axiom,
zero(int),
c_0_1273 ).
fof(c_0_1929,axiom,
power(int),
c_0_1274 ).
fof(c_0_1930,axiom,
ord(int),
c_0_1275 ).
fof(c_0_1931,axiom,
number_ring(int),
c_0_1276 ).
fof(c_0_1932,axiom,
ring_char_0(int),
c_0_1277 ).
fof(c_0_1933,axiom,
order(int),
c_0_1278 ).
fof(c_0_1934,axiom,
mult_zero(int),
c_0_1279 ).
fof(c_0_1935,axiom,
semiring_0(int),
c_0_1280 ).
fof(c_0_1936,axiom,
semiring_1(int),
c_0_1281 ).
fof(c_0_1937,axiom,
monoid_add(int),
c_0_1282 ).
fof(c_0_1938,axiom,
monoid_mult(int),
c_0_1283 ).
fof(c_0_1939,axiom,
linorder(int),
c_0_1284 ).
fof(c_0_1940,axiom,
preorder(int),
c_0_1285 ).
fof(c_0_1941,axiom,
zero_neq_one(int),
c_0_1286 ).
fof(c_0_1942,axiom,
number_semiring(int),
c_0_1287 ).
fof(c_0_1943,axiom,
semiring_char_0(int),
c_0_1288 ).
fof(c_0_1944,axiom,
comm_semiring_1(int),
c_0_1289 ).
fof(c_0_1945,axiom,
linordered_idom(int),
c_0_1290 ).
fof(c_0_1946,axiom,
linordered_ring(int),
c_0_1291 ).
fof(c_0_1947,axiom,
comm_monoid_add(int),
c_0_1292 ).
fof(c_0_1948,axiom,
no_zero_divisors(int),
c_0_1293 ).
fof(c_0_1949,axiom,
ab_semigroup_add(int),
c_0_1294 ).
fof(c_0_1950,axiom,
linordered_semidom(int),
c_0_1295 ).
fof(c_0_1951,axiom,
linordered_semiring(int),
c_0_1296 ).
fof(c_0_1952,axiom,
cancel_semigroup_add(int),
c_0_1297 ).
fof(c_0_1953,axiom,
linord581940658strict(int),
c_0_1298 ).
fof(c_0_1954,axiom,
ring_11004092258visors(int),
c_0_1299 ).
fof(c_0_1955,axiom,
cancel146912293up_add(int),
c_0_1300 ).
fof(c_0_1956,axiom,
linord219039673up_add(int),
c_0_1301 ).
fof(c_0_1957,axiom,
ordere216010020id_add(int),
c_0_1302 ).
fof(c_0_1958,axiom,
ordere779506340up_add(int),
c_0_1303 ).
fof(c_0_1959,axiom,
linord20386208strict(int),
c_0_1304 ).
fof(c_0_1960,axiom,
linord893533164strict(int),
c_0_1305 ).
fof(c_0_1961,axiom,
ordere236663937imp_le(int),
c_0_1306 ).
fof(c_0_1962,axiom,
ordere223160158up_add(int),
c_0_1307 ).
fof(c_0_1963,axiom,
semiri456707255roduct(int),
c_0_1308 ).
fof(c_0_1964,axiom,
pls = zero_zero(int),
c_0_1309 ).
cnf(c_0_1965,plain,
hAPP(nat,int,power_power(int,hAPP(int,int,plus_plus(int,X1),X2)),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,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,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),number_number_of(int,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),X1)),X2))),hAPP(nat,int,power_power(int,X2),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),
inference(split_conjunct,[status(thm)],[c_0_1310]) ).
cnf(c_0_1966,plain,
( ti(X1,X2) = zero_zero(X1)
| ~ linordered_idom(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,plus_plus(X1,hAPP(nat,X1,power_power(X1,X2),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,X1,power_power(X1,X3),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),zero_zero(X1))) ),
inference(split_conjunct,[status(thm)],[c_0_1311]) ).
cnf(c_0_1967,plain,
( ti(X1,X3) = zero_zero(X1)
| ~ linordered_idom(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,plus_plus(X1,hAPP(nat,X1,power_power(X1,X2),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,X1,power_power(X1,X3),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),zero_zero(X1))) ),
inference(split_conjunct,[status(thm)],[c_0_1311]) ).
cnf(c_0_1968,plain,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,plus_plus(X1,hAPP(nat,X1,power_power(X1,X2),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,X1,power_power(X1,X3),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),zero_zero(X1)))
| ~ linordered_idom(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1312]) ).
cnf(c_0_1969,plain,
( hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),hAPP(X1,X2,X3,X6)),X5))
| ~ order(X1)
| ~ order(X2)
| ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),hAPP(X1,X2,X3,X4)),X5))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X6),X4))
| ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less_eq(X2),hAPP(X1,X2,X3,esk44_6(X1,X2,X6,X3,X4,X5))),hAPP(X1,X2,X3,esk43_6(X1,X2,X6,X3,X4,X5)))) ),
inference(split_conjunct,[status(thm)],[c_0_1313]) ).
cnf(c_0_1970,plain,
( hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),hAPP(X1,X2,X5,X3)),X6))
| ~ order(X1)
| ~ order(X2)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X4))
| ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),hAPP(X1,X2,X5,X4)),X6))
| ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less_eq(X2),hAPP(X1,X2,X5,esk39_6(X1,X2,X5,X6,X3,X4))),hAPP(X1,X2,X5,esk40_6(X1,X2,X5,X6,X3,X4)))) ),
inference(split_conjunct,[status(thm)],[c_0_1314]) ).
cnf(c_0_1971,plain,
( hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),hAPP(X1,X2,X3,X6)),X5))
| ~ ord(X1)
| ~ order(X2)
| ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less_eq(X2),hAPP(X1,X2,X3,X4)),X5))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X6),X4))
| ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),hAPP(X1,X2,X3,esk38_6(X1,X2,X6,X3,X4,X5))),hAPP(X1,X2,X3,esk37_6(X1,X2,X6,X3,X4,X5)))) ),
inference(split_conjunct,[status(thm)],[c_0_1315]) ).
cnf(c_0_1972,plain,
( hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),hAPP(X1,X2,X5,X3)),X6))
| ~ order(X1)
| ~ order(X2)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X4))
| ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less_eq(X2),hAPP(X1,X2,X5,X4)),X6))
| ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),hAPP(X1,X2,X5,esk34_6(X1,X2,X5,X6,X3,X4))),hAPP(X1,X2,X5,esk35_6(X1,X2,X5,X6,X3,X4)))) ),
inference(split_conjunct,[status(thm)],[c_0_1316]) ).
cnf(c_0_1973,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),hAPP(X2,X1,X4,X6)))
| ~ order(X1)
| ~ order(X2)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),hAPP(X2,X1,X4,X5)))
| ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),X5),X6))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X2,X1,X4,esk45_6(X1,X2,X6,X3,X4,X5))),hAPP(X2,X1,X4,esk46_6(X1,X2,X6,X3,X4,X5)))) ),
inference(split_conjunct,[status(thm)],[c_0_1317]) ).
cnf(c_0_1974,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),hAPP(X2,X1,X4,X6)))
| ~ order(X1)
| ~ order(X2)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),hAPP(X2,X1,X4,X5)))
| ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less_eq(X2),X5),X6))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X2,X1,X4,esk41_6(X1,X2,X6,X3,X4,X5))),hAPP(X2,X1,X4,esk42_6(X1,X2,X6,X3,X4,X5)))) ),
inference(split_conjunct,[status(thm)],[c_0_1318]) ).
cnf(c_0_1975,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X5),hAPP(X2,X1,X6,X4)))
| ~ order(X1)
| ~ order(X2)
| ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less_eq(X2),X3),X4))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X5),hAPP(X2,X1,X6,X3)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X2,X1,X6,esk33_6(X1,X2,X5,X6,X3,X4))),hAPP(X2,X1,X6,esk32_6(X1,X2,X5,X6,X3,X4)))) ),
inference(split_conjunct,[status(thm)],[c_0_1319]) ).
cnf(c_0_1976,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X5),hAPP(X2,X1,X6,X4)))
| ~ order(X1)
| ~ order(X2)
| ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),X3),X4))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X5),hAPP(X2,X1,X6,X3)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X2,X1,X6,esk29_6(X1,X2,X5,X6,X3,X4))),hAPP(X2,X1,X6,esk28_6(X1,X2,X5,X6,X3,X4)))) ),
inference(split_conjunct,[status(thm)],[c_0_1320]) ).
cnf(c_0_1977,plain,
hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),hAPP(real,real,sqrt,hAPP(real,real,plus_plus(real,hAPP(nat,real,power_power(real,X1),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,real,power_power(real,X2),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))))),
inference(split_conjunct,[status(thm)],[c_0_1321]) ).
cnf(c_0_1978,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,plus_plus(X1,hAPP(nat,X1,power_power(X1,X2),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,X1,power_power(X1,X3),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),zero_zero(X1)))
| ~ linordered_idom(X1)
| ti(X1,X3) != zero_zero(X1)
| ti(X1,X2) != zero_zero(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1311]) ).
cnf(c_0_1979,plain,
( ~ linordered_idom(X1)
| ti(X1,X2) != zero_zero(X1)
| ti(X1,X3) != zero_zero(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),hAPP(X1,X1,plus_plus(X1,hAPP(nat,X1,power_power(X1,X3),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,X1,power_power(X1,X2),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))) ),
inference(split_conjunct,[status(thm)],[c_0_1322]) ).
cnf(c_0_1980,plain,
( hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),hAPP(X1,X2,X3,X6)),X5))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),esk44_6(X1,X2,X6,X3,X4,X5)),esk43_6(X1,X2,X6,X3,X4,X5)))
| ~ order(X1)
| ~ order(X2)
| ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),hAPP(X1,X2,X3,X4)),X5))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X6),X4)) ),
inference(split_conjunct,[status(thm)],[c_0_1313]) ).
cnf(c_0_1981,plain,
( hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),hAPP(X1,X2,X5,X3)),X6))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),esk39_6(X1,X2,X5,X6,X3,X4)),esk40_6(X1,X2,X5,X6,X3,X4)))
| ~ order(X1)
| ~ order(X2)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X4))
| ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),hAPP(X1,X2,X5,X4)),X6)) ),
inference(split_conjunct,[status(thm)],[c_0_1314]) ).
cnf(c_0_1982,plain,
( hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),hAPP(X1,X2,X3,X6)),X5))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),esk38_6(X1,X2,X6,X3,X4,X5)),esk37_6(X1,X2,X6,X3,X4,X5)))
| ~ ord(X1)
| ~ order(X2)
| ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less_eq(X2),hAPP(X1,X2,X3,X4)),X5))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X6),X4)) ),
inference(split_conjunct,[status(thm)],[c_0_1315]) ).
cnf(c_0_1983,plain,
( hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),hAPP(X1,X2,X5,X3)),X6))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),esk34_6(X1,X2,X5,X6,X3,X4)),esk35_6(X1,X2,X5,X6,X3,X4)))
| ~ order(X1)
| ~ order(X2)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X4))
| ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less_eq(X2),hAPP(X1,X2,X5,X4)),X6)) ),
inference(split_conjunct,[status(thm)],[c_0_1316]) ).
cnf(c_0_1984,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),hAPP(X2,X1,X4,X6)))
| hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),esk45_6(X1,X2,X6,X3,X4,X5)),esk46_6(X1,X2,X6,X3,X4,X5)))
| ~ order(X1)
| ~ order(X2)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),hAPP(X2,X1,X4,X5)))
| ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),X5),X6)) ),
inference(split_conjunct,[status(thm)],[c_0_1317]) ).
cnf(c_0_1985,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),hAPP(X2,X1,X4,X6)))
| hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less_eq(X2),esk41_6(X1,X2,X6,X3,X4,X5)),esk42_6(X1,X2,X6,X3,X4,X5)))
| ~ order(X1)
| ~ order(X2)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),hAPP(X2,X1,X4,X5)))
| ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less_eq(X2),X5),X6)) ),
inference(split_conjunct,[status(thm)],[c_0_1318]) ).
cnf(c_0_1986,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X5),hAPP(X2,X1,X6,X4)))
| hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less_eq(X2),esk33_6(X1,X2,X5,X6,X3,X4)),esk32_6(X1,X2,X5,X6,X3,X4)))
| ~ order(X1)
| ~ order(X2)
| ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less_eq(X2),X3),X4))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X5),hAPP(X2,X1,X6,X3))) ),
inference(split_conjunct,[status(thm)],[c_0_1319]) ).
cnf(c_0_1987,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X5),hAPP(X2,X1,X6,X4)))
| hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),esk29_6(X1,X2,X5,X6,X3,X4)),esk28_6(X1,X2,X5,X6,X3,X4)))
| ~ order(X1)
| ~ order(X2)
| ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),X3),X4))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X5),hAPP(X2,X1,X6,X3))) ),
inference(split_conjunct,[status(thm)],[c_0_1320]) ).
cnf(c_0_1988,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),hAPP(X1,X1,plus_plus(X1,hAPP(nat,X1,power_power(X1,X2),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,X1,power_power(X1,X3),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))))
| ti(X1,X2) = zero_zero(X1)
| ~ linordered_idom(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1322]) ).
cnf(c_0_1989,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),hAPP(X1,X1,plus_plus(X1,hAPP(nat,X1,power_power(X1,X2),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,X1,power_power(X1,X3),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))))
| ti(X1,X3) = zero_zero(X1)
| ~ linordered_idom(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1322]) ).
cnf(c_0_1990,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),hAPP(X1,X1,plus_plus(X1,hAPP(nat,X1,power_power(X1,X2),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,X1,power_power(X1,X3),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))))
| ~ linordered_idom(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1323]) ).
cnf(c_0_1991,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(nat,X1,power_power(X1,X2),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,X1,power_power(X1,X3),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))
| ~ linordered_semidom(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1324]) ).
cnf(c_0_1992,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(nat,X1,power_power(X1,X2),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,X1,power_power(X1,X3),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))
| ~ linordered_semidom(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1325]) ).
cnf(c_0_1993,plain,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,plus_plus(X1,hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X2)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X3),X3))),zero_zero(X1)))
| ~ linordered_ring(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1326]) ).
cnf(c_0_1994,plain,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(nat,X1,power_power(X1,X2),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),zero_zero(X1)))
| ~ linordered_idom(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1327]) ).
cnf(c_0_1995,plain,
( ~ linord581940658strict(X1)
| ti(X1,X2) != zero_zero(X1)
| ti(X1,X3) != zero_zero(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),hAPP(X1,X1,plus_plus(X1,hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X3),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X2)))) ),
inference(split_conjunct,[status(thm)],[c_0_1328]) ).
cnf(c_0_1996,plain,
( ti(X1,X2) = zero_zero(X1)
| ~ linordered_idom(X1)
| hAPP(X1,X1,plus_plus(X1,hAPP(nat,X1,power_power(X1,X2),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,X1,power_power(X1,X3),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) != zero_zero(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1329]) ).
cnf(c_0_1997,plain,
( ti(X1,X3) = zero_zero(X1)
| ~ linordered_idom(X1)
| hAPP(X1,X1,plus_plus(X1,hAPP(nat,X1,power_power(X1,X2),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,X1,power_power(X1,X3),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) != zero_zero(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1329]) ).
cnf(c_0_1998,plain,
( X1 = zero_zero(real)
| hAPP(real,real,plus_plus(real,hAPP(nat,real,power_power(real,X1),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,real,power_power(real,X2),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) != zero_zero(real) ),
inference(split_conjunct,[status(thm)],[c_0_1330]) ).
cnf(c_0_1999,plain,
( X2 = zero_zero(real)
| hAPP(real,real,plus_plus(real,hAPP(nat,real,power_power(real,X1),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,real,power_power(real,X2),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) != zero_zero(real) ),
inference(split_conjunct,[status(thm)],[c_0_1330]) ).
cnf(c_0_2000,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(nat,X1,semiring_1_of_nat(X1),X2)),hAPP(nat,X1,power_power(X1,number_number_of(X1,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),X2)))
| ~ linordered_idom(X1)
| ~ number_ring(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1331]) ).
cnf(c_0_2001,plain,
hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),one_one(real)),hAPP(nat,real,power_power(real,number_number_of(real,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),X1))),
inference(split_conjunct,[status(thm)],[c_0_1332]) ).
cnf(c_0_2002,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,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(nat,fun(nat,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_1333]) ).
cnf(c_0_2003,plain,
hAPP(nat,int,power_power(int,hAPP(nat,int,power_power(int,X1),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) = hAPP(nat,int,power_power(int,X1),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),
inference(split_conjunct,[status(thm)],[c_0_1334]) ).
cnf(c_0_2004,plain,
( ~ linordered_idom(X1)
| ti(X1,X2) != zero_zero(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),hAPP(nat,X1,power_power(X1,X2),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))) ),
inference(split_conjunct,[status(thm)],[c_0_1335]) ).
cnf(c_0_2005,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),hAPP(X1,X1,plus_plus(X1,hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X2)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X3),X3))))
| ti(X1,X2) = zero_zero(X1)
| ~ linord581940658strict(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1328]) ).
cnf(c_0_2006,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),hAPP(X1,X1,plus_plus(X1,hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X2)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X3),X3))))
| ti(X1,X3) = zero_zero(X1)
| ~ linord581940658strict(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1328]) ).
cnf(c_0_2007,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X4))
| ~ linord581940658strict(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X2))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X4))) ),
inference(split_conjunct,[status(thm)],[c_0_1336]) ).
cnf(c_0_2008,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X4))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X4)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X3),X4)))
| ~ linordered_semiring(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1337]) ).
cnf(c_0_2009,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X4))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X4)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X3),X4)))
| ~ linord20386208strict(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1338]) ).
cnf(c_0_2010,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X4))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X2)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X3)))
| ~ linordered_semiring(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1339]) ).
cnf(c_0_2011,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X4))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X2)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X3)))
| ~ linord20386208strict(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1340]) ).
cnf(c_0_2012,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X4))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X4)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X3),X4)))
| ~ linord20386208strict(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1341]) ).
cnf(c_0_2013,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X4))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X2)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X3)))
| ~ linord20386208strict(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1342]) ).
cnf(c_0_2014,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X4))
| ~ linord581940658strict(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),zero_zero(X1)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X4)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3))) ),
inference(split_conjunct,[status(thm)],[c_0_1343]) ).
cnf(c_0_2015,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X4))
| ~ linord581940658strict(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),zero_zero(X1)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X4)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3))) ),
inference(split_conjunct,[status(thm)],[c_0_1344]) ).
cnf(c_0_2016,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X5)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X4))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X5))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X4))
| ~ linord20386208strict(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1345]) ).
cnf(c_0_2017,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X5)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X2))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X5))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X4))
| ~ linord20386208strict(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1346]) ).
cnf(c_0_2018,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X5)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X2))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X5))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X4))
| ~ linord20386208strict(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1347]) ).
cnf(c_0_2019,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X5)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X2))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X5))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X4))
| ~ linord20386208strict(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1348]) ).
cnf(c_0_2020,plain,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X1),zero_zero(int)))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,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_1349]) ).
cnf(c_0_2021,plain,
( hAPP(X1,X1,plus_plus(X1,hAPP(nat,X1,power_power(X1,X2),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,X1,power_power(X1,X3),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) = zero_zero(X1)
| ~ linordered_idom(X1)
| ti(X1,X3) != zero_zero(X1)
| ti(X1,X2) != zero_zero(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1329]) ).
cnf(c_0_2022,plain,
( hAPP(real,real,plus_plus(real,hAPP(nat,real,power_power(real,X1),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,real,power_power(real,X2),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) = zero_zero(real)
| X2 != zero_zero(real)
| X1 != zero_zero(real) ),
inference(split_conjunct,[status(thm)],[c_0_1330]) ).
cnf(c_0_2023,plain,
( hBOOL(hAPP(fun(X1,X2),bool,hAPP(fun(X1,X2),fun(fun(X1,X2),bool),ord_less_eq(fun(X1,X2)),X3),X4))
| ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less_eq(X2),hAPP(X1,X2,X3,esk25_4(X1,X2,X3,X4))),hAPP(X1,X2,X4,esk25_4(X1,X2,X3,X4))))
| ~ ord(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1350]) ).
cnf(c_0_2024,plain,
( hBOOL(hAPP(fun(X2,X1),bool,hAPP(fun(X2,X1),fun(fun(X2,X1),bool),ord_less_eq(fun(X2,X1)),X3),X4))
| ~ ord(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X2,X1,X3,esk22_4(X2,X1,X3,X4))),hAPP(X2,X1,X4,esk22_4(X2,X1,X3,X4)))) ),
inference(split_conjunct,[status(thm)],[c_0_1351]) ).
cnf(c_0_2025,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,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(nat,fun(nat,bool),ord_less(nat),esk16_3(X2,X3,X1)),esk17_3(X2,X3,X1))) ),
inference(split_conjunct,[status(thm)],[c_0_1333]) ).
cnf(c_0_2026,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X3)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X4))
| ~ linord20386208strict(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1352]) ).
cnf(c_0_2027,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X4)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X2))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X4))
| ~ linord20386208strict(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1353]) ).
cnf(c_0_2028,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X4)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X2))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X4))
| ~ linord893533164strict(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1354]) ).
cnf(c_0_2029,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X4)))
| ~ linord581940658strict(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X2))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X4)) ),
inference(split_conjunct,[status(thm)],[c_0_1336]) ).
cnf(c_0_2030,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X4)))
| ~ linord581940658strict(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),zero_zero(X1)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X4),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_1343]) ).
cnf(c_0_2031,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X3)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),zero_zero(X1)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X4),X2))
| ~ linord581940658strict(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1355]) ).
cnf(c_0_2032,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X4)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),zero_zero(X1)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X4),X3))
| ~ linord581940658strict(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1356]) ).
cnf(c_0_2033,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X4)))
| ~ linord581940658strict(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),zero_zero(X1)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X4),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_1344]) ).
cnf(c_0_2034,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,X1,X2)),hAPP(nat,nat,X1,X3)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X2),X3))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,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_1357]) ).
cnf(c_0_2035,plain,
( ti(X1,X2) = ti(X1,X3)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X2))
| hAPP(nat,X1,power_power(X1,X2),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) != hAPP(nat,X1,power_power(X1,X3),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))
| ~ linordered_semidom(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1358]) ).
cnf(c_0_2036,plain,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,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(int,fun(int,bool),ord_less(int),X1),zero_zero(int))) ),
inference(split_conjunct,[status(thm)],[c_0_1349]) ).
cnf(c_0_2037,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),hAPP(nat,X1,power_power(X1,X2),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))
| ti(X1,X2) = zero_zero(X1)
| ~ linordered_idom(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1335]) ).
cnf(c_0_2038,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),hAPP(nat,X1,power_power(X1,X2),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))
| ~ linordered_idom(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1359]) ).
cnf(c_0_2039,plain,
hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X1),hAPP(nat,int,power_power(int,X1),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),
inference(split_conjunct,[status(thm)],[c_0_1360]) ).
cnf(c_0_2040,plain,
( X1 = one_one(int)
| X1 = zero_zero(int)
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X1),number_number_of(int,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X1)) ),
inference(split_conjunct,[status(thm)],[c_0_1361]) ).
cnf(c_0_2041,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),zero_zero(X1)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),zero_zero(X1)))
| ~ linord20386208strict(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1362]) ).
cnf(c_0_2042,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(nat,X1,power_power(X1,X2),X3)),hAPP(nat,X1,power_power(X1,X4),X3)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X2))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X4))
| ~ linordered_semidom(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1363]) ).
cnf(c_0_2043,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(nat,X1,power_power(X1,X2),X3)),hAPP(nat,X1,power_power(X1,X2),X4)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),one_one(X1)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X2))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X4),X3))
| ~ linordered_semidom(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1364]) ).
cnf(c_0_2044,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(nat,X1,power_power(X1,X2),X3)),hAPP(nat,X1,power_power(X1,X2),X4)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),one_one(X1)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X2))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X4),X3))
| ~ linordered_semidom(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1365]) ).
cnf(c_0_2045,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X2))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)))
| ~ linord20386208strict(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1366]) ).
cnf(c_0_2046,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(nat,X1,power_power(X1,X2),X4)),hAPP(nat,X1,power_power(X1,X3),X4)))
| ~ linordered_semidom(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1367]) ).
cnf(c_0_2047,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2))
| ~ hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),hAPP(nat,X3,power_power(X3,X4),X1)),hAPP(nat,X3,power_power(X3,X4),X2)))
| ~ hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),one_one(X3)),X4))
| ~ linordered_semidom(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1368]) ).
cnf(c_0_2048,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X3),X4))
| ~ linordered_semidom(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),one_one(X1)),X2))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(nat,X1,power_power(X1,X2),X3)),hAPP(nat,X1,power_power(X1,X2),X4))) ),
inference(split_conjunct,[status(thm)],[c_0_1369]) ).
cnf(c_0_2049,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2))
| ~ hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),hAPP(nat,X3,power_power(X3,X4),X1)),hAPP(nat,X3,power_power(X3,X4),X2)))
| ~ hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),one_one(X3)),X4))
| ~ linordered_semidom(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1370]) ).
cnf(c_0_2050,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X3),X4))
| ~ linordered_semidom(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),one_one(X1)),X2))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(nat,X1,power_power(X1,X2),X3)),hAPP(nat,X1,power_power(X1,X2),X4))) ),
inference(split_conjunct,[status(thm)],[c_0_1371]) ).
cnf(c_0_2051,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(nat,X1,power_power(X1,X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),hAPP(nat,X1,power_power(X1,X2),X3))))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),one_one(X1)),X2))
| ~ linordered_semidom(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1372]) ).
cnf(c_0_2052,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,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(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_1373]) ).
cnf(c_0_2053,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(nat,X1,power_power(X1,X2),X3)),hAPP(nat,X1,power_power(X1,X4),X3)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X2))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X4))
| ~ linordered_semidom(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1374]) ).
cnf(c_0_2054,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),zero_zero(X1)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),zero_zero(X1)))
| ~ linord581940658strict(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1375]) ).
cnf(c_0_2055,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,plus_plus(X1,X2),X3)),hAPP(X1,X1,plus_plus(X1,X4),X5)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X5))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X4))
| ~ ordere223160158up_add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1376]) ).
cnf(c_0_2056,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,plus_plus(X1,X2),X3)),hAPP(X1,X1,plus_plus(X1,X4),X5)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X5))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X4))
| ~ ordere223160158up_add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1377]) ).
cnf(c_0_2057,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,plus_plus(X1,X2),X3)),hAPP(X1,X1,plus_plus(X1,X4),X5)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X5))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X4))
| ~ ordere779506340up_add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1378]) ).
cnf(c_0_2058,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,plus_plus(X1,X2),X3)),hAPP(X1,X1,plus_plus(X1,X4),X5)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X5))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X4))
| ~ ordere223160158up_add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1379]) ).
cnf(c_0_2059,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(nat,X1,power_power(X1,X2),X3)),hAPP(nat,X1,power_power(X1,X2),X4)))
| ~ linordered_semidom(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),one_one(X1)),X2))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X3),X4)) ),
inference(split_conjunct,[status(thm)],[c_0_1369]) ).
cnf(c_0_2060,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(nat,X1,power_power(X1,X2),X3)),hAPP(nat,X1,power_power(X1,X2),X4)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),one_one(X1)),X2))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X3),X4))
| ~ linordered_semidom(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1380]) ).
cnf(c_0_2061,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(nat,X1,power_power(X1,X2),X3)),hAPP(nat,X1,power_power(X1,X2),X4)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),one_one(X1)),X2))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X3),X4))
| ~ linordered_semidom(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1381]) ).
cnf(c_0_2062,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(nat,X1,power_power(X1,X2),X3)),hAPP(nat,X1,power_power(X1,X2),X4)))
| ~ linordered_semidom(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),one_one(X1)),X2))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X3),X4)) ),
inference(split_conjunct,[status(thm)],[c_0_1371]) ).
cnf(c_0_2063,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X4))
| ~ dense_linorder(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),esk27_4(X1,X4,X2,X3)),X4)) ),
inference(split_conjunct,[status(thm)],[c_0_1382]) ).
cnf(c_0_2064,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,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(nat,fun(nat,bool),ord_less_eq(nat),X2),X4))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_1383]) ).
cnf(c_0_2065,plain,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,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(int,fun(int,bool),ord_less_eq(int),X2),X4))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X1),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_1384]) ).
cnf(c_0_2066,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,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(nat,fun(nat,bool),ord_less(nat),X2),X4))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_1385]) ).
cnf(c_0_2067,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),one_one(X1)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),hAPP(nat,X1,power_power(X1,X2),X3))))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),one_one(X1)),X2))
| ~ linordered_semidom(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1386]) ).
cnf(c_0_2068,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,plus_plus(X1,X4),X2)),hAPP(X1,X1,plus_plus(X1,X4),X3)))
| ~ ordere236663937imp_le(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1387]) ).
cnf(c_0_2069,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,plus_plus(X1,X2),X4)),hAPP(X1,X1,plus_plus(X1,X3),X4)))
| ~ ordere236663937imp_le(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1388]) ).
cnf(c_0_2070,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
| ~ ordere236663937imp_le(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,plus_plus(X1,X4),X2)),hAPP(X1,X1,plus_plus(X1,X4),X3))) ),
inference(split_conjunct,[status(thm)],[c_0_1389]) ).
cnf(c_0_2071,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
| ~ ordere236663937imp_le(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,plus_plus(X1,X2),X4)),hAPP(X1,X1,plus_plus(X1,X3),X4))) ),
inference(split_conjunct,[status(thm)],[c_0_1390]) ).
cnf(c_0_2072,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| ~ ordere236663937imp_le(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,plus_plus(X1,X2),X4)),hAPP(X1,X1,plus_plus(X1,X3),X4))) ),
inference(split_conjunct,[status(thm)],[c_0_1391]) ).
cnf(c_0_2073,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| ~ ordere236663937imp_le(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,plus_plus(X1,X4),X2)),hAPP(X1,X1,plus_plus(X1,X4),X3))) ),
inference(split_conjunct,[status(thm)],[c_0_1392]) ).
cnf(c_0_2074,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,plus_plus(X1,X2),X4)),hAPP(X1,X1,plus_plus(X1,X3),X4)))
| ~ ordere236663937imp_le(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1393]) ).
cnf(c_0_2075,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,plus_plus(X1,X4),X2)),hAPP(X1,X1,plus_plus(X1,X4),X3)))
| ~ ordere236663937imp_le(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1394]) ).
cnf(c_0_2076,plain,
( hBOOL(hAPP(int,bool,X3,X2))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,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_1395]) ).
cnf(c_0_2077,plain,
hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,bit1,X1)),X2) = hAPP(int,int,plus_plus(int,hAPP(int,int,bit0,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),X1),X2))),X2),
inference(split_conjunct,[status(thm)],[c_0_1396]) ).
cnf(c_0_2078,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,X1,X2)),hAPP(nat,nat,X1,X3)))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),esk20_3(X2,X3,X1)),esk21_3(X2,X3,X1)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X2),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_1357]) ).
cnf(c_0_2079,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,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_1397]) ).
cnf(c_0_2080,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,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_1398]) ).
cnf(c_0_2081,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X1,X2),X3))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X1,X2),X3))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X1,X2),X3))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X1,X2),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_1399]) ).
cnf(c_0_2082,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,plus_plus(X1,X2),X3)),zero_zero(X1)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),zero_zero(X1)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),zero_zero(X1)))
| ~ ordere216010020id_add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1400]) ).
cnf(c_0_2083,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,plus_plus(X1,X2),X3)),zero_zero(X1)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),zero_zero(X1)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),zero_zero(X1)))
| ~ ordere216010020id_add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1401]) ).
cnf(c_0_2084,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,plus_plus(X1,X2),X3)),zero_zero(X1)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),zero_zero(X1)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),zero_zero(X1)))
| ~ ordere216010020id_add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1402]) ).
cnf(c_0_2085,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,plus_plus(X1,X2),X3)),zero_zero(X1)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),zero_zero(X1)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),zero_zero(X1)))
| ~ ordere216010020id_add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1403]) ).
cnf(c_0_2086,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X2),X3))
| ~ linordered_semidom(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(nat,X1,semiring_1_of_nat(X1),X2)),hAPP(nat,X1,semiring_1_of_nat(X1),X3))) ),
inference(split_conjunct,[status(thm)],[c_0_1404]) ).
cnf(c_0_2087,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2))
| ~ hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),hAPP(nat,X3,semiring_1_of_nat(X3),X1)),hAPP(nat,X3,semiring_1_of_nat(X3),X2)))
| ~ linordered_semidom(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1405]) ).
cnf(c_0_2088,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X2),X3))
| ~ linordered_semidom(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(nat,X1,semiring_1_of_nat(X1),X2)),hAPP(nat,X1,semiring_1_of_nat(X1),X3))) ),
inference(split_conjunct,[status(thm)],[c_0_1406]) ).
cnf(c_0_2089,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(nat,int,semiring_1_of_nat(int),X1)),hAPP(nat,int,semiring_1_of_nat(int),X2))) ),
inference(split_conjunct,[status(thm)],[c_0_1407]) ).
cnf(c_0_2090,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(nat,int,semiring_1_of_nat(int),X1)),hAPP(nat,int,semiring_1_of_nat(int),X2))) ),
inference(split_conjunct,[status(thm)],[c_0_1408]) ).
cnf(c_0_2091,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(nat,int,semiring_1_of_nat(int),X1)),hAPP(nat,int,semiring_1_of_nat(int),X2))) ),
inference(split_conjunct,[status(thm)],[c_0_1409]) ).
cnf(c_0_2092,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(nat,int,semiring_1_of_nat(int),X1)),hAPP(nat,int,semiring_1_of_nat(int),X2))) ),
inference(split_conjunct,[status(thm)],[c_0_1410]) ).
cnf(c_0_2093,plain,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X1),X2))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,bit1,X1)),hAPP(int,int,bit0,X2))) ),
inference(split_conjunct,[status(thm)],[c_0_1411]) ).
cnf(c_0_2094,plain,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X1),X2))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,bit1,X1)),hAPP(int,int,bit0,X2))) ),
inference(split_conjunct,[status(thm)],[c_0_1412]) ).
cnf(c_0_2095,plain,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X1),X2))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit0,X1)),hAPP(int,int,bit1,X2))) ),
inference(split_conjunct,[status(thm)],[c_0_1413]) ).
cnf(c_0_2096,plain,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X1),X2))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit0,X1)),hAPP(int,int,bit1,X2))) ),
inference(split_conjunct,[status(thm)],[c_0_1414]) ).
cnf(c_0_2097,plain,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X1),X2))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,bit0,X1)),hAPP(int,int,bit1,X2))) ),
inference(split_conjunct,[status(thm)],[c_0_1415]) ).
cnf(c_0_2098,plain,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X1),X2))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,bit0,X1)),hAPP(int,int,bit1,X2))) ),
inference(split_conjunct,[status(thm)],[c_0_1416]) ).
cnf(c_0_2099,plain,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X1),X2))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,bit0,X1)),hAPP(int,int,bit0,X2))) ),
inference(split_conjunct,[status(thm)],[c_0_1417]) ).
cnf(c_0_2100,plain,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X1),X2))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,bit0,X1)),hAPP(int,int,bit0,X2))) ),
inference(split_conjunct,[status(thm)],[c_0_1418]) ).
cnf(c_0_2101,plain,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X1),X2))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,bit1,X1)),hAPP(int,int,bit1,X2))) ),
inference(split_conjunct,[status(thm)],[c_0_1419]) ).
cnf(c_0_2102,plain,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X1),X2))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,bit1,X1)),hAPP(int,int,bit1,X2))) ),
inference(split_conjunct,[status(thm)],[c_0_1420]) ).
cnf(c_0_2103,plain,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X1),X2))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit1,X1)),hAPP(int,int,bit0,X2))) ),
inference(split_conjunct,[status(thm)],[c_0_1421]) ).
cnf(c_0_2104,plain,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X1),X2))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit1,X1)),hAPP(int,int,bit0,X2))) ),
inference(split_conjunct,[status(thm)],[c_0_1422]) ).
cnf(c_0_2105,plain,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X1),X2))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit0,X1)),hAPP(int,int,bit0,X2))) ),
inference(split_conjunct,[status(thm)],[c_0_1423]) ).
cnf(c_0_2106,plain,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X1),X2))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit0,X1)),hAPP(int,int,bit0,X2))) ),
inference(split_conjunct,[status(thm)],[c_0_1424]) ).
cnf(c_0_2107,plain,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X1),X2))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit1,X1)),hAPP(int,int,bit1,X2))) ),
inference(split_conjunct,[status(thm)],[c_0_1425]) ).
cnf(c_0_2108,plain,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X1),X2))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit1,X1)),hAPP(int,int,bit1,X2))) ),
inference(split_conjunct,[status(thm)],[c_0_1426]) ).
cnf(c_0_2109,plain,
( ti(X1,X2) = ti(X1,X3)
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X4))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X2))
| hAPP(nat,X1,power_power(X1,X2),X4) != hAPP(nat,X1,power_power(X1,X3),X4)
| ~ linordered_semidom(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1427]) ).
cnf(c_0_2110,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X3,X2),X1))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X3,X2),X1))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X3,X2),X1)) ),
inference(split_conjunct,[status(thm)],[c_0_1399]) ).
cnf(c_0_2111,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X1,X2),X3))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X2),X3))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X1,X2),X3))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X1,X2),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_1399]) ).
cnf(c_0_2112,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X2,X1,X3,X4)),hAPP(X2,X1,X5,X4)))
| ~ ord(X1)
| ~ hBOOL(hAPP(fun(X2,X1),bool,hAPP(fun(X2,X1),fun(fun(X2,X1),bool),ord_less_eq(fun(X2,X1)),X3),X5)) ),
inference(split_conjunct,[status(thm)],[c_0_1351]) ).
cnf(c_0_2113,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X2,X1,X3,X4)),hAPP(X2,X1,X5,X4)))
| ~ hBOOL(hAPP(fun(X2,X1),bool,hAPP(fun(X2,X1),fun(fun(X2,X1),bool),ord_less_eq(fun(X2,X1)),X3),X5))
| ~ ord(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1428]) ).
cnf(c_0_2114,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X2,X1,X3,X4)),hAPP(X2,X1,X5,X4)))
| ~ hBOOL(hAPP(fun(X2,X1),bool,hAPP(fun(X2,X1),fun(fun(X2,X1),bool),ord_less_eq(fun(X2,X1)),X3),X5))
| ~ ord(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1429]) ).
cnf(c_0_2115,plain,
( X3 = esk4_2(X2,X1)
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X1))
| ~ hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X2))
| hAPP(nat,real,power_power(real,X3),X1) != X2
| ~ hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_1430]) ).
cnf(c_0_2116,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),hAPP(X1,X1,plus_plus(X1,X2),X3)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X2))
| ~ ordere216010020id_add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1431]) ).
cnf(c_0_2117,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),hAPP(X1,X1,plus_plus(X1,X2),X3)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X2))
| ~ ordere216010020id_add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1432]) ).
cnf(c_0_2118,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),hAPP(X1,X1,plus_plus(X1,X2),X3)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X2))
| ~ ordere216010020id_add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1433]) ).
cnf(c_0_2119,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),hAPP(X1,X1,plus_plus(X1,X2),X3)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X2))
| ~ ordere216010020id_add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1434]) ).
cnf(c_0_2120,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),hAPP(X1,X1,plus_plus(X1,X3),X4)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X4))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X3))
| ~ ordere216010020id_add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1435]) ).
cnf(c_0_2121,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),hAPP(X1,X1,plus_plus(X1,X3),X4)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X4))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X3))
| ~ ordere216010020id_add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1436]) ).
cnf(c_0_2122,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),hAPP(X1,X1,plus_plus(X1,X3),X4)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X4))
| ~ ordere216010020id_add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1437]) ).
cnf(c_0_2123,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),hAPP(X1,X1,plus_plus(X1,X3),X4)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X4))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X3))
| ~ ordere216010020id_add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1438]) ).
cnf(c_0_2124,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),hAPP(X1,X1,plus_plus(X1,X3),X4)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X4))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X3))
| ~ linordered_semidom(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1439]) ).
cnf(c_0_2125,plain,
( hBOOL(hAPP(fun(X2,X1),bool,hAPP(fun(X2,X1),fun(fun(X2,X1),bool),ord_less(fun(X2,X1)),X3),X4))
| hBOOL(hAPP(fun(X2,X1),bool,hAPP(fun(X2,X1),fun(fun(X2,X1),bool),ord_less_eq(fun(X2,X1)),X4),X3))
| ~ ord(X1)
| ~ hBOOL(hAPP(fun(X2,X1),bool,hAPP(fun(X2,X1),fun(fun(X2,X1),bool),ord_less_eq(fun(X2,X1)),X3),X4)) ),
inference(split_conjunct,[status(thm)],[c_0_1440]) ).
cnf(c_0_2126,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),one_one(X1)),hAPP(nat,X1,power_power(X1,X2),X3)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),one_one(X1)),X2))
| ~ linordered_semidom(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1441]) ).
cnf(c_0_2127,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X4))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),esk27_4(X1,X4,X2,X3)),X3))
| ~ dense_linorder(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_1382]) ).
cnf(c_0_2128,plain,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,plus_plus(int,X1),X2)))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X2))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X1)) ),
inference(split_conjunct,[status(thm)],[c_0_1442]) ).
cnf(c_0_2129,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),zero_zero(X1)))
| ~ linord219039673up_add(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,plus_plus(X1,X2),X2)),zero_zero(X1))) ),
inference(split_conjunct,[status(thm)],[c_0_1443]) ).
cnf(c_0_2130,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),zero_zero(X1)))
| ~ linord219039673up_add(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,plus_plus(X1,X2),X2)),zero_zero(X1))) ),
inference(split_conjunct,[status(thm)],[c_0_1444]) ).
cnf(c_0_2131,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),zero_zero(X1)))
| ~ linordered_idom(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,plus_plus(X1,X2),X2)),zero_zero(X1))) ),
inference(split_conjunct,[status(thm)],[c_0_1445]) ).
cnf(c_0_2132,plain,
( hBOOL(hAPP(int,bool,X3,X2))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,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_1446]) ).
cnf(c_0_2133,plain,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X1),X2))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,plus_plus(int,X1),one_one(int))),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_1447]) ).
cnf(c_0_2134,plain,
hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),number_number_of(int,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),
inference(split_conjunct,[status(thm)],[c_0_1448]) ).
cnf(c_0_2135,plain,
hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),number_number_of(int,hAPP(int,int,bit1,hAPP(int,int,bit1,pls))))),
inference(split_conjunct,[status(thm)],[c_0_1449]) ).
cnf(c_0_2136,plain,
hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),
inference(split_conjunct,[status(thm)],[c_0_1450]) ).
cnf(c_0_2137,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,plus_plus(X1,X2),X3)),hAPP(X1,X1,plus_plus(X1,X2),X4)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X4))
| ~ ordere779506340up_add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1451]) ).
cnf(c_0_2138,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,plus_plus(X1,X2),X3)),hAPP(X1,X1,plus_plus(X1,X4),X3)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X4))
| ~ ordere779506340up_add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1452]) ).
cnf(c_0_2139,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,plus_plus(X1,X2),X3)),hAPP(X1,X1,plus_plus(X1,X2),X4)))
| ~ ordere236663937imp_le(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X4)) ),
inference(split_conjunct,[status(thm)],[c_0_1389]) ).
cnf(c_0_2140,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,plus_plus(X1,X2),X3)),hAPP(X1,X1,plus_plus(X1,X4),X3)))
| ~ ordere236663937imp_le(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X4)) ),
inference(split_conjunct,[status(thm)],[c_0_1390]) ).
cnf(c_0_2141,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,plus_plus(X1,X2),X3)),hAPP(X1,X1,plus_plus(X1,X4),X3)))
| ~ ordere236663937imp_le(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X4)) ),
inference(split_conjunct,[status(thm)],[c_0_1391]) ).
cnf(c_0_2142,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,plus_plus(X1,X2),X3)),hAPP(X1,X1,plus_plus(X1,X2),X4)))
| ~ ordere236663937imp_le(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X4)) ),
inference(split_conjunct,[status(thm)],[c_0_1392]) ).
cnf(c_0_2143,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,plus_plus(X1,X2),X3)),hAPP(X1,X1,plus_plus(X1,X4),X3)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X4))
| ~ ordere223160158up_add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1453]) ).
cnf(c_0_2144,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,plus_plus(X1,X2),X3)),hAPP(X1,X1,plus_plus(X1,X2),X4)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X4))
| ~ ordere223160158up_add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1454]) ).
cnf(c_0_2145,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X3))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,plus_plus(nat,X1),X2)),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_1455]) ).
cnf(c_0_2146,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X2),X3))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,plus_plus(nat,X1),X2)),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_1455]) ).
cnf(c_0_2147,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,plus_plus(nat,X1),X3)),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_1456]) ).
cnf(c_0_2148,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,plus_plus(nat,X3),X1)),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_1457]) ).
cnf(c_0_2149,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,plus_plus(nat,X1),X3)),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_1458]) ).
cnf(c_0_2150,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X1))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X2))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,plus_plus(nat,X2),X1))) ),
inference(split_conjunct,[status(thm)],[c_0_1459]) ).
cnf(c_0_2151,plain,
( hBOOL(hAPP(real,bool,hAPP(real,fun(real,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(real,fun(real,bool),ord_less_eq(real),X2),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_1460]) ).
cnf(c_0_2152,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,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(nat,fun(nat,bool),ord_less_eq(nat),X1),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_1461]) ).
cnf(c_0_2153,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,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(nat,fun(nat,bool),ord_less_eq(nat),X2),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_1397]) ).
cnf(c_0_2154,plain,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,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(int,fun(int,bool),ord_less_eq(int),X2),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_1462]) ).
cnf(c_0_2155,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,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(nat,fun(nat,bool),ord_less(nat),X1),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_1463]) ).
cnf(c_0_2156,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,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(nat,fun(nat,bool),ord_less(nat),X2),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_1398]) ).
cnf(c_0_2157,plain,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,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(int,fun(int,bool),ord_less(int),X1),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_1464]) ).
cnf(c_0_2158,plain,
( hBOOL(hAPP(int,bool,X3,X2))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X1),esk1_3(X3,X1,X2)))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,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_1395]) ).
cnf(c_0_2159,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),one_one(X1)),number_number_of(X1,X2)))
| ~ linordered_idom(X1)
| ~ number_ring(X1)
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,bit1,pls)),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_1465]) ).
cnf(c_0_2160,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),one_one(X1)),number_number_of(X1,X2)))
| ~ linordered_idom(X1)
| ~ number_ring(X1)
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit1,pls)),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_1466]) ).
cnf(c_0_2161,plain,
hAPP(int,int,plus_plus(int,hAPP(nat,int,semiring_1_of_nat(int),X1)),hAPP(int,int,plus_plus(int,hAPP(nat,int,semiring_1_of_nat(int),X2)),X3)) = hAPP(int,int,plus_plus(int,hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,plus_plus(nat,X1),X2))),X3),
inference(split_conjunct,[status(thm)],[c_0_1467]) ).
cnf(c_0_2162,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X3,X2),X1))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X2),X1))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X3,X2),X1)) ),
inference(split_conjunct,[status(thm)],[c_0_1399]) ).
cnf(c_0_2163,plain,
( hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X1),one_one(real)))
| ~ hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,sqrt,X1)),one_one(real))) ),
inference(split_conjunct,[status(thm)],[c_0_1468]) ).
cnf(c_0_2164,plain,
( hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X1),zero_zero(real)))
| ~ hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,sqrt,X1)),zero_zero(real))) ),
inference(split_conjunct,[status(thm)],[c_0_1469]) ).
cnf(c_0_2165,plain,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X1),zero_zero(int)))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit0,X1)),zero_zero(int))) ),
inference(split_conjunct,[status(thm)],[c_0_1470]) ).
cnf(c_0_2166,plain,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X1),zero_zero(int)))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit1,X1)),zero_zero(int))) ),
inference(split_conjunct,[status(thm)],[c_0_1471]) ).
cnf(c_0_2167,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(nat,X1,semiring_1_of_nat(X1),X2)),hAPP(nat,X1,semiring_1_of_nat(X1),X3)))
| ~ linordered_semidom(X1)
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X2),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_1404]) ).
cnf(c_0_2168,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(nat,X1,semiring_1_of_nat(X1),X2)),hAPP(nat,X1,semiring_1_of_nat(X1),X3)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X2),X3))
| ~ linordered_semidom(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1472]) ).
cnf(c_0_2169,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(nat,X1,semiring_1_of_nat(X1),X2)),hAPP(nat,X1,semiring_1_of_nat(X1),X3)))
| ~ linordered_semidom(X1)
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X2),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_1406]) ).
cnf(c_0_2170,plain,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X1),pls))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,bit1,X1)),pls)) ),
inference(split_conjunct,[status(thm)],[c_0_1473]) ).
cnf(c_0_2171,plain,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X1),pls))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,bit0,X1)),pls)) ),
inference(split_conjunct,[status(thm)],[c_0_1474]) ).
cnf(c_0_2172,plain,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X1),pls))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit0,X1)),pls)) ),
inference(split_conjunct,[status(thm)],[c_0_1475]) ).
cnf(c_0_2173,plain,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X1),pls))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit1,X1)),pls)) ),
inference(split_conjunct,[status(thm)],[c_0_1476]) ).
cnf(c_0_2174,plain,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(nat,int,semiring_1_of_nat(int),X1)),hAPP(nat,int,semiring_1_of_nat(int),X2)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_1407]) ).
cnf(c_0_2175,plain,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(nat,int,semiring_1_of_nat(int),X1)),hAPP(nat,int,semiring_1_of_nat(int),X2)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_1408]) ).
cnf(c_0_2176,plain,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(nat,int,semiring_1_of_nat(int),X1)),hAPP(nat,int,semiring_1_of_nat(int),X2)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_1409]) ).
cnf(c_0_2177,plain,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(nat,int,semiring_1_of_nat(int),X1)),hAPP(nat,int,semiring_1_of_nat(int),X2)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_1410]) ).
cnf(c_0_2178,plain,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,bit1,X1)),hAPP(int,int,bit0,X2)))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X1),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_1411]) ).
cnf(c_0_2179,plain,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,bit1,X1)),hAPP(int,int,bit0,X2)))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X1),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_1412]) ).
cnf(c_0_2180,plain,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit0,X1)),hAPP(int,int,bit1,X2)))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X1),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_1413]) ).
cnf(c_0_2181,plain,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit0,X1)),hAPP(int,int,bit1,X2)))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X1),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_1414]) ).
cnf(c_0_2182,plain,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,bit0,X1)),hAPP(int,int,bit1,X2)))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X1),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_1415]) ).
cnf(c_0_2183,plain,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,bit0,X1)),hAPP(int,int,bit1,X2)))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X1),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_1416]) ).
cnf(c_0_2184,plain,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,bit0,X1)),hAPP(int,int,bit0,X2)))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X1),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_1417]) ).
cnf(c_0_2185,plain,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,bit0,X1)),hAPP(int,int,bit0,X2)))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X1),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_1418]) ).
cnf(c_0_2186,plain,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,bit1,X1)),hAPP(int,int,bit1,X2)))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X1),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_1419]) ).
cnf(c_0_2187,plain,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,bit1,X1)),hAPP(int,int,bit1,X2)))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X1),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_1420]) ).
cnf(c_0_2188,plain,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit1,X1)),hAPP(int,int,bit0,X2)))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X1),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_1421]) ).
cnf(c_0_2189,plain,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit1,X1)),hAPP(int,int,bit0,X2)))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X1),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_1422]) ).
cnf(c_0_2190,plain,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit0,X1)),hAPP(int,int,bit0,X2)))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X1),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_1423]) ).
cnf(c_0_2191,plain,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit0,X1)),hAPP(int,int,bit0,X2)))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X1),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_1424]) ).
cnf(c_0_2192,plain,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit1,X1)),hAPP(int,int,bit1,X2)))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X1),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_1425]) ).
cnf(c_0_2193,plain,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit1,X1)),hAPP(int,int,bit1,X2)))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X1),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_1426]) ).
cnf(c_0_2194,plain,
( ~ ord(X1)
| ~ hBOOL(hAPP(fun(X2,X1),bool,hAPP(fun(X2,X1),fun(fun(X2,X1),bool),ord_less(fun(X2,X1)),X3),X4))
| ~ hBOOL(hAPP(fun(X2,X1),bool,hAPP(fun(X2,X1),fun(fun(X2,X1),bool),ord_less_eq(fun(X2,X1)),X4),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_1440]) ).
cnf(c_0_2195,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X4))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),esk27_4(X1,X4,X2,X3)))
| ~ dense_linorder(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_1382]) ).
cnf(c_0_2196,plain,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),X2))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),number_number_of(nat,X1)),number_number_of(nat,X2)))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X1),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_1477]) ).
cnf(c_0_2197,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X4))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X4),X3))
| ~ order(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1478]) ).
cnf(c_0_2198,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X4),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X4))
| ~ preorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1479]) ).
cnf(c_0_2199,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X4))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X4),X3))
| ~ order(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1480]) ).
cnf(c_0_2200,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X4),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X4))
| ~ preorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1481]) ).
cnf(c_0_2201,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X4),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X4))
| ~ preorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1482]) ).
cnf(c_0_2202,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X4))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X4),X3))
| ~ order(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1483]) ).
cnf(c_0_2203,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X4),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X4))
| ~ preorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1484]) ).
cnf(c_0_2204,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X4))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X4),X3))
| ~ order(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1485]) ).
cnf(c_0_2205,plain,
( hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),esk23_2(X2,X1)),X1))
| ~ hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X1))
| ~ hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_1486]) ).
cnf(c_0_2206,plain,
( hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),esk23_2(X2,X1)),X2))
| ~ hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X1))
| ~ hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_1486]) ).
cnf(c_0_2207,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),number_number_of(nat,X1)),number_number_of(nat,X2)))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X1),X2))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_1477]) ).
cnf(c_0_2208,plain,
( hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),esk23_2(X2,X1)))
| ~ hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X1))
| ~ hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_1486]) ).
cnf(c_0_2209,plain,
( hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),esk5_2(X2,X1)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X1))
| ~ hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_1487]) ).
cnf(c_0_2210,plain,
( hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),esk4_2(X2,X1)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X1))
| ~ hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_1430]) ).
cnf(c_0_2211,plain,
( hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X1),X2))
| ~ hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X3),X2))
| ~ hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X1),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_1488]) ).
cnf(c_0_2212,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X3),X2))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_1489]) ).
cnf(c_0_2213,plain,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X1),X2))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X3),X2))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X1),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_1490]) ).
cnf(c_0_2214,plain,
( X3 = X2
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X1,X2),X3))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X1,X2),X3))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X1,X2),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_1399]) ).
cnf(c_0_2215,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,plus_plus(X1,X2),X2)),zero_zero(X1)))
| ~ linord219039673up_add(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),zero_zero(X1))) ),
inference(split_conjunct,[status(thm)],[c_0_1443]) ).
cnf(c_0_2216,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,plus_plus(X1,X2),X2)),zero_zero(X1)))
| ~ linord219039673up_add(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),zero_zero(X1))) ),
inference(split_conjunct,[status(thm)],[c_0_1444]) ).
cnf(c_0_2217,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,plus_plus(X1,X2),X2)),zero_zero(X1)))
| ~ linordered_idom(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),zero_zero(X1))) ),
inference(split_conjunct,[status(thm)],[c_0_1445]) ).
cnf(c_0_2218,plain,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,plus_plus(int,X1),one_one(int))),X2))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X1),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_1491]) ).
cnf(c_0_2219,plain,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,plus_plus(int,X1),one_one(int))),X2))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X1),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_1447]) ).
cnf(c_0_2220,plain,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,bit1,pls)),X2))
| ~ linordered_idom(X1)
| ~ number_ring(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),one_one(X1)),number_number_of(X1,X2))) ),
inference(split_conjunct,[status(thm)],[c_0_1465]) ).
cnf(c_0_2221,plain,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit1,pls)),X2))
| ~ linordered_idom(X1)
| ~ number_ring(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),one_one(X1)),number_number_of(X1,X2))) ),
inference(split_conjunct,[status(thm)],[c_0_1466]) ).
cnf(c_0_2222,plain,
( hBOOL(hAPP(int,bool,X3,X2))
| hBOOL(hAPP(int,bool,X3,esk1_3(X3,X1,X2)))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,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_1395]) ).
cnf(c_0_2223,plain,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),number_number_of(int,hAPP(int,int,bit0,X1))))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),number_number_of(int,X1))) ),
inference(split_conjunct,[status(thm)],[c_0_1492]) ).
cnf(c_0_2224,plain,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),number_number_of(int,hAPP(int,int,bit1,X1))))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),number_number_of(int,X1))) ),
inference(split_conjunct,[status(thm)],[c_0_1492]) ).
cnf(c_0_2225,plain,
( hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,sqrt,X1)),one_one(real)))
| ~ hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X1),one_one(real))) ),
inference(split_conjunct,[status(thm)],[c_0_1468]) ).
cnf(c_0_2226,plain,
( hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,sqrt,X1)),zero_zero(real)))
| ~ hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X1),zero_zero(real))) ),
inference(split_conjunct,[status(thm)],[c_0_1469]) ).
cnf(c_0_2227,plain,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit0,X1)),zero_zero(int)))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X1),zero_zero(int))) ),
inference(split_conjunct,[status(thm)],[c_0_1470]) ).
cnf(c_0_2228,plain,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit1,X1)),zero_zero(int)))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X1),zero_zero(int))) ),
inference(split_conjunct,[status(thm)],[c_0_1471]) ).
cnf(c_0_2229,plain,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,bit1,X1)),pls))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X1),pls)) ),
inference(split_conjunct,[status(thm)],[c_0_1473]) ).
cnf(c_0_2230,plain,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,bit0,X1)),pls))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X1),pls)) ),
inference(split_conjunct,[status(thm)],[c_0_1474]) ).
cnf(c_0_2231,plain,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit0,X1)),pls))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X1),pls)) ),
inference(split_conjunct,[status(thm)],[c_0_1475]) ).
cnf(c_0_2232,plain,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit1,X1)),pls))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X1),pls)) ),
inference(split_conjunct,[status(thm)],[c_0_1476]) ).
cnf(c_0_2233,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X2))
| ~ linord219039673up_add(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),hAPP(X1,X1,plus_plus(X1,X2),X2))) ),
inference(split_conjunct,[status(thm)],[c_0_1493]) ).
cnf(c_0_2234,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X2))
| ~ linord219039673up_add(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),hAPP(X1,X1,plus_plus(X1,X2),X2))) ),
inference(split_conjunct,[status(thm)],[c_0_1494]) ).
cnf(c_0_2235,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X1))
| number_number_of(nat,X2) = zero_zero(nat)
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,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_1495]) ).
cnf(c_0_2236,plain,
~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,plus_plus(nat,X1),X2)),X2)),
inference(split_conjunct,[status(thm)],[c_0_1496]) ).
cnf(c_0_2237,plain,
~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,plus_plus(nat,X1),X2)),X1)),
inference(split_conjunct,[status(thm)],[c_0_1497]) ).
cnf(c_0_2238,plain,
( hAPP(X1,X1,plus_plus(X1,number_number_of(X1,X2)),number_number_of(X1,X3)) = number_number_of(X1,hAPP(int,int,plus_plus(int,X2),X3))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),X3))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),X2))
| ~ number_semiring(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1498]) ).
cnf(c_0_2239,plain,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X1),pls))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X1),X2))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),number_number_of(nat,X1)),number_number_of(nat,X2))) ),
inference(split_conjunct,[status(thm)],[c_0_1499]) ).
cnf(c_0_2240,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X1))
| X2 = zero_zero(nat)
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,power_power(nat,X1),X2))) ),
inference(split_conjunct,[status(thm)],[c_0_1500]) ).
cnf(c_0_2241,plain,
( X1 = zero_zero(nat)
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X2))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,power_power(nat,X2),X1))) ),
inference(split_conjunct,[status(thm)],[c_0_1501]) ).
cnf(c_0_2242,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),number_number_of(nat,X1)),number_number_of(nat,X2)))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X1),X2))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X1),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_1477]) ).
cnf(c_0_2243,plain,
( X1 = X2
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X1),X2))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X1),hAPP(int,int,plus_plus(int,X2),one_one(int)))) ),
inference(split_conjunct,[status(thm)],[c_0_1502]) ).
cnf(c_0_2244,plain,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X1),X2))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X1),hAPP(int,int,plus_plus(int,X2),one_one(int)))) ),
inference(split_conjunct,[status(thm)],[c_0_1503]) ).
cnf(c_0_2245,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X2))
| ~ preorder(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_1504]) ).
cnf(c_0_2246,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X2))
| ~ linordered_semidom(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),hAPP(nat,X1,semiring_1_of_nat(X1),X2))) ),
inference(split_conjunct,[status(thm)],[c_0_1505]) ).
cnf(c_0_2247,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),number_number_of(X1,X2)),one_one(X1)))
| ~ linordered_idom(X1)
| ~ number_ring(X1)
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X2),hAPP(int,int,bit1,pls))) ),
inference(split_conjunct,[status(thm)],[c_0_1506]) ).
cnf(c_0_2248,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),number_number_of(X1,X2)),one_one(X1)))
| ~ linordered_idom(X1)
| ~ number_ring(X1)
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X2),hAPP(int,int,bit1,pls))) ),
inference(split_conjunct,[status(thm)],[c_0_1507]) ).
cnf(c_0_2249,plain,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(nat,X1,semiring_1_of_nat(X1),X2)),zero_zero(X1)))
| ~ linordered_semidom(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1508]) ).
cnf(c_0_2250,plain,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X1))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X1))
| ~ hBOOL(X2)
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X1)) ),
inference(split_conjunct,[status(thm)],[c_0_1509]) ).
cnf(c_0_2251,plain,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X1))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X1))
| ~ hBOOL(X2)
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X1)) ),
inference(split_conjunct,[status(thm)],[c_0_1509]) ).
cnf(c_0_2252,plain,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X1))
| hBOOL(X2)
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X1))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X1)) ),
inference(split_conjunct,[status(thm)],[c_0_1510]) ).
cnf(c_0_2253,plain,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X1))
| hBOOL(X2)
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X1))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X1)) ),
inference(split_conjunct,[status(thm)],[c_0_1510]) ).
cnf(c_0_2254,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X1))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(nat,int,semiring_1_of_nat(int),X1))) ),
inference(split_conjunct,[status(thm)],[c_0_1511]) ).
cnf(c_0_2255,plain,
( hBOOL(hAPP(fun(X2,X1),bool,hAPP(fun(X2,X1),fun(fun(X2,X1),bool),ord_less_eq(fun(X2,X1)),X3),X4))
| ~ ord(X1)
| ~ hBOOL(hAPP(fun(X2,X1),bool,hAPP(fun(X2,X1),fun(fun(X2,X1),bool),ord_less(fun(X2,X1)),X3),X4)) ),
inference(split_conjunct,[status(thm)],[c_0_1440]) ).
cnf(c_0_2256,plain,
( hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),one_one(real)),X1))
| ~ hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),one_one(real)),hAPP(real,real,sqrt,X1))) ),
inference(split_conjunct,[status(thm)],[c_0_1512]) ).
cnf(c_0_2257,plain,
( hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X1))
| ~ hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(real,real,sqrt,X1))) ),
inference(split_conjunct,[status(thm)],[c_0_1513]) ).
cnf(c_0_2258,plain,
( X1 = zero_zero(nat)
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(nat,int,semiring_1_of_nat(int),X1)),zero_zero(int))) ),
inference(split_conjunct,[status(thm)],[c_0_1514]) ).
cnf(c_0_2259,plain,
~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(nat,int,semiring_1_of_nat(int),X1)),zero_zero(int))),
inference(split_conjunct,[status(thm)],[c_0_1515]) ).
cnf(c_0_2260,plain,
( ti(X1,X2) = zero_zero(X1)
| ~ ordere216010020id_add(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X2))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X3))
| hAPP(X1,X1,plus_plus(X1,X2),X3) != zero_zero(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1516]) ).
cnf(c_0_2261,plain,
( ti(X1,X3) = zero_zero(X1)
| ~ ordere216010020id_add(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X2))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X3))
| hAPP(X1,X1,plus_plus(X1,X2),X3) != zero_zero(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1516]) ).
cnf(c_0_2262,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2))
| X1 = X2
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X3,X2),X1))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X3,X2),X1)) ),
inference(split_conjunct,[status(thm)],[c_0_1399]) ).
cnf(c_0_2263,plain,
( X3 = X2
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X1,X2),X3))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X2),X3))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X1,X2),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_1399]) ).
cnf(c_0_2264,plain,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),X1))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),hAPP(int,int,bit1,X1))) ),
inference(split_conjunct,[status(thm)],[c_0_1517]) ).
cnf(c_0_2265,plain,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),X1))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),hAPP(int,int,bit0,X1))) ),
inference(split_conjunct,[status(thm)],[c_0_1518]) ).
cnf(c_0_2266,plain,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),X1))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),hAPP(int,int,bit1,X1))) ),
inference(split_conjunct,[status(thm)],[c_0_1519]) ).
cnf(c_0_2267,plain,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),X1))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),hAPP(int,int,bit0,X1))) ),
inference(split_conjunct,[status(thm)],[c_0_1520]) ).
cnf(c_0_2268,plain,
( ~ linorder(X1)
| ~ number(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),number_number_of(X1,X2)),number_number_of(X1,X3)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),number_number_of(X1,X3)),number_number_of(X1,X2))) ),
inference(split_conjunct,[status(thm)],[c_0_1521]) ).
cnf(c_0_2269,plain,
( hBOOL(hAPP(int,bool,X3,X2))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X1),esk18_3(X3,X1,X2)))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X1),X2))
| ~ hBOOL(hAPP(int,bool,X3,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_1446]) ).
cnf(c_0_2270,plain,
( hAPP(X1,X1,plus_plus(X1,X2),X3) = zero_zero(X1)
| ~ ordere216010020id_add(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X2))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X3))
| ti(X1,X3) != zero_zero(X1)
| ti(X1,X2) != zero_zero(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1516]) ).
cnf(c_0_2271,plain,
( hBOOL(hAPP(int,bool,X1,X2))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X2))
| ~ hBOOL(hAPP(int,bool,X1,hAPP(nat,int,semiring_1_of_nat(int),esk9_1(X1)))) ),
inference(split_conjunct,[status(thm)],[c_0_1522]) ).
cnf(c_0_2272,plain,
( hAPP(nat,real,power_power(real,esk5_2(X2,X1)),X1) = X2
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X1))
| ~ hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_1487]) ).
cnf(c_0_2273,plain,
( hAPP(nat,real,power_power(real,esk4_2(X2,X1)),X1) = X2
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X1))
| ~ hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_1430]) ).
cnf(c_0_2274,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),hAPP(X1,X1,plus_plus(X1,X2),X2)))
| ~ linord219039673up_add(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_1493]) ).
cnf(c_0_2275,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),hAPP(X1,X1,plus_plus(X1,X2),X2)))
| ~ linord219039673up_add(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_1494]) ).
cnf(c_0_2276,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),one_one(X1)),hAPP(nat,X1,power_power(X1,X2),X3)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),one_one(X1)),X2))
| ~ linordered_semidom(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1523]) ).
cnf(c_0_2277,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),hAPP(nat,X1,power_power(X1,X2),X3)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X2))
| ~ linordered_semidom(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1524]) ).
cnf(c_0_2278,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),hAPP(nat,X1,power_power(X1,X2),X3)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X2))
| ~ linordered_semidom(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1525]) ).
cnf(c_0_2279,plain,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X2),hAPP(int,int,bit1,pls)))
| ~ linordered_idom(X1)
| ~ number_ring(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),number_number_of(X1,X2)),one_one(X1))) ),
inference(split_conjunct,[status(thm)],[c_0_1506]) ).
cnf(c_0_2280,plain,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X2),hAPP(int,int,bit1,pls)))
| ~ linordered_idom(X1)
| ~ number_ring(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),number_number_of(X1,X2)),one_one(X1))) ),
inference(split_conjunct,[status(thm)],[c_0_1507]) ).
cnf(c_0_2281,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,power_power(nat,X1),number_number_of(nat,X2))))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X1)) ),
inference(split_conjunct,[status(thm)],[c_0_1495]) ).
cnf(c_0_2282,plain,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),esk26_2(X1,X3)),X2))
| ~ linorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1526]) ).
cnf(c_0_2283,plain,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(int,int,plus_plus(int,one_one(int)),X1)))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X1)) ),
inference(split_conjunct,[status(thm)],[c_0_1527]) ).
cnf(c_0_2284,plain,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(nat,int,power_power(int,X1),X2)))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X1)) ),
inference(split_conjunct,[status(thm)],[c_0_1528]) ).
cnf(c_0_2285,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,power_power(nat,X1),X2)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X1)) ),
inference(split_conjunct,[status(thm)],[c_0_1500]) ).
cnf(c_0_2286,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,plus_plus(nat,X1),X2)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X1)) ),
inference(split_conjunct,[status(thm)],[c_0_1459]) ).
cnf(c_0_2287,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,plus_plus(nat,X1),X2)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_1459]) ).
cnf(c_0_2288,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,power_power(nat,X1),X2)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X1)) ),
inference(split_conjunct,[status(thm)],[c_0_1501]) ).
cnf(c_0_2289,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),hAPP(nat,X1,semiring_1_of_nat(X1),X2)))
| ~ linordered_semidom(X1)
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_1505]) ).
cnf(c_0_2290,plain,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),esk36_2(X1,X2)))
| ~ linorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1529]) ).
cnf(c_0_2291,plain,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X1),hAPP(int,int,plus_plus(int,X2),one_one(int))))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X1),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_1503]) ).
cnf(c_0_2292,plain,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X1),hAPP(int,int,plus_plus(int,X2),one_one(int))))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X1),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_1502]) ).
cnf(c_0_2293,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),hAPP(nat,nat,plus_plus(nat,X2),X3)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_1530]) ).
cnf(c_0_2294,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),hAPP(nat,nat,plus_plus(nat,X2),X3)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_1531]) ).
cnf(c_0_2295,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),hAPP(nat,nat,plus_plus(nat,X2),X3)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_1532]) ).
cnf(c_0_2296,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),hAPP(nat,nat,plus_plus(nat,X2),X3)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_1533]) ).
cnf(c_0_2297,plain,
( ~ linorder(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| ti(X1,X2) != ti(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_1534]) ).
cnf(c_0_2298,plain,
( ti(X1,X2) = ti(X1,X3)
| ~ order(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X2))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_1535]) ).
cnf(c_0_2299,plain,
( ti(X1,X3) = ti(X1,X2)
| ~ order(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_1536]) ).
cnf(c_0_2300,plain,
( ti(X1,X2) = ti(X1,X3)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X2))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
| ~ order(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1537]) ).
cnf(c_0_2301,plain,
( ti(X1,X2) = ti(X1,X3)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X2))
| ~ order(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1538]) ).
cnf(c_0_2302,plain,
( ti(X1,X2) = zero_zero(X1)
| ~ ring_11004092258visors(X1)
| hAPP(nat,X1,power_power(X1,X2),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) != zero_zero(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1539]) ).
cnf(c_0_2303,plain,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(nat,int,semiring_1_of_nat(int),X1)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X1)) ),
inference(split_conjunct,[status(thm)],[c_0_1511]) ).
cnf(c_0_2304,plain,
( hBOOL(X1)
| ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),X3),X4))
| ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),X4),X3))
| ~ preorder(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1540]) ).
cnf(c_0_2305,plain,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X2))
| ~ linorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1541]) ).
cnf(c_0_2306,plain,
( ~ preorder(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_1504]) ).
cnf(c_0_2307,plain,
( ~ linorder(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_1542]) ).
cnf(c_0_2308,plain,
( ~ linorder(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_1543]) ).
cnf(c_0_2309,plain,
( ~ linorder(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_1544]) ).
cnf(c_0_2310,plain,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X2))
| ~ preorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1545]) ).
cnf(c_0_2311,plain,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X2))
| ~ preorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1546]) ).
cnf(c_0_2312,plain,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X2))
| ~ preorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1547]) ).
cnf(c_0_2313,plain,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X2))
| ~ order(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1548]) ).
cnf(c_0_2314,plain,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X2))
| ~ preorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1549]) ).
cnf(c_0_2315,plain,
( hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),one_one(real)),hAPP(real,real,sqrt,X1)))
| ~ hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),one_one(real)),X1)) ),
inference(split_conjunct,[status(thm)],[c_0_1512]) ).
cnf(c_0_2316,plain,
( hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(real,real,sqrt,X1)))
| ~ hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X1)) ),
inference(split_conjunct,[status(thm)],[c_0_1513]) ).
cnf(c_0_2317,plain,
( hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(real,real,sqrt,X1)))
| ~ hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X1)) ),
inference(split_conjunct,[status(thm)],[c_0_1550]) ).
cnf(c_0_2318,plain,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),hAPP(int,int,bit1,X1)))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),X1)) ),
inference(split_conjunct,[status(thm)],[c_0_1517]) ).
cnf(c_0_2319,plain,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),hAPP(int,int,bit0,X1)))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),X1)) ),
inference(split_conjunct,[status(thm)],[c_0_1518]) ).
cnf(c_0_2320,plain,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),hAPP(int,int,bit1,X1)))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),X1)) ),
inference(split_conjunct,[status(thm)],[c_0_1519]) ).
cnf(c_0_2321,plain,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),hAPP(int,int,bit0,X1)))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),X1)) ),
inference(split_conjunct,[status(thm)],[c_0_1520]) ).
cnf(c_0_2322,plain,
( X1 = X2
| ~ hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X2),X1))
| ~ hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X1),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_1551]) ).
cnf(c_0_2323,plain,
( X1 = X2
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X2),X1))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_1552]) ).
cnf(c_0_2324,plain,
( X1 = X2
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X2),X1))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X1),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_1553]) ).
cnf(c_0_2325,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,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(nat,fun(nat,bool),ord_less(nat),X4),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_1554]) ).
cnf(c_0_2326,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
| ~ dense_linorder(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),esk24_3(X1,X3,X2)),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_1555]) ).
cnf(c_0_2327,plain,
( hBOOL(hAPP(int,bool,X1,hAPP(nat,int,semiring_1_of_nat(int),esk6_1(X1))))
| ~ hBOOL(hAPP(int,bool,X1,X2))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_1556]) ).
cnf(c_0_2328,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2))
| X1 = X2
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X3,X2),X1))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X2),X1)) ),
inference(split_conjunct,[status(thm)],[c_0_1399]) ).
cnf(c_0_2329,plain,
hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(int,int,plus_plus(int,one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),n)))),
inference(split_conjunct,[status(thm)],[c_0_1557]) ).
cnf(c_0_2330,plain,
number_number_of(int,hAPP(int,int,bit1,hAPP(int,int,bit1,pls))) = hAPP(nat,int,semiring_1_of_nat(int),number_number_of(nat,hAPP(int,int,bit1,hAPP(int,int,bit1,pls)))),
inference(split_conjunct,[status(thm)],[c_0_1558]) ).
cnf(c_0_2331,plain,
number_number_of(int,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))) = hAPP(nat,int,semiring_1_of_nat(int),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),
inference(split_conjunct,[status(thm)],[c_0_1559]) ).
cnf(c_0_2332,plain,
hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),m1),hAPP(int,int,plus_plus(int,one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),n)))),
inference(split_conjunct,[status(thm)],[c_0_1560]) ).
cnf(c_0_2333,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(nat,fun(nat,bool),ord_less(nat),X3),esk19_2(X2,X1))) ),
inference(split_conjunct,[status(thm)],[c_0_1561]) ).
cnf(c_0_2334,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(nat,fun(nat,bool),ord_less_eq(nat),X3),esk14_2(X2,X1))) ),
inference(split_conjunct,[status(thm)],[c_0_1562]) ).
cnf(c_0_2335,plain,
( hAPP(nat,int,semiring_1_of_nat(int),X1) = hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),hAPP(bool,fun(nat,fun(nat,nat)),if(nat),X2),X1),X3))
| ~ hBOOL(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1563]) ).
cnf(c_0_2336,plain,
( hAPP(nat,int,semiring_1_of_nat(int),X1) = hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),hAPP(bool,fun(nat,fun(nat,nat)),if(nat),X2),X3),X1))
| hBOOL(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1563]) ).
cnf(c_0_2337,plain,
( hBOOL(hAPP(int,bool,X3,X2))
| hBOOL(hAPP(int,bool,X3,esk18_3(X3,X1,X2)))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X1),X2))
| ~ hBOOL(hAPP(int,bool,X3,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_1446]) ).
cnf(c_0_2338,plain,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,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(int,fun(int,bool),ord_less(int),X2),pls)) ),
inference(split_conjunct,[status(thm)],[c_0_1564]) ).
cnf(c_0_2339,plain,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X2),X3))
| ~ linordered_idom(X1)
| ~ number_ring(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),number_number_of(X1,X2)),number_number_of(X1,X3))) ),
inference(split_conjunct,[status(thm)],[c_0_1565]) ).
cnf(c_0_2340,plain,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X2),X3))
| ~ linordered_idom(X1)
| ~ number_ring(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),number_number_of(X1,X2)),number_number_of(X1,X3))) ),
inference(split_conjunct,[status(thm)],[c_0_1566]) ).
cnf(c_0_2341,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),esk31_2(X1,X2)),X3))
| ~ linorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1567]) ).
cnf(c_0_2342,plain,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X2),pls))
| ~ linordered_idom(X1)
| ~ number_ring(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),number_number_of(X1,X2)),zero_zero(X1))) ),
inference(split_conjunct,[status(thm)],[c_0_1568]) ).
cnf(c_0_2343,plain,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X2),pls))
| ~ linordered_idom(X1)
| ~ number_ring(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),number_number_of(X1,X2)),zero_zero(X1))) ),
inference(split_conjunct,[status(thm)],[c_0_1569]) ).
cnf(c_0_2344,plain,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X1),X2))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),number_number_of(int,X1)),number_number_of(int,X2))) ),
inference(split_conjunct,[status(thm)],[c_0_1570]) ).
cnf(c_0_2345,plain,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X1),X2))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),number_number_of(nat,X1)),number_number_of(nat,X2))) ),
inference(split_conjunct,[status(thm)],[c_0_1477]) ).
cnf(c_0_2346,plain,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X1),X2))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),number_number_of(int,X1)),number_number_of(int,X2))) ),
inference(split_conjunct,[status(thm)],[c_0_1571]) ).
cnf(c_0_2347,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),number_number_of(X1,X2)),number_number_of(X1,X3)))
| ~ linordered_idom(X1)
| ~ number_ring(X1)
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X2),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_1565]) ).
cnf(c_0_2348,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),number_number_of(X1,X2)),number_number_of(X1,X3)))
| ~ linordered_idom(X1)
| ~ number_ring(X1)
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X2),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_1566]) ).
cnf(c_0_2349,plain,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),X2))
| ~ linordered_idom(X1)
| ~ number_ring(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),number_number_of(X1,X2))) ),
inference(split_conjunct,[status(thm)],[c_0_1572]) ).
cnf(c_0_2350,plain,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),X2))
| ~ linordered_idom(X1)
| ~ number_ring(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),number_number_of(X1,X2))) ),
inference(split_conjunct,[status(thm)],[c_0_1573]) ).
cnf(c_0_2351,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),esk30_2(X1,X3)))
| ~ linorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1574]) ).
cnf(c_0_2352,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),number_number_of(X1,X2)),zero_zero(X1)))
| ~ linordered_idom(X1)
| ~ number_ring(X1)
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X2),pls)) ),
inference(split_conjunct,[status(thm)],[c_0_1568]) ).
cnf(c_0_2353,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),number_number_of(X1,X2)),zero_zero(X1)))
| ~ linordered_idom(X1)
| ~ number_ring(X1)
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X2),pls)) ),
inference(split_conjunct,[status(thm)],[c_0_1569]) ).
cnf(c_0_2354,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| ~ linorder(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X2))
| ti(X1,X3) != ti(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_1575]) ).
cnf(c_0_2355,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X4))
| ti(X1,X3) != ti(X1,X4)
| ~ order(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1576]) ).
cnf(c_0_2356,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| ti(X1,X4) != ti(X1,X2)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X4),X3))
| ~ order(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1577]) ).
cnf(c_0_2357,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X2))
| ~ order(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
| ti(X1,X3) != ti(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_1536]) ).
cnf(c_0_2358,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X4))
| ti(X1,X3) != ti(X1,X4)
| ~ order(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1578]) ).
cnf(c_0_2359,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
| ti(X1,X4) != ti(X1,X2)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X4),X3))
| ~ order(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1579]) ).
cnf(c_0_2360,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),number_number_of(nat,X1)),number_number_of(nat,X2)))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X1),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_1499]) ).
cnf(c_0_2361,plain,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),number_number_of(int,X1)),number_number_of(int,X2)))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X1),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_1570]) ).
cnf(c_0_2362,plain,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),number_number_of(int,X1)),number_number_of(int,X2)))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X1),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_1571]) ).
cnf(c_0_2363,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),number_number_of(nat,X1)),number_number_of(nat,X2)))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X1),pls)) ),
inference(split_conjunct,[status(thm)],[c_0_1499]) ).
cnf(c_0_2364,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| ti(X1,X3) = ti(X1,X2)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
| ~ order(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1580]) ).
cnf(c_0_2365,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| ti(X1,X2) = ti(X1,X3)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
| ~ order(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1581]) ).
cnf(c_0_2366,plain,
( ti(X1,X2) = ti(X1,X3)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
| ~ order(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1582]) ).
cnf(c_0_2367,plain,
( ti(X1,X2) = ti(X1,X3)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| ~ linorder(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_1534]) ).
cnf(c_0_2368,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| ti(X1,X3) = ti(X1,X2)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
| ~ order(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1583]) ).
cnf(c_0_2369,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| ti(X1,X2) = ti(X1,X3)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
| ~ order(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1584]) ).
cnf(c_0_2370,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| ti(X1,X2) = ti(X1,X3)
| ~ linorder(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_1585]) ).
cnf(c_0_2371,plain,
( ti(X1,X2) = ti(X1,X3)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| ~ order(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_1586]) ).
cnf(c_0_2372,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| ti(X1,X2) = ti(X1,X3)
| ~ order(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_1587]) ).
cnf(c_0_2373,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),number_number_of(X1,X2)))
| ~ linordered_idom(X1)
| ~ number_ring(X1)
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_1572]) ).
cnf(c_0_2374,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),number_number_of(X1,X2)))
| ~ linordered_idom(X1)
| ~ number_ring(X1)
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_1573]) ).
cnf(c_0_2375,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X4),X3))
| X2 != X4
| ~ ord(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1588]) ).
cnf(c_0_2376,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| X4 != X3
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X4))
| ~ ord(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1589]) ).
cnf(c_0_2377,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X4),X3))
| X2 != X4
| ~ ord(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1590]) ).
cnf(c_0_2378,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
| X4 != X3
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X4))
| ~ ord(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1591]) ).
cnf(c_0_2379,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| ~ preorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1592]) ).
cnf(c_0_2380,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
| ~ order(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_1586]) ).
cnf(c_0_2381,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
| ~ preorder(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_1504]) ).
cnf(c_0_2382,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
| ~ order(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_1587]) ).
cnf(c_0_2383,plain,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),X1))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),number_number_of(nat,X1))) ),
inference(split_conjunct,[status(thm)],[c_0_1593]) ).
cnf(c_0_2384,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),esk3_2(X1,X2)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_1594]) ).
cnf(c_0_2385,plain,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X3))
| ~ hBOOL(X1)
| ~ hBOOL(X2)
| ~ hBOOL(X2)
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_1509]) ).
cnf(c_0_2386,plain,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X3))
| ~ hBOOL(X1)
| ~ hBOOL(X2)
| ~ hBOOL(X1)
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_1509]) ).
cnf(c_0_2387,plain,
( hBOOL(X1)
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X3))
| ~ hBOOL(X1)
| ~ hBOOL(X2)
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_1510]) ).
cnf(c_0_2388,plain,
( hBOOL(X2)
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X3))
| ~ hBOOL(X1)
| ~ hBOOL(X2)
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_1510]) ).
cnf(c_0_2389,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),number_number_of(nat,X1)))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),X1)) ),
inference(split_conjunct,[status(thm)],[c_0_1593]) ).
cnf(c_0_2390,plain,
( hBOOL(X1)
| hBOOL(X2)
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X3))
| ~ hBOOL(X2)
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_1509]) ).
cnf(c_0_2391,plain,
( hBOOL(X1)
| hBOOL(X2)
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X3))
| ~ hBOOL(X1)
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_1509]) ).
cnf(c_0_2392,plain,
( hBOOL(X1)
| hBOOL(X2)
| hBOOL(X1)
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X3))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_1510]) ).
cnf(c_0_2393,plain,
( hBOOL(X1)
| hBOOL(X2)
| hBOOL(X2)
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X3))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_1510]) ).
cnf(c_0_2394,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),esk2_1(X1)))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),X1)) ),
inference(split_conjunct,[status(thm)],[c_0_1595]) ).
cnf(c_0_2395,plain,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X1))
| hBOOL(X2)
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X1))
| ~ hBOOL(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1510]) ).
cnf(c_0_2396,plain,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X1))
| hBOOL(X2)
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X1))
| ~ hBOOL(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1510]) ).
cnf(c_0_2397,plain,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X1))
| hBOOL(X3)
| ~ hBOOL(X2)
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X1)) ),
inference(split_conjunct,[status(thm)],[c_0_1509]) ).
cnf(c_0_2398,plain,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X1))
| hBOOL(X3)
| ~ hBOOL(X2)
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X1)) ),
inference(split_conjunct,[status(thm)],[c_0_1509]) ).
cnf(c_0_2399,plain,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),X1))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),one_one(int)),X1)) ),
inference(split_conjunct,[status(thm)],[c_0_1596]) ).
cnf(c_0_2400,plain,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),one_one(int)),X1))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),X1)) ),
inference(split_conjunct,[status(thm)],[c_0_1596]) ).
cnf(c_0_2401,plain,
( hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X1),X2))
| X1 = X2
| ~ hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X1),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_1597]) ).
cnf(c_0_2402,plain,
( X1 = X2
| hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X1),X2))
| ~ hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X1),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_1598]) ).
cnf(c_0_2403,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2))
| X1 = X2
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_1599]) ).
cnf(c_0_2404,plain,
( X1 = X2
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_1600]) ).
cnf(c_0_2405,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2))
| X1 = X2
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_1601]) ).
cnf(c_0_2406,plain,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X1),X2))
| X1 = X2
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X1),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_1602]) ).
cnf(c_0_2407,plain,
( hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X1),X2))
| ~ hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X1),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_1597]) ).
cnf(c_0_2408,plain,
( hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X1),X2))
| ~ hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X1),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_1598]) ).
cnf(c_0_2409,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_1599]) ).
cnf(c_0_2410,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_1600]) ).
cnf(c_0_2411,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_1603]) ).
cnf(c_0_2412,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_1604]) ).
cnf(c_0_2413,plain,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X1),X2))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X1),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_1602]) ).
cnf(c_0_2414,plain,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,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(int,fun(int,bool),ord_less(int),X2),pls)) ),
inference(split_conjunct,[status(thm)],[c_0_1564]) ).
cnf(c_0_2415,plain,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),esk7_1(X1)))
| ~ hBOOL(hAPP(int,bool,X1,hAPP(nat,int,semiring_1_of_nat(int),X2))) ),
inference(split_conjunct,[status(thm)],[c_0_1556]) ).
cnf(c_0_2416,plain,
( hAPP(X1,X1,plus_plus(X1,hAPP(X1,X1,plus_plus(X1,X2),X3)),hAPP(X1,X1,plus_plus(X1,X4),X5)) = hAPP(X1,X1,plus_plus(X1,hAPP(X1,X1,plus_plus(X1,X2),X4)),hAPP(X1,X1,plus_plus(X1,X3),X5))
| ~ comm_semiring_1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1605]) ).
cnf(c_0_2417,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),esk24_3(X1,X3,X2)),X2))
| ~ dense_linorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1555]) ).
cnf(c_0_2418,plain,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(nat,int,semiring_1_of_nat(int),X1)),zero_zero(int)))
| X1 != zero_zero(nat) ),
inference(split_conjunct,[status(thm)],[c_0_1514]) ).
cnf(c_0_2419,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),number_number_of(X1,X2)),number_number_of(X1,X3)))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),number_number_of(X1,X3)),number_number_of(X1,X2)))
| ~ linorder(X1)
| ~ number(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1521]) ).
cnf(c_0_2420,plain,
hAPP(int,int,plus_plus(int,hAPP(int,int,bit1,X1)),hAPP(int,int,bit1,X2)) = hAPP(int,int,bit0,hAPP(int,int,plus_plus(int,X1),hAPP(int,int,succ,X2))),
inference(split_conjunct,[status(thm)],[c_0_1606]) ).
cnf(c_0_2421,plain,
( hAPP(X1,X1,plus_plus(X1,number_number_of(X1,X2)),hAPP(X1,X1,plus_plus(X1,number_number_of(X1,X3)),X4)) = hAPP(X1,X1,plus_plus(X1,number_number_of(X1,hAPP(int,int,plus_plus(int,X2),X3))),X4)
| ~ number_ring(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1607]) ).
cnf(c_0_2422,plain,
( X3 = X4
| ~ linordered_semidom(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),one_one(X1)),X2))
| hAPP(nat,X1,power_power(X1,X2),X3) != hAPP(nat,X1,power_power(X1,X2),X4) ),
inference(split_conjunct,[status(thm)],[c_0_1608]) ).
cnf(c_0_2423,plain,
( hAPP(X1,X1,plus_plus(X1,number_number_of(X1,X2)),one_one(X1)) = number_number_of(X1,hAPP(int,int,succ,X2))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),X2))
| ~ number_semiring(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1609]) ).
cnf(c_0_2424,plain,
( X1 = hAPP(int,int,plus_plus(int,X2),hAPP(nat,int,semiring_1_of_nat(int),esk10_2(X2,X1)))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X2),X1)) ),
inference(split_conjunct,[status(thm)],[c_0_1610]) ).
cnf(c_0_2425,plain,
( hAPP(X1,X1,plus_plus(X1,one_one(X1)),number_number_of(X1,X2)) = number_number_of(X1,hAPP(int,int,succ,X2))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),X2))
| ~ number_semiring(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1611]) ).
cnf(c_0_2426,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
| ~ linorder(X1)
| ti(X1,X2) != ti(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_1585]) ).
cnf(c_0_2427,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X2))
| ti(X1,X3) = ti(X1,X2)
| ~ linorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1612]) ).
cnf(c_0_2428,plain,
( ti(X1,X2) = ti(X1,X3)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X2))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| ~ linorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1544]) ).
cnf(c_0_2429,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| ti(X1,X3) = ti(X1,X2)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X2))
| ~ linorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1613]) ).
cnf(c_0_2430,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| ti(X1,X3) = ti(X1,X2)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X2))
| ~ linorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1575]) ).
cnf(c_0_2431,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X2))
| ti(X1,X3) = ti(X1,X2)
| ~ linorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1614]) ).
cnf(c_0_2432,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| ti(X1,X3) = ti(X1,X2)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X2))
| ~ linorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1615]) ).
cnf(c_0_2433,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X2))
| ti(X1,X3) = ti(X1,X2)
| ~ linordered_idom(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1616]) ).
cnf(c_0_2434,plain,
( hAPP(nat,X1,power_power(X1,X2),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) = zero_zero(X1)
| ~ ring_11004092258visors(X1)
| ti(X1,X2) != zero_zero(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1539]) ).
cnf(c_0_2435,plain,
( hAPP(nat,X1,power_power(X1,zero_zero(X1)),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) = zero_zero(X1)
| ~ semiring_1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1617]) ).
cnf(c_0_2436,plain,
( hAPP(nat,X1,power_power(X1,one_one(X1)),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) = one_one(X1)
| ~ semiring_1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1618]) ).
cnf(c_0_2437,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X2))
| ~ linorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1619]) ).
cnf(c_0_2438,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X2))
| ~ linorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1620]) ).
cnf(c_0_2439,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X2))
| ~ linorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1621]) ).
cnf(c_0_2440,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X2))
| ~ linorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1542]) ).
cnf(c_0_2441,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X2))
| ~ linorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1543]) ).
cnf(c_0_2442,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X2))
| ~ linorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1622]) ).
cnf(c_0_2443,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X2))
| ~ linorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1623]) ).
cnf(c_0_2444,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X2),X1))
| X2 = X1 ),
inference(split_conjunct,[status(thm)],[c_0_1624]) ).
cnf(c_0_2445,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X2),X1))
| X2 = X1 ),
inference(split_conjunct,[status(thm)],[c_0_1625]) ).
cnf(c_0_2446,plain,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X1),X2))
| X2 = X1
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X2),X1)) ),
inference(split_conjunct,[status(thm)],[c_0_1626]) ).
cnf(c_0_2447,plain,
( hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X1),X2))
| hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X2),X1)) ),
inference(split_conjunct,[status(thm)],[c_0_1627]) ).
cnf(c_0_2448,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X2),X1)) ),
inference(split_conjunct,[status(thm)],[c_0_1628]) ).
cnf(c_0_2449,plain,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X1),X2))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X2),X1)) ),
inference(split_conjunct,[status(thm)],[c_0_1629]) ).
cnf(c_0_2450,plain,
( hAPP(nat,X1,power_power(X1,X2),X3) = hAPP(nat,X1,power_power(X1,X2),X4)
| ~ linordered_semidom(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),one_one(X1)),X2))
| X3 != X4 ),
inference(split_conjunct,[status(thm)],[c_0_1608]) ).
cnf(c_0_2451,plain,
( hBOOL(hAPP(int,bool,X1,hAPP(nat,int,semiring_1_of_nat(int),X2)))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),esk8_1(X1))) ),
inference(split_conjunct,[status(thm)],[c_0_1522]) ).
cnf(c_0_2452,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_1562]) ).
cnf(c_0_2453,plain,
( hBOOL(hAPP(nat,bool,X1,zero_zero(nat)))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),esk19_2(X2,X1)),X2))
| ~ hBOOL(hAPP(nat,bool,X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_1561]) ).
cnf(c_0_2454,plain,
( hBOOL(hAPP(nat,bool,X1,zero_zero(nat)))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),esk14_2(X2,X1)),X2))
| ~ hBOOL(hAPP(nat,bool,X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_1562]) ).
cnf(c_0_2455,plain,
( hAPP(real,real,sqrt,X1) != zero_zero(real)
| ~ hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X1)) ),
inference(split_conjunct,[status(thm)],[c_0_1630]) ).
cnf(c_0_2456,plain,
( hAPP(nat,X1,semiring_1_of_nat(X1),number_number_of(nat,X2)) = number_number_of(X1,X2)
| ~ number_ring(X1)
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),number_number_of(int,X2))) ),
inference(split_conjunct,[status(thm)],[c_0_1631]) ).
cnf(c_0_2457,plain,
( hBOOL(hAPP(int,bool,X1,esk7_1(X1)))
| ~ hBOOL(hAPP(int,bool,X1,hAPP(nat,int,semiring_1_of_nat(int),X2))) ),
inference(split_conjunct,[status(thm)],[c_0_1556]) ).
cnf(c_0_2458,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(int,fun(int,bool),ord_less(int),X1),pls)) ),
inference(split_conjunct,[status(thm)],[c_0_1564]) ).
cnf(c_0_2459,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),hAPP(X1,X1,plus_plus(X1,one_one(X1)),one_one(X1))))
| ~ linordered_semidom(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1632]) ).
cnf(c_0_2460,plain,
( hAPP(X1,X1,plus_plus(X1,one_one(X1)),number_number_of(X1,X2)) = number_number_of(X1,hAPP(int,int,plus_plus(int,hAPP(int,int,bit1,pls)),X2))
| ~ number_ring(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1633]) ).
cnf(c_0_2461,plain,
( hAPP(nat,nat,plus_plus(nat,number_number_of(nat,X1)),one_one(nat)) = one_one(nat)
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X1),pls)) ),
inference(split_conjunct,[status(thm)],[c_0_1634]) ).
cnf(c_0_2462,plain,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X1),X2))
| X2 != hAPP(int,int,plus_plus(int,X1),hAPP(nat,int,semiring_1_of_nat(int),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_1610]) ).
cnf(c_0_2463,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,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_1495]) ).
cnf(c_0_2464,plain,
( X1 = hAPP(nat,nat,plus_plus(nat,X2),esk13_2(X2,X1))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X2),X1)) ),
inference(split_conjunct,[status(thm)],[c_0_1635]) ).
cnf(c_0_2465,plain,
( hAPP(nat,nat,plus_plus(nat,X1),esk3_2(X1,X2)) = X2
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_1594]) ).
cnf(c_0_2466,plain,
( hAPP(nat,nat,plus_plus(nat,one_one(nat)),number_number_of(nat,X1)) = one_one(nat)
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X1),pls)) ),
inference(split_conjunct,[status(thm)],[c_0_1636]) ).
cnf(c_0_2467,plain,
( hAPP(X1,X1,plus_plus(X1,hAPP(X1,X1,plus_plus(X1,X2),X3)),X4) = hAPP(X1,X1,plus_plus(X1,hAPP(X1,X1,plus_plus(X1,X2),X4)),X3)
| ~ comm_semiring_1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1637]) ).
cnf(c_0_2468,plain,
( X1 = hAPP(nat,int,semiring_1_of_nat(int),esk15_1(X1))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X1)) ),
inference(split_conjunct,[status(thm)],[c_0_1638]) ).
cnf(c_0_2469,plain,
( X1 = hAPP(nat,int,semiring_1_of_nat(int),esk12_1(X1))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X1)) ),
inference(split_conjunct,[status(thm)],[c_0_1639]) ).
cnf(c_0_2470,plain,
( X1 = hAPP(nat,int,semiring_1_of_nat(int),esk11_1(X1))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X1)) ),
inference(split_conjunct,[status(thm)],[c_0_1640]) ).
cnf(c_0_2471,plain,
( X1 = hAPP(nat,int,semiring_1_of_nat(int),esk2_1(X1))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),X1)) ),
inference(split_conjunct,[status(thm)],[c_0_1595]) ).
cnf(c_0_2472,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),hAPP(X1,X1,plus_plus(X1,X2),one_one(X1))))
| ~ linordered_semidom(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1641]) ).
cnf(c_0_2473,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,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_1500]) ).
cnf(c_0_2474,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,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_1501]) ).
cnf(c_0_2475,plain,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X1),hAPP(int,int,plus_plus(int,X2),one_one(int))))
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[c_0_1502]) ).
cnf(c_0_2476,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),hAPP(nat,X1,semiring_1_of_nat(X1),X2)))
| ~ linordered_semidom(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1642]) ).
cnf(c_0_2477,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),hAPP(nat,X1,semiring_1_of_nat(X1),X2)))
| ~ linordered_semidom(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1643]) ).
cnf(c_0_2478,plain,
hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),hAPP(nat,nat,plus_plus(nat,X1),X2))),
inference(split_conjunct,[status(thm)],[c_0_1644]) ).
cnf(c_0_2479,plain,
hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),hAPP(nat,nat,plus_plus(nat,X2),X1))),
inference(split_conjunct,[status(thm)],[c_0_1645]) ).
cnf(c_0_2480,plain,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),one_one(X1)),zero_zero(X1)))
| ~ linordered_semidom(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1646]) ).
cnf(c_0_2481,plain,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),one_one(X1)),zero_zero(X1)))
| ~ linordered_semidom(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1647]) ).
cnf(c_0_2482,plain,
( hAPP(nat,X1,semiring_1_of_nat(X1),hAPP(nat,nat,plus_plus(nat,X2),X3)) = hAPP(X1,X1,plus_plus(X1,hAPP(nat,X1,semiring_1_of_nat(X1),X2)),hAPP(nat,X1,semiring_1_of_nat(X1),X3))
| ~ semiring_1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1648]) ).
cnf(c_0_2483,plain,
hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(nat,int,semiring_1_of_nat(int),X1))),
inference(split_conjunct,[status(thm)],[c_0_1649]) ).
cnf(c_0_2484,plain,
hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(nat,int,semiring_1_of_nat(int),X1))),
inference(split_conjunct,[status(thm)],[c_0_1650]) ).
cnf(c_0_2485,plain,
( ~ order(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| ti(X1,X2) != ti(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_1587]) ).
cnf(c_0_2486,plain,
( ~ linorder(X1)
| ti(X1,X2) != ti(X1,X3)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_1612]) ).
cnf(c_0_2487,plain,
( ~ linorder(X1)
| ti(X1,X2) != ti(X1,X3)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_1612]) ).
cnf(c_0_2488,plain,
( ~ linorder(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| ti(X1,X2) != ti(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_1544]) ).
cnf(c_0_2489,plain,
( ti(X1,X2) != ti(X1,X3)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| ~ order(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1651]) ).
cnf(c_0_2490,plain,
( ti(X1,X2) != ti(X1,X3)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| ~ order(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1652]) ).
cnf(c_0_2491,plain,
( ti(X1,X2) != ti(X1,X3)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X2))
| ~ order(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1653]) ).
cnf(c_0_2492,plain,
hAPP(int,int,plus_plus(int,hAPP(nat,int,semiring_1_of_nat(int),X1)),hAPP(nat,int,semiring_1_of_nat(int),X2)) = hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,plus_plus(nat,X1),X2)),
inference(split_conjunct,[status(thm)],[c_0_1654]) ).
cnf(c_0_2493,plain,
hAPP(int,int,plus_plus(int,hAPP(nat,int,semiring_1_of_nat(int),X1)),hAPP(nat,int,semiring_1_of_nat(int),X2)) = hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,plus_plus(nat,X1),X2)),
inference(split_conjunct,[status(thm)],[c_0_1655]) ).
cnf(c_0_2494,plain,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X2))
| ~ preorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1656]) ).
cnf(c_0_2495,plain,
( hBOOL(X1)
| ~ hBOOL(X1)
| ~ hBOOL(X2)
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X3))
| ~ hBOOL(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1510]) ).
cnf(c_0_2496,plain,
( hBOOL(X2)
| ~ hBOOL(X1)
| ~ hBOOL(X2)
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X3))
| ~ hBOOL(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1510]) ).
cnf(c_0_2497,plain,
( hBOOL(X1)
| ~ hBOOL(X1)
| ~ hBOOL(X2)
| ~ hBOOL(X2)
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_1509]) ).
cnf(c_0_2498,plain,
( hBOOL(X2)
| ~ hBOOL(X1)
| ~ hBOOL(X2)
| ~ hBOOL(X1)
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_1509]) ).
cnf(c_0_2499,plain,
( hBOOL(X1)
| hBOOL(X2)
| hBOOL(X1)
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X3))
| ~ hBOOL(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1510]) ).
cnf(c_0_2500,plain,
( hBOOL(X1)
| hBOOL(X2)
| hBOOL(X2)
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X3))
| ~ hBOOL(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1510]) ).
cnf(c_0_2501,plain,
( hBOOL(X1)
| hBOOL(X2)
| hBOOL(X1)
| ~ hBOOL(X2)
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_1509]) ).
cnf(c_0_2502,plain,
( hBOOL(X1)
| hBOOL(X2)
| hBOOL(X2)
| ~ hBOOL(X1)
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_1509]) ).
cnf(c_0_2503,plain,
hAPP(int,int,plus_plus(int,hAPP(int,int,bit0,X1)),hAPP(int,int,bit1,X2)) = hAPP(int,int,bit1,hAPP(int,int,plus_plus(int,X1),X2)),
inference(split_conjunct,[status(thm)],[c_0_1657]) ).
cnf(c_0_2504,plain,
hAPP(int,int,plus_plus(int,hAPP(int,int,bit1,X1)),hAPP(int,int,bit0,X2)) = hAPP(int,int,bit1,hAPP(int,int,plus_plus(int,X1),X2)),
inference(split_conjunct,[status(thm)],[c_0_1658]) ).
cnf(c_0_2505,plain,
hAPP(int,int,plus_plus(int,hAPP(int,int,bit0,X1)),hAPP(int,int,bit0,X2)) = hAPP(int,int,bit0,hAPP(int,int,plus_plus(int,X1),X2)),
inference(split_conjunct,[status(thm)],[c_0_1659]) ).
cnf(c_0_2506,plain,
( X1 != zero_zero(nat)
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X1)) ),
inference(split_conjunct,[status(thm)],[c_0_1660]) ).
cnf(c_0_2507,plain,
( X1 = zero_zero(nat)
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),zero_zero(nat))) ),
inference(split_conjunct,[status(thm)],[c_0_1661]) ).
cnf(c_0_2508,plain,
( number_number_of(nat,X1) = zero_zero(nat)
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X1),pls)) ),
inference(split_conjunct,[status(thm)],[c_0_1662]) ).
cnf(c_0_2509,plain,
( zero_zero(nat) = number_number_of(nat,X1)
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X1),pls)) ),
inference(split_conjunct,[status(thm)],[c_0_1663]) ).
cnf(c_0_2510,plain,
~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),zero_zero(nat))),
inference(split_conjunct,[status(thm)],[c_0_1664]) ).
cnf(c_0_2511,plain,
~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),zero_zero(nat))),
inference(split_conjunct,[status(thm)],[c_0_1665]) ).
cnf(c_0_2512,plain,
~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),zero_zero(nat))),
inference(split_conjunct,[status(thm)],[c_0_1666]) ).
cnf(c_0_2513,plain,
( X1 != zero_zero(nat)
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X2),X1)) ),
inference(split_conjunct,[status(thm)],[c_0_1667]) ).
cnf(c_0_2514,plain,
( ~ hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X1),X2))
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[c_0_1597]) ).
cnf(c_0_2515,plain,
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2))
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[c_0_1599]) ).
cnf(c_0_2516,plain,
( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X1),X2))
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[c_0_1602]) ).
cnf(c_0_2517,plain,
( X1 != X2
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_1668]) ).
cnf(c_0_2518,plain,
( X1 != X2
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X2),X1)) ),
inference(split_conjunct,[status(thm)],[c_0_1669]) ).
cnf(c_0_2519,plain,
( X1 != X2
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_1625]) ).
cnf(c_0_2520,plain,
( X1 != X2
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X2),X1)) ),
inference(split_conjunct,[status(thm)],[c_0_1625]) ).
cnf(c_0_2521,plain,
~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X1)),
inference(split_conjunct,[status(thm)],[c_0_1670]) ).
cnf(c_0_2522,plain,
~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X1)),
inference(split_conjunct,[status(thm)],[c_0_1671]) ).
cnf(c_0_2523,plain,
~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),zero_zero(int))),
inference(split_conjunct,[status(thm)],[c_0_1672]) ).
cnf(c_0_2524,plain,
~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),pls)),
inference(split_conjunct,[status(thm)],[c_0_1673]) ).
cnf(c_0_2525,plain,
( hAPP(nat,nat,plus_plus(nat,number_number_of(nat,X1)),one_one(nat)) = number_number_of(nat,hAPP(int,int,succ,X1))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X1),pls)) ),
inference(split_conjunct,[status(thm)],[c_0_1634]) ).
cnf(c_0_2526,plain,
( hAPP(nat,nat,plus_plus(nat,one_one(nat)),number_number_of(nat,X1)) = number_number_of(nat,hAPP(int,int,succ,X1))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X1),pls)) ),
inference(split_conjunct,[status(thm)],[c_0_1636]) ).
cnf(c_0_2527,plain,
( hBOOL(hAPP(int,bool,X1,hAPP(nat,int,semiring_1_of_nat(int),X2)))
| ~ hBOOL(hAPP(int,bool,X1,esk8_1(X1))) ),
inference(split_conjunct,[status(thm)],[c_0_1522]) ).
cnf(c_0_2528,plain,
( hAPP(X1,X1,plus_plus(X1,X2),hAPP(X1,X1,plus_plus(X1,X3),X4)) = hAPP(X1,X1,plus_plus(X1,hAPP(X1,X1,plus_plus(X1,X2),X3)),X4)
| ~ comm_semiring_1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1674]) ).
cnf(c_0_2529,plain,
( hAPP(X1,X1,plus_plus(X1,hAPP(X1,X1,plus_plus(X1,X2),X3)),X4) = hAPP(X1,X1,plus_plus(X1,X2),hAPP(X1,X1,plus_plus(X1,X3),X4))
| ~ comm_semiring_1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1675]) ).
cnf(c_0_2530,plain,
( hAPP(X1,X1,plus_plus(X1,hAPP(X1,X1,plus_plus(X1,X2),X3)),X4) = hAPP(X1,X1,plus_plus(X1,X2),hAPP(X1,X1,plus_plus(X1,X3),X4))
| ~ ab_semigroup_add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1676]) ).
cnf(c_0_2531,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_1677]) ).
cnf(c_0_2532,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_1678]) ).
cnf(c_0_2533,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_1679]) ).
cnf(c_0_2534,plain,
hAPP(X1,X1,hAPP(X1,fun(X1,X1),hAPP(bool,fun(X1,fun(X1,X1)),if(X1),fFalse),X2),X3) = ti(X1,X3),
inference(split_conjunct,[status(thm)],[c_0_1680]) ).
cnf(c_0_2535,plain,
hAPP(X1,X1,hAPP(X1,fun(X1,X1),hAPP(bool,fun(X1,fun(X1,X1)),if(X1),fTrue),X2),X3) = ti(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_1681]) ).
cnf(c_0_2536,plain,
( hAPP(nat,X1,semiring_1_of_nat(X1),hAPP(nat,nat,power_power(nat,X2),X3)) = hAPP(nat,X1,power_power(X1,hAPP(nat,X1,semiring_1_of_nat(X1),X2)),X3)
| ~ semiring_1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1682]) ).
cnf(c_0_2537,plain,
( number_number_of(X1,hAPP(int,int,bit1,X2)) = hAPP(X1,X1,plus_plus(X1,hAPP(X1,X1,plus_plus(X1,one_one(X1)),number_number_of(X1,X2))),number_number_of(X1,X2))
| ~ number_ring(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1683]) ).
cnf(c_0_2538,plain,
( number_number_of(X1,hAPP(int,int,bit0,X2)) = hAPP(X1,X1,plus_plus(X1,hAPP(X1,X1,plus_plus(X1,zero_zero(X1)),number_number_of(X1,X2))),number_number_of(X1,X2))
| ~ number_ring(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1684]) ).
cnf(c_0_2539,plain,
hAPP(nat,int,power_power(int,hAPP(nat,int,semiring_1_of_nat(int),X1)),X2) = hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,power_power(nat,X1),X2)),
inference(split_conjunct,[status(thm)],[c_0_1685]) ).
cnf(c_0_2540,plain,
hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,power_power(nat,X1),X2)) = hAPP(nat,int,power_power(int,hAPP(nat,int,semiring_1_of_nat(int),X1)),X2),
inference(split_conjunct,[status(thm)],[c_0_1686]) ).
cnf(c_0_2541,plain,
hAPP(nat,int,power_power(int,hAPP(nat,int,semiring_1_of_nat(int),X1)),X2) = hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,power_power(nat,X1),X2)),
inference(split_conjunct,[status(thm)],[c_0_1687]) ).
cnf(c_0_2542,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2))
| X2 != hAPP(nat,nat,plus_plus(nat,X1),X3) ),
inference(split_conjunct,[status(thm)],[c_0_1635]) ).
cnf(c_0_2543,plain,
( hAPP(nat,X1,semiring_1_of_nat(X1),number_number_of(nat,X2)) = zero_zero(X1)
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),number_number_of(int,X2)))
| ~ number_ring(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1631]) ).
cnf(c_0_2544,plain,
( hAPP(X1,X1,plus_plus(X1,number_number_of(X1,X2)),one_one(X1)) = number_number_of(X1,hAPP(int,int,plus_plus(int,X2),hAPP(int,int,bit1,pls)))
| ~ number_ring(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1688]) ).
cnf(c_0_2545,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_1561]) ).
cnf(c_0_2546,plain,
( hAPP(X1,X1,plus_plus(X1,one_one(X1)),one_one(X1)) = number_number_of(X1,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))
| ~ number_semiring(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1689]) ).
cnf(c_0_2547,plain,
( hAPP(X1,X1,plus_plus(X1,one_one(X1)),one_one(X1)) = number_number_of(X1,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))
| ~ number_ring(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1690]) ).
cnf(c_0_2548,plain,
hAPP(nat,nat,plus_plus(nat,one_one(nat)),one_one(nat)) = number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))),
inference(split_conjunct,[status(thm)],[c_0_1691]) ).
cnf(c_0_2549,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
| ~ order(X1)
| ti(X1,X2) != ti(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_1586]) ).
cnf(c_0_2550,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
| ~ order(X1)
| ti(X1,X2) != ti(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_1535]) ).
cnf(c_0_2551,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X2))
| ~ order(X1)
| ti(X1,X2) != ti(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_1535]) ).
cnf(c_0_2552,plain,
( hAPP(X1,X1,plus_plus(X1,X2),hAPP(X1,X1,plus_plus(X1,X3),X4)) = hAPP(X1,X1,plus_plus(X1,X3),hAPP(X1,X1,plus_plus(X1,X2),X4))
| ~ comm_semiring_1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1692]) ).
cnf(c_0_2553,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),one_one(X1)))
| ~ linordered_semidom(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1693]) ).
cnf(c_0_2554,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),one_one(X1)))
| ~ linordered_semidom(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1694]) ).
cnf(c_0_2555,plain,
hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),number_number_of(int,pls))),
inference(split_conjunct,[status(thm)],[c_0_1695]) ).
cnf(c_0_2556,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
| X2 != X3
| ~ preorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1696]) ).
cnf(c_0_2557,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X2))
| ~ preorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1697]) ).
cnf(c_0_2558,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_1698]) ).
cnf(c_0_2559,plain,
hAPP(int,int,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_1699]) ).
cnf(c_0_2560,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_1700]) ).
cnf(c_0_2561,plain,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X1),pls))
| number_number_of(nat,X1) != zero_zero(nat) ),
inference(split_conjunct,[status(thm)],[c_0_1662]) ).
cnf(c_0_2562,plain,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X1),pls))
| zero_zero(nat) != number_number_of(nat,X1) ),
inference(split_conjunct,[status(thm)],[c_0_1663]) ).
cnf(c_0_2563,plain,
hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),one_one(int))),
inference(split_conjunct,[status(thm)],[c_0_1701]) ).
cnf(c_0_2564,plain,
hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),zero_zero(int))),
inference(split_conjunct,[status(thm)],[c_0_1702]) ).
cnf(c_0_2565,plain,
hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),one_one(int))),
inference(split_conjunct,[status(thm)],[c_0_1703]) ).
cnf(c_0_2566,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X1))
| X1 = zero_zero(nat) ),
inference(split_conjunct,[status(thm)],[c_0_1660]) ).
cnf(c_0_2567,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X1))
| X1 = zero_zero(nat) ),
inference(split_conjunct,[status(thm)],[c_0_1704]) ).
cnf(c_0_2568,plain,
hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),zero_zero(nat)),X1)),
inference(split_conjunct,[status(thm)],[c_0_1705]) ).
cnf(c_0_2569,plain,
hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),zero_zero(nat)),X1)),
inference(split_conjunct,[status(thm)],[c_0_1706]) ).
cnf(c_0_2570,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),zero_zero(nat)))
| X1 != zero_zero(nat) ),
inference(split_conjunct,[status(thm)],[c_0_1661]) ).
cnf(c_0_2571,plain,
hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),one_one(int)),t)),
inference(split_conjunct,[status(thm)],[c_0_1707]) ).
cnf(c_0_2572,plain,
hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),tn)),
inference(split_conjunct,[status(thm)],[c_0_1708]) ).
cnf(c_0_2573,plain,
hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),n)),
inference(split_conjunct,[status(thm)],[c_0_1709]) ).
cnf(c_0_2574,plain,
hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),t)),
inference(split_conjunct,[status(thm)],[c_0_1710]) ).
cnf(c_0_2575,plain,
( hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X1),X2))
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[c_0_1598]) ).
cnf(c_0_2576,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2))
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[c_0_1711]) ).
cnf(c_0_2577,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2))
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[c_0_1600]) ).
cnf(c_0_2578,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2))
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[c_0_1604]) ).
cnf(c_0_2579,plain,
hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X1),X1)),
inference(split_conjunct,[status(thm)],[c_0_1712]) ).
cnf(c_0_2580,plain,
hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X1)),
inference(split_conjunct,[status(thm)],[c_0_1713]) ).
cnf(c_0_2581,plain,
hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X1),X1)),
inference(split_conjunct,[status(thm)],[c_0_1714]) ).
cnf(c_0_2582,plain,
hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),pls)),
inference(split_conjunct,[status(thm)],[c_0_1715]) ).
cnf(c_0_2583,plain,
hAPP(int,int,succ,hAPP(int,int,bit1,X1)) = hAPP(int,int,bit0,hAPP(int,int,succ,X1)),
inference(split_conjunct,[status(thm)],[c_0_1716]) ).
cnf(c_0_2584,plain,
ti(fun(X1,fun(X1,X1)),hAPP(bool,fun(X1,fun(X1,X1)),X2,X3)) = hAPP(bool,fun(X1,fun(X1,X1)),X2,X3),
inference(split_conjunct,[status(thm)],[c_0_1717]) ).
cnf(c_0_2585,plain,
hAPP(bool,fun(X1,fun(X1,X1)),ti(fun(bool,fun(X1,fun(X1,X1))),X2),X3) = hAPP(bool,fun(X1,fun(X1,X1)),X2,X3),
inference(split_conjunct,[status(thm)],[c_0_1718]) ).
cnf(c_0_2586,plain,
hAPP(int,int,succ,hAPP(int,int,bit0,X1)) = hAPP(int,int,bit1,X1),
inference(split_conjunct,[status(thm)],[c_0_1719]) ).
cnf(c_0_2587,plain,
( number_number_of(X1,hAPP(int,int,plus_plus(int,X2),X3)) = hAPP(X1,X1,plus_plus(X1,number_number_of(X1,X2)),number_number_of(X1,X3))
| ~ number_ring(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1720]) ).
cnf(c_0_2588,plain,
( hAPP(X1,X1,plus_plus(X1,number_number_of(X1,X2)),number_number_of(X1,X3)) = number_number_of(X1,hAPP(int,int,plus_plus(int,X2),X3))
| ~ number_ring(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1721]) ).
cnf(c_0_2589,plain,
( ti(X1,X2) = ti(X1,X3)
| ~ cancel_semigroup_add(X1)
| hAPP(X1,X1,plus_plus(X1,X4),X2) != hAPP(X1,X1,plus_plus(X1,X4),X3) ),
inference(split_conjunct,[status(thm)],[c_0_1722]) ).
cnf(c_0_2590,plain,
( ti(X1,X2) = ti(X1,X3)
| ~ cancel_semigroup_add(X1)
| hAPP(X1,X1,plus_plus(X1,X2),X4) != hAPP(X1,X1,plus_plus(X1,X3),X4) ),
inference(split_conjunct,[status(thm)],[c_0_1723]) ).
cnf(c_0_2591,plain,
( ti(X1,X2) = ti(X1,X3)
| hAPP(X1,X1,plus_plus(X1,X4),X2) != hAPP(X1,X1,plus_plus(X1,X4),X3)
| ~ cancel_semigroup_add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1724]) ).
cnf(c_0_2592,plain,
( ti(X1,X2) = ti(X1,X3)
| hAPP(X1,X1,plus_plus(X1,X4),X2) != hAPP(X1,X1,plus_plus(X1,X4),X3)
| ~ cancel146912293up_add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1725]) ).
cnf(c_0_2593,plain,
( ti(X1,X2) = ti(X1,X3)
| hAPP(X1,X1,plus_plus(X1,X2),X4) != hAPP(X1,X1,plus_plus(X1,X3),X4)
| ~ cancel_semigroup_add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1726]) ).
cnf(c_0_2594,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_1727]) ).
cnf(c_0_2595,plain,
ti(fun(X1,X1),hAPP(X1,fun(X1,X1),X2,X3)) = hAPP(X1,fun(X1,X1),X2,X3),
inference(split_conjunct,[status(thm)],[c_0_1728]) ).
cnf(c_0_2596,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_1729]) ).
cnf(c_0_2597,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_1730]) ).
cnf(c_0_2598,plain,
( number_number_of(X1,hAPP(int,int,succ,X2)) = hAPP(X1,X1,plus_plus(X1,one_one(X1)),number_number_of(X1,X2))
| ~ number_ring(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1731]) ).
cnf(c_0_2599,plain,
( X2 = X3
| ~ semiring_char_0(X1)
| hAPP(nat,X1,semiring_1_of_nat(X1),X2) != hAPP(nat,X1,semiring_1_of_nat(X1),X3) ),
inference(split_conjunct,[status(thm)],[c_0_1732]) ).
cnf(c_0_2600,plain,
( X1 = X2
| hAPP(nat,int,semiring_1_of_nat(int),X1) != hAPP(nat,int,semiring_1_of_nat(int),X2) ),
inference(split_conjunct,[status(thm)],[c_0_1733]) ).
cnf(c_0_2601,plain,
( X1 = X2
| hAPP(nat,int,semiring_1_of_nat(int),X1) != hAPP(nat,int,semiring_1_of_nat(int),X2) ),
inference(split_conjunct,[status(thm)],[c_0_1734]) ).
cnf(c_0_2602,plain,
( number_number_of(X1,hAPP(nat,int,semiring_1_of_nat(int),X2)) = hAPP(nat,X1,semiring_1_of_nat(X1),X2)
| ~ number_semiring(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1735]) ).
cnf(c_0_2603,plain,
( X1 = X2
| hAPP(int,int,bit0,X1) != hAPP(int,int,bit0,X2) ),
inference(split_conjunct,[status(thm)],[c_0_1736]) ).
cnf(c_0_2604,plain,
( X1 = X2
| hAPP(int,int,bit1,X1) != hAPP(int,int,bit1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_1737]) ).
cnf(c_0_2605,plain,
hAPP(int,int,bit0,X1) != hAPP(int,int,bit1,X2),
inference(split_conjunct,[status(thm)],[c_0_1738]) ).
cnf(c_0_2606,plain,
hAPP(int,int,bit1,X1) != hAPP(int,int,bit0,X2),
inference(split_conjunct,[status(thm)],[c_0_1739]) ).
cnf(c_0_2607,plain,
( ti(X1,hAPP(X2,X1,X3,X4)) = hAPP(X2,X1,X3,X4)
| ~ ord(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1740]) ).
cnf(c_0_2608,plain,
( ti(X1,hAPP(nat,X1,X2,X3)) = hAPP(nat,X1,X2,X3)
| ~ power(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1741]) ).
cnf(c_0_2609,plain,
ti(X1,hAPP(X1,X1,X2,X3)) = hAPP(X1,X1,X2,X3),
inference(split_conjunct,[status(thm)],[c_0_1742]) ).
cnf(c_0_2610,plain,
hAPP(X1,fun(X1,X1),ti(fun(X1,fun(X1,X1)),X2),X3) = hAPP(X1,fun(X1,X1),X2,X3),
inference(split_conjunct,[status(thm)],[c_0_1743]) ).
cnf(c_0_2611,plain,
hAPP(bool,fun(X1,fun(X1,X1)),X2,ti(bool,X3)) = hAPP(bool,fun(X1,fun(X1,X1)),X2,X3),
inference(split_conjunct,[status(thm)],[c_0_1744]) ).
cnf(c_0_2612,plain,
( hAPP(X1,X1,plus_plus(X1,X2),X3) = hAPP(X1,X1,plus_plus(X1,X2),X4)
| ~ cancel_semigroup_add(X1)
| ti(X1,X3) != ti(X1,X4) ),
inference(split_conjunct,[status(thm)],[c_0_1722]) ).
cnf(c_0_2613,plain,
( hAPP(X1,X1,plus_plus(X1,X2),X3) = hAPP(X1,X1,plus_plus(X1,X4),X3)
| ~ cancel_semigroup_add(X1)
| ti(X1,X2) != ti(X1,X4) ),
inference(split_conjunct,[status(thm)],[c_0_1723]) ).
cnf(c_0_2614,plain,
( hAPP(X1,X2,ti(fun(X1,X2),X3),X4) = hAPP(X1,X2,X3,X4)
| ~ ord(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1745]) ).
cnf(c_0_2615,plain,
hAPP(X1,X1,ti(fun(X1,X1),X2),X3) = hAPP(X1,X1,X2,X3),
inference(split_conjunct,[status(thm)],[c_0_1746]) ).
cnf(c_0_2616,plain,
hAPP(X1,fun(X1,X1),X2,ti(X1,X3)) = hAPP(X1,fun(X1,X1),X2,X3),
inference(split_conjunct,[status(thm)],[c_0_1747]) ).
cnf(c_0_2617,plain,
( hAPP(nat,X1,ti(fun(nat,X1),X2),X3) = hAPP(nat,X1,X2,X3)
| ~ power(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1748]) ).
cnf(c_0_2618,plain,
( hAPP(X1,X1,plus_plus(X1,X2),X3) = hAPP(X1,X1,plus_plus(X1,X3),X2)
| ~ comm_semiring_1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1749]) ).
cnf(c_0_2619,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_1729]) ).
cnf(c_0_2620,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_1730]) ).
cnf(c_0_2621,plain,
hAPP(nat,nat,plus_plus(nat,X1),X2) = hAPP(nat,nat,plus_plus(nat,X2),X1),
inference(split_conjunct,[status(thm)],[c_0_1750]) ).
cnf(c_0_2622,plain,
hAPP(int,int,plus_plus(int,X1),X2) = hAPP(int,int,plus_plus(int,X2),X1),
inference(split_conjunct,[status(thm)],[c_0_1751]) ).
cnf(c_0_2623,plain,
( hAPP(X1,X2,X3,ti(X1,X4)) = hAPP(X1,X2,X3,X4)
| ~ ord(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1752]) ).
cnf(c_0_2624,plain,
( ~ zero_neq_one(X1)
| ~ no_zero_divisors(X1)
| ~ mult_zero(X1)
| ~ power(X1)
| hAPP(nat,X1,power_power(X1,X2),number_number_of(nat,X3)) != zero_zero(X1)
| number_number_of(nat,X3) != zero_zero(nat) ),
inference(split_conjunct,[status(thm)],[c_0_1753]) ).
cnf(c_0_2625,plain,
( hAPP(nat,X1,X2,ti(nat,X3)) = hAPP(nat,X1,X2,X3)
| ~ power(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1754]) ).
cnf(c_0_2626,plain,
hAPP(X1,X1,X2,ti(X1,X3)) = hAPP(X1,X1,X2,X3),
inference(split_conjunct,[status(thm)],[c_0_1755]) ).
cnf(c_0_2627,plain,
( ti(X1,X2) = zero_zero(X1)
| ~ zero_neq_one(X1)
| ~ no_zero_divisors(X1)
| ~ mult_zero(X1)
| ~ power(X1)
| hAPP(nat,X1,power_power(X1,X2),number_number_of(nat,X3)) != zero_zero(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1753]) ).
cnf(c_0_2628,plain,
( hAPP(nat,X1,semiring_1_of_nat(X1),X2) = hAPP(nat,X1,semiring_1_of_nat(X1),X3)
| ~ semiring_char_0(X1)
| X2 != X3 ),
inference(split_conjunct,[status(thm)],[c_0_1732]) ).
cnf(c_0_2629,plain,
hAPP(int,int,succ,X1) = hAPP(int,int,plus_plus(int,X1),one_one(int)),
inference(split_conjunct,[status(thm)],[c_0_1756]) ).
cnf(c_0_2630,plain,
hAPP(int,int,bit0,X1) = hAPP(int,int,plus_plus(int,X1),X1),
inference(split_conjunct,[status(thm)],[c_0_1757]) ).
cnf(c_0_2631,plain,
( number_number_of(X1,hAPP(int,int,bit1,pls)) = one_one(X1)
| ~ number_semiring(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1758]) ).
cnf(c_0_2632,plain,
( number_number_of(X1,hAPP(int,int,bit1,pls)) = one_one(X1)
| ~ number_ring(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1759]) ).
cnf(c_0_2633,plain,
( one_one(X1) = number_number_of(X1,hAPP(int,int,bit1,pls))
| ~ number_ring(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1760]) ).
cnf(c_0_2634,plain,
( hAPP(nat,int,semiring_1_of_nat(int),X1) = hAPP(nat,int,semiring_1_of_nat(int),X2)
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[c_0_1733]) ).
cnf(c_0_2635,plain,
( hAPP(nat,int,semiring_1_of_nat(int),X1) = hAPP(nat,int,semiring_1_of_nat(int),X2)
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[c_0_1734]) ).
cnf(c_0_2636,plain,
one_one(nat) = number_number_of(nat,hAPP(int,int,bit1,pls)),
inference(split_conjunct,[status(thm)],[c_0_1761]) ).
cnf(c_0_2637,plain,
number_number_of(nat,hAPP(int,int,bit1,pls)) = one_one(nat),
inference(split_conjunct,[status(thm)],[c_0_1762]) ).
cnf(c_0_2638,plain,
one_one(int) = number_number_of(int,hAPP(int,int,bit1,pls)),
inference(split_conjunct,[status(thm)],[c_0_1763]) ).
cnf(c_0_2639,plain,
( hAPP(int,int,bit0,X1) = hAPP(int,int,bit0,X2)
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[c_0_1736]) ).
cnf(c_0_2640,plain,
( hAPP(int,int,bit1,X1) = hAPP(int,int,bit1,X2)
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[c_0_1737]) ).
cnf(c_0_2641,plain,
hAPP(int,int,succ,pls) = hAPP(int,int,bit1,pls),
inference(split_conjunct,[status(thm)],[c_0_1764]) ).
cnf(c_0_2642,plain,
( ti(X1,X2) = zero_zero(X1)
| ~ zero_neq_one(X1)
| ~ no_zero_divisors(X1)
| ~ mult_zero(X1)
| ~ power(X1)
| hAPP(nat,X1,power_power(X1,X2),X3) != zero_zero(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1765]) ).
cnf(c_0_2643,plain,
( ti(X1,X2) = zero_zero(X1)
| ~ semiri456707255roduct(X1)
| ti(X1,X3) != hAPP(X1,X1,plus_plus(X1,X3),X2) ),
inference(split_conjunct,[status(thm)],[c_0_1766]) ).
cnf(c_0_2644,plain,
( ~ zero_neq_one(X1)
| ~ no_zero_divisors(X1)
| ~ mult_zero(X1)
| ~ power(X1)
| hAPP(nat,X1,power_power(X1,X2),X3) != zero_zero(X1)
| X3 != zero_zero(nat) ),
inference(split_conjunct,[status(thm)],[c_0_1765]) ).
cnf(c_0_2645,plain,
( ti(X1,X2) = zero_zero(X1)
| ~ linord219039673up_add(X1)
| zero_zero(X1) != hAPP(X1,X1,plus_plus(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[c_0_1767]) ).
cnf(c_0_2646,plain,
( ti(X1,X2) = zero_zero(X1)
| ~ linord219039673up_add(X1)
| hAPP(X1,X1,plus_plus(X1,X2),X2) != zero_zero(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1768]) ).
cnf(c_0_2647,plain,
( ti(X1,X2) = zero_zero(X1)
| hAPP(nat,X1,power_power(X1,X2),X3) != zero_zero(X1)
| ~ ring_11004092258visors(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1769]) ).
cnf(c_0_2648,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_1770]) ).
cnf(c_0_2649,plain,
( hAPP(nat,nat,power_power(nat,X1),X2) != zero_zero(nat)
| X2 != zero_zero(nat) ),
inference(split_conjunct,[status(thm)],[c_0_1771]) ).
cnf(c_0_2650,plain,
( X1 = zero_zero(nat)
| hAPP(nat,nat,power_power(nat,X1),X2) != zero_zero(nat) ),
inference(split_conjunct,[status(thm)],[c_0_1771]) ).
cnf(c_0_2651,plain,
( X1 = zero_zero(nat)
| hAPP(nat,nat,plus_plus(nat,X1),X2) != zero_zero(nat) ),
inference(split_conjunct,[status(thm)],[c_0_1772]) ).
cnf(c_0_2652,plain,
( X2 = zero_zero(nat)
| hAPP(nat,nat,plus_plus(nat,X1),X2) != zero_zero(nat) ),
inference(split_conjunct,[status(thm)],[c_0_1772]) ).
cnf(c_0_2653,plain,
( X1 = zero_zero(nat)
| hAPP(nat,nat,plus_plus(nat,X2),X1) != X2 ),
inference(split_conjunct,[status(thm)],[c_0_1773]) ).
cnf(c_0_2654,plain,
( X1 = zero_zero(nat)
| hAPP(nat,int,semiring_1_of_nat(int),X1) != zero_zero(int) ),
inference(split_conjunct,[status(thm)],[c_0_1774]) ).
cnf(c_0_2655,plain,
( pls = X1
| pls != hAPP(int,int,bit0,X1) ),
inference(split_conjunct,[status(thm)],[c_0_1775]) ).
cnf(c_0_2656,plain,
( X1 = pls
| hAPP(int,int,bit0,X1) != pls ),
inference(split_conjunct,[status(thm)],[c_0_1776]) ).
cnf(c_0_2657,plain,
pls != hAPP(int,int,bit1,X1),
inference(split_conjunct,[status(thm)],[c_0_1777]) ).
cnf(c_0_2658,plain,
hAPP(int,int,bit1,X1) != pls,
inference(split_conjunct,[status(thm)],[c_0_1778]) ).
cnf(c_0_2659,plain,
( hAPP(nat,X1,power_power(X1,X2),number_number_of(nat,X3)) = zero_zero(X1)
| number_number_of(nat,X3) = zero_zero(nat)
| ~ zero_neq_one(X1)
| ~ no_zero_divisors(X1)
| ~ mult_zero(X1)
| ~ power(X1)
| ti(X1,X2) != zero_zero(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1753]) ).
cnf(c_0_2660,plain,
( hAPP(nat,X1,power_power(X1,zero_zero(X1)),number_number_of(nat,X2)) = one_one(X1)
| ~ semiring_0(X1)
| ~ power(X1)
| number_number_of(nat,X2) != zero_zero(nat) ),
inference(split_conjunct,[status(thm)],[c_0_1779]) ).
cnf(c_0_2661,plain,
( hAPP(nat,X1,power_power(X1,zero_zero(X1)),number_number_of(nat,X2)) = zero_zero(X1)
| number_number_of(nat,X2) = zero_zero(nat)
| ~ semiring_0(X1)
| ~ power(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1779]) ).
cnf(c_0_2662,plain,
( hAPP(X1,X1,plus_plus(X1,number_number_of(X1,pls)),X2) = ti(X1,X2)
| ~ number_ring(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1780]) ).
cnf(c_0_2663,plain,
( hAPP(nat,X1,power_power(X1,X2),X3) = zero_zero(X1)
| X3 = zero_zero(nat)
| ~ zero_neq_one(X1)
| ~ no_zero_divisors(X1)
| ~ mult_zero(X1)
| ~ power(X1)
| ti(X1,X2) != zero_zero(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1765]) ).
cnf(c_0_2664,plain,
( ti(X1,X2) = hAPP(X1,X1,plus_plus(X1,X2),X3)
| ~ semiri456707255roduct(X1)
| ti(X1,X3) != zero_zero(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1766]) ).
cnf(c_0_2665,plain,
( hAPP(X1,X1,plus_plus(X1,X2),number_number_of(X1,pls)) = ti(X1,X2)
| ~ number_ring(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1781]) ).
cnf(c_0_2666,plain,
( zero_zero(X1) = hAPP(X1,X1,plus_plus(X1,X2),X2)
| ~ linord219039673up_add(X1)
| ti(X1,X2) != zero_zero(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1767]) ).
cnf(c_0_2667,plain,
( hAPP(X1,X1,plus_plus(X1,X2),X2) = zero_zero(X1)
| ~ linord219039673up_add(X1)
| ti(X1,X2) != zero_zero(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1768]) ).
cnf(c_0_2668,plain,
( hAPP(nat,X1,power_power(X1,zero_zero(X1)),X2) = one_one(X1)
| ~ semiring_0(X1)
| ~ power(X1)
| X2 != zero_zero(nat) ),
inference(split_conjunct,[status(thm)],[c_0_1782]) ).
cnf(c_0_2669,plain,
( hAPP(X1,X1,plus_plus(X1,zero_zero(X1)),X2) = ti(X1,X2)
| ~ monoid_add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1783]) ).
cnf(c_0_2670,plain,
( hAPP(X1,X1,plus_plus(X1,zero_zero(X1)),X2) = ti(X1,X2)
| ~ comm_semiring_1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1784]) ).
cnf(c_0_2671,plain,
( hAPP(X1,X1,plus_plus(X1,zero_zero(X1)),X2) = ti(X1,X2)
| ~ comm_monoid_add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1785]) ).
cnf(c_0_2672,plain,
( hAPP(nat,X1,power_power(X1,zero_zero(X1)),X2) = zero_zero(X1)
| X2 = zero_zero(nat)
| ~ semiring_0(X1)
| ~ power(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1782]) ).
cnf(c_0_2673,plain,
( hAPP(X1,X1,plus_plus(X1,X2),zero_zero(X1)) = ti(X1,X2)
| ~ monoid_add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1786]) ).
cnf(c_0_2674,plain,
( hAPP(X1,X1,plus_plus(X1,X2),zero_zero(X1)) = ti(X1,X2)
| ~ comm_semiring_1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1787]) ).
cnf(c_0_2675,plain,
( hAPP(X1,X1,plus_plus(X1,X2),zero_zero(X1)) = ti(X1,X2)
| ~ comm_monoid_add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1788]) ).
cnf(c_0_2676,plain,
( hAPP(nat,X1,power_power(X1,X2),one_one(nat)) = ti(X1,X2)
| ~ comm_semiring_1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1789]) ).
cnf(c_0_2677,plain,
( hAPP(nat,X1,power_power(X1,X2),one_one(nat)) = ti(X1,X2)
| ~ monoid_mult(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1790]) ).
cnf(c_0_2678,plain,
( hAPP(nat,X1,power_power(X1,one_one(X1)),X2) = one_one(X1)
| ~ monoid_mult(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1791]) ).
cnf(c_0_2679,plain,
( hAPP(nat,X1,power_power(X1,X2),zero_zero(nat)) = one_one(X1)
| ~ comm_semiring_1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1792]) ).
cnf(c_0_2680,plain,
( hAPP(nat,X1,power_power(X1,X2),zero_zero(nat)) = one_one(X1)
| ~ power(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1793]) ).
cnf(c_0_2681,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_1772]) ).
cnf(c_0_2682,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_1771]) ).
cnf(c_0_2683,plain,
( hAPP(nat,nat,power_power(nat,X1),X2) = one_one(nat)
| X1 != one_one(nat) ),
inference(split_conjunct,[status(thm)],[c_0_1770]) ).
cnf(c_0_2684,plain,
( hAPP(nat,nat,power_power(nat,X1),X2) = one_one(nat)
| X2 != zero_zero(nat) ),
inference(split_conjunct,[status(thm)],[c_0_1770]) ).
cnf(c_0_2685,plain,
hAPP(nat,nat,plus_plus(nat,zero_zero(nat)),X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_1794]) ).
cnf(c_0_2686,plain,
hAPP(int,int,plus_plus(int,zero_zero(int)),X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_1795]) ).
cnf(c_0_2687,plain,
hAPP(nat,nat,plus_plus(nat,X1),zero_zero(nat)) = X1,
inference(split_conjunct,[status(thm)],[c_0_1796]) ).
cnf(c_0_2688,plain,
hAPP(int,int,plus_plus(int,X1),zero_zero(int)) = X1,
inference(split_conjunct,[status(thm)],[c_0_1797]) ).
cnf(c_0_2689,plain,
hAPP(int,int,plus_plus(int,X1),pls) = X1,
inference(split_conjunct,[status(thm)],[c_0_1798]) ).
cnf(c_0_2690,plain,
( hAPP(nat,X1,semiring_1_of_nat(X1),zero_zero(nat)) = zero_zero(X1)
| ~ semiring_1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1799]) ).
cnf(c_0_2691,plain,
( hAPP(nat,X1,semiring_1_of_nat(X1),one_one(nat)) = one_one(X1)
| ~ semiring_1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1800]) ).
cnf(c_0_2692,plain,
hAPP(int,int,plus_plus(int,pls),X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_1801]) ).
cnf(c_0_2693,plain,
( hAPP(nat,int,semiring_1_of_nat(int),X1) = zero_zero(int)
| X1 != zero_zero(nat) ),
inference(split_conjunct,[status(thm)],[c_0_1774]) ).
cnf(c_0_2694,plain,
zero_zero(int) = hAPP(nat,int,semiring_1_of_nat(int),zero_zero(nat)),
inference(split_conjunct,[status(thm)],[c_0_1802]) ).
cnf(c_0_2695,plain,
one_one(int) = hAPP(nat,int,semiring_1_of_nat(int),one_one(nat)),
inference(split_conjunct,[status(thm)],[c_0_1803]) ).
cnf(c_0_2696,plain,
hAPP(nat,int,semiring_1_of_nat(int),zero_zero(nat)) = zero_zero(int),
inference(split_conjunct,[status(thm)],[c_0_1804]) ).
cnf(c_0_2697,plain,
hAPP(nat,int,semiring_1_of_nat(int),one_one(nat)) = one_one(int),
inference(split_conjunct,[status(thm)],[c_0_1805]) ).
cnf(c_0_2698,plain,
( pls = hAPP(int,int,bit0,X1)
| pls != X1 ),
inference(split_conjunct,[status(thm)],[c_0_1775]) ).
cnf(c_0_2699,plain,
( hAPP(int,int,bit0,X1) = pls
| X1 != pls ),
inference(split_conjunct,[status(thm)],[c_0_1776]) ).
cnf(c_0_2700,plain,
hAPP(int,int,bit0,pls) = pls,
inference(split_conjunct,[status(thm)],[c_0_1806]) ).
cnf(c_0_2701,plain,
ti(fun(bool,fun(X1,fun(X1,X1))),if(X1)) = if(X1),
inference(split_conjunct,[status(thm)],[c_0_1807]) ).
cnf(c_0_2702,plain,
( ti(fun(X1,fun(X1,X1)),times_times(X1)) = times_times(X1)
| ~ linordered_semiring(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1808]) ).
cnf(c_0_2703,plain,
( ti(fun(X1,fun(X1,bool)),ord_less_eq(X1)) = ord_less_eq(X1)
| ~ ord(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1809]) ).
cnf(c_0_2704,plain,
( ti(fun(X1,fun(X1,bool)),ord_less(X1)) = ord_less(X1)
| ~ ord(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1810]) ).
cnf(c_0_2705,plain,
( ti(fun(X1,X1),plus_plus(X1,X2)) = plus_plus(X1,X2)
| ~ cancel_semigroup_add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1811]) ).
cnf(c_0_2706,plain,
( ti(fun(X1,X1),plus_plus(X1,X2)) = plus_plus(X1,X2)
| ~ ab_semigroup_add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1812]) ).
cnf(c_0_2707,plain,
( ti(fun(X1,X1),plus_plus(X1,X2)) = plus_plus(X1,X2)
| ~ monoid_add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1813]) ).
cnf(c_0_2708,plain,
( ti(fun(nat,X1),power_power(X1,X2)) = power_power(X1,X2)
| ~ power(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1814]) ).
cnf(c_0_2709,plain,
( ti(X1,X2) = number_number_of(X1,X3)
| ~ number(X1)
| number_number_of(X1,X3) != ti(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_1815]) ).
cnf(c_0_2710,plain,
( number_number_of(X1,X2) = ti(X1,X3)
| ~ number(X1)
| ti(X1,X3) != number_number_of(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_1815]) ).
cnf(c_0_2711,plain,
( power_power(X1,ti(X1,X2)) = power_power(X1,X2)
| ~ power(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1816]) ).
cnf(c_0_2712,plain,
( ti(X1,number_number_of(X1,X2)) = number_number_of(X1,X2)
| ~ number(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1817]) ).
cnf(c_0_2713,plain,
( plus_plus(X1,ti(X1,X2)) = plus_plus(X1,X2)
| ~ cancel_semigroup_add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1818]) ).
cnf(c_0_2714,plain,
( plus_plus(X1,ti(X1,X2)) = plus_plus(X1,X2)
| ~ ab_semigroup_add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1819]) ).
cnf(c_0_2715,plain,
( plus_plus(X1,ti(X1,X2)) = plus_plus(X1,X2)
| ~ monoid_add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1820]) ).
cnf(c_0_2716,plain,
( X2 = X3
| ~ ring_char_0(X1)
| ~ number_ring(X1)
| number_number_of(X1,X2) != number_number_of(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_1821]) ).
cnf(c_0_2717,plain,
( number_number_of(X1,ti(int,X2)) = number_number_of(X1,X2)
| ~ number(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1822]) ).
cnf(c_0_2718,plain,
( ti(fun(nat,X1),semiring_1_of_nat(X1)) = semiring_1_of_nat(X1)
| ~ semiring_1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1823]) ).
cnf(c_0_2719,plain,
( ti(X1,X2) = one_one(X1)
| ~ one(X1)
| one_one(X1) != ti(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_1824]) ).
cnf(c_0_2720,plain,
( one_one(X1) = ti(X1,X2)
| ~ one(X1)
| ti(X1,X2) != one_one(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1824]) ).
cnf(c_0_2721,plain,
( ti(X1,X2) = zero_zero(X1)
| ~ zero(X1)
| zero_zero(X1) != ti(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_1825]) ).
cnf(c_0_2722,plain,
( zero_zero(X1) = ti(X1,X2)
| ~ zero(X1)
| ti(X1,X2) != zero_zero(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1825]) ).
cnf(c_0_2723,plain,
ti(X1,ti(X1,X2)) = ti(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_1826]) ).
cnf(c_0_2724,plain,
( hBOOL(X1)
| ~ hBOOL(ti(bool,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_1827]) ).
cnf(c_0_2725,plain,
( number_number_of(X1,X2) = number_number_of(X1,X3)
| ~ ring_char_0(X1)
| ~ number_ring(X1)
| X2 != X3 ),
inference(split_conjunct,[status(thm)],[c_0_1821]) ).
cnf(c_0_2726,plain,
( ord(fun(X1,X2))
| ~ ord(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1828]) ).
cnf(c_0_2727,plain,
( order(fun(X1,X2))
| ~ order(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1829]) ).
cnf(c_0_2728,plain,
( preorder(fun(X1,X2))
| ~ preorder(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1830]) ).
cnf(c_0_2729,plain,
( hBOOL(ti(bool,X1))
| ~ hBOOL(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1827]) ).
cnf(c_0_2730,plain,
ti(fun(real,real),sqrt) = sqrt,
inference(split_conjunct,[status(thm)],[c_0_1831]) ).
cnf(c_0_2731,plain,
ti(fun(int,int),succ) = succ,
inference(split_conjunct,[status(thm)],[c_0_1832]) ).
cnf(c_0_2732,plain,
( ti(X1,zero_zero(X1)) = zero_zero(X1)
| ~ zero(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1833]) ).
cnf(c_0_2733,plain,
( ti(X1,one_one(X1)) = one_one(X1)
| ~ one(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1834]) ).
cnf(c_0_2734,plain,
( ti(bool,X1) = fFalse
| ti(bool,X1) = fTrue ),
inference(split_conjunct,[status(thm)],[c_0_1835]) ).
cnf(c_0_2735,plain,
ti(X1,undefined(X1)) = undefined(X1),
inference(split_conjunct,[status(thm)],[c_0_1836]) ).
cnf(c_0_2736,plain,
( zero_zero(X1) = number_number_of(X1,pls)
| ~ number_ring(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1837]) ).
cnf(c_0_2737,plain,
( number_number_of(X1,pls) = zero_zero(X1)
| ~ number_ring(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1838]) ).
cnf(c_0_2738,plain,
( number_number_of(X1,pls) = zero_zero(X1)
| ~ number_semiring(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1839]) ).
cnf(c_0_2739,plain,
( zero_zero(X1) != one_one(X1)
| ~ zero_neq_one(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1840]) ).
cnf(c_0_2740,plain,
( one_one(X1) != zero_zero(X1)
| ~ zero_neq_one(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1841]) ).
cnf(c_0_2741,plain,
number_number_of(int,X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_1842]) ).
cnf(c_0_2742,plain,
zero_zero(nat) = number_number_of(nat,pls),
inference(split_conjunct,[status(thm)],[c_0_1843]) ).
cnf(c_0_2743,plain,
number_number_of(nat,pls) = zero_zero(nat),
inference(split_conjunct,[status(thm)],[c_0_1844]) ).
cnf(c_0_2744,plain,
zero_zero(int) = number_number_of(int,pls),
inference(split_conjunct,[status(thm)],[c_0_1845]) ).
cnf(c_0_2745,plain,
ti(nat,tn) = tn,
inference(split_conjunct,[status(thm)],[c_0_1846]) ).
cnf(c_0_2746,plain,
ti(int,t) = t,
inference(split_conjunct,[status(thm)],[c_0_1847]) ).
cnf(c_0_2747,plain,
ti(int,m1) = m1,
inference(split_conjunct,[status(thm)],[c_0_1848]) ).
cnf(c_0_2748,plain,
ti(bool,fTrue) = fTrue,
inference(split_conjunct,[status(thm)],[c_0_1849]) ).
cnf(c_0_2749,plain,
ti(bool,fFalse) = fFalse,
inference(split_conjunct,[status(thm)],[c_0_1850]) ).
cnf(c_0_2750,plain,
zero_zero(real) != one_one(real),
inference(split_conjunct,[status(thm)],[c_0_1851]) ).
cnf(c_0_2751,plain,
zero_zero(int) != one_one(int),
inference(split_conjunct,[status(thm)],[c_0_1852]) ).
cnf(c_0_2752,plain,
one(real),
inference(split_conjunct,[status(thm)],[c_0_1853]) ).
cnf(c_0_2753,plain,
number(real),
inference(split_conjunct,[status(thm)],[c_0_1854]) ).
cnf(c_0_2754,plain,
zero(real),
inference(split_conjunct,[status(thm)],[c_0_1855]) ).
cnf(c_0_2755,plain,
power(real),
inference(split_conjunct,[status(thm)],[c_0_1856]) ).
cnf(c_0_2756,plain,
ord(real),
inference(split_conjunct,[status(thm)],[c_0_1857]) ).
cnf(c_0_2757,plain,
number_ring(real),
inference(split_conjunct,[status(thm)],[c_0_1858]) ).
cnf(c_0_2758,plain,
ring_char_0(real),
inference(split_conjunct,[status(thm)],[c_0_1859]) ).
cnf(c_0_2759,plain,
order(real),
inference(split_conjunct,[status(thm)],[c_0_1860]) ).
cnf(c_0_2760,plain,
mult_zero(real),
inference(split_conjunct,[status(thm)],[c_0_1861]) ).
cnf(c_0_2761,plain,
semiring_0(real),
inference(split_conjunct,[status(thm)],[c_0_1862]) ).
cnf(c_0_2762,plain,
semiring_1(real),
inference(split_conjunct,[status(thm)],[c_0_1863]) ).
cnf(c_0_2763,plain,
monoid_add(real),
inference(split_conjunct,[status(thm)],[c_0_1864]) ).
cnf(c_0_2764,plain,
monoid_mult(real),
inference(split_conjunct,[status(thm)],[c_0_1865]) ).
cnf(c_0_2765,plain,
linorder(real),
inference(split_conjunct,[status(thm)],[c_0_1866]) ).
cnf(c_0_2766,plain,
preorder(real),
inference(split_conjunct,[status(thm)],[c_0_1867]) ).
cnf(c_0_2767,plain,
zero_neq_one(real),
inference(split_conjunct,[status(thm)],[c_0_1868]) ).
cnf(c_0_2768,plain,
number_semiring(real),
inference(split_conjunct,[status(thm)],[c_0_1869]) ).
cnf(c_0_2769,plain,
semiring_char_0(real),
inference(split_conjunct,[status(thm)],[c_0_1870]) ).
cnf(c_0_2770,plain,
comm_semiring_1(real),
inference(split_conjunct,[status(thm)],[c_0_1871]) ).
cnf(c_0_2771,plain,
linordered_idom(real),
inference(split_conjunct,[status(thm)],[c_0_1872]) ).
cnf(c_0_2772,plain,
linordered_ring(real),
inference(split_conjunct,[status(thm)],[c_0_1873]) ).
cnf(c_0_2773,plain,
comm_monoid_add(real),
inference(split_conjunct,[status(thm)],[c_0_1874]) ).
cnf(c_0_2774,plain,
no_zero_divisors(real),
inference(split_conjunct,[status(thm)],[c_0_1875]) ).
cnf(c_0_2775,plain,
ab_semigroup_add(real),
inference(split_conjunct,[status(thm)],[c_0_1876]) ).
cnf(c_0_2776,plain,
dense_linorder(real),
inference(split_conjunct,[status(thm)],[c_0_1877]) ).
cnf(c_0_2777,plain,
linordered_semidom(real),
inference(split_conjunct,[status(thm)],[c_0_1878]) ).
cnf(c_0_2778,plain,
linordered_semiring(real),
inference(split_conjunct,[status(thm)],[c_0_1879]) ).
cnf(c_0_2779,plain,
cancel_semigroup_add(real),
inference(split_conjunct,[status(thm)],[c_0_1880]) ).
cnf(c_0_2780,plain,
linord581940658strict(real),
inference(split_conjunct,[status(thm)],[c_0_1881]) ).
cnf(c_0_2781,plain,
ring_11004092258visors(real),
inference(split_conjunct,[status(thm)],[c_0_1882]) ).
cnf(c_0_2782,plain,
cancel146912293up_add(real),
inference(split_conjunct,[status(thm)],[c_0_1883]) ).
cnf(c_0_2783,plain,
linord219039673up_add(real),
inference(split_conjunct,[status(thm)],[c_0_1884]) ).
cnf(c_0_2784,plain,
ordere216010020id_add(real),
inference(split_conjunct,[status(thm)],[c_0_1885]) ).
cnf(c_0_2785,plain,
ordere779506340up_add(real),
inference(split_conjunct,[status(thm)],[c_0_1886]) ).
cnf(c_0_2786,plain,
linord20386208strict(real),
inference(split_conjunct,[status(thm)],[c_0_1887]) ).
cnf(c_0_2787,plain,
linord893533164strict(real),
inference(split_conjunct,[status(thm)],[c_0_1888]) ).
cnf(c_0_2788,plain,
ordere236663937imp_le(real),
inference(split_conjunct,[status(thm)],[c_0_1889]) ).
cnf(c_0_2789,plain,
ordere223160158up_add(real),
inference(split_conjunct,[status(thm)],[c_0_1890]) ).
cnf(c_0_2790,plain,
semiri456707255roduct(real),
inference(split_conjunct,[status(thm)],[c_0_1891]) ).
cnf(c_0_2791,plain,
ord(bool),
inference(split_conjunct,[status(thm)],[c_0_1892]) ).
cnf(c_0_2792,plain,
order(bool),
inference(split_conjunct,[status(thm)],[c_0_1893]) ).
cnf(c_0_2793,plain,
preorder(bool),
inference(split_conjunct,[status(thm)],[c_0_1894]) ).
cnf(c_0_2794,plain,
one(nat),
inference(split_conjunct,[status(thm)],[c_0_1895]) ).
cnf(c_0_2795,plain,
number(nat),
inference(split_conjunct,[status(thm)],[c_0_1896]) ).
cnf(c_0_2796,plain,
zero(nat),
inference(split_conjunct,[status(thm)],[c_0_1897]) ).
cnf(c_0_2797,plain,
power(nat),
inference(split_conjunct,[status(thm)],[c_0_1898]) ).
cnf(c_0_2798,plain,
ord(nat),
inference(split_conjunct,[status(thm)],[c_0_1899]) ).
cnf(c_0_2799,plain,
order(nat),
inference(split_conjunct,[status(thm)],[c_0_1900]) ).
cnf(c_0_2800,plain,
mult_zero(nat),
inference(split_conjunct,[status(thm)],[c_0_1901]) ).
cnf(c_0_2801,plain,
semiring_0(nat),
inference(split_conjunct,[status(thm)],[c_0_1902]) ).
cnf(c_0_2802,plain,
semiring_1(nat),
inference(split_conjunct,[status(thm)],[c_0_1903]) ).
cnf(c_0_2803,plain,
monoid_add(nat),
inference(split_conjunct,[status(thm)],[c_0_1904]) ).
cnf(c_0_2804,plain,
monoid_mult(nat),
inference(split_conjunct,[status(thm)],[c_0_1905]) ).
cnf(c_0_2805,plain,
linorder(nat),
inference(split_conjunct,[status(thm)],[c_0_1906]) ).
cnf(c_0_2806,plain,
preorder(nat),
inference(split_conjunct,[status(thm)],[c_0_1907]) ).
cnf(c_0_2807,plain,
zero_neq_one(nat),
inference(split_conjunct,[status(thm)],[c_0_1908]) ).
cnf(c_0_2808,plain,
number_semiring(nat),
inference(split_conjunct,[status(thm)],[c_0_1909]) ).
cnf(c_0_2809,plain,
semiring_char_0(nat),
inference(split_conjunct,[status(thm)],[c_0_1910]) ).
cnf(c_0_2810,plain,
comm_semiring_1(nat),
inference(split_conjunct,[status(thm)],[c_0_1911]) ).
cnf(c_0_2811,plain,
comm_monoid_add(nat),
inference(split_conjunct,[status(thm)],[c_0_1912]) ).
cnf(c_0_2812,plain,
no_zero_divisors(nat),
inference(split_conjunct,[status(thm)],[c_0_1913]) ).
cnf(c_0_2813,plain,
ab_semigroup_add(nat),
inference(split_conjunct,[status(thm)],[c_0_1914]) ).
cnf(c_0_2814,plain,
linordered_semidom(nat),
inference(split_conjunct,[status(thm)],[c_0_1915]) ).
cnf(c_0_2815,plain,
linordered_semiring(nat),
inference(split_conjunct,[status(thm)],[c_0_1916]) ).
cnf(c_0_2816,plain,
cancel_semigroup_add(nat),
inference(split_conjunct,[status(thm)],[c_0_1917]) ).
cnf(c_0_2817,plain,
cancel146912293up_add(nat),
inference(split_conjunct,[status(thm)],[c_0_1918]) ).
cnf(c_0_2818,plain,
ordere216010020id_add(nat),
inference(split_conjunct,[status(thm)],[c_0_1919]) ).
cnf(c_0_2819,plain,
ordere779506340up_add(nat),
inference(split_conjunct,[status(thm)],[c_0_1920]) ).
cnf(c_0_2820,plain,
linord20386208strict(nat),
inference(split_conjunct,[status(thm)],[c_0_1921]) ).
cnf(c_0_2821,plain,
linord893533164strict(nat),
inference(split_conjunct,[status(thm)],[c_0_1922]) ).
cnf(c_0_2822,plain,
ordere236663937imp_le(nat),
inference(split_conjunct,[status(thm)],[c_0_1923]) ).
cnf(c_0_2823,plain,
ordere223160158up_add(nat),
inference(split_conjunct,[status(thm)],[c_0_1924]) ).
cnf(c_0_2824,plain,
semiri456707255roduct(nat),
inference(split_conjunct,[status(thm)],[c_0_1925]) ).
cnf(c_0_2825,plain,
one(int),
inference(split_conjunct,[status(thm)],[c_0_1926]) ).
cnf(c_0_2826,plain,
number(int),
inference(split_conjunct,[status(thm)],[c_0_1927]) ).
cnf(c_0_2827,plain,
zero(int),
inference(split_conjunct,[status(thm)],[c_0_1928]) ).
cnf(c_0_2828,plain,
power(int),
inference(split_conjunct,[status(thm)],[c_0_1929]) ).
cnf(c_0_2829,plain,
ord(int),
inference(split_conjunct,[status(thm)],[c_0_1930]) ).
cnf(c_0_2830,plain,
number_ring(int),
inference(split_conjunct,[status(thm)],[c_0_1931]) ).
cnf(c_0_2831,plain,
ring_char_0(int),
inference(split_conjunct,[status(thm)],[c_0_1932]) ).
cnf(c_0_2832,plain,
order(int),
inference(split_conjunct,[status(thm)],[c_0_1933]) ).
cnf(c_0_2833,plain,
mult_zero(int),
inference(split_conjunct,[status(thm)],[c_0_1934]) ).
cnf(c_0_2834,plain,
semiring_0(int),
inference(split_conjunct,[status(thm)],[c_0_1935]) ).
cnf(c_0_2835,plain,
semiring_1(int),
inference(split_conjunct,[status(thm)],[c_0_1936]) ).
cnf(c_0_2836,plain,
monoid_add(int),
inference(split_conjunct,[status(thm)],[c_0_1937]) ).
cnf(c_0_2837,plain,
monoid_mult(int),
inference(split_conjunct,[status(thm)],[c_0_1938]) ).
cnf(c_0_2838,plain,
linorder(int),
inference(split_conjunct,[status(thm)],[c_0_1939]) ).
cnf(c_0_2839,plain,
preorder(int),
inference(split_conjunct,[status(thm)],[c_0_1940]) ).
cnf(c_0_2840,plain,
zero_neq_one(int),
inference(split_conjunct,[status(thm)],[c_0_1941]) ).
cnf(c_0_2841,plain,
number_semiring(int),
inference(split_conjunct,[status(thm)],[c_0_1942]) ).
cnf(c_0_2842,plain,
semiring_char_0(int),
inference(split_conjunct,[status(thm)],[c_0_1943]) ).
cnf(c_0_2843,plain,
comm_semiring_1(int),
inference(split_conjunct,[status(thm)],[c_0_1944]) ).
cnf(c_0_2844,plain,
linordered_idom(int),
inference(split_conjunct,[status(thm)],[c_0_1945]) ).
cnf(c_0_2845,plain,
linordered_ring(int),
inference(split_conjunct,[status(thm)],[c_0_1946]) ).
cnf(c_0_2846,plain,
comm_monoid_add(int),
inference(split_conjunct,[status(thm)],[c_0_1947]) ).
cnf(c_0_2847,plain,
no_zero_divisors(int),
inference(split_conjunct,[status(thm)],[c_0_1948]) ).
cnf(c_0_2848,plain,
ab_semigroup_add(int),
inference(split_conjunct,[status(thm)],[c_0_1949]) ).
cnf(c_0_2849,plain,
linordered_semidom(int),
inference(split_conjunct,[status(thm)],[c_0_1950]) ).
cnf(c_0_2850,plain,
linordered_semiring(int),
inference(split_conjunct,[status(thm)],[c_0_1951]) ).
cnf(c_0_2851,plain,
cancel_semigroup_add(int),
inference(split_conjunct,[status(thm)],[c_0_1952]) ).
cnf(c_0_2852,plain,
linord581940658strict(int),
inference(split_conjunct,[status(thm)],[c_0_1953]) ).
cnf(c_0_2853,plain,
ring_11004092258visors(int),
inference(split_conjunct,[status(thm)],[c_0_1954]) ).
cnf(c_0_2854,plain,
cancel146912293up_add(int),
inference(split_conjunct,[status(thm)],[c_0_1955]) ).
cnf(c_0_2855,plain,
linord219039673up_add(int),
inference(split_conjunct,[status(thm)],[c_0_1956]) ).
cnf(c_0_2856,plain,
ordere216010020id_add(int),
inference(split_conjunct,[status(thm)],[c_0_1957]) ).
cnf(c_0_2857,plain,
ordere779506340up_add(int),
inference(split_conjunct,[status(thm)],[c_0_1958]) ).
cnf(c_0_2858,plain,
linord20386208strict(int),
inference(split_conjunct,[status(thm)],[c_0_1959]) ).
cnf(c_0_2859,plain,
linord893533164strict(int),
inference(split_conjunct,[status(thm)],[c_0_1960]) ).
cnf(c_0_2860,plain,
ordere236663937imp_le(int),
inference(split_conjunct,[status(thm)],[c_0_1961]) ).
cnf(c_0_2861,plain,
ordere223160158up_add(int),
inference(split_conjunct,[status(thm)],[c_0_1962]) ).
cnf(c_0_2862,plain,
semiri456707255roduct(int),
inference(split_conjunct,[status(thm)],[c_0_1963]) ).
cnf(c_0_2863,plain,
pls = zero_zero(int),
inference(split_conjunct,[status(thm)],[c_0_1964]) ).
cnf(c_0_2864,plain,
hAPP(int,int,plus_plus(int,hAPP(int,int,plus_plus(int,hAPP(nat,int,power_power(int,X1),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),number_number_of(int,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),X1)),X2))),hAPP(nat,int,power_power(int,X2),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) = hAPP(nat,int,power_power(int,hAPP(int,int,plus_plus(int,X1),X2)),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),
c_0_1965,
[final] ).
cnf(c_0_2865,plain,
( ti(X1,X2) = zero_zero(X1)
| ~ linordered_idom(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,plus_plus(X1,hAPP(nat,X1,power_power(X1,X2),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,X1,power_power(X1,X3),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),zero_zero(X1))) ),
c_0_1966,
[final] ).
cnf(c_0_2866,plain,
( ti(X1,X3) = zero_zero(X1)
| ~ linordered_idom(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,plus_plus(X1,hAPP(nat,X1,power_power(X1,X2),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,X1,power_power(X1,X3),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),zero_zero(X1))) ),
c_0_1967,
[final] ).
cnf(c_0_2867,plain,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,plus_plus(X1,hAPP(nat,X1,power_power(X1,X2),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,X1,power_power(X1,X3),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),zero_zero(X1)))
| ~ linordered_idom(X1) ),
c_0_1968,
[final] ).
cnf(c_0_2868,plain,
( hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),hAPP(X1,X2,X3,X6)),X5))
| ~ order(X1)
| ~ order(X2)
| ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),hAPP(X1,X2,X3,X4)),X5))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X6),X4))
| ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less_eq(X2),hAPP(X1,X2,X3,esk44_6(X1,X2,X6,X3,X4,X5))),hAPP(X1,X2,X3,esk43_6(X1,X2,X6,X3,X4,X5)))) ),
c_0_1969,
[final] ).
cnf(c_0_2869,plain,
( hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),hAPP(X1,X2,X5,X3)),X6))
| ~ order(X1)
| ~ order(X2)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X4))
| ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),hAPP(X1,X2,X5,X4)),X6))
| ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less_eq(X2),hAPP(X1,X2,X5,esk39_6(X1,X2,X5,X6,X3,X4))),hAPP(X1,X2,X5,esk40_6(X1,X2,X5,X6,X3,X4)))) ),
c_0_1970,
[final] ).
cnf(c_0_2870,plain,
( hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),hAPP(X1,X2,X3,X6)),X5))
| ~ ord(X1)
| ~ order(X2)
| ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less_eq(X2),hAPP(X1,X2,X3,X4)),X5))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X6),X4))
| ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),hAPP(X1,X2,X3,esk38_6(X1,X2,X6,X3,X4,X5))),hAPP(X1,X2,X3,esk37_6(X1,X2,X6,X3,X4,X5)))) ),
c_0_1971,
[final] ).
cnf(c_0_2871,plain,
( hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),hAPP(X1,X2,X5,X3)),X6))
| ~ order(X1)
| ~ order(X2)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X4))
| ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less_eq(X2),hAPP(X1,X2,X5,X4)),X6))
| ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),hAPP(X1,X2,X5,esk34_6(X1,X2,X5,X6,X3,X4))),hAPP(X1,X2,X5,esk35_6(X1,X2,X5,X6,X3,X4)))) ),
c_0_1972,
[final] ).
cnf(c_0_2872,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),hAPP(X2,X1,X4,X6)))
| ~ order(X1)
| ~ order(X2)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),hAPP(X2,X1,X4,X5)))
| ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),X5),X6))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X2,X1,X4,esk45_6(X1,X2,X6,X3,X4,X5))),hAPP(X2,X1,X4,esk46_6(X1,X2,X6,X3,X4,X5)))) ),
c_0_1973,
[final] ).
cnf(c_0_2873,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),hAPP(X2,X1,X4,X6)))
| ~ order(X1)
| ~ order(X2)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),hAPP(X2,X1,X4,X5)))
| ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less_eq(X2),X5),X6))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X2,X1,X4,esk41_6(X1,X2,X6,X3,X4,X5))),hAPP(X2,X1,X4,esk42_6(X1,X2,X6,X3,X4,X5)))) ),
c_0_1974,
[final] ).
cnf(c_0_2874,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X5),hAPP(X2,X1,X6,X4)))
| ~ order(X1)
| ~ order(X2)
| ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less_eq(X2),X3),X4))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X5),hAPP(X2,X1,X6,X3)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X2,X1,X6,esk33_6(X1,X2,X5,X6,X3,X4))),hAPP(X2,X1,X6,esk32_6(X1,X2,X5,X6,X3,X4)))) ),
c_0_1975,
[final] ).
cnf(c_0_2875,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X5),hAPP(X2,X1,X6,X4)))
| ~ order(X1)
| ~ order(X2)
| ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),X3),X4))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X5),hAPP(X2,X1,X6,X3)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X2,X1,X6,esk29_6(X1,X2,X5,X6,X3,X4))),hAPP(X2,X1,X6,esk28_6(X1,X2,X5,X6,X3,X4)))) ),
c_0_1976,
[final] ).
cnf(c_0_2876,plain,
hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),hAPP(real,real,sqrt,hAPP(real,real,plus_plus(real,hAPP(nat,real,power_power(real,X1),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,real,power_power(real,X2),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))))),
c_0_1977,
[final] ).
cnf(c_0_2877,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,plus_plus(X1,hAPP(nat,X1,power_power(X1,X2),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,X1,power_power(X1,X3),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),zero_zero(X1)))
| ~ linordered_idom(X1)
| ti(X1,X3) != zero_zero(X1)
| ti(X1,X2) != zero_zero(X1) ),
c_0_1978,
[final] ).
cnf(c_0_2878,plain,
( ~ linordered_idom(X1)
| ti(X1,X2) != zero_zero(X1)
| ti(X1,X3) != zero_zero(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),hAPP(X1,X1,plus_plus(X1,hAPP(nat,X1,power_power(X1,X3),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,X1,power_power(X1,X2),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))) ),
c_0_1979,
[final] ).
cnf(c_0_2879,plain,
( hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),hAPP(X1,X2,X3,X6)),X5))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),esk44_6(X1,X2,X6,X3,X4,X5)),esk43_6(X1,X2,X6,X3,X4,X5)))
| ~ order(X1)
| ~ order(X2)
| ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),hAPP(X1,X2,X3,X4)),X5))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X6),X4)) ),
c_0_1980,
[final] ).
cnf(c_0_2880,plain,
( hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),hAPP(X1,X2,X5,X3)),X6))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),esk39_6(X1,X2,X5,X6,X3,X4)),esk40_6(X1,X2,X5,X6,X3,X4)))
| ~ order(X1)
| ~ order(X2)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X4))
| ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),hAPP(X1,X2,X5,X4)),X6)) ),
c_0_1981,
[final] ).
cnf(c_0_2881,plain,
( hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),hAPP(X1,X2,X3,X6)),X5))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),esk38_6(X1,X2,X6,X3,X4,X5)),esk37_6(X1,X2,X6,X3,X4,X5)))
| ~ ord(X1)
| ~ order(X2)
| ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less_eq(X2),hAPP(X1,X2,X3,X4)),X5))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X6),X4)) ),
c_0_1982,
[final] ).
cnf(c_0_2882,plain,
( hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),hAPP(X1,X2,X5,X3)),X6))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),esk34_6(X1,X2,X5,X6,X3,X4)),esk35_6(X1,X2,X5,X6,X3,X4)))
| ~ order(X1)
| ~ order(X2)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X4))
| ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less_eq(X2),hAPP(X1,X2,X5,X4)),X6)) ),
c_0_1983,
[final] ).
cnf(c_0_2883,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),hAPP(X2,X1,X4,X6)))
| hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),esk45_6(X1,X2,X6,X3,X4,X5)),esk46_6(X1,X2,X6,X3,X4,X5)))
| ~ order(X1)
| ~ order(X2)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),hAPP(X2,X1,X4,X5)))
| ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),X5),X6)) ),
c_0_1984,
[final] ).
cnf(c_0_2884,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),hAPP(X2,X1,X4,X6)))
| hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less_eq(X2),esk41_6(X1,X2,X6,X3,X4,X5)),esk42_6(X1,X2,X6,X3,X4,X5)))
| ~ order(X1)
| ~ order(X2)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),hAPP(X2,X1,X4,X5)))
| ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less_eq(X2),X5),X6)) ),
c_0_1985,
[final] ).
cnf(c_0_2885,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X5),hAPP(X2,X1,X6,X4)))
| hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less_eq(X2),esk33_6(X1,X2,X5,X6,X3,X4)),esk32_6(X1,X2,X5,X6,X3,X4)))
| ~ order(X1)
| ~ order(X2)
| ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less_eq(X2),X3),X4))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X5),hAPP(X2,X1,X6,X3))) ),
c_0_1986,
[final] ).
cnf(c_0_2886,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X5),hAPP(X2,X1,X6,X4)))
| hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),esk29_6(X1,X2,X5,X6,X3,X4)),esk28_6(X1,X2,X5,X6,X3,X4)))
| ~ order(X1)
| ~ order(X2)
| ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),X3),X4))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X5),hAPP(X2,X1,X6,X3))) ),
c_0_1987,
[final] ).
cnf(c_0_2887,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),hAPP(X1,X1,plus_plus(X1,hAPP(nat,X1,power_power(X1,X2),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,X1,power_power(X1,X3),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))))
| ti(X1,X2) = zero_zero(X1)
| ~ linordered_idom(X1) ),
c_0_1988,
[final] ).
cnf(c_0_2888,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),hAPP(X1,X1,plus_plus(X1,hAPP(nat,X1,power_power(X1,X2),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,X1,power_power(X1,X3),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))))
| ti(X1,X3) = zero_zero(X1)
| ~ linordered_idom(X1) ),
c_0_1989,
[final] ).
cnf(c_0_2889,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),hAPP(X1,X1,plus_plus(X1,hAPP(nat,X1,power_power(X1,X2),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,X1,power_power(X1,X3),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))))
| ~ linordered_idom(X1) ),
c_0_1990,
[final] ).
cnf(c_0_2890,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(nat,X1,power_power(X1,X2),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,X1,power_power(X1,X3),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))
| ~ linordered_semidom(X1) ),
c_0_1991,
[final] ).
cnf(c_0_2891,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(nat,X1,power_power(X1,X2),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,X1,power_power(X1,X3),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))
| ~ linordered_semidom(X1) ),
c_0_1992,
[final] ).
cnf(c_0_2892,plain,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,plus_plus(X1,hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X2)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X3),X3))),zero_zero(X1)))
| ~ linordered_ring(X1) ),
c_0_1993,
[final] ).
cnf(c_0_2893,plain,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(nat,X1,power_power(X1,X2),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),zero_zero(X1)))
| ~ linordered_idom(X1) ),
c_0_1994,
[final] ).
cnf(c_0_2894,plain,
( ~ linord581940658strict(X1)
| ti(X1,X2) != zero_zero(X1)
| ti(X1,X3) != zero_zero(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),hAPP(X1,X1,plus_plus(X1,hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X3),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X2)))) ),
c_0_1995,
[final] ).
cnf(c_0_2895,plain,
( ti(X1,X2) = zero_zero(X1)
| ~ linordered_idom(X1)
| hAPP(X1,X1,plus_plus(X1,hAPP(nat,X1,power_power(X1,X2),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,X1,power_power(X1,X3),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) != zero_zero(X1) ),
c_0_1996,
[final] ).
cnf(c_0_2896,plain,
( ti(X1,X3) = zero_zero(X1)
| ~ linordered_idom(X1)
| hAPP(X1,X1,plus_plus(X1,hAPP(nat,X1,power_power(X1,X2),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,X1,power_power(X1,X3),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) != zero_zero(X1) ),
c_0_1997,
[final] ).
cnf(c_0_2897,plain,
( X1 = zero_zero(real)
| hAPP(real,real,plus_plus(real,hAPP(nat,real,power_power(real,X1),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,real,power_power(real,X2),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) != zero_zero(real) ),
c_0_1998,
[final] ).
cnf(c_0_2898,plain,
( X2 = zero_zero(real)
| hAPP(real,real,plus_plus(real,hAPP(nat,real,power_power(real,X1),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,real,power_power(real,X2),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) != zero_zero(real) ),
c_0_1999,
[final] ).
cnf(c_0_2899,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(nat,X1,semiring_1_of_nat(X1),X2)),hAPP(nat,X1,power_power(X1,number_number_of(X1,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),X2)))
| ~ linordered_idom(X1)
| ~ number_ring(X1) ),
c_0_2000,
[final] ).
cnf(c_0_2900,plain,
hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),one_one(real)),hAPP(nat,real,power_power(real,number_number_of(real,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),X1))),
c_0_2001,
[final] ).
cnf(c_0_2901,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,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(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,X1,esk16_3(X2,X3,X1))),hAPP(nat,nat,X1,esk17_3(X2,X3,X1)))) ),
c_0_2002,
[final] ).
cnf(c_0_2902,plain,
hAPP(nat,int,power_power(int,hAPP(nat,int,power_power(int,X1),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) = hAPP(nat,int,power_power(int,X1),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),
c_0_2003,
[final] ).
cnf(c_0_2903,plain,
( ~ linordered_idom(X1)
| ti(X1,X2) != zero_zero(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),hAPP(nat,X1,power_power(X1,X2),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))) ),
c_0_2004,
[final] ).
cnf(c_0_2904,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),hAPP(X1,X1,plus_plus(X1,hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X2)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X3),X3))))
| ti(X1,X2) = zero_zero(X1)
| ~ linord581940658strict(X1) ),
c_0_2005,
[final] ).
cnf(c_0_2905,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),hAPP(X1,X1,plus_plus(X1,hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X2)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X3),X3))))
| ti(X1,X3) = zero_zero(X1)
| ~ linord581940658strict(X1) ),
c_0_2006,
[final] ).
cnf(c_0_2906,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X4))
| ~ linord581940658strict(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X2))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X4))) ),
c_0_2007,
[final] ).
cnf(c_0_2907,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X4))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X4)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X3),X4)))
| ~ linordered_semiring(X1) ),
c_0_2008,
[final] ).
cnf(c_0_2908,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X4))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X4)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X3),X4)))
| ~ linord20386208strict(X1) ),
c_0_2009,
[final] ).
cnf(c_0_2909,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X4))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X2)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X3)))
| ~ linordered_semiring(X1) ),
c_0_2010,
[final] ).
cnf(c_0_2910,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X4))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X2)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X3)))
| ~ linord20386208strict(X1) ),
c_0_2011,
[final] ).
cnf(c_0_2911,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X4))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X4)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X3),X4)))
| ~ linord20386208strict(X1) ),
c_0_2012,
[final] ).
cnf(c_0_2912,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X4))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X2)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X3)))
| ~ linord20386208strict(X1) ),
c_0_2013,
[final] ).
cnf(c_0_2913,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X4))
| ~ linord581940658strict(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),zero_zero(X1)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X4)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3))) ),
c_0_2014,
[final] ).
cnf(c_0_2914,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X4))
| ~ linord581940658strict(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),zero_zero(X1)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X4)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3))) ),
c_0_2015,
[final] ).
cnf(c_0_2915,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X5)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X4))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X5))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X4))
| ~ linord20386208strict(X1) ),
c_0_2016,
[final] ).
cnf(c_0_2916,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X5)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X2))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X5))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X4))
| ~ linord20386208strict(X1) ),
c_0_2017,
[final] ).
cnf(c_0_2917,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X5)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X2))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X5))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X4))
| ~ linord20386208strict(X1) ),
c_0_2018,
[final] ).
cnf(c_0_2918,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X5)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X2))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X5))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X4))
| ~ linord20386208strict(X1) ),
c_0_2019,
[final] ).
cnf(c_0_2919,plain,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X1),zero_zero(int)))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,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_2020,
[final] ).
cnf(c_0_2920,plain,
( hAPP(X1,X1,plus_plus(X1,hAPP(nat,X1,power_power(X1,X2),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,X1,power_power(X1,X3),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) = zero_zero(X1)
| ~ linordered_idom(X1)
| ti(X1,X3) != zero_zero(X1)
| ti(X1,X2) != zero_zero(X1) ),
c_0_2021,
[final] ).
cnf(c_0_2921,plain,
( hAPP(real,real,plus_plus(real,hAPP(nat,real,power_power(real,X1),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,real,power_power(real,X2),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) = zero_zero(real)
| X2 != zero_zero(real)
| X1 != zero_zero(real) ),
c_0_2022,
[final] ).
cnf(c_0_2922,plain,
( hBOOL(hAPP(fun(X1,X2),bool,hAPP(fun(X1,X2),fun(fun(X1,X2),bool),ord_less_eq(fun(X1,X2)),X3),X4))
| ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less_eq(X2),hAPP(X1,X2,X3,esk25_4(X1,X2,X3,X4))),hAPP(X1,X2,X4,esk25_4(X1,X2,X3,X4))))
| ~ ord(X2) ),
c_0_2023,
[final] ).
cnf(c_0_2923,plain,
( hBOOL(hAPP(fun(X2,X1),bool,hAPP(fun(X2,X1),fun(fun(X2,X1),bool),ord_less_eq(fun(X2,X1)),X3),X4))
| ~ ord(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X2,X1,X3,esk22_4(X2,X1,X3,X4))),hAPP(X2,X1,X4,esk22_4(X2,X1,X3,X4)))) ),
c_0_2024,
[final] ).
cnf(c_0_2924,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,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(nat,fun(nat,bool),ord_less(nat),esk16_3(X2,X3,X1)),esk17_3(X2,X3,X1))) ),
c_0_2025,
[final] ).
cnf(c_0_2925,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X3)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X4))
| ~ linord20386208strict(X1) ),
c_0_2026,
[final] ).
cnf(c_0_2926,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X4)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X2))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X4))
| ~ linord20386208strict(X1) ),
c_0_2027,
[final] ).
cnf(c_0_2927,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X4)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X2))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X4))
| ~ linord893533164strict(X1) ),
c_0_2028,
[final] ).
cnf(c_0_2928,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X4)))
| ~ linord581940658strict(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X2))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X4)) ),
c_0_2029,
[final] ).
cnf(c_0_2929,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X4)))
| ~ linord581940658strict(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),zero_zero(X1)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X4),X3)) ),
c_0_2030,
[final] ).
cnf(c_0_2930,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X3)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),zero_zero(X1)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X4),X2))
| ~ linord581940658strict(X1) ),
c_0_2031,
[final] ).
cnf(c_0_2931,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X4)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),zero_zero(X1)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X4),X3))
| ~ linord581940658strict(X1) ),
c_0_2032,
[final] ).
cnf(c_0_2932,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X4)))
| ~ linord581940658strict(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),zero_zero(X1)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X4),X3)) ),
c_0_2033,
[final] ).
cnf(c_0_2933,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,X1,X2)),hAPP(nat,nat,X1,X3)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X2),X3))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,X1,esk20_3(X2,X3,X1))),hAPP(nat,nat,X1,esk21_3(X2,X3,X1)))) ),
c_0_2034,
[final] ).
cnf(c_0_2934,plain,
( ti(X1,X2) = ti(X1,X3)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X2))
| hAPP(nat,X1,power_power(X1,X2),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) != hAPP(nat,X1,power_power(X1,X3),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))
| ~ linordered_semidom(X1) ),
c_0_2035,
[final] ).
cnf(c_0_2935,plain,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,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(int,fun(int,bool),ord_less(int),X1),zero_zero(int))) ),
c_0_2036,
[final] ).
cnf(c_0_2936,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),hAPP(nat,X1,power_power(X1,X2),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))
| ti(X1,X2) = zero_zero(X1)
| ~ linordered_idom(X1) ),
c_0_2037,
[final] ).
cnf(c_0_2937,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),hAPP(nat,X1,power_power(X1,X2),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))
| ~ linordered_idom(X1) ),
c_0_2038,
[final] ).
cnf(c_0_2938,plain,
hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X1),hAPP(nat,int,power_power(int,X1),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),
c_0_2039,
[final] ).
cnf(c_0_2939,plain,
( X1 = one_one(int)
| X1 = zero_zero(int)
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X1),number_number_of(int,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X1)) ),
c_0_2040,
[final] ).
cnf(c_0_2940,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),zero_zero(X1)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),zero_zero(X1)))
| ~ linord20386208strict(X1) ),
c_0_2041,
[final] ).
cnf(c_0_2941,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(nat,X1,power_power(X1,X2),X3)),hAPP(nat,X1,power_power(X1,X4),X3)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X2))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X4))
| ~ linordered_semidom(X1) ),
c_0_2042,
[final] ).
cnf(c_0_2942,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(nat,X1,power_power(X1,X2),X3)),hAPP(nat,X1,power_power(X1,X2),X4)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),one_one(X1)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X2))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X4),X3))
| ~ linordered_semidom(X1) ),
c_0_2043,
[final] ).
cnf(c_0_2943,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(nat,X1,power_power(X1,X2),X3)),hAPP(nat,X1,power_power(X1,X2),X4)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),one_one(X1)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X2))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X4),X3))
| ~ linordered_semidom(X1) ),
c_0_2044,
[final] ).
cnf(c_0_2944,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X2))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)))
| ~ linord20386208strict(X1) ),
c_0_2045,
[final] ).
cnf(c_0_2945,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(nat,X1,power_power(X1,X2),X4)),hAPP(nat,X1,power_power(X1,X3),X4)))
| ~ linordered_semidom(X1) ),
c_0_2046,
[final] ).
cnf(c_0_2946,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2))
| ~ hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),hAPP(nat,X3,power_power(X3,X4),X1)),hAPP(nat,X3,power_power(X3,X4),X2)))
| ~ hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),one_one(X3)),X4))
| ~ linordered_semidom(X3) ),
c_0_2047,
[final] ).
cnf(c_0_2947,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X3),X4))
| ~ linordered_semidom(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),one_one(X1)),X2))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(nat,X1,power_power(X1,X2),X3)),hAPP(nat,X1,power_power(X1,X2),X4))) ),
c_0_2048,
[final] ).
cnf(c_0_2948,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2))
| ~ hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),hAPP(nat,X3,power_power(X3,X4),X1)),hAPP(nat,X3,power_power(X3,X4),X2)))
| ~ hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),one_one(X3)),X4))
| ~ linordered_semidom(X3) ),
c_0_2049,
[final] ).
cnf(c_0_2949,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X3),X4))
| ~ linordered_semidom(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),one_one(X1)),X2))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(nat,X1,power_power(X1,X2),X3)),hAPP(nat,X1,power_power(X1,X2),X4))) ),
c_0_2050,
[final] ).
cnf(c_0_2950,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(nat,X1,power_power(X1,X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),hAPP(nat,X1,power_power(X1,X2),X3))))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),one_one(X1)),X2))
| ~ linordered_semidom(X1) ),
c_0_2051,
[final] ).
cnf(c_0_2951,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,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(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X3)) ),
c_0_2052,
[final] ).
cnf(c_0_2952,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(nat,X1,power_power(X1,X2),X3)),hAPP(nat,X1,power_power(X1,X4),X3)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X2))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X4))
| ~ linordered_semidom(X1) ),
c_0_2053,
[final] ).
cnf(c_0_2953,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),zero_zero(X1)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),zero_zero(X1)))
| ~ linord581940658strict(X1) ),
c_0_2054,
[final] ).
cnf(c_0_2954,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,plus_plus(X1,X2),X3)),hAPP(X1,X1,plus_plus(X1,X4),X5)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X5))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X4))
| ~ ordere223160158up_add(X1) ),
c_0_2055,
[final] ).
cnf(c_0_2955,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,plus_plus(X1,X2),X3)),hAPP(X1,X1,plus_plus(X1,X4),X5)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X5))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X4))
| ~ ordere223160158up_add(X1) ),
c_0_2056,
[final] ).
cnf(c_0_2956,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,plus_plus(X1,X2),X3)),hAPP(X1,X1,plus_plus(X1,X4),X5)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X5))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X4))
| ~ ordere779506340up_add(X1) ),
c_0_2057,
[final] ).
cnf(c_0_2957,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,plus_plus(X1,X2),X3)),hAPP(X1,X1,plus_plus(X1,X4),X5)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X5))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X4))
| ~ ordere223160158up_add(X1) ),
c_0_2058,
[final] ).
cnf(c_0_2958,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(nat,X1,power_power(X1,X2),X3)),hAPP(nat,X1,power_power(X1,X2),X4)))
| ~ linordered_semidom(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),one_one(X1)),X2))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X3),X4)) ),
c_0_2059,
[final] ).
cnf(c_0_2959,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(nat,X1,power_power(X1,X2),X3)),hAPP(nat,X1,power_power(X1,X2),X4)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),one_one(X1)),X2))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X3),X4))
| ~ linordered_semidom(X1) ),
c_0_2060,
[final] ).
cnf(c_0_2960,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(nat,X1,power_power(X1,X2),X3)),hAPP(nat,X1,power_power(X1,X2),X4)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),one_one(X1)),X2))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X3),X4))
| ~ linordered_semidom(X1) ),
c_0_2061,
[final] ).
cnf(c_0_2961,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(nat,X1,power_power(X1,X2),X3)),hAPP(nat,X1,power_power(X1,X2),X4)))
| ~ linordered_semidom(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),one_one(X1)),X2))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X3),X4)) ),
c_0_2062,
[final] ).
cnf(c_0_2962,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X4))
| ~ dense_linorder(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),esk27_4(X1,X4,X2,X3)),X4)) ),
c_0_2063,
[final] ).
cnf(c_0_2963,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,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(nat,fun(nat,bool),ord_less_eq(nat),X2),X4))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X3)) ),
c_0_2064,
[final] ).
cnf(c_0_2964,plain,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,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(int,fun(int,bool),ord_less_eq(int),X2),X4))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X1),X3)) ),
c_0_2065,
[final] ).
cnf(c_0_2965,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,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(nat,fun(nat,bool),ord_less(nat),X2),X4))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X3)) ),
c_0_2066,
[final] ).
cnf(c_0_2966,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),one_one(X1)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),hAPP(nat,X1,power_power(X1,X2),X3))))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),one_one(X1)),X2))
| ~ linordered_semidom(X1) ),
c_0_2067,
[final] ).
cnf(c_0_2967,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,plus_plus(X1,X4),X2)),hAPP(X1,X1,plus_plus(X1,X4),X3)))
| ~ ordere236663937imp_le(X1) ),
c_0_2068,
[final] ).
cnf(c_0_2968,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,plus_plus(X1,X2),X4)),hAPP(X1,X1,plus_plus(X1,X3),X4)))
| ~ ordere236663937imp_le(X1) ),
c_0_2069,
[final] ).
cnf(c_0_2969,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
| ~ ordere236663937imp_le(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,plus_plus(X1,X4),X2)),hAPP(X1,X1,plus_plus(X1,X4),X3))) ),
c_0_2070,
[final] ).
cnf(c_0_2970,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
| ~ ordere236663937imp_le(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,plus_plus(X1,X2),X4)),hAPP(X1,X1,plus_plus(X1,X3),X4))) ),
c_0_2071,
[final] ).
cnf(c_0_2971,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| ~ ordere236663937imp_le(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,plus_plus(X1,X2),X4)),hAPP(X1,X1,plus_plus(X1,X3),X4))) ),
c_0_2072,
[final] ).
cnf(c_0_2972,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| ~ ordere236663937imp_le(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,plus_plus(X1,X4),X2)),hAPP(X1,X1,plus_plus(X1,X4),X3))) ),
c_0_2073,
[final] ).
cnf(c_0_2973,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,plus_plus(X1,X2),X4)),hAPP(X1,X1,plus_plus(X1,X3),X4)))
| ~ ordere236663937imp_le(X1) ),
c_0_2074,
[final] ).
cnf(c_0_2974,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,plus_plus(X1,X4),X2)),hAPP(X1,X1,plus_plus(X1,X4),X3)))
| ~ ordere236663937imp_le(X1) ),
c_0_2075,
[final] ).
cnf(c_0_2975,plain,
( hBOOL(hAPP(int,bool,X3,X2))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,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_2076,
[final] ).
cnf(c_0_2976,plain,
hAPP(int,int,plus_plus(int,hAPP(int,int,bit0,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),X1),X2))),X2) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,bit1,X1)),X2),
c_0_2077,
[final] ).
cnf(c_0_2977,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,X1,X2)),hAPP(nat,nat,X1,X3)))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),esk20_3(X2,X3,X1)),esk21_3(X2,X3,X1)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X2),X3)) ),
c_0_2078,
[final] ).
cnf(c_0_2978,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,plus_plus(nat,X3),X1)),hAPP(nat,nat,plus_plus(nat,X3),X2))) ),
c_0_2079,
[final] ).
cnf(c_0_2979,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,plus_plus(nat,X3),X1)),hAPP(nat,nat,plus_plus(nat,X3),X2))) ),
c_0_2080,
[final] ).
cnf(c_0_2980,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X1,X2),X3))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X1,X2),X3))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X1,X2),X3))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X1,X2),X3)) ),
c_0_2081,
[final] ).
cnf(c_0_2981,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,plus_plus(X1,X2),X3)),zero_zero(X1)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),zero_zero(X1)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),zero_zero(X1)))
| ~ ordere216010020id_add(X1) ),
c_0_2082,
[final] ).
cnf(c_0_2982,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,plus_plus(X1,X2),X3)),zero_zero(X1)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),zero_zero(X1)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),zero_zero(X1)))
| ~ ordere216010020id_add(X1) ),
c_0_2083,
[final] ).
cnf(c_0_2983,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,plus_plus(X1,X2),X3)),zero_zero(X1)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),zero_zero(X1)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),zero_zero(X1)))
| ~ ordere216010020id_add(X1) ),
c_0_2084,
[final] ).
cnf(c_0_2984,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,plus_plus(X1,X2),X3)),zero_zero(X1)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),zero_zero(X1)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),zero_zero(X1)))
| ~ ordere216010020id_add(X1) ),
c_0_2085,
[final] ).
cnf(c_0_2985,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X2),X3))
| ~ linordered_semidom(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(nat,X1,semiring_1_of_nat(X1),X2)),hAPP(nat,X1,semiring_1_of_nat(X1),X3))) ),
c_0_2086,
[final] ).
cnf(c_0_2986,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2))
| ~ hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),hAPP(nat,X3,semiring_1_of_nat(X3),X1)),hAPP(nat,X3,semiring_1_of_nat(X3),X2)))
| ~ linordered_semidom(X3) ),
c_0_2087,
[final] ).
cnf(c_0_2987,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X2),X3))
| ~ linordered_semidom(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(nat,X1,semiring_1_of_nat(X1),X2)),hAPP(nat,X1,semiring_1_of_nat(X1),X3))) ),
c_0_2088,
[final] ).
cnf(c_0_2988,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(nat,int,semiring_1_of_nat(int),X1)),hAPP(nat,int,semiring_1_of_nat(int),X2))) ),
c_0_2089,
[final] ).
cnf(c_0_2989,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(nat,int,semiring_1_of_nat(int),X1)),hAPP(nat,int,semiring_1_of_nat(int),X2))) ),
c_0_2090,
[final] ).
cnf(c_0_2990,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(nat,int,semiring_1_of_nat(int),X1)),hAPP(nat,int,semiring_1_of_nat(int),X2))) ),
c_0_2091,
[final] ).
cnf(c_0_2991,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(nat,int,semiring_1_of_nat(int),X1)),hAPP(nat,int,semiring_1_of_nat(int),X2))) ),
c_0_2092,
[final] ).
cnf(c_0_2992,plain,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X1),X2))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,bit1,X1)),hAPP(int,int,bit0,X2))) ),
c_0_2093,
[final] ).
cnf(c_0_2993,plain,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X1),X2))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,bit1,X1)),hAPP(int,int,bit0,X2))) ),
c_0_2094,
[final] ).
cnf(c_0_2994,plain,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X1),X2))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit0,X1)),hAPP(int,int,bit1,X2))) ),
c_0_2095,
[final] ).
cnf(c_0_2995,plain,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X1),X2))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit0,X1)),hAPP(int,int,bit1,X2))) ),
c_0_2096,
[final] ).
cnf(c_0_2996,plain,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X1),X2))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,bit0,X1)),hAPP(int,int,bit1,X2))) ),
c_0_2097,
[final] ).
cnf(c_0_2997,plain,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X1),X2))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,bit0,X1)),hAPP(int,int,bit1,X2))) ),
c_0_2098,
[final] ).
cnf(c_0_2998,plain,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X1),X2))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,bit0,X1)),hAPP(int,int,bit0,X2))) ),
c_0_2099,
[final] ).
cnf(c_0_2999,plain,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X1),X2))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,bit0,X1)),hAPP(int,int,bit0,X2))) ),
c_0_2100,
[final] ).
cnf(c_0_3000,plain,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X1),X2))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,bit1,X1)),hAPP(int,int,bit1,X2))) ),
c_0_2101,
[final] ).
cnf(c_0_3001,plain,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X1),X2))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,bit1,X1)),hAPP(int,int,bit1,X2))) ),
c_0_2102,
[final] ).
cnf(c_0_3002,plain,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X1),X2))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit1,X1)),hAPP(int,int,bit0,X2))) ),
c_0_2103,
[final] ).
cnf(c_0_3003,plain,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X1),X2))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit1,X1)),hAPP(int,int,bit0,X2))) ),
c_0_2104,
[final] ).
cnf(c_0_3004,plain,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X1),X2))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit0,X1)),hAPP(int,int,bit0,X2))) ),
c_0_2105,
[final] ).
cnf(c_0_3005,plain,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X1),X2))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit0,X1)),hAPP(int,int,bit0,X2))) ),
c_0_2106,
[final] ).
cnf(c_0_3006,plain,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X1),X2))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit1,X1)),hAPP(int,int,bit1,X2))) ),
c_0_2107,
[final] ).
cnf(c_0_3007,plain,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X1),X2))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit1,X1)),hAPP(int,int,bit1,X2))) ),
c_0_2108,
[final] ).
cnf(c_0_3008,plain,
( ti(X1,X2) = ti(X1,X3)
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X4))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X2))
| hAPP(nat,X1,power_power(X1,X2),X4) != hAPP(nat,X1,power_power(X1,X3),X4)
| ~ linordered_semidom(X1) ),
c_0_2109,
[final] ).
cnf(c_0_3009,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X3,X2),X1))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X3,X2),X1))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X3,X2),X1)) ),
c_0_2110,
[final] ).
cnf(c_0_3010,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X1,X2),X3))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X2),X3))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X1,X2),X3))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X1,X2),X3)) ),
c_0_2111,
[final] ).
cnf(c_0_3011,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X2,X1,X3,X4)),hAPP(X2,X1,X5,X4)))
| ~ ord(X1)
| ~ hBOOL(hAPP(fun(X2,X1),bool,hAPP(fun(X2,X1),fun(fun(X2,X1),bool),ord_less_eq(fun(X2,X1)),X3),X5)) ),
c_0_2112,
[final] ).
cnf(c_0_3012,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X2,X1,X3,X4)),hAPP(X2,X1,X5,X4)))
| ~ hBOOL(hAPP(fun(X2,X1),bool,hAPP(fun(X2,X1),fun(fun(X2,X1),bool),ord_less_eq(fun(X2,X1)),X3),X5))
| ~ ord(X1) ),
c_0_2113,
[final] ).
cnf(c_0_3013,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X2,X1,X3,X4)),hAPP(X2,X1,X5,X4)))
| ~ hBOOL(hAPP(fun(X2,X1),bool,hAPP(fun(X2,X1),fun(fun(X2,X1),bool),ord_less_eq(fun(X2,X1)),X3),X5))
| ~ ord(X1) ),
c_0_2114,
[final] ).
cnf(c_0_3014,plain,
( X3 = esk4_2(X2,X1)
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X1))
| ~ hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X2))
| hAPP(nat,real,power_power(real,X3),X1) != X2
| ~ hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X3)) ),
c_0_2115,
[final] ).
cnf(c_0_3015,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),hAPP(X1,X1,plus_plus(X1,X2),X3)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X2))
| ~ ordere216010020id_add(X1) ),
c_0_2116,
[final] ).
cnf(c_0_3016,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),hAPP(X1,X1,plus_plus(X1,X2),X3)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X2))
| ~ ordere216010020id_add(X1) ),
c_0_2117,
[final] ).
cnf(c_0_3017,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),hAPP(X1,X1,plus_plus(X1,X2),X3)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X2))
| ~ ordere216010020id_add(X1) ),
c_0_2118,
[final] ).
cnf(c_0_3018,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),hAPP(X1,X1,plus_plus(X1,X2),X3)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X2))
| ~ ordere216010020id_add(X1) ),
c_0_2119,
[final] ).
cnf(c_0_3019,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),hAPP(X1,X1,plus_plus(X1,X3),X4)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X4))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X3))
| ~ ordere216010020id_add(X1) ),
c_0_2120,
[final] ).
cnf(c_0_3020,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),hAPP(X1,X1,plus_plus(X1,X3),X4)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X4))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X3))
| ~ ordere216010020id_add(X1) ),
c_0_2121,
[final] ).
cnf(c_0_3021,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),hAPP(X1,X1,plus_plus(X1,X3),X4)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X4))
| ~ ordere216010020id_add(X1) ),
c_0_2122,
[final] ).
cnf(c_0_3022,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),hAPP(X1,X1,plus_plus(X1,X3),X4)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X4))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X3))
| ~ ordere216010020id_add(X1) ),
c_0_2123,
[final] ).
cnf(c_0_3023,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),hAPP(X1,X1,plus_plus(X1,X3),X4)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X4))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X3))
| ~ linordered_semidom(X1) ),
c_0_2124,
[final] ).
cnf(c_0_3024,plain,
( hBOOL(hAPP(fun(X2,X1),bool,hAPP(fun(X2,X1),fun(fun(X2,X1),bool),ord_less(fun(X2,X1)),X3),X4))
| hBOOL(hAPP(fun(X2,X1),bool,hAPP(fun(X2,X1),fun(fun(X2,X1),bool),ord_less_eq(fun(X2,X1)),X4),X3))
| ~ ord(X1)
| ~ hBOOL(hAPP(fun(X2,X1),bool,hAPP(fun(X2,X1),fun(fun(X2,X1),bool),ord_less_eq(fun(X2,X1)),X3),X4)) ),
c_0_2125,
[final] ).
cnf(c_0_3025,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),one_one(X1)),hAPP(nat,X1,power_power(X1,X2),X3)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),one_one(X1)),X2))
| ~ linordered_semidom(X1) ),
c_0_2126,
[final] ).
cnf(c_0_3026,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X4))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),esk27_4(X1,X4,X2,X3)),X3))
| ~ dense_linorder(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3)) ),
c_0_2127,
[final] ).
cnf(c_0_3027,plain,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,plus_plus(int,X1),X2)))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X2))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X1)) ),
c_0_2128,
[final] ).
cnf(c_0_3028,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),zero_zero(X1)))
| ~ linord219039673up_add(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,plus_plus(X1,X2),X2)),zero_zero(X1))) ),
c_0_2129,
[final] ).
cnf(c_0_3029,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),zero_zero(X1)))
| ~ linord219039673up_add(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,plus_plus(X1,X2),X2)),zero_zero(X1))) ),
c_0_2130,
[final] ).
cnf(c_0_3030,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),zero_zero(X1)))
| ~ linordered_idom(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,plus_plus(X1,X2),X2)),zero_zero(X1))) ),
c_0_2131,
[final] ).
cnf(c_0_3031,plain,
( hBOOL(hAPP(int,bool,X3,X2))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,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_2132,
[final] ).
cnf(c_0_3032,plain,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X1),X2))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,plus_plus(int,X1),one_one(int))),X2)) ),
c_0_2133,
[final] ).
cnf(c_0_3033,plain,
hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),number_number_of(int,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),
c_0_2134,
[final] ).
cnf(c_0_3034,plain,
hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),number_number_of(int,hAPP(int,int,bit1,hAPP(int,int,bit1,pls))))),
c_0_2135,
[final] ).
cnf(c_0_3035,plain,
hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),
c_0_2136,
[final] ).
cnf(c_0_3036,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,plus_plus(X1,X2),X3)),hAPP(X1,X1,plus_plus(X1,X2),X4)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X4))
| ~ ordere779506340up_add(X1) ),
c_0_2137,
[final] ).
cnf(c_0_3037,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,plus_plus(X1,X2),X3)),hAPP(X1,X1,plus_plus(X1,X4),X3)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X4))
| ~ ordere779506340up_add(X1) ),
c_0_2138,
[final] ).
cnf(c_0_3038,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,plus_plus(X1,X2),X3)),hAPP(X1,X1,plus_plus(X1,X2),X4)))
| ~ ordere236663937imp_le(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X4)) ),
c_0_2139,
[final] ).
cnf(c_0_3039,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,plus_plus(X1,X2),X3)),hAPP(X1,X1,plus_plus(X1,X4),X3)))
| ~ ordere236663937imp_le(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X4)) ),
c_0_2140,
[final] ).
cnf(c_0_3040,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,plus_plus(X1,X2),X3)),hAPP(X1,X1,plus_plus(X1,X4),X3)))
| ~ ordere236663937imp_le(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X4)) ),
c_0_2141,
[final] ).
cnf(c_0_3041,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,plus_plus(X1,X2),X3)),hAPP(X1,X1,plus_plus(X1,X2),X4)))
| ~ ordere236663937imp_le(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X4)) ),
c_0_2142,
[final] ).
cnf(c_0_3042,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,plus_plus(X1,X2),X3)),hAPP(X1,X1,plus_plus(X1,X4),X3)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X4))
| ~ ordere223160158up_add(X1) ),
c_0_2143,
[final] ).
cnf(c_0_3043,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,plus_plus(X1,X2),X3)),hAPP(X1,X1,plus_plus(X1,X2),X4)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X4))
| ~ ordere223160158up_add(X1) ),
c_0_2144,
[final] ).
cnf(c_0_3044,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X3))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,plus_plus(nat,X1),X2)),X3)) ),
c_0_2145,
[final] ).
cnf(c_0_3045,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X2),X3))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,plus_plus(nat,X1),X2)),X3)) ),
c_0_2146,
[final] ).
cnf(c_0_3046,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,plus_plus(nat,X1),X3)),X2)) ),
c_0_2147,
[final] ).
cnf(c_0_3047,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,plus_plus(nat,X3),X1)),X2)) ),
c_0_2148,
[final] ).
cnf(c_0_3048,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,plus_plus(nat,X1),X3)),X2)) ),
c_0_2149,
[final] ).
cnf(c_0_3049,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X1))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X2))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,plus_plus(nat,X2),X1))) ),
c_0_2150,
[final] ).
cnf(c_0_3050,plain,
( hBOOL(hAPP(real,bool,hAPP(real,fun(real,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(real,fun(real,bool),ord_less_eq(real),X2),X3)) ),
c_0_2151,
[final] ).
cnf(c_0_3051,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,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(nat,fun(nat,bool),ord_less_eq(nat),X1),X3)) ),
c_0_2152,
[final] ).
cnf(c_0_3052,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,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(nat,fun(nat,bool),ord_less_eq(nat),X2),X3)) ),
c_0_2153,
[final] ).
cnf(c_0_3053,plain,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,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(int,fun(int,bool),ord_less_eq(int),X2),X3)) ),
c_0_2154,
[final] ).
cnf(c_0_3054,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,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(nat,fun(nat,bool),ord_less(nat),X1),X3)) ),
c_0_2155,
[final] ).
cnf(c_0_3055,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,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(nat,fun(nat,bool),ord_less(nat),X2),X3)) ),
c_0_2156,
[final] ).
cnf(c_0_3056,plain,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,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(int,fun(int,bool),ord_less(int),X1),X3)) ),
c_0_2157,
[final] ).
cnf(c_0_3057,plain,
( hBOOL(hAPP(int,bool,X3,X2))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X1),esk1_3(X3,X1,X2)))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X1),X2))
| ~ hBOOL(hAPP(int,bool,X3,hAPP(int,int,plus_plus(int,X1),one_one(int)))) ),
c_0_2158,
[final] ).
cnf(c_0_3058,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),one_one(X1)),number_number_of(X1,X2)))
| ~ linordered_idom(X1)
| ~ number_ring(X1)
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,bit1,pls)),X2)) ),
c_0_2159,
[final] ).
cnf(c_0_3059,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),one_one(X1)),number_number_of(X1,X2)))
| ~ linordered_idom(X1)
| ~ number_ring(X1)
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit1,pls)),X2)) ),
c_0_2160,
[final] ).
cnf(c_0_3060,plain,
hAPP(int,int,plus_plus(int,hAPP(nat,int,semiring_1_of_nat(int),X1)),hAPP(int,int,plus_plus(int,hAPP(nat,int,semiring_1_of_nat(int),X2)),X3)) = hAPP(int,int,plus_plus(int,hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,plus_plus(nat,X1),X2))),X3),
c_0_2161,
[final] ).
cnf(c_0_3061,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X3,X2),X1))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X2),X1))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X3,X2),X1)) ),
c_0_2162,
[final] ).
cnf(c_0_3062,plain,
( hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X1),one_one(real)))
| ~ hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,sqrt,X1)),one_one(real))) ),
c_0_2163,
[final] ).
cnf(c_0_3063,plain,
( hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X1),zero_zero(real)))
| ~ hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,sqrt,X1)),zero_zero(real))) ),
c_0_2164,
[final] ).
cnf(c_0_3064,plain,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X1),zero_zero(int)))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit0,X1)),zero_zero(int))) ),
c_0_2165,
[final] ).
cnf(c_0_3065,plain,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X1),zero_zero(int)))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit1,X1)),zero_zero(int))) ),
c_0_2166,
[final] ).
cnf(c_0_3066,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(nat,X1,semiring_1_of_nat(X1),X2)),hAPP(nat,X1,semiring_1_of_nat(X1),X3)))
| ~ linordered_semidom(X1)
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X2),X3)) ),
c_0_2167,
[final] ).
cnf(c_0_3067,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(nat,X1,semiring_1_of_nat(X1),X2)),hAPP(nat,X1,semiring_1_of_nat(X1),X3)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X2),X3))
| ~ linordered_semidom(X1) ),
c_0_2168,
[final] ).
cnf(c_0_3068,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(nat,X1,semiring_1_of_nat(X1),X2)),hAPP(nat,X1,semiring_1_of_nat(X1),X3)))
| ~ linordered_semidom(X1)
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X2),X3)) ),
c_0_2169,
[final] ).
cnf(c_0_3069,plain,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X1),pls))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,bit1,X1)),pls)) ),
c_0_2170,
[final] ).
cnf(c_0_3070,plain,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X1),pls))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,bit0,X1)),pls)) ),
c_0_2171,
[final] ).
cnf(c_0_3071,plain,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X1),pls))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit0,X1)),pls)) ),
c_0_2172,
[final] ).
cnf(c_0_3072,plain,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X1),pls))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit1,X1)),pls)) ),
c_0_2173,
[final] ).
cnf(c_0_3073,plain,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(nat,int,semiring_1_of_nat(int),X1)),hAPP(nat,int,semiring_1_of_nat(int),X2)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2)) ),
c_0_2174,
[final] ).
cnf(c_0_3074,plain,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(nat,int,semiring_1_of_nat(int),X1)),hAPP(nat,int,semiring_1_of_nat(int),X2)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2)) ),
c_0_2175,
[final] ).
cnf(c_0_3075,plain,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(nat,int,semiring_1_of_nat(int),X1)),hAPP(nat,int,semiring_1_of_nat(int),X2)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2)) ),
c_0_2176,
[final] ).
cnf(c_0_3076,plain,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(nat,int,semiring_1_of_nat(int),X1)),hAPP(nat,int,semiring_1_of_nat(int),X2)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2)) ),
c_0_2177,
[final] ).
cnf(c_0_3077,plain,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,bit1,X1)),hAPP(int,int,bit0,X2)))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X1),X2)) ),
c_0_2178,
[final] ).
cnf(c_0_3078,plain,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,bit1,X1)),hAPP(int,int,bit0,X2)))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X1),X2)) ),
c_0_2179,
[final] ).
cnf(c_0_3079,plain,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit0,X1)),hAPP(int,int,bit1,X2)))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X1),X2)) ),
c_0_2180,
[final] ).
cnf(c_0_3080,plain,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit0,X1)),hAPP(int,int,bit1,X2)))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X1),X2)) ),
c_0_2181,
[final] ).
cnf(c_0_3081,plain,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,bit0,X1)),hAPP(int,int,bit1,X2)))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X1),X2)) ),
c_0_2182,
[final] ).
cnf(c_0_3082,plain,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,bit0,X1)),hAPP(int,int,bit1,X2)))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X1),X2)) ),
c_0_2183,
[final] ).
cnf(c_0_3083,plain,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,bit0,X1)),hAPP(int,int,bit0,X2)))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X1),X2)) ),
c_0_2184,
[final] ).
cnf(c_0_3084,plain,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,bit0,X1)),hAPP(int,int,bit0,X2)))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X1),X2)) ),
c_0_2185,
[final] ).
cnf(c_0_3085,plain,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,bit1,X1)),hAPP(int,int,bit1,X2)))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X1),X2)) ),
c_0_2186,
[final] ).
cnf(c_0_3086,plain,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,bit1,X1)),hAPP(int,int,bit1,X2)))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X1),X2)) ),
c_0_2187,
[final] ).
cnf(c_0_3087,plain,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit1,X1)),hAPP(int,int,bit0,X2)))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X1),X2)) ),
c_0_2188,
[final] ).
cnf(c_0_3088,plain,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit1,X1)),hAPP(int,int,bit0,X2)))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X1),X2)) ),
c_0_2189,
[final] ).
cnf(c_0_3089,plain,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit0,X1)),hAPP(int,int,bit0,X2)))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X1),X2)) ),
c_0_2190,
[final] ).
cnf(c_0_3090,plain,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit0,X1)),hAPP(int,int,bit0,X2)))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X1),X2)) ),
c_0_2191,
[final] ).
cnf(c_0_3091,plain,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit1,X1)),hAPP(int,int,bit1,X2)))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X1),X2)) ),
c_0_2192,
[final] ).
cnf(c_0_3092,plain,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit1,X1)),hAPP(int,int,bit1,X2)))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X1),X2)) ),
c_0_2193,
[final] ).
cnf(c_0_3093,plain,
( ~ ord(X1)
| ~ hBOOL(hAPP(fun(X2,X1),bool,hAPP(fun(X2,X1),fun(fun(X2,X1),bool),ord_less(fun(X2,X1)),X3),X4))
| ~ hBOOL(hAPP(fun(X2,X1),bool,hAPP(fun(X2,X1),fun(fun(X2,X1),bool),ord_less_eq(fun(X2,X1)),X4),X3)) ),
c_0_2194,
[final] ).
cnf(c_0_3094,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X4))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),esk27_4(X1,X4,X2,X3)))
| ~ dense_linorder(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3)) ),
c_0_2195,
[final] ).
cnf(c_0_3095,plain,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),X2))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),number_number_of(nat,X1)),number_number_of(nat,X2)))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X1),X2)) ),
c_0_2196,
[final] ).
cnf(c_0_3096,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X4))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X4),X3))
| ~ order(X1) ),
c_0_2197,
[final] ).
cnf(c_0_3097,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X4),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X4))
| ~ preorder(X1) ),
c_0_2198,
[final] ).
cnf(c_0_3098,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X4))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X4),X3))
| ~ order(X1) ),
c_0_2199,
[final] ).
cnf(c_0_3099,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X4),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X4))
| ~ preorder(X1) ),
c_0_2200,
[final] ).
cnf(c_0_3100,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X4),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X4))
| ~ preorder(X1) ),
c_0_2201,
[final] ).
cnf(c_0_3101,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X4))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X4),X3))
| ~ order(X1) ),
c_0_2202,
[final] ).
cnf(c_0_3102,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X4),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X4))
| ~ preorder(X1) ),
c_0_2203,
[final] ).
cnf(c_0_3103,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X4))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X4),X3))
| ~ order(X1) ),
c_0_2204,
[final] ).
cnf(c_0_3104,plain,
( hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),esk23_2(X2,X1)),X1))
| ~ hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X1))
| ~ hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X2)) ),
c_0_2205,
[final] ).
cnf(c_0_3105,plain,
( hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),esk23_2(X2,X1)),X2))
| ~ hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X1))
| ~ hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X2)) ),
c_0_2206,
[final] ).
cnf(c_0_3106,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),number_number_of(nat,X1)),number_number_of(nat,X2)))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X1),X2))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),X2)) ),
c_0_2207,
[final] ).
cnf(c_0_3107,plain,
( hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),esk23_2(X2,X1)))
| ~ hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X1))
| ~ hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X2)) ),
c_0_2208,
[final] ).
cnf(c_0_3108,plain,
( hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),esk5_2(X2,X1)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X1))
| ~ hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X2)) ),
c_0_2209,
[final] ).
cnf(c_0_3109,plain,
( hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),esk4_2(X2,X1)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X1))
| ~ hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X2)) ),
c_0_2210,
[final] ).
cnf(c_0_3110,plain,
( hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X1),X2))
| ~ hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X3),X2))
| ~ hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X1),X3)) ),
c_0_2211,
[final] ).
cnf(c_0_3111,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X3),X2))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X3)) ),
c_0_2212,
[final] ).
cnf(c_0_3112,plain,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X1),X2))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X3),X2))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X1),X3)) ),
c_0_2213,
[final] ).
cnf(c_0_3113,plain,
( X3 = X2
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X1,X2),X3))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X1,X2),X3))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X1,X2),X3)) ),
c_0_2214,
[final] ).
cnf(c_0_3114,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,plus_plus(X1,X2),X2)),zero_zero(X1)))
| ~ linord219039673up_add(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),zero_zero(X1))) ),
c_0_2215,
[final] ).
cnf(c_0_3115,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,plus_plus(X1,X2),X2)),zero_zero(X1)))
| ~ linord219039673up_add(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),zero_zero(X1))) ),
c_0_2216,
[final] ).
cnf(c_0_3116,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,plus_plus(X1,X2),X2)),zero_zero(X1)))
| ~ linordered_idom(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),zero_zero(X1))) ),
c_0_2217,
[final] ).
cnf(c_0_3117,plain,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,plus_plus(int,X1),one_one(int))),X2))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X1),X2)) ),
c_0_2218,
[final] ).
cnf(c_0_3118,plain,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,plus_plus(int,X1),one_one(int))),X2))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X1),X2)) ),
c_0_2219,
[final] ).
cnf(c_0_3119,plain,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,bit1,pls)),X2))
| ~ linordered_idom(X1)
| ~ number_ring(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),one_one(X1)),number_number_of(X1,X2))) ),
c_0_2220,
[final] ).
cnf(c_0_3120,plain,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit1,pls)),X2))
| ~ linordered_idom(X1)
| ~ number_ring(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),one_one(X1)),number_number_of(X1,X2))) ),
c_0_2221,
[final] ).
cnf(c_0_3121,plain,
( hBOOL(hAPP(int,bool,X3,X2))
| hBOOL(hAPP(int,bool,X3,esk1_3(X3,X1,X2)))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X1),X2))
| ~ hBOOL(hAPP(int,bool,X3,hAPP(int,int,plus_plus(int,X1),one_one(int)))) ),
c_0_2222,
[final] ).
cnf(c_0_3122,plain,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),number_number_of(int,hAPP(int,int,bit0,X1))))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),number_number_of(int,X1))) ),
c_0_2223,
[final] ).
cnf(c_0_3123,plain,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),number_number_of(int,hAPP(int,int,bit1,X1))))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),number_number_of(int,X1))) ),
c_0_2224,
[final] ).
cnf(c_0_3124,plain,
( hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,sqrt,X1)),one_one(real)))
| ~ hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X1),one_one(real))) ),
c_0_2225,
[final] ).
cnf(c_0_3125,plain,
( hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,sqrt,X1)),zero_zero(real)))
| ~ hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X1),zero_zero(real))) ),
c_0_2226,
[final] ).
cnf(c_0_3126,plain,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit0,X1)),zero_zero(int)))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X1),zero_zero(int))) ),
c_0_2227,
[final] ).
cnf(c_0_3127,plain,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit1,X1)),zero_zero(int)))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X1),zero_zero(int))) ),
c_0_2228,
[final] ).
cnf(c_0_3128,plain,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,bit1,X1)),pls))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X1),pls)) ),
c_0_2229,
[final] ).
cnf(c_0_3129,plain,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,bit0,X1)),pls))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X1),pls)) ),
c_0_2230,
[final] ).
cnf(c_0_3130,plain,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit0,X1)),pls))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X1),pls)) ),
c_0_2231,
[final] ).
cnf(c_0_3131,plain,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit1,X1)),pls))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X1),pls)) ),
c_0_2232,
[final] ).
cnf(c_0_3132,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X2))
| ~ linord219039673up_add(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),hAPP(X1,X1,plus_plus(X1,X2),X2))) ),
c_0_2233,
[final] ).
cnf(c_0_3133,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X2))
| ~ linord219039673up_add(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),hAPP(X1,X1,plus_plus(X1,X2),X2))) ),
c_0_2234,
[final] ).
cnf(c_0_3134,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X1))
| number_number_of(nat,X2) = zero_zero(nat)
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,power_power(nat,X1),number_number_of(nat,X2)))) ),
c_0_2235,
[final] ).
cnf(c_0_3135,plain,
~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,plus_plus(nat,X1),X2)),X2)),
c_0_2236,
[final] ).
cnf(c_0_3136,plain,
~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,plus_plus(nat,X1),X2)),X1)),
c_0_2237,
[final] ).
cnf(c_0_3137,plain,
( hAPP(X1,X1,plus_plus(X1,number_number_of(X1,X2)),number_number_of(X1,X3)) = number_number_of(X1,hAPP(int,int,plus_plus(int,X2),X3))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),X3))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),X2))
| ~ number_semiring(X1) ),
c_0_2238,
[final] ).
cnf(c_0_3138,plain,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X1),pls))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X1),X2))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),number_number_of(nat,X1)),number_number_of(nat,X2))) ),
c_0_2239,
[final] ).
cnf(c_0_3139,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X1))
| X2 = zero_zero(nat)
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,power_power(nat,X1),X2))) ),
c_0_2240,
[final] ).
cnf(c_0_3140,plain,
( X1 = zero_zero(nat)
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X2))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,power_power(nat,X2),X1))) ),
c_0_2241,
[final] ).
cnf(c_0_3141,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),number_number_of(nat,X1)),number_number_of(nat,X2)))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X1),X2))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X1),X2)) ),
c_0_2242,
[final] ).
cnf(c_0_3142,plain,
( X1 = X2
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X1),X2))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X1),hAPP(int,int,plus_plus(int,X2),one_one(int)))) ),
c_0_2243,
[final] ).
cnf(c_0_3143,plain,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X1),X2))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X1),hAPP(int,int,plus_plus(int,X2),one_one(int)))) ),
c_0_2244,
[final] ).
cnf(c_0_3144,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X2))
| ~ preorder(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3)) ),
c_0_2245,
[final] ).
cnf(c_0_3145,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X2))
| ~ linordered_semidom(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),hAPP(nat,X1,semiring_1_of_nat(X1),X2))) ),
c_0_2246,
[final] ).
cnf(c_0_3146,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),number_number_of(X1,X2)),one_one(X1)))
| ~ linordered_idom(X1)
| ~ number_ring(X1)
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X2),hAPP(int,int,bit1,pls))) ),
c_0_2247,
[final] ).
cnf(c_0_3147,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),number_number_of(X1,X2)),one_one(X1)))
| ~ linordered_idom(X1)
| ~ number_ring(X1)
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X2),hAPP(int,int,bit1,pls))) ),
c_0_2248,
[final] ).
cnf(c_0_3148,plain,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(nat,X1,semiring_1_of_nat(X1),X2)),zero_zero(X1)))
| ~ linordered_semidom(X1) ),
c_0_2249,
[final] ).
cnf(c_0_3149,plain,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X1))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X1))
| ~ hBOOL(X2)
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X1)) ),
c_0_2250,
[final] ).
cnf(c_0_3150,plain,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X1))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X1))
| ~ hBOOL(X2)
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X1)) ),
c_0_2251,
[final] ).
cnf(c_0_3151,plain,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X1))
| hBOOL(X2)
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X1))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X1)) ),
c_0_2252,
[final] ).
cnf(c_0_3152,plain,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X1))
| hBOOL(X2)
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X1))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X1)) ),
c_0_2253,
[final] ).
cnf(c_0_3153,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X1))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(nat,int,semiring_1_of_nat(int),X1))) ),
c_0_2254,
[final] ).
cnf(c_0_3154,plain,
( hBOOL(hAPP(fun(X2,X1),bool,hAPP(fun(X2,X1),fun(fun(X2,X1),bool),ord_less_eq(fun(X2,X1)),X3),X4))
| ~ ord(X1)
| ~ hBOOL(hAPP(fun(X2,X1),bool,hAPP(fun(X2,X1),fun(fun(X2,X1),bool),ord_less(fun(X2,X1)),X3),X4)) ),
c_0_2255,
[final] ).
cnf(c_0_3155,plain,
( hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),one_one(real)),X1))
| ~ hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),one_one(real)),hAPP(real,real,sqrt,X1))) ),
c_0_2256,
[final] ).
cnf(c_0_3156,plain,
( hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X1))
| ~ hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(real,real,sqrt,X1))) ),
c_0_2257,
[final] ).
cnf(c_0_3157,plain,
( X1 = zero_zero(nat)
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(nat,int,semiring_1_of_nat(int),X1)),zero_zero(int))) ),
c_0_2258,
[final] ).
cnf(c_0_3158,plain,
~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(nat,int,semiring_1_of_nat(int),X1)),zero_zero(int))),
c_0_2259,
[final] ).
cnf(c_0_3159,plain,
( ti(X1,X2) = zero_zero(X1)
| ~ ordere216010020id_add(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X2))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X3))
| hAPP(X1,X1,plus_plus(X1,X2),X3) != zero_zero(X1) ),
c_0_2260,
[final] ).
cnf(c_0_3160,plain,
( ti(X1,X3) = zero_zero(X1)
| ~ ordere216010020id_add(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X2))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X3))
| hAPP(X1,X1,plus_plus(X1,X2),X3) != zero_zero(X1) ),
c_0_2261,
[final] ).
cnf(c_0_3161,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2))
| X1 = X2
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X3,X2),X1))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X3,X2),X1)) ),
c_0_2262,
[final] ).
cnf(c_0_3162,plain,
( X3 = X2
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X1,X2),X3))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X2),X3))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X1,X2),X3)) ),
c_0_2263,
[final] ).
cnf(c_0_3163,plain,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),X1))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),hAPP(int,int,bit1,X1))) ),
c_0_2264,
[final] ).
cnf(c_0_3164,plain,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),X1))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),hAPP(int,int,bit0,X1))) ),
c_0_2265,
[final] ).
cnf(c_0_3165,plain,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),X1))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),hAPP(int,int,bit1,X1))) ),
c_0_2266,
[final] ).
cnf(c_0_3166,plain,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),X1))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),hAPP(int,int,bit0,X1))) ),
c_0_2267,
[final] ).
cnf(c_0_3167,plain,
( ~ linorder(X1)
| ~ number(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),number_number_of(X1,X2)),number_number_of(X1,X3)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),number_number_of(X1,X3)),number_number_of(X1,X2))) ),
c_0_2268,
[final] ).
cnf(c_0_3168,plain,
( hBOOL(hAPP(int,bool,X3,X2))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X1),esk18_3(X3,X1,X2)))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X1),X2))
| ~ hBOOL(hAPP(int,bool,X3,X1)) ),
c_0_2269,
[final] ).
cnf(c_0_3169,plain,
( hAPP(X1,X1,plus_plus(X1,X2),X3) = zero_zero(X1)
| ~ ordere216010020id_add(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X2))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X3))
| ti(X1,X3) != zero_zero(X1)
| ti(X1,X2) != zero_zero(X1) ),
c_0_2270,
[final] ).
cnf(c_0_3170,plain,
( hBOOL(hAPP(int,bool,X1,X2))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X2))
| ~ hBOOL(hAPP(int,bool,X1,hAPP(nat,int,semiring_1_of_nat(int),esk9_1(X1)))) ),
c_0_2271,
[final] ).
cnf(c_0_3171,plain,
( hAPP(nat,real,power_power(real,esk5_2(X2,X1)),X1) = X2
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X1))
| ~ hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X2)) ),
c_0_2272,
[final] ).
cnf(c_0_3172,plain,
( hAPP(nat,real,power_power(real,esk4_2(X2,X1)),X1) = X2
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X1))
| ~ hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X2)) ),
c_0_2273,
[final] ).
cnf(c_0_3173,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),hAPP(X1,X1,plus_plus(X1,X2),X2)))
| ~ linord219039673up_add(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X2)) ),
c_0_2274,
[final] ).
cnf(c_0_3174,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),hAPP(X1,X1,plus_plus(X1,X2),X2)))
| ~ linord219039673up_add(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X2)) ),
c_0_2275,
[final] ).
cnf(c_0_3175,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),one_one(X1)),hAPP(nat,X1,power_power(X1,X2),X3)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),one_one(X1)),X2))
| ~ linordered_semidom(X1) ),
c_0_2276,
[final] ).
cnf(c_0_3176,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),hAPP(nat,X1,power_power(X1,X2),X3)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X2))
| ~ linordered_semidom(X1) ),
c_0_2277,
[final] ).
cnf(c_0_3177,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),hAPP(nat,X1,power_power(X1,X2),X3)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X2))
| ~ linordered_semidom(X1) ),
c_0_2278,
[final] ).
cnf(c_0_3178,plain,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X2),hAPP(int,int,bit1,pls)))
| ~ linordered_idom(X1)
| ~ number_ring(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),number_number_of(X1,X2)),one_one(X1))) ),
c_0_2279,
[final] ).
cnf(c_0_3179,plain,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X2),hAPP(int,int,bit1,pls)))
| ~ linordered_idom(X1)
| ~ number_ring(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),number_number_of(X1,X2)),one_one(X1))) ),
c_0_2280,
[final] ).
cnf(c_0_3180,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,power_power(nat,X1),number_number_of(nat,X2))))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X1)) ),
c_0_2281,
[final] ).
cnf(c_0_3181,plain,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),esk26_2(X1,X3)),X2))
| ~ linorder(X1) ),
c_0_2282,
[final] ).
cnf(c_0_3182,plain,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(int,int,plus_plus(int,one_one(int)),X1)))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X1)) ),
c_0_2283,
[final] ).
cnf(c_0_3183,plain,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(nat,int,power_power(int,X1),X2)))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X1)) ),
c_0_2284,
[final] ).
cnf(c_0_3184,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,power_power(nat,X1),X2)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X1)) ),
c_0_2285,
[final] ).
cnf(c_0_3185,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,plus_plus(nat,X1),X2)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X1)) ),
c_0_2286,
[final] ).
cnf(c_0_3186,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,plus_plus(nat,X1),X2)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X2)) ),
c_0_2287,
[final] ).
cnf(c_0_3187,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,power_power(nat,X1),X2)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X1)) ),
c_0_2288,
[final] ).
cnf(c_0_3188,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),hAPP(nat,X1,semiring_1_of_nat(X1),X2)))
| ~ linordered_semidom(X1)
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X2)) ),
c_0_2289,
[final] ).
cnf(c_0_3189,plain,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),esk36_2(X1,X2)))
| ~ linorder(X1) ),
c_0_2290,
[final] ).
cnf(c_0_3190,plain,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X1),hAPP(int,int,plus_plus(int,X2),one_one(int))))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X1),X2)) ),
c_0_2291,
[final] ).
cnf(c_0_3191,plain,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X1),hAPP(int,int,plus_plus(int,X2),one_one(int))))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X1),X2)) ),
c_0_2292,
[final] ).
cnf(c_0_3192,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),hAPP(nat,nat,plus_plus(nat,X2),X3)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X3)) ),
c_0_2293,
[final] ).
cnf(c_0_3193,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),hAPP(nat,nat,plus_plus(nat,X2),X3)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2)) ),
c_0_2294,
[final] ).
cnf(c_0_3194,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),hAPP(nat,nat,plus_plus(nat,X2),X3)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X3)) ),
c_0_2295,
[final] ).
cnf(c_0_3195,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),hAPP(nat,nat,plus_plus(nat,X2),X3)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2)) ),
c_0_2296,
[final] ).
cnf(c_0_3196,plain,
( ~ linorder(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| ti(X1,X2) != ti(X1,X3) ),
c_0_2297,
[final] ).
cnf(c_0_3197,plain,
( ti(X1,X2) = ti(X1,X3)
| ~ order(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X2))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3)) ),
c_0_2298,
[final] ).
cnf(c_0_3198,plain,
( ti(X1,X3) = ti(X1,X2)
| ~ order(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X2)) ),
c_0_2299,
[final] ).
cnf(c_0_3199,plain,
( ti(X1,X2) = ti(X1,X3)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X2))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
| ~ order(X1) ),
c_0_2300,
[final] ).
cnf(c_0_3200,plain,
( ti(X1,X2) = ti(X1,X3)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X2))
| ~ order(X1) ),
c_0_2301,
[final] ).
cnf(c_0_3201,plain,
( ti(X1,X2) = zero_zero(X1)
| ~ ring_11004092258visors(X1)
| hAPP(nat,X1,power_power(X1,X2),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) != zero_zero(X1) ),
c_0_2302,
[final] ).
cnf(c_0_3202,plain,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(nat,int,semiring_1_of_nat(int),X1)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X1)) ),
c_0_2303,
[final] ).
cnf(c_0_3203,plain,
( hBOOL(X1)
| ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),X3),X4))
| ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),X4),X3))
| ~ preorder(X2) ),
c_0_2304,
[final] ).
cnf(c_0_3204,plain,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X2))
| ~ linorder(X1) ),
c_0_2305,
[final] ).
cnf(c_0_3205,plain,
( ~ preorder(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X2)) ),
c_0_2306,
[final] ).
cnf(c_0_3206,plain,
( ~ linorder(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X2)) ),
c_0_2307,
[final] ).
cnf(c_0_3207,plain,
( ~ linorder(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X2)) ),
c_0_2308,
[final] ).
cnf(c_0_3208,plain,
( ~ linorder(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X2)) ),
c_0_2309,
[final] ).
cnf(c_0_3209,plain,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X2))
| ~ preorder(X1) ),
c_0_2310,
[final] ).
cnf(c_0_3210,plain,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X2))
| ~ preorder(X1) ),
c_0_2311,
[final] ).
cnf(c_0_3211,plain,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X2))
| ~ preorder(X1) ),
c_0_2312,
[final] ).
cnf(c_0_3212,plain,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X2))
| ~ order(X1) ),
c_0_2313,
[final] ).
cnf(c_0_3213,plain,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X2))
| ~ preorder(X1) ),
c_0_2314,
[final] ).
cnf(c_0_3214,plain,
( hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),one_one(real)),hAPP(real,real,sqrt,X1)))
| ~ hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),one_one(real)),X1)) ),
c_0_2315,
[final] ).
cnf(c_0_3215,plain,
( hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(real,real,sqrt,X1)))
| ~ hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X1)) ),
c_0_2316,
[final] ).
cnf(c_0_3216,plain,
( hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(real,real,sqrt,X1)))
| ~ hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X1)) ),
c_0_2317,
[final] ).
cnf(c_0_3217,plain,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),hAPP(int,int,bit1,X1)))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),X1)) ),
c_0_2318,
[final] ).
cnf(c_0_3218,plain,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),hAPP(int,int,bit0,X1)))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),X1)) ),
c_0_2319,
[final] ).
cnf(c_0_3219,plain,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),hAPP(int,int,bit1,X1)))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),X1)) ),
c_0_2320,
[final] ).
cnf(c_0_3220,plain,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),hAPP(int,int,bit0,X1)))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),X1)) ),
c_0_2321,
[final] ).
cnf(c_0_3221,plain,
( X1 = X2
| ~ hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X2),X1))
| ~ hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X1),X2)) ),
c_0_2322,
[final] ).
cnf(c_0_3222,plain,
( X1 = X2
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X2),X1))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2)) ),
c_0_2323,
[final] ).
cnf(c_0_3223,plain,
( X1 = X2
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X2),X1))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X1),X2)) ),
c_0_2324,
[final] ).
cnf(c_0_3224,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,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(nat,fun(nat,bool),ord_less(nat),X4),X3)) ),
c_0_2325,
[final] ).
cnf(c_0_3225,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
| ~ dense_linorder(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),esk24_3(X1,X3,X2)),X3)) ),
c_0_2326,
[final] ).
cnf(c_0_3226,plain,
( hBOOL(hAPP(int,bool,X1,hAPP(nat,int,semiring_1_of_nat(int),esk6_1(X1))))
| ~ hBOOL(hAPP(int,bool,X1,X2))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X2)) ),
c_0_2327,
[final] ).
cnf(c_0_3227,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2))
| X1 = X2
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X3,X2),X1))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X2),X1)) ),
c_0_2328,
[final] ).
cnf(c_0_3228,plain,
hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(int,int,plus_plus(int,one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),n)))),
c_0_2329,
[final] ).
cnf(c_0_3229,plain,
hAPP(nat,int,semiring_1_of_nat(int),number_number_of(nat,hAPP(int,int,bit1,hAPP(int,int,bit1,pls)))) = number_number_of(int,hAPP(int,int,bit1,hAPP(int,int,bit1,pls))),
c_0_2330,
[final] ).
cnf(c_0_3230,plain,
hAPP(nat,int,semiring_1_of_nat(int),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) = number_number_of(int,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))),
c_0_2331,
[final] ).
cnf(c_0_3231,plain,
hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),m1),hAPP(int,int,plus_plus(int,one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),n)))),
c_0_2332,
[final] ).
cnf(c_0_3232,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(nat,fun(nat,bool),ord_less(nat),X3),esk19_2(X2,X1))) ),
c_0_2333,
[final] ).
cnf(c_0_3233,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(nat,fun(nat,bool),ord_less_eq(nat),X3),esk14_2(X2,X1))) ),
c_0_2334,
[final] ).
cnf(c_0_3234,plain,
( hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),hAPP(bool,fun(nat,fun(nat,nat)),if(nat),X2),X1),X3)) = hAPP(nat,int,semiring_1_of_nat(int),X1)
| ~ hBOOL(X2) ),
c_0_2335,
[final] ).
cnf(c_0_3235,plain,
( hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),hAPP(bool,fun(nat,fun(nat,nat)),if(nat),X2),X3),X1)) = hAPP(nat,int,semiring_1_of_nat(int),X1)
| hBOOL(X2) ),
c_0_2336,
[final] ).
cnf(c_0_3236,plain,
( hBOOL(hAPP(int,bool,X3,X2))
| hBOOL(hAPP(int,bool,X3,esk18_3(X3,X1,X2)))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X1),X2))
| ~ hBOOL(hAPP(int,bool,X3,X1)) ),
c_0_2337,
[final] ).
cnf(c_0_3237,plain,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,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(int,fun(int,bool),ord_less(int),X2),pls)) ),
c_0_2338,
[final] ).
cnf(c_0_3238,plain,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X2),X3))
| ~ linordered_idom(X1)
| ~ number_ring(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),number_number_of(X1,X2)),number_number_of(X1,X3))) ),
c_0_2339,
[final] ).
cnf(c_0_3239,plain,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X2),X3))
| ~ linordered_idom(X1)
| ~ number_ring(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),number_number_of(X1,X2)),number_number_of(X1,X3))) ),
c_0_2340,
[final] ).
cnf(c_0_3240,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),esk31_2(X1,X2)),X3))
| ~ linorder(X1) ),
c_0_2341,
[final] ).
cnf(c_0_3241,plain,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X2),pls))
| ~ linordered_idom(X1)
| ~ number_ring(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),number_number_of(X1,X2)),zero_zero(X1))) ),
c_0_2342,
[final] ).
cnf(c_0_3242,plain,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X2),pls))
| ~ linordered_idom(X1)
| ~ number_ring(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),number_number_of(X1,X2)),zero_zero(X1))) ),
c_0_2343,
[final] ).
cnf(c_0_3243,plain,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X1),X2))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),number_number_of(int,X1)),number_number_of(int,X2))) ),
c_0_2344,
[final] ).
cnf(c_0_3244,plain,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X1),X2))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),number_number_of(nat,X1)),number_number_of(nat,X2))) ),
c_0_2345,
[final] ).
cnf(c_0_3245,plain,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X1),X2))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),number_number_of(int,X1)),number_number_of(int,X2))) ),
c_0_2346,
[final] ).
cnf(c_0_3246,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),number_number_of(X1,X2)),number_number_of(X1,X3)))
| ~ linordered_idom(X1)
| ~ number_ring(X1)
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X2),X3)) ),
c_0_2347,
[final] ).
cnf(c_0_3247,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),number_number_of(X1,X2)),number_number_of(X1,X3)))
| ~ linordered_idom(X1)
| ~ number_ring(X1)
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X2),X3)) ),
c_0_2348,
[final] ).
cnf(c_0_3248,plain,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),X2))
| ~ linordered_idom(X1)
| ~ number_ring(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),number_number_of(X1,X2))) ),
c_0_2349,
[final] ).
cnf(c_0_3249,plain,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),X2))
| ~ linordered_idom(X1)
| ~ number_ring(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),number_number_of(X1,X2))) ),
c_0_2350,
[final] ).
cnf(c_0_3250,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),esk30_2(X1,X3)))
| ~ linorder(X1) ),
c_0_2351,
[final] ).
cnf(c_0_3251,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),number_number_of(X1,X2)),zero_zero(X1)))
| ~ linordered_idom(X1)
| ~ number_ring(X1)
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X2),pls)) ),
c_0_2352,
[final] ).
cnf(c_0_3252,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),number_number_of(X1,X2)),zero_zero(X1)))
| ~ linordered_idom(X1)
| ~ number_ring(X1)
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X2),pls)) ),
c_0_2353,
[final] ).
cnf(c_0_3253,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| ~ linorder(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X2))
| ti(X1,X3) != ti(X1,X2) ),
c_0_2354,
[final] ).
cnf(c_0_3254,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X4))
| ti(X1,X3) != ti(X1,X4)
| ~ order(X1) ),
c_0_2355,
[final] ).
cnf(c_0_3255,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| ti(X1,X4) != ti(X1,X2)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X4),X3))
| ~ order(X1) ),
c_0_2356,
[final] ).
cnf(c_0_3256,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X2))
| ~ order(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
| ti(X1,X3) != ti(X1,X2) ),
c_0_2357,
[final] ).
cnf(c_0_3257,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X4))
| ti(X1,X3) != ti(X1,X4)
| ~ order(X1) ),
c_0_2358,
[final] ).
cnf(c_0_3258,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
| ti(X1,X4) != ti(X1,X2)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X4),X3))
| ~ order(X1) ),
c_0_2359,
[final] ).
cnf(c_0_3259,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),number_number_of(nat,X1)),number_number_of(nat,X2)))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X1),X2)) ),
c_0_2360,
[final] ).
cnf(c_0_3260,plain,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),number_number_of(int,X1)),number_number_of(int,X2)))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X1),X2)) ),
c_0_2361,
[final] ).
cnf(c_0_3261,plain,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),number_number_of(int,X1)),number_number_of(int,X2)))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X1),X2)) ),
c_0_2362,
[final] ).
cnf(c_0_3262,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),number_number_of(nat,X1)),number_number_of(nat,X2)))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X1),pls)) ),
c_0_2363,
[final] ).
cnf(c_0_3263,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| ti(X1,X3) = ti(X1,X2)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
| ~ order(X1) ),
c_0_2364,
[final] ).
cnf(c_0_3264,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| ti(X1,X2) = ti(X1,X3)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
| ~ order(X1) ),
c_0_2365,
[final] ).
cnf(c_0_3265,plain,
( ti(X1,X2) = ti(X1,X3)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
| ~ order(X1) ),
c_0_2366,
[final] ).
cnf(c_0_3266,plain,
( ti(X1,X2) = ti(X1,X3)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| ~ linorder(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3)) ),
c_0_2367,
[final] ).
cnf(c_0_3267,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| ti(X1,X3) = ti(X1,X2)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
| ~ order(X1) ),
c_0_2368,
[final] ).
cnf(c_0_3268,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| ti(X1,X2) = ti(X1,X3)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
| ~ order(X1) ),
c_0_2369,
[final] ).
cnf(c_0_3269,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| ti(X1,X2) = ti(X1,X3)
| ~ linorder(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3)) ),
c_0_2370,
[final] ).
cnf(c_0_3270,plain,
( ti(X1,X2) = ti(X1,X3)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| ~ order(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3)) ),
c_0_2371,
[final] ).
cnf(c_0_3271,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| ti(X1,X2) = ti(X1,X3)
| ~ order(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3)) ),
c_0_2372,
[final] ).
cnf(c_0_3272,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),number_number_of(X1,X2)))
| ~ linordered_idom(X1)
| ~ number_ring(X1)
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),X2)) ),
c_0_2373,
[final] ).
cnf(c_0_3273,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),number_number_of(X1,X2)))
| ~ linordered_idom(X1)
| ~ number_ring(X1)
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),X2)) ),
c_0_2374,
[final] ).
cnf(c_0_3274,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X4),X3))
| X2 != X4
| ~ ord(X1) ),
c_0_2375,
[final] ).
cnf(c_0_3275,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| X4 != X3
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X4))
| ~ ord(X1) ),
c_0_2376,
[final] ).
cnf(c_0_3276,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X4),X3))
| X2 != X4
| ~ ord(X1) ),
c_0_2377,
[final] ).
cnf(c_0_3277,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
| X4 != X3
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X4))
| ~ ord(X1) ),
c_0_2378,
[final] ).
cnf(c_0_3278,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| ~ preorder(X1) ),
c_0_2379,
[final] ).
cnf(c_0_3279,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
| ~ order(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3)) ),
c_0_2380,
[final] ).
cnf(c_0_3280,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
| ~ preorder(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3)) ),
c_0_2381,
[final] ).
cnf(c_0_3281,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
| ~ order(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3)) ),
c_0_2382,
[final] ).
cnf(c_0_3282,plain,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),X1))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),number_number_of(nat,X1))) ),
c_0_2383,
[final] ).
cnf(c_0_3283,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),esk3_2(X1,X2)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2)) ),
c_0_2384,
[final] ).
cnf(c_0_3284,plain,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X3))
| ~ hBOOL(X1)
| ~ hBOOL(X2)
| ~ hBOOL(X2)
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X3)) ),
c_0_2385,
[final] ).
cnf(c_0_3285,plain,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X3))
| ~ hBOOL(X1)
| ~ hBOOL(X2)
| ~ hBOOL(X1)
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X3)) ),
c_0_2386,
[final] ).
cnf(c_0_3286,plain,
( hBOOL(X1)
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X3))
| ~ hBOOL(X1)
| ~ hBOOL(X2)
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X3)) ),
c_0_2387,
[final] ).
cnf(c_0_3287,plain,
( hBOOL(X2)
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X3))
| ~ hBOOL(X1)
| ~ hBOOL(X2)
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X3)) ),
c_0_2388,
[final] ).
cnf(c_0_3288,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),number_number_of(nat,X1)))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),X1)) ),
c_0_2389,
[final] ).
cnf(c_0_3289,plain,
( hBOOL(X1)
| hBOOL(X2)
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X3))
| ~ hBOOL(X2)
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X3)) ),
c_0_2390,
[final] ).
cnf(c_0_3290,plain,
( hBOOL(X1)
| hBOOL(X2)
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X3))
| ~ hBOOL(X1)
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X3)) ),
c_0_2391,
[final] ).
cnf(c_0_3291,plain,
( hBOOL(X1)
| hBOOL(X2)
| hBOOL(X1)
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X3))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X3)) ),
c_0_2392,
[final] ).
cnf(c_0_3292,plain,
( hBOOL(X1)
| hBOOL(X2)
| hBOOL(X2)
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X3))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X3)) ),
c_0_2393,
[final] ).
cnf(c_0_3293,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),esk2_1(X1)))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),X1)) ),
c_0_2394,
[final] ).
cnf(c_0_3294,plain,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X1))
| hBOOL(X2)
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X1))
| ~ hBOOL(X3) ),
c_0_2395,
[final] ).
cnf(c_0_3295,plain,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X1))
| hBOOL(X2)
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X1))
| ~ hBOOL(X3) ),
c_0_2396,
[final] ).
cnf(c_0_3296,plain,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X1))
| hBOOL(X3)
| ~ hBOOL(X2)
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X1)) ),
c_0_2397,
[final] ).
cnf(c_0_3297,plain,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X1))
| hBOOL(X3)
| ~ hBOOL(X2)
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X1)) ),
c_0_2398,
[final] ).
cnf(c_0_3298,plain,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),X1))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),one_one(int)),X1)) ),
c_0_2399,
[final] ).
cnf(c_0_3299,plain,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),one_one(int)),X1))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),X1)) ),
c_0_2400,
[final] ).
cnf(c_0_3300,plain,
( hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X1),X2))
| X1 = X2
| ~ hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X1),X2)) ),
c_0_2401,
[final] ).
cnf(c_0_3301,plain,
( X1 = X2
| hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X1),X2))
| ~ hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X1),X2)) ),
c_0_2402,
[final] ).
cnf(c_0_3302,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2))
| X1 = X2
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2)) ),
c_0_2403,
[final] ).
cnf(c_0_3303,plain,
( X1 = X2
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2)) ),
c_0_2404,
[final] ).
cnf(c_0_3304,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2))
| X1 = X2
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2)) ),
c_0_2405,
[final] ).
cnf(c_0_3305,plain,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X1),X2))
| X1 = X2
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X1),X2)) ),
c_0_2406,
[final] ).
cnf(c_0_3306,plain,
( hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X1),X2))
| ~ hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X1),X2)) ),
c_0_2407,
[final] ).
cnf(c_0_3307,plain,
( hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X1),X2))
| ~ hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X1),X2)) ),
c_0_2408,
[final] ).
cnf(c_0_3308,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2)) ),
c_0_2409,
[final] ).
cnf(c_0_3309,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2)) ),
c_0_2410,
[final] ).
cnf(c_0_3310,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2)) ),
c_0_2411,
[final] ).
cnf(c_0_3311,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2)) ),
c_0_2412,
[final] ).
cnf(c_0_3312,plain,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X1),X2))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X1),X2)) ),
c_0_2413,
[final] ).
cnf(c_0_3313,plain,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,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(int,fun(int,bool),ord_less(int),X2),pls)) ),
c_0_2414,
[final] ).
cnf(c_0_3314,plain,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),esk7_1(X1)))
| ~ hBOOL(hAPP(int,bool,X1,hAPP(nat,int,semiring_1_of_nat(int),X2))) ),
c_0_2415,
[final] ).
cnf(c_0_3315,plain,
( hAPP(X1,X1,plus_plus(X1,hAPP(X1,X1,plus_plus(X1,X2),X3)),hAPP(X1,X1,plus_plus(X1,X4),X5)) = hAPP(X1,X1,plus_plus(X1,hAPP(X1,X1,plus_plus(X1,X2),X4)),hAPP(X1,X1,plus_plus(X1,X3),X5))
| ~ comm_semiring_1(X1) ),
c_0_2416,
[final] ).
cnf(c_0_3316,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),esk24_3(X1,X3,X2)),X2))
| ~ dense_linorder(X1) ),
c_0_2417,
[final] ).
cnf(c_0_3317,plain,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(nat,int,semiring_1_of_nat(int),X1)),zero_zero(int)))
| X1 != zero_zero(nat) ),
c_0_2418,
[final] ).
cnf(c_0_3318,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),number_number_of(X1,X2)),number_number_of(X1,X3)))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),number_number_of(X1,X3)),number_number_of(X1,X2)))
| ~ linorder(X1)
| ~ number(X1) ),
c_0_2419,
[final] ).
cnf(c_0_3319,plain,
hAPP(int,int,plus_plus(int,hAPP(int,int,bit1,X1)),hAPP(int,int,bit1,X2)) = hAPP(int,int,bit0,hAPP(int,int,plus_plus(int,X1),hAPP(int,int,succ,X2))),
c_0_2420,
[final] ).
cnf(c_0_3320,plain,
( hAPP(X1,X1,plus_plus(X1,number_number_of(X1,X2)),hAPP(X1,X1,plus_plus(X1,number_number_of(X1,X3)),X4)) = hAPP(X1,X1,plus_plus(X1,number_number_of(X1,hAPP(int,int,plus_plus(int,X2),X3))),X4)
| ~ number_ring(X1) ),
c_0_2421,
[final] ).
cnf(c_0_3321,plain,
( X3 = X4
| ~ linordered_semidom(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),one_one(X1)),X2))
| hAPP(nat,X1,power_power(X1,X2),X3) != hAPP(nat,X1,power_power(X1,X2),X4) ),
c_0_2422,
[final] ).
cnf(c_0_3322,plain,
( hAPP(X1,X1,plus_plus(X1,number_number_of(X1,X2)),one_one(X1)) = number_number_of(X1,hAPP(int,int,succ,X2))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),X2))
| ~ number_semiring(X1) ),
c_0_2423,
[final] ).
cnf(c_0_3323,plain,
( hAPP(int,int,plus_plus(int,X2),hAPP(nat,int,semiring_1_of_nat(int),esk10_2(X2,X1))) = X1
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X2),X1)) ),
c_0_2424,
[final] ).
cnf(c_0_3324,plain,
( hAPP(X1,X1,plus_plus(X1,one_one(X1)),number_number_of(X1,X2)) = number_number_of(X1,hAPP(int,int,succ,X2))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),X2))
| ~ number_semiring(X1) ),
c_0_2425,
[final] ).
cnf(c_0_3325,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
| ~ linorder(X1)
| ti(X1,X2) != ti(X1,X3) ),
c_0_2426,
[final] ).
cnf(c_0_3326,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X2))
| ti(X1,X3) = ti(X1,X2)
| ~ linorder(X1) ),
c_0_2427,
[final] ).
cnf(c_0_3327,plain,
( ti(X1,X2) = ti(X1,X3)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X2))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| ~ linorder(X1) ),
c_0_2428,
[final] ).
cnf(c_0_3328,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| ti(X1,X3) = ti(X1,X2)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X2))
| ~ linorder(X1) ),
c_0_2429,
[final] ).
cnf(c_0_3329,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| ti(X1,X3) = ti(X1,X2)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X2))
| ~ linorder(X1) ),
c_0_2430,
[final] ).
cnf(c_0_3330,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X2))
| ti(X1,X3) = ti(X1,X2)
| ~ linorder(X1) ),
c_0_2431,
[final] ).
cnf(c_0_3331,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| ti(X1,X3) = ti(X1,X2)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X2))
| ~ linorder(X1) ),
c_0_2432,
[final] ).
cnf(c_0_3332,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X2))
| ti(X1,X3) = ti(X1,X2)
| ~ linordered_idom(X1) ),
c_0_2433,
[final] ).
cnf(c_0_3333,plain,
( hAPP(nat,X1,power_power(X1,X2),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) = zero_zero(X1)
| ~ ring_11004092258visors(X1)
| ti(X1,X2) != zero_zero(X1) ),
c_0_2434,
[final] ).
cnf(c_0_3334,plain,
( hAPP(nat,X1,power_power(X1,zero_zero(X1)),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) = zero_zero(X1)
| ~ semiring_1(X1) ),
c_0_2435,
[final] ).
cnf(c_0_3335,plain,
( hAPP(nat,X1,power_power(X1,one_one(X1)),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) = one_one(X1)
| ~ semiring_1(X1) ),
c_0_2436,
[final] ).
cnf(c_0_3336,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X2))
| ~ linorder(X1) ),
c_0_2437,
[final] ).
cnf(c_0_3337,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X2))
| ~ linorder(X1) ),
c_0_2438,
[final] ).
cnf(c_0_3338,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X2))
| ~ linorder(X1) ),
c_0_2439,
[final] ).
cnf(c_0_3339,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X2))
| ~ linorder(X1) ),
c_0_2440,
[final] ).
cnf(c_0_3340,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X2))
| ~ linorder(X1) ),
c_0_2441,
[final] ).
cnf(c_0_3341,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X2))
| ~ linorder(X1) ),
c_0_2442,
[final] ).
cnf(c_0_3342,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X2))
| ~ linorder(X1) ),
c_0_2443,
[final] ).
cnf(c_0_3343,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X2),X1))
| X2 = X1 ),
c_0_2444,
[final] ).
cnf(c_0_3344,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X2),X1))
| X2 = X1 ),
c_0_2445,
[final] ).
cnf(c_0_3345,plain,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X1),X2))
| X2 = X1
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X2),X1)) ),
c_0_2446,
[final] ).
cnf(c_0_3346,plain,
( hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X1),X2))
| hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X2),X1)) ),
c_0_2447,
[final] ).
cnf(c_0_3347,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X2),X1)) ),
c_0_2448,
[final] ).
cnf(c_0_3348,plain,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X1),X2))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X2),X1)) ),
c_0_2449,
[final] ).
cnf(c_0_3349,plain,
( hAPP(nat,X1,power_power(X1,X2),X3) = hAPP(nat,X1,power_power(X1,X2),X4)
| ~ linordered_semidom(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),one_one(X1)),X2))
| X3 != X4 ),
c_0_2450,
[final] ).
cnf(c_0_3350,plain,
( hBOOL(hAPP(int,bool,X1,hAPP(nat,int,semiring_1_of_nat(int),X2)))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),esk8_1(X1))) ),
c_0_2451,
[final] ).
cnf(c_0_3351,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_2452,
[final] ).
cnf(c_0_3352,plain,
( hBOOL(hAPP(nat,bool,X1,zero_zero(nat)))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),esk19_2(X2,X1)),X2))
| ~ hBOOL(hAPP(nat,bool,X1,X2)) ),
c_0_2453,
[final] ).
cnf(c_0_3353,plain,
( hBOOL(hAPP(nat,bool,X1,zero_zero(nat)))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),esk14_2(X2,X1)),X2))
| ~ hBOOL(hAPP(nat,bool,X1,X2)) ),
c_0_2454,
[final] ).
cnf(c_0_3354,plain,
( hAPP(real,real,sqrt,X1) != zero_zero(real)
| ~ hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X1)) ),
c_0_2455,
[final] ).
cnf(c_0_3355,plain,
( hAPP(nat,X1,semiring_1_of_nat(X1),number_number_of(nat,X2)) = number_number_of(X1,X2)
| ~ number_ring(X1)
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),number_number_of(int,X2))) ),
c_0_2456,
[final] ).
cnf(c_0_3356,plain,
( hBOOL(hAPP(int,bool,X1,esk7_1(X1)))
| ~ hBOOL(hAPP(int,bool,X1,hAPP(nat,int,semiring_1_of_nat(int),X2))) ),
c_0_2457,
[final] ).
cnf(c_0_3357,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(int,fun(int,bool),ord_less(int),X1),pls)) ),
c_0_2458,
[final] ).
cnf(c_0_3358,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),hAPP(X1,X1,plus_plus(X1,one_one(X1)),one_one(X1))))
| ~ linordered_semidom(X1) ),
c_0_2459,
[final] ).
cnf(c_0_3359,plain,
( hAPP(X1,X1,plus_plus(X1,one_one(X1)),number_number_of(X1,X2)) = number_number_of(X1,hAPP(int,int,plus_plus(int,hAPP(int,int,bit1,pls)),X2))
| ~ number_ring(X1) ),
c_0_2460,
[final] ).
cnf(c_0_3360,plain,
( hAPP(nat,nat,plus_plus(nat,number_number_of(nat,X1)),one_one(nat)) = one_one(nat)
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X1),pls)) ),
c_0_2461,
[final] ).
cnf(c_0_3361,plain,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X1),X2))
| X2 != hAPP(int,int,plus_plus(int,X1),hAPP(nat,int,semiring_1_of_nat(int),X3)) ),
c_0_2462,
[final] ).
cnf(c_0_3362,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,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_2463,
[final] ).
cnf(c_0_3363,plain,
( hAPP(nat,nat,plus_plus(nat,X2),esk13_2(X2,X1)) = X1
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X2),X1)) ),
c_0_2464,
[final] ).
cnf(c_0_3364,plain,
( hAPP(nat,nat,plus_plus(nat,X1),esk3_2(X1,X2)) = X2
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2)) ),
c_0_2465,
[final] ).
cnf(c_0_3365,plain,
( hAPP(nat,nat,plus_plus(nat,one_one(nat)),number_number_of(nat,X1)) = one_one(nat)
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X1),pls)) ),
c_0_2466,
[final] ).
cnf(c_0_3366,plain,
( hAPP(X1,X1,plus_plus(X1,hAPP(X1,X1,plus_plus(X1,X2),X3)),X4) = hAPP(X1,X1,plus_plus(X1,hAPP(X1,X1,plus_plus(X1,X2),X4)),X3)
| ~ comm_semiring_1(X1) ),
c_0_2467,
[final] ).
cnf(c_0_3367,plain,
( hAPP(nat,int,semiring_1_of_nat(int),esk15_1(X1)) = X1
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X1)) ),
c_0_2468,
[final] ).
cnf(c_0_3368,plain,
( hAPP(nat,int,semiring_1_of_nat(int),esk12_1(X1)) = X1
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X1)) ),
c_0_2469,
[final] ).
cnf(c_0_3369,plain,
( hAPP(nat,int,semiring_1_of_nat(int),esk11_1(X1)) = X1
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X1)) ),
c_0_2470,
[final] ).
cnf(c_0_3370,plain,
( hAPP(nat,int,semiring_1_of_nat(int),esk2_1(X1)) = X1
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),X1)) ),
c_0_2471,
[final] ).
cnf(c_0_3371,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),hAPP(X1,X1,plus_plus(X1,X2),one_one(X1))))
| ~ linordered_semidom(X1) ),
c_0_2472,
[final] ).
cnf(c_0_3372,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,power_power(nat,X1),X2)))
| X2 != zero_zero(nat) ),
c_0_2473,
[final] ).
cnf(c_0_3373,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,power_power(nat,X1),X2)))
| X2 != zero_zero(nat) ),
c_0_2474,
[final] ).
cnf(c_0_3374,plain,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X1),hAPP(int,int,plus_plus(int,X2),one_one(int))))
| X1 != X2 ),
c_0_2475,
[final] ).
cnf(c_0_3375,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),hAPP(nat,X1,semiring_1_of_nat(X1),X2)))
| ~ linordered_semidom(X1) ),
c_0_2476,
[final] ).
cnf(c_0_3376,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),hAPP(nat,X1,semiring_1_of_nat(X1),X2)))
| ~ linordered_semidom(X1) ),
c_0_2477,
[final] ).
cnf(c_0_3377,plain,
hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),hAPP(nat,nat,plus_plus(nat,X1),X2))),
c_0_2478,
[final] ).
cnf(c_0_3378,plain,
hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),hAPP(nat,nat,plus_plus(nat,X2),X1))),
c_0_2479,
[final] ).
cnf(c_0_3379,plain,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),one_one(X1)),zero_zero(X1)))
| ~ linordered_semidom(X1) ),
c_0_2480,
[final] ).
cnf(c_0_3380,plain,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),one_one(X1)),zero_zero(X1)))
| ~ linordered_semidom(X1) ),
c_0_2481,
[final] ).
cnf(c_0_3381,plain,
( hAPP(X1,X1,plus_plus(X1,hAPP(nat,X1,semiring_1_of_nat(X1),X2)),hAPP(nat,X1,semiring_1_of_nat(X1),X3)) = hAPP(nat,X1,semiring_1_of_nat(X1),hAPP(nat,nat,plus_plus(nat,X2),X3))
| ~ semiring_1(X1) ),
c_0_2482,
[final] ).
cnf(c_0_3382,plain,
hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(nat,int,semiring_1_of_nat(int),X1))),
c_0_2483,
[final] ).
cnf(c_0_3383,plain,
hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(nat,int,semiring_1_of_nat(int),X1))),
c_0_2484,
[final] ).
cnf(c_0_3384,plain,
( ~ order(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| ti(X1,X2) != ti(X1,X3) ),
c_0_2485,
[final] ).
cnf(c_0_3385,plain,
( ~ linorder(X1)
| ti(X1,X2) != ti(X1,X3)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3)) ),
c_0_2486,
[final] ).
cnf(c_0_3386,plain,
( ~ linorder(X1)
| ti(X1,X2) != ti(X1,X3)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X2)) ),
c_0_2487,
[final] ).
cnf(c_0_3387,plain,
( ~ linorder(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| ti(X1,X2) != ti(X1,X3) ),
c_0_2488,
[final] ).
cnf(c_0_3388,plain,
( ti(X1,X2) != ti(X1,X3)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| ~ order(X1) ),
c_0_2489,
[final] ).
cnf(c_0_3389,plain,
( ti(X1,X2) != ti(X1,X3)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| ~ order(X1) ),
c_0_2490,
[final] ).
cnf(c_0_3390,plain,
( ti(X1,X2) != ti(X1,X3)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X2))
| ~ order(X1) ),
c_0_2491,
[final] ).
cnf(c_0_3391,plain,
hAPP(int,int,plus_plus(int,hAPP(nat,int,semiring_1_of_nat(int),X1)),hAPP(nat,int,semiring_1_of_nat(int),X2)) = hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,plus_plus(nat,X1),X2)),
c_0_2492,
[final] ).
cnf(c_0_3392,plain,
hAPP(int,int,plus_plus(int,hAPP(nat,int,semiring_1_of_nat(int),X1)),hAPP(nat,int,semiring_1_of_nat(int),X2)) = hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,plus_plus(nat,X1),X2)),
c_0_2493,
[final] ).
cnf(c_0_3393,plain,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X2))
| ~ preorder(X1) ),
c_0_2494,
[final] ).
cnf(c_0_3394,plain,
( hBOOL(X1)
| ~ hBOOL(X1)
| ~ hBOOL(X2)
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X3))
| ~ hBOOL(X2) ),
c_0_2495,
[final] ).
cnf(c_0_3395,plain,
( hBOOL(X2)
| ~ hBOOL(X1)
| ~ hBOOL(X2)
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X3))
| ~ hBOOL(X1) ),
c_0_2496,
[final] ).
cnf(c_0_3396,plain,
( hBOOL(X1)
| ~ hBOOL(X1)
| ~ hBOOL(X2)
| ~ hBOOL(X2)
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X3)) ),
c_0_2497,
[final] ).
cnf(c_0_3397,plain,
( hBOOL(X2)
| ~ hBOOL(X1)
| ~ hBOOL(X2)
| ~ hBOOL(X1)
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X3)) ),
c_0_2498,
[final] ).
cnf(c_0_3398,plain,
( hBOOL(X1)
| hBOOL(X2)
| hBOOL(X1)
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X3))
| ~ hBOOL(X2) ),
c_0_2499,
[final] ).
cnf(c_0_3399,plain,
( hBOOL(X1)
| hBOOL(X2)
| hBOOL(X2)
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X3))
| ~ hBOOL(X1) ),
c_0_2500,
[final] ).
cnf(c_0_3400,plain,
( hBOOL(X1)
| hBOOL(X2)
| hBOOL(X1)
| ~ hBOOL(X2)
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X3)) ),
c_0_2501,
[final] ).
cnf(c_0_3401,plain,
( hBOOL(X1)
| hBOOL(X2)
| hBOOL(X2)
| ~ hBOOL(X1)
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X3)) ),
c_0_2502,
[final] ).
cnf(c_0_3402,plain,
hAPP(int,int,plus_plus(int,hAPP(int,int,bit0,X1)),hAPP(int,int,bit1,X2)) = hAPP(int,int,bit1,hAPP(int,int,plus_plus(int,X1),X2)),
c_0_2503,
[final] ).
cnf(c_0_3403,plain,
hAPP(int,int,plus_plus(int,hAPP(int,int,bit1,X1)),hAPP(int,int,bit0,X2)) = hAPP(int,int,bit1,hAPP(int,int,plus_plus(int,X1),X2)),
c_0_2504,
[final] ).
cnf(c_0_3404,plain,
hAPP(int,int,plus_plus(int,hAPP(int,int,bit0,X1)),hAPP(int,int,bit0,X2)) = hAPP(int,int,bit0,hAPP(int,int,plus_plus(int,X1),X2)),
c_0_2505,
[final] ).
cnf(c_0_3405,plain,
( X1 != zero_zero(nat)
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X1)) ),
c_0_2506,
[final] ).
cnf(c_0_3406,plain,
( X1 = zero_zero(nat)
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),zero_zero(nat))) ),
c_0_2507,
[final] ).
cnf(c_0_3407,plain,
( number_number_of(nat,X1) = zero_zero(nat)
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X1),pls)) ),
c_0_2508,
[final] ).
cnf(c_0_3408,plain,
( number_number_of(nat,X1) = zero_zero(nat)
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X1),pls)) ),
c_0_2509,
[final] ).
cnf(c_0_3409,plain,
~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),zero_zero(nat))),
c_0_2510,
[final] ).
cnf(c_0_3410,plain,
~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),zero_zero(nat))),
c_0_2511,
[final] ).
cnf(c_0_3411,plain,
~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),zero_zero(nat))),
c_0_2512,
[final] ).
cnf(c_0_3412,plain,
( X1 != zero_zero(nat)
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X2),X1)) ),
c_0_2513,
[final] ).
cnf(c_0_3413,plain,
( ~ hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X1),X2))
| X1 != X2 ),
c_0_2514,
[final] ).
cnf(c_0_3414,plain,
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2))
| X1 != X2 ),
c_0_2515,
[final] ).
cnf(c_0_3415,plain,
( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X1),X2))
| X1 != X2 ),
c_0_2516,
[final] ).
cnf(c_0_3416,plain,
( X1 != X2
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2)) ),
c_0_2517,
[final] ).
cnf(c_0_3417,plain,
( X1 != X2
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X2),X1)) ),
c_0_2518,
[final] ).
cnf(c_0_3418,plain,
( X1 != X2
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2)) ),
c_0_2519,
[final] ).
cnf(c_0_3419,plain,
( X1 != X2
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X2),X1)) ),
c_0_2520,
[final] ).
cnf(c_0_3420,plain,
~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X1)),
c_0_2521,
[final] ).
cnf(c_0_3421,plain,
~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X1)),
c_0_2522,
[final] ).
cnf(c_0_3422,plain,
~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),zero_zero(int))),
c_0_2523,
[final] ).
cnf(c_0_3423,plain,
~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),pls)),
c_0_2524,
[final] ).
cnf(c_0_3424,plain,
( hAPP(nat,nat,plus_plus(nat,number_number_of(nat,X1)),one_one(nat)) = number_number_of(nat,hAPP(int,int,succ,X1))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X1),pls)) ),
c_0_2525,
[final] ).
cnf(c_0_3425,plain,
( hAPP(nat,nat,plus_plus(nat,one_one(nat)),number_number_of(nat,X1)) = number_number_of(nat,hAPP(int,int,succ,X1))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X1),pls)) ),
c_0_2526,
[final] ).
cnf(c_0_3426,plain,
( hBOOL(hAPP(int,bool,X1,hAPP(nat,int,semiring_1_of_nat(int),X2)))
| ~ hBOOL(hAPP(int,bool,X1,esk8_1(X1))) ),
c_0_2527,
[final] ).
cnf(c_0_3427,plain,
( hAPP(X1,X1,plus_plus(X1,hAPP(X1,X1,plus_plus(X1,X2),X3)),X4) = hAPP(X1,X1,plus_plus(X1,X2),hAPP(X1,X1,plus_plus(X1,X3),X4))
| ~ comm_semiring_1(X1) ),
c_0_2528,
[final] ).
cnf(c_0_3428,plain,
( hAPP(X1,X1,plus_plus(X1,hAPP(X1,X1,plus_plus(X1,X2),X3)),X4) = hAPP(X1,X1,plus_plus(X1,X2),hAPP(X1,X1,plus_plus(X1,X3),X4))
| ~ comm_semiring_1(X1) ),
c_0_2529,
[final] ).
cnf(c_0_3429,plain,
( hAPP(X1,X1,plus_plus(X1,hAPP(X1,X1,plus_plus(X1,X2),X3)),X4) = hAPP(X1,X1,plus_plus(X1,X2),hAPP(X1,X1,plus_plus(X1,X3),X4))
| ~ ab_semigroup_add(X1) ),
c_0_2530,
[final] ).
cnf(c_0_3430,plain,
hAPP(int,int,plus_plus(int,hAPP(int,int,plus_plus(int,one_one(int)),X1)),X1) != zero_zero(int),
c_0_2531,
[final] ).
cnf(c_0_3431,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_2532,
[final] ).
cnf(c_0_3432,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_2533,
[final] ).
cnf(c_0_3433,plain,
hAPP(X1,X1,hAPP(X1,fun(X1,X1),hAPP(bool,fun(X1,fun(X1,X1)),if(X1),fFalse),X2),X3) = ti(X1,X3),
c_0_2534,
[final] ).
cnf(c_0_3434,plain,
hAPP(X1,X1,hAPP(X1,fun(X1,X1),hAPP(bool,fun(X1,fun(X1,X1)),if(X1),fTrue),X2),X3) = ti(X1,X2),
c_0_2535,
[final] ).
cnf(c_0_3435,plain,
( hAPP(nat,X1,power_power(X1,hAPP(nat,X1,semiring_1_of_nat(X1),X2)),X3) = hAPP(nat,X1,semiring_1_of_nat(X1),hAPP(nat,nat,power_power(nat,X2),X3))
| ~ semiring_1(X1) ),
c_0_2536,
[final] ).
cnf(c_0_3436,plain,
( hAPP(X1,X1,plus_plus(X1,hAPP(X1,X1,plus_plus(X1,one_one(X1)),number_number_of(X1,X2))),number_number_of(X1,X2)) = number_number_of(X1,hAPP(int,int,bit1,X2))
| ~ number_ring(X1) ),
c_0_2537,
[final] ).
cnf(c_0_3437,plain,
( hAPP(X1,X1,plus_plus(X1,hAPP(X1,X1,plus_plus(X1,zero_zero(X1)),number_number_of(X1,X2))),number_number_of(X1,X2)) = number_number_of(X1,hAPP(int,int,bit0,X2))
| ~ number_ring(X1) ),
c_0_2538,
[final] ).
cnf(c_0_3438,plain,
hAPP(nat,int,power_power(int,hAPP(nat,int,semiring_1_of_nat(int),X1)),X2) = hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,power_power(nat,X1),X2)),
c_0_2539,
[final] ).
cnf(c_0_3439,plain,
hAPP(nat,int,power_power(int,hAPP(nat,int,semiring_1_of_nat(int),X1)),X2) = hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,power_power(nat,X1),X2)),
c_0_2540,
[final] ).
cnf(c_0_3440,plain,
hAPP(nat,int,power_power(int,hAPP(nat,int,semiring_1_of_nat(int),X1)),X2) = hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,power_power(nat,X1),X2)),
c_0_2541,
[final] ).
cnf(c_0_3441,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2))
| X2 != hAPP(nat,nat,plus_plus(nat,X1),X3) ),
c_0_2542,
[final] ).
cnf(c_0_3442,plain,
( hAPP(nat,X1,semiring_1_of_nat(X1),number_number_of(nat,X2)) = zero_zero(X1)
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),number_number_of(int,X2)))
| ~ number_ring(X1) ),
c_0_2543,
[final] ).
cnf(c_0_3443,plain,
( hAPP(X1,X1,plus_plus(X1,number_number_of(X1,X2)),one_one(X1)) = number_number_of(X1,hAPP(int,int,plus_plus(int,X2),hAPP(int,int,bit1,pls)))
| ~ number_ring(X1) ),
c_0_2544,
[final] ).
cnf(c_0_3444,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_2545,
[final] ).
cnf(c_0_3445,plain,
( hAPP(X1,X1,plus_plus(X1,one_one(X1)),one_one(X1)) = number_number_of(X1,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))
| ~ number_semiring(X1) ),
c_0_2546,
[final] ).
cnf(c_0_3446,plain,
( hAPP(X1,X1,plus_plus(X1,one_one(X1)),one_one(X1)) = number_number_of(X1,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))
| ~ number_ring(X1) ),
c_0_2547,
[final] ).
cnf(c_0_3447,plain,
number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))) = hAPP(nat,nat,plus_plus(nat,one_one(nat)),one_one(nat)),
c_0_2548,
[final] ).
cnf(c_0_3448,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
| ~ order(X1)
| ti(X1,X2) != ti(X1,X3) ),
c_0_2549,
[final] ).
cnf(c_0_3449,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
| ~ order(X1)
| ti(X1,X2) != ti(X1,X3) ),
c_0_2550,
[final] ).
cnf(c_0_3450,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X2))
| ~ order(X1)
| ti(X1,X2) != ti(X1,X3) ),
c_0_2551,
[final] ).
cnf(c_0_3451,plain,
( hAPP(X1,X1,plus_plus(X1,X2),hAPP(X1,X1,plus_plus(X1,X3),X4)) = hAPP(X1,X1,plus_plus(X1,X3),hAPP(X1,X1,plus_plus(X1,X2),X4))
| ~ comm_semiring_1(X1) ),
c_0_2552,
[final] ).
cnf(c_0_3452,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),one_one(X1)))
| ~ linordered_semidom(X1) ),
c_0_2553,
[final] ).
cnf(c_0_3453,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),one_one(X1)))
| ~ linordered_semidom(X1) ),
c_0_2554,
[final] ).
cnf(c_0_3454,plain,
hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),number_number_of(int,pls))),
c_0_2555,
[final] ).
cnf(c_0_3455,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
| X2 != X3
| ~ preorder(X1) ),
c_0_2556,
[final] ).
cnf(c_0_3456,plain,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X2))
| ~ preorder(X1) ),
c_0_2557,
[final] ).
cnf(c_0_3457,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_2558,
[final] ).
cnf(c_0_3458,plain,
hAPP(int,int,plus_plus(int,hAPP(int,int,plus_plus(int,one_one(int)),X1)),X1) = hAPP(int,int,bit1,X1),
c_0_2559,
[final] ).
cnf(c_0_3459,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_2560,
[final] ).
cnf(c_0_3460,plain,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X1),pls))
| number_number_of(nat,X1) != zero_zero(nat) ),
c_0_2561,
[final] ).
cnf(c_0_3461,plain,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X1),pls))
| number_number_of(nat,X1) != zero_zero(nat) ),
c_0_2562,
[final] ).
cnf(c_0_3462,plain,
hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),one_one(int))),
c_0_2563,
[final] ).
cnf(c_0_3463,plain,
hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),zero_zero(int))),
c_0_2564,
[final] ).
cnf(c_0_3464,plain,
hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),one_one(int))),
c_0_2565,
[final] ).
cnf(c_0_3465,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X1))
| X1 = zero_zero(nat) ),
c_0_2566,
[final] ).
cnf(c_0_3466,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X1))
| X1 = zero_zero(nat) ),
c_0_2567,
[final] ).
cnf(c_0_3467,plain,
hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),zero_zero(nat)),X1)),
c_0_2568,
[final] ).
cnf(c_0_3468,plain,
hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),zero_zero(nat)),X1)),
c_0_2569,
[final] ).
cnf(c_0_3469,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),zero_zero(nat)))
| X1 != zero_zero(nat) ),
c_0_2570,
[final] ).
cnf(c_0_3470,plain,
hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),one_one(int)),t)),
c_0_2571,
[final] ).
cnf(c_0_3471,plain,
hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),tn)),
c_0_2572,
[final] ).
cnf(c_0_3472,plain,
hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),n)),
c_0_2573,
[final] ).
cnf(c_0_3473,plain,
hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),t)),
c_0_2574,
[final] ).
cnf(c_0_3474,plain,
( hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X1),X2))
| X1 != X2 ),
c_0_2575,
[final] ).
cnf(c_0_3475,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2))
| X1 != X2 ),
c_0_2576,
[final] ).
cnf(c_0_3476,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2))
| X1 != X2 ),
c_0_2577,
[final] ).
cnf(c_0_3477,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2))
| X1 != X2 ),
c_0_2578,
[final] ).
cnf(c_0_3478,plain,
hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X1),X1)),
c_0_2579,
[final] ).
cnf(c_0_3479,plain,
hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X1)),
c_0_2580,
[final] ).
cnf(c_0_3480,plain,
hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X1),X1)),
c_0_2581,
[final] ).
cnf(c_0_3481,plain,
hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),pls)),
c_0_2582,
[final] ).
cnf(c_0_3482,plain,
hAPP(int,int,bit0,hAPP(int,int,succ,X1)) = hAPP(int,int,succ,hAPP(int,int,bit1,X1)),
c_0_2583,
[final] ).
cnf(c_0_3483,plain,
ti(fun(X1,fun(X1,X1)),hAPP(bool,fun(X1,fun(X1,X1)),X2,X3)) = hAPP(bool,fun(X1,fun(X1,X1)),X2,X3),
c_0_2584,
[final] ).
cnf(c_0_3484,plain,
hAPP(bool,fun(X1,fun(X1,X1)),ti(fun(bool,fun(X1,fun(X1,X1))),X2),X3) = hAPP(bool,fun(X1,fun(X1,X1)),X2,X3),
c_0_2585,
[final] ).
cnf(c_0_3485,plain,
hAPP(int,int,succ,hAPP(int,int,bit0,X1)) = hAPP(int,int,bit1,X1),
c_0_2586,
[final] ).
cnf(c_0_3486,plain,
( hAPP(X1,X1,plus_plus(X1,number_number_of(X1,X2)),number_number_of(X1,X3)) = number_number_of(X1,hAPP(int,int,plus_plus(int,X2),X3))
| ~ number_ring(X1) ),
c_0_2587,
[final] ).
cnf(c_0_3487,plain,
( hAPP(X1,X1,plus_plus(X1,number_number_of(X1,X2)),number_number_of(X1,X3)) = number_number_of(X1,hAPP(int,int,plus_plus(int,X2),X3))
| ~ number_ring(X1) ),
c_0_2588,
[final] ).
cnf(c_0_3488,plain,
( ti(X1,X2) = ti(X1,X3)
| ~ cancel_semigroup_add(X1)
| hAPP(X1,X1,plus_plus(X1,X4),X2) != hAPP(X1,X1,plus_plus(X1,X4),X3) ),
c_0_2589,
[final] ).
cnf(c_0_3489,plain,
( ti(X1,X2) = ti(X1,X3)
| ~ cancel_semigroup_add(X1)
| hAPP(X1,X1,plus_plus(X1,X2),X4) != hAPP(X1,X1,plus_plus(X1,X3),X4) ),
c_0_2590,
[final] ).
cnf(c_0_3490,plain,
( ti(X1,X2) = ti(X1,X3)
| hAPP(X1,X1,plus_plus(X1,X4),X2) != hAPP(X1,X1,plus_plus(X1,X4),X3)
| ~ cancel_semigroup_add(X1) ),
c_0_2591,
[final] ).
cnf(c_0_3491,plain,
( ti(X1,X2) = ti(X1,X3)
| hAPP(X1,X1,plus_plus(X1,X4),X2) != hAPP(X1,X1,plus_plus(X1,X4),X3)
| ~ cancel146912293up_add(X1) ),
c_0_2592,
[final] ).
cnf(c_0_3492,plain,
( ti(X1,X2) = ti(X1,X3)
| hAPP(X1,X1,plus_plus(X1,X2),X4) != hAPP(X1,X1,plus_plus(X1,X3),X4)
| ~ cancel_semigroup_add(X1) ),
c_0_2593,
[final] ).
cnf(c_0_3493,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_2594,
[final] ).
cnf(c_0_3494,plain,
ti(fun(X1,X1),hAPP(X1,fun(X1,X1),X2,X3)) = hAPP(X1,fun(X1,X1),X2,X3),
c_0_2595,
[final] ).
cnf(c_0_3495,plain,
( X1 = X2
| hAPP(nat,nat,plus_plus(nat,X1),X3) != hAPP(nat,nat,plus_plus(nat,X2),X3) ),
c_0_2596,
[final] ).
cnf(c_0_3496,plain,
( X1 = X2
| hAPP(nat,nat,plus_plus(nat,X3),X1) != hAPP(nat,nat,plus_plus(nat,X3),X2) ),
c_0_2597,
[final] ).
cnf(c_0_3497,plain,
( hAPP(X1,X1,plus_plus(X1,one_one(X1)),number_number_of(X1,X2)) = number_number_of(X1,hAPP(int,int,succ,X2))
| ~ number_ring(X1) ),
c_0_2598,
[final] ).
cnf(c_0_3498,plain,
( X2 = X3
| ~ semiring_char_0(X1)
| hAPP(nat,X1,semiring_1_of_nat(X1),X2) != hAPP(nat,X1,semiring_1_of_nat(X1),X3) ),
c_0_2599,
[final] ).
cnf(c_0_3499,plain,
( X1 = X2
| hAPP(nat,int,semiring_1_of_nat(int),X1) != hAPP(nat,int,semiring_1_of_nat(int),X2) ),
c_0_2600,
[final] ).
cnf(c_0_3500,plain,
( X1 = X2
| hAPP(nat,int,semiring_1_of_nat(int),X1) != hAPP(nat,int,semiring_1_of_nat(int),X2) ),
c_0_2601,
[final] ).
cnf(c_0_3501,plain,
( number_number_of(X1,hAPP(nat,int,semiring_1_of_nat(int),X2)) = hAPP(nat,X1,semiring_1_of_nat(X1),X2)
| ~ number_semiring(X1) ),
c_0_2602,
[final] ).
cnf(c_0_3502,plain,
( X1 = X2
| hAPP(int,int,bit0,X1) != hAPP(int,int,bit0,X2) ),
c_0_2603,
[final] ).
cnf(c_0_3503,plain,
( X1 = X2
| hAPP(int,int,bit1,X1) != hAPP(int,int,bit1,X2) ),
c_0_2604,
[final] ).
cnf(c_0_3504,plain,
hAPP(int,int,bit0,X1) != hAPP(int,int,bit1,X2),
c_0_2605,
[final] ).
cnf(c_0_3505,plain,
hAPP(int,int,bit1,X1) != hAPP(int,int,bit0,X2),
c_0_2606,
[final] ).
cnf(c_0_3506,plain,
( ti(X1,hAPP(X2,X1,X3,X4)) = hAPP(X2,X1,X3,X4)
| ~ ord(X1) ),
c_0_2607,
[final] ).
cnf(c_0_3507,plain,
( ti(X1,hAPP(nat,X1,X2,X3)) = hAPP(nat,X1,X2,X3)
| ~ power(X1) ),
c_0_2608,
[final] ).
cnf(c_0_3508,plain,
ti(X1,hAPP(X1,X1,X2,X3)) = hAPP(X1,X1,X2,X3),
c_0_2609,
[final] ).
cnf(c_0_3509,plain,
hAPP(X1,fun(X1,X1),ti(fun(X1,fun(X1,X1)),X2),X3) = hAPP(X1,fun(X1,X1),X2,X3),
c_0_2610,
[final] ).
cnf(c_0_3510,plain,
hAPP(bool,fun(X1,fun(X1,X1)),X2,ti(bool,X3)) = hAPP(bool,fun(X1,fun(X1,X1)),X2,X3),
c_0_2611,
[final] ).
cnf(c_0_3511,plain,
( hAPP(X1,X1,plus_plus(X1,X2),X3) = hAPP(X1,X1,plus_plus(X1,X2),X4)
| ~ cancel_semigroup_add(X1)
| ti(X1,X3) != ti(X1,X4) ),
c_0_2612,
[final] ).
cnf(c_0_3512,plain,
( hAPP(X1,X1,plus_plus(X1,X2),X3) = hAPP(X1,X1,plus_plus(X1,X4),X3)
| ~ cancel_semigroup_add(X1)
| ti(X1,X2) != ti(X1,X4) ),
c_0_2613,
[final] ).
cnf(c_0_3513,plain,
( hAPP(X1,X2,ti(fun(X1,X2),X3),X4) = hAPP(X1,X2,X3,X4)
| ~ ord(X2) ),
c_0_2614,
[final] ).
cnf(c_0_3514,plain,
hAPP(X1,X1,ti(fun(X1,X1),X2),X3) = hAPP(X1,X1,X2,X3),
c_0_2615,
[final] ).
cnf(c_0_3515,plain,
hAPP(X1,fun(X1,X1),X2,ti(X1,X3)) = hAPP(X1,fun(X1,X1),X2,X3),
c_0_2616,
[final] ).
cnf(c_0_3516,plain,
( hAPP(nat,X1,ti(fun(nat,X1),X2),X3) = hAPP(nat,X1,X2,X3)
| ~ power(X1) ),
c_0_2617,
[final] ).
cnf(c_0_3517,plain,
( hAPP(X1,X1,plus_plus(X1,X2),X3) = hAPP(X1,X1,plus_plus(X1,X3),X2)
| ~ comm_semiring_1(X1) ),
c_0_2618,
[final] ).
cnf(c_0_3518,plain,
( hAPP(nat,nat,plus_plus(nat,X1),X2) = hAPP(nat,nat,plus_plus(nat,X3),X2)
| X1 != X3 ),
c_0_2619,
[final] ).
cnf(c_0_3519,plain,
( hAPP(nat,nat,plus_plus(nat,X1),X2) = hAPP(nat,nat,plus_plus(nat,X1),X3)
| X2 != X3 ),
c_0_2620,
[final] ).
cnf(c_0_3520,plain,
hAPP(nat,nat,plus_plus(nat,X1),X2) = hAPP(nat,nat,plus_plus(nat,X2),X1),
c_0_2621,
[final] ).
cnf(c_0_3521,plain,
hAPP(int,int,plus_plus(int,X1),X2) = hAPP(int,int,plus_plus(int,X2),X1),
c_0_2622,
[final] ).
cnf(c_0_3522,plain,
( hAPP(X1,X2,X3,ti(X1,X4)) = hAPP(X1,X2,X3,X4)
| ~ ord(X2) ),
c_0_2623,
[final] ).
cnf(c_0_3523,plain,
( ~ zero_neq_one(X1)
| ~ no_zero_divisors(X1)
| ~ mult_zero(X1)
| ~ power(X1)
| hAPP(nat,X1,power_power(X1,X2),number_number_of(nat,X3)) != zero_zero(X1)
| number_number_of(nat,X3) != zero_zero(nat) ),
c_0_2624,
[final] ).
cnf(c_0_3524,plain,
( hAPP(nat,X1,X2,ti(nat,X3)) = hAPP(nat,X1,X2,X3)
| ~ power(X1) ),
c_0_2625,
[final] ).
cnf(c_0_3525,plain,
hAPP(X1,X1,X2,ti(X1,X3)) = hAPP(X1,X1,X2,X3),
c_0_2626,
[final] ).
cnf(c_0_3526,plain,
( ti(X1,X2) = zero_zero(X1)
| ~ zero_neq_one(X1)
| ~ no_zero_divisors(X1)
| ~ mult_zero(X1)
| ~ power(X1)
| hAPP(nat,X1,power_power(X1,X2),number_number_of(nat,X3)) != zero_zero(X1) ),
c_0_2627,
[final] ).
cnf(c_0_3527,plain,
( hAPP(nat,X1,semiring_1_of_nat(X1),X2) = hAPP(nat,X1,semiring_1_of_nat(X1),X3)
| ~ semiring_char_0(X1)
| X2 != X3 ),
c_0_2628,
[final] ).
cnf(c_0_3528,plain,
hAPP(int,int,plus_plus(int,X1),one_one(int)) = hAPP(int,int,succ,X1),
c_0_2629,
[final] ).
cnf(c_0_3529,plain,
hAPP(int,int,plus_plus(int,X1),X1) = hAPP(int,int,bit0,X1),
c_0_2630,
[final] ).
cnf(c_0_3530,plain,
( number_number_of(X1,hAPP(int,int,bit1,pls)) = one_one(X1)
| ~ number_semiring(X1) ),
c_0_2631,
[final] ).
cnf(c_0_3531,plain,
( number_number_of(X1,hAPP(int,int,bit1,pls)) = one_one(X1)
| ~ number_ring(X1) ),
c_0_2632,
[final] ).
cnf(c_0_3532,plain,
( number_number_of(X1,hAPP(int,int,bit1,pls)) = one_one(X1)
| ~ number_ring(X1) ),
c_0_2633,
[final] ).
cnf(c_0_3533,plain,
( hAPP(nat,int,semiring_1_of_nat(int),X1) = hAPP(nat,int,semiring_1_of_nat(int),X2)
| X1 != X2 ),
c_0_2634,
[final] ).
cnf(c_0_3534,plain,
( hAPP(nat,int,semiring_1_of_nat(int),X1) = hAPP(nat,int,semiring_1_of_nat(int),X2)
| X1 != X2 ),
c_0_2635,
[final] ).
cnf(c_0_3535,plain,
number_number_of(nat,hAPP(int,int,bit1,pls)) = one_one(nat),
c_0_2636,
[final] ).
cnf(c_0_3536,plain,
number_number_of(nat,hAPP(int,int,bit1,pls)) = one_one(nat),
c_0_2637,
[final] ).
cnf(c_0_3537,plain,
number_number_of(int,hAPP(int,int,bit1,pls)) = one_one(int),
c_0_2638,
[final] ).
cnf(c_0_3538,plain,
( hAPP(int,int,bit0,X1) = hAPP(int,int,bit0,X2)
| X1 != X2 ),
c_0_2639,
[final] ).
cnf(c_0_3539,plain,
( hAPP(int,int,bit1,X1) = hAPP(int,int,bit1,X2)
| X1 != X2 ),
c_0_2640,
[final] ).
cnf(c_0_3540,plain,
hAPP(int,int,bit1,pls) = hAPP(int,int,succ,pls),
c_0_2641,
[final] ).
cnf(c_0_3541,plain,
( ti(X1,X2) = zero_zero(X1)
| ~ zero_neq_one(X1)
| ~ no_zero_divisors(X1)
| ~ mult_zero(X1)
| ~ power(X1)
| hAPP(nat,X1,power_power(X1,X2),X3) != zero_zero(X1) ),
c_0_2642,
[final] ).
cnf(c_0_3542,plain,
( ti(X1,X2) = zero_zero(X1)
| ~ semiri456707255roduct(X1)
| hAPP(X1,X1,plus_plus(X1,X3),X2) != ti(X1,X3) ),
c_0_2643,
[final] ).
cnf(c_0_3543,plain,
( ~ zero_neq_one(X1)
| ~ no_zero_divisors(X1)
| ~ mult_zero(X1)
| ~ power(X1)
| hAPP(nat,X1,power_power(X1,X2),X3) != zero_zero(X1)
| X3 != zero_zero(nat) ),
c_0_2644,
[final] ).
cnf(c_0_3544,plain,
( ti(X1,X2) = zero_zero(X1)
| ~ linord219039673up_add(X1)
| hAPP(X1,X1,plus_plus(X1,X2),X2) != zero_zero(X1) ),
c_0_2645,
[final] ).
cnf(c_0_3545,plain,
( ti(X1,X2) = zero_zero(X1)
| ~ linord219039673up_add(X1)
| hAPP(X1,X1,plus_plus(X1,X2),X2) != zero_zero(X1) ),
c_0_2646,
[final] ).
cnf(c_0_3546,plain,
( ti(X1,X2) = zero_zero(X1)
| hAPP(nat,X1,power_power(X1,X2),X3) != zero_zero(X1)
| ~ ring_11004092258visors(X1) ),
c_0_2647,
[final] ).
cnf(c_0_3547,plain,
( X1 = zero_zero(nat)
| X2 = one_one(nat)
| hAPP(nat,nat,power_power(nat,X2),X1) != one_one(nat) ),
c_0_2648,
[final] ).
cnf(c_0_3548,plain,
( hAPP(nat,nat,power_power(nat,X1),X2) != zero_zero(nat)
| X2 != zero_zero(nat) ),
c_0_2649,
[final] ).
cnf(c_0_3549,plain,
( X1 = zero_zero(nat)
| hAPP(nat,nat,power_power(nat,X1),X2) != zero_zero(nat) ),
c_0_2650,
[final] ).
cnf(c_0_3550,plain,
( X1 = zero_zero(nat)
| hAPP(nat,nat,plus_plus(nat,X1),X2) != zero_zero(nat) ),
c_0_2651,
[final] ).
cnf(c_0_3551,plain,
( X2 = zero_zero(nat)
| hAPP(nat,nat,plus_plus(nat,X1),X2) != zero_zero(nat) ),
c_0_2652,
[final] ).
cnf(c_0_3552,plain,
( X1 = zero_zero(nat)
| hAPP(nat,nat,plus_plus(nat,X2),X1) != X2 ),
c_0_2653,
[final] ).
cnf(c_0_3553,plain,
( X1 = zero_zero(nat)
| hAPP(nat,int,semiring_1_of_nat(int),X1) != zero_zero(int) ),
c_0_2654,
[final] ).
cnf(c_0_3554,plain,
( pls = X1
| hAPP(int,int,bit0,X1) != pls ),
c_0_2655,
[final] ).
cnf(c_0_3555,plain,
( X1 = pls
| hAPP(int,int,bit0,X1) != pls ),
c_0_2656,
[final] ).
cnf(c_0_3556,plain,
hAPP(int,int,bit1,X1) != pls,
c_0_2657,
[final] ).
cnf(c_0_3557,plain,
hAPP(int,int,bit1,X1) != pls,
c_0_2658,
[final] ).
cnf(c_0_3558,plain,
( hAPP(nat,X1,power_power(X1,X2),number_number_of(nat,X3)) = zero_zero(X1)
| number_number_of(nat,X3) = zero_zero(nat)
| ~ zero_neq_one(X1)
| ~ no_zero_divisors(X1)
| ~ mult_zero(X1)
| ~ power(X1)
| ti(X1,X2) != zero_zero(X1) ),
c_0_2659,
[final] ).
cnf(c_0_3559,plain,
( hAPP(nat,X1,power_power(X1,zero_zero(X1)),number_number_of(nat,X2)) = one_one(X1)
| ~ semiring_0(X1)
| ~ power(X1)
| number_number_of(nat,X2) != zero_zero(nat) ),
c_0_2660,
[final] ).
cnf(c_0_3560,plain,
( hAPP(nat,X1,power_power(X1,zero_zero(X1)),number_number_of(nat,X2)) = zero_zero(X1)
| number_number_of(nat,X2) = zero_zero(nat)
| ~ semiring_0(X1)
| ~ power(X1) ),
c_0_2661,
[final] ).
cnf(c_0_3561,plain,
( hAPP(X1,X1,plus_plus(X1,number_number_of(X1,pls)),X2) = ti(X1,X2)
| ~ number_ring(X1) ),
c_0_2662,
[final] ).
cnf(c_0_3562,plain,
( hAPP(nat,X1,power_power(X1,X2),X3) = zero_zero(X1)
| X3 = zero_zero(nat)
| ~ zero_neq_one(X1)
| ~ no_zero_divisors(X1)
| ~ mult_zero(X1)
| ~ power(X1)
| ti(X1,X2) != zero_zero(X1) ),
c_0_2663,
[final] ).
cnf(c_0_3563,plain,
( hAPP(X1,X1,plus_plus(X1,X2),X3) = ti(X1,X2)
| ~ semiri456707255roduct(X1)
| ti(X1,X3) != zero_zero(X1) ),
c_0_2664,
[final] ).
cnf(c_0_3564,plain,
( hAPP(X1,X1,plus_plus(X1,X2),number_number_of(X1,pls)) = ti(X1,X2)
| ~ number_ring(X1) ),
c_0_2665,
[final] ).
cnf(c_0_3565,plain,
( hAPP(X1,X1,plus_plus(X1,X2),X2) = zero_zero(X1)
| ~ linord219039673up_add(X1)
| ti(X1,X2) != zero_zero(X1) ),
c_0_2666,
[final] ).
cnf(c_0_3566,plain,
( hAPP(X1,X1,plus_plus(X1,X2),X2) = zero_zero(X1)
| ~ linord219039673up_add(X1)
| ti(X1,X2) != zero_zero(X1) ),
c_0_2667,
[final] ).
cnf(c_0_3567,plain,
( hAPP(nat,X1,power_power(X1,zero_zero(X1)),X2) = one_one(X1)
| ~ semiring_0(X1)
| ~ power(X1)
| X2 != zero_zero(nat) ),
c_0_2668,
[final] ).
cnf(c_0_3568,plain,
( hAPP(X1,X1,plus_plus(X1,zero_zero(X1)),X2) = ti(X1,X2)
| ~ monoid_add(X1) ),
c_0_2669,
[final] ).
cnf(c_0_3569,plain,
( hAPP(X1,X1,plus_plus(X1,zero_zero(X1)),X2) = ti(X1,X2)
| ~ comm_semiring_1(X1) ),
c_0_2670,
[final] ).
cnf(c_0_3570,plain,
( hAPP(X1,X1,plus_plus(X1,zero_zero(X1)),X2) = ti(X1,X2)
| ~ comm_monoid_add(X1) ),
c_0_2671,
[final] ).
cnf(c_0_3571,plain,
( hAPP(nat,X1,power_power(X1,zero_zero(X1)),X2) = zero_zero(X1)
| X2 = zero_zero(nat)
| ~ semiring_0(X1)
| ~ power(X1) ),
c_0_2672,
[final] ).
cnf(c_0_3572,plain,
( hAPP(X1,X1,plus_plus(X1,X2),zero_zero(X1)) = ti(X1,X2)
| ~ monoid_add(X1) ),
c_0_2673,
[final] ).
cnf(c_0_3573,plain,
( hAPP(X1,X1,plus_plus(X1,X2),zero_zero(X1)) = ti(X1,X2)
| ~ comm_semiring_1(X1) ),
c_0_2674,
[final] ).
cnf(c_0_3574,plain,
( hAPP(X1,X1,plus_plus(X1,X2),zero_zero(X1)) = ti(X1,X2)
| ~ comm_monoid_add(X1) ),
c_0_2675,
[final] ).
cnf(c_0_3575,plain,
( hAPP(nat,X1,power_power(X1,X2),one_one(nat)) = ti(X1,X2)
| ~ comm_semiring_1(X1) ),
c_0_2676,
[final] ).
cnf(c_0_3576,plain,
( hAPP(nat,X1,power_power(X1,X2),one_one(nat)) = ti(X1,X2)
| ~ monoid_mult(X1) ),
c_0_2677,
[final] ).
cnf(c_0_3577,plain,
( hAPP(nat,X1,power_power(X1,one_one(X1)),X2) = one_one(X1)
| ~ monoid_mult(X1) ),
c_0_2678,
[final] ).
cnf(c_0_3578,plain,
( hAPP(nat,X1,power_power(X1,X2),zero_zero(nat)) = one_one(X1)
| ~ comm_semiring_1(X1) ),
c_0_2679,
[final] ).
cnf(c_0_3579,plain,
( hAPP(nat,X1,power_power(X1,X2),zero_zero(nat)) = one_one(X1)
| ~ power(X1) ),
c_0_2680,
[final] ).
cnf(c_0_3580,plain,
( hAPP(nat,nat,plus_plus(nat,X1),X2) = zero_zero(nat)
| X2 != zero_zero(nat)
| X1 != zero_zero(nat) ),
c_0_2681,
[final] ).
cnf(c_0_3581,plain,
( hAPP(nat,nat,power_power(nat,X1),X2) = zero_zero(nat)
| X2 = zero_zero(nat)
| X1 != zero_zero(nat) ),
c_0_2682,
[final] ).
cnf(c_0_3582,plain,
( hAPP(nat,nat,power_power(nat,X1),X2) = one_one(nat)
| X1 != one_one(nat) ),
c_0_2683,
[final] ).
cnf(c_0_3583,plain,
( hAPP(nat,nat,power_power(nat,X1),X2) = one_one(nat)
| X2 != zero_zero(nat) ),
c_0_2684,
[final] ).
cnf(c_0_3584,plain,
hAPP(nat,nat,plus_plus(nat,zero_zero(nat)),X1) = X1,
c_0_2685,
[final] ).
cnf(c_0_3585,plain,
hAPP(int,int,plus_plus(int,zero_zero(int)),X1) = X1,
c_0_2686,
[final] ).
cnf(c_0_3586,plain,
hAPP(nat,nat,plus_plus(nat,X1),zero_zero(nat)) = X1,
c_0_2687,
[final] ).
cnf(c_0_3587,plain,
hAPP(int,int,plus_plus(int,X1),zero_zero(int)) = X1,
c_0_2688,
[final] ).
cnf(c_0_3588,plain,
hAPP(int,int,plus_plus(int,X1),pls) = X1,
c_0_2689,
[final] ).
cnf(c_0_3589,plain,
( hAPP(nat,X1,semiring_1_of_nat(X1),zero_zero(nat)) = zero_zero(X1)
| ~ semiring_1(X1) ),
c_0_2690,
[final] ).
cnf(c_0_3590,plain,
( hAPP(nat,X1,semiring_1_of_nat(X1),one_one(nat)) = one_one(X1)
| ~ semiring_1(X1) ),
c_0_2691,
[final] ).
cnf(c_0_3591,plain,
hAPP(int,int,plus_plus(int,pls),X1) = X1,
c_0_2692,
[final] ).
cnf(c_0_3592,plain,
( hAPP(nat,int,semiring_1_of_nat(int),X1) = zero_zero(int)
| X1 != zero_zero(nat) ),
c_0_2693,
[final] ).
cnf(c_0_3593,plain,
hAPP(nat,int,semiring_1_of_nat(int),zero_zero(nat)) = zero_zero(int),
c_0_2694,
[final] ).
cnf(c_0_3594,plain,
hAPP(nat,int,semiring_1_of_nat(int),one_one(nat)) = one_one(int),
c_0_2695,
[final] ).
cnf(c_0_3595,plain,
hAPP(nat,int,semiring_1_of_nat(int),zero_zero(nat)) = zero_zero(int),
c_0_2696,
[final] ).
cnf(c_0_3596,plain,
hAPP(nat,int,semiring_1_of_nat(int),one_one(nat)) = one_one(int),
c_0_2697,
[final] ).
cnf(c_0_3597,plain,
( hAPP(int,int,bit0,X1) = pls
| pls != X1 ),
c_0_2698,
[final] ).
cnf(c_0_3598,plain,
( hAPP(int,int,bit0,X1) = pls
| X1 != pls ),
c_0_2699,
[final] ).
cnf(c_0_3599,plain,
hAPP(int,int,bit0,pls) = pls,
c_0_2700,
[final] ).
cnf(c_0_3600,plain,
ti(fun(bool,fun(X1,fun(X1,X1))),if(X1)) = if(X1),
c_0_2701,
[final] ).
cnf(c_0_3601,plain,
( ti(fun(X1,fun(X1,X1)),times_times(X1)) = times_times(X1)
| ~ linordered_semiring(X1) ),
c_0_2702,
[final] ).
cnf(c_0_3602,plain,
( ti(fun(X1,fun(X1,bool)),ord_less_eq(X1)) = ord_less_eq(X1)
| ~ ord(X1) ),
c_0_2703,
[final] ).
cnf(c_0_3603,plain,
( ti(fun(X1,fun(X1,bool)),ord_less(X1)) = ord_less(X1)
| ~ ord(X1) ),
c_0_2704,
[final] ).
cnf(c_0_3604,plain,
( ti(fun(X1,X1),plus_plus(X1,X2)) = plus_plus(X1,X2)
| ~ cancel_semigroup_add(X1) ),
c_0_2705,
[final] ).
cnf(c_0_3605,plain,
( ti(fun(X1,X1),plus_plus(X1,X2)) = plus_plus(X1,X2)
| ~ ab_semigroup_add(X1) ),
c_0_2706,
[final] ).
cnf(c_0_3606,plain,
( ti(fun(X1,X1),plus_plus(X1,X2)) = plus_plus(X1,X2)
| ~ monoid_add(X1) ),
c_0_2707,
[final] ).
cnf(c_0_3607,plain,
( ti(fun(nat,X1),power_power(X1,X2)) = power_power(X1,X2)
| ~ power(X1) ),
c_0_2708,
[final] ).
cnf(c_0_3608,plain,
( ti(X1,X2) = number_number_of(X1,X3)
| ~ number(X1)
| number_number_of(X1,X3) != ti(X1,X2) ),
c_0_2709,
[final] ).
cnf(c_0_3609,plain,
( number_number_of(X1,X2) = ti(X1,X3)
| ~ number(X1)
| ti(X1,X3) != number_number_of(X1,X2) ),
c_0_2710,
[final] ).
cnf(c_0_3610,plain,
( power_power(X1,ti(X1,X2)) = power_power(X1,X2)
| ~ power(X1) ),
c_0_2711,
[final] ).
cnf(c_0_3611,plain,
( ti(X1,number_number_of(X1,X2)) = number_number_of(X1,X2)
| ~ number(X1) ),
c_0_2712,
[final] ).
cnf(c_0_3612,plain,
( plus_plus(X1,ti(X1,X2)) = plus_plus(X1,X2)
| ~ cancel_semigroup_add(X1) ),
c_0_2713,
[final] ).
cnf(c_0_3613,plain,
( plus_plus(X1,ti(X1,X2)) = plus_plus(X1,X2)
| ~ ab_semigroup_add(X1) ),
c_0_2714,
[final] ).
cnf(c_0_3614,plain,
( plus_plus(X1,ti(X1,X2)) = plus_plus(X1,X2)
| ~ monoid_add(X1) ),
c_0_2715,
[final] ).
cnf(c_0_3615,plain,
( X2 = X3
| ~ ring_char_0(X1)
| ~ number_ring(X1)
| number_number_of(X1,X2) != number_number_of(X1,X3) ),
c_0_2716,
[final] ).
cnf(c_0_3616,plain,
( number_number_of(X1,ti(int,X2)) = number_number_of(X1,X2)
| ~ number(X1) ),
c_0_2717,
[final] ).
cnf(c_0_3617,plain,
( ti(fun(nat,X1),semiring_1_of_nat(X1)) = semiring_1_of_nat(X1)
| ~ semiring_1(X1) ),
c_0_2718,
[final] ).
cnf(c_0_3618,plain,
( ti(X1,X2) = one_one(X1)
| ~ one(X1)
| ti(X1,X2) != one_one(X1) ),
c_0_2719,
[final] ).
cnf(c_0_3619,plain,
( ti(X1,X2) = one_one(X1)
| ~ one(X1)
| ti(X1,X2) != one_one(X1) ),
c_0_2720,
[final] ).
cnf(c_0_3620,plain,
( ti(X1,X2) = zero_zero(X1)
| ~ zero(X1)
| ti(X1,X2) != zero_zero(X1) ),
c_0_2721,
[final] ).
cnf(c_0_3621,plain,
( ti(X1,X2) = zero_zero(X1)
| ~ zero(X1)
| ti(X1,X2) != zero_zero(X1) ),
c_0_2722,
[final] ).
cnf(c_0_3622,plain,
ti(X1,ti(X1,X2)) = ti(X1,X2),
c_0_2723,
[final] ).
cnf(c_0_3623,plain,
( hBOOL(X1)
| ~ hBOOL(ti(bool,X1)) ),
c_0_2724,
[final] ).
cnf(c_0_3624,plain,
( number_number_of(X1,X2) = number_number_of(X1,X3)
| ~ ring_char_0(X1)
| ~ number_ring(X1)
| X2 != X3 ),
c_0_2725,
[final] ).
cnf(c_0_3625,plain,
( ord(fun(X1,X2))
| ~ ord(X2) ),
c_0_2726,
[final] ).
cnf(c_0_3626,plain,
( order(fun(X1,X2))
| ~ order(X2) ),
c_0_2727,
[final] ).
cnf(c_0_3627,plain,
( preorder(fun(X1,X2))
| ~ preorder(X2) ),
c_0_2728,
[final] ).
cnf(c_0_3628,plain,
( hBOOL(ti(bool,X1))
| ~ hBOOL(X1) ),
c_0_2729,
[final] ).
cnf(c_0_3629,plain,
ti(fun(real,real),sqrt) = sqrt,
c_0_2730,
[final] ).
cnf(c_0_3630,plain,
ti(fun(int,int),succ) = succ,
c_0_2731,
[final] ).
cnf(c_0_3631,plain,
( ti(X1,zero_zero(X1)) = zero_zero(X1)
| ~ zero(X1) ),
c_0_2732,
[final] ).
cnf(c_0_3632,plain,
( ti(X1,one_one(X1)) = one_one(X1)
| ~ one(X1) ),
c_0_2733,
[final] ).
cnf(c_0_3633,plain,
( ti(bool,X1) = fFalse
| ti(bool,X1) = fTrue ),
c_0_2734,
[final] ).
cnf(c_0_3634,plain,
ti(X1,undefined(X1)) = undefined(X1),
c_0_2735,
[final] ).
cnf(c_0_3635,plain,
( number_number_of(X1,pls) = zero_zero(X1)
| ~ number_ring(X1) ),
c_0_2736,
[final] ).
cnf(c_0_3636,plain,
( number_number_of(X1,pls) = zero_zero(X1)
| ~ number_ring(X1) ),
c_0_2737,
[final] ).
cnf(c_0_3637,plain,
( number_number_of(X1,pls) = zero_zero(X1)
| ~ number_semiring(X1) ),
c_0_2738,
[final] ).
cnf(c_0_3638,plain,
( zero_zero(X1) != one_one(X1)
| ~ zero_neq_one(X1) ),
c_0_2739,
[final] ).
cnf(c_0_3639,plain,
( zero_zero(X1) != one_one(X1)
| ~ zero_neq_one(X1) ),
c_0_2740,
[final] ).
cnf(c_0_3640,plain,
number_number_of(int,X1) = X1,
c_0_2741,
[final] ).
cnf(c_0_3641,plain,
number_number_of(nat,pls) = zero_zero(nat),
c_0_2742,
[final] ).
cnf(c_0_3642,plain,
number_number_of(nat,pls) = zero_zero(nat),
c_0_2743,
[final] ).
cnf(c_0_3643,plain,
number_number_of(int,pls) = zero_zero(int),
c_0_2744,
[final] ).
cnf(c_0_3644,plain,
ti(nat,tn) = tn,
c_0_2745,
[final] ).
cnf(c_0_3645,plain,
ti(int,t) = t,
c_0_2746,
[final] ).
cnf(c_0_3646,plain,
ti(int,m1) = m1,
c_0_2747,
[final] ).
cnf(c_0_3647,plain,
ti(bool,fTrue) = fTrue,
c_0_2748,
[final] ).
cnf(c_0_3648,plain,
ti(bool,fFalse) = fFalse,
c_0_2749,
[final] ).
cnf(c_0_3649,plain,
zero_zero(real) != one_one(real),
c_0_2750,
[final] ).
cnf(c_0_3650,plain,
zero_zero(int) != one_one(int),
c_0_2751,
[final] ).
cnf(c_0_3651,plain,
one(real),
c_0_2752,
[final] ).
cnf(c_0_3652,plain,
number(real),
c_0_2753,
[final] ).
cnf(c_0_3653,plain,
zero(real),
c_0_2754,
[final] ).
cnf(c_0_3654,plain,
power(real),
c_0_2755,
[final] ).
cnf(c_0_3655,plain,
ord(real),
c_0_2756,
[final] ).
cnf(c_0_3656,plain,
number_ring(real),
c_0_2757,
[final] ).
cnf(c_0_3657,plain,
ring_char_0(real),
c_0_2758,
[final] ).
cnf(c_0_3658,plain,
order(real),
c_0_2759,
[final] ).
cnf(c_0_3659,plain,
mult_zero(real),
c_0_2760,
[final] ).
cnf(c_0_3660,plain,
semiring_0(real),
c_0_2761,
[final] ).
cnf(c_0_3661,plain,
semiring_1(real),
c_0_2762,
[final] ).
cnf(c_0_3662,plain,
monoid_add(real),
c_0_2763,
[final] ).
cnf(c_0_3663,plain,
monoid_mult(real),
c_0_2764,
[final] ).
cnf(c_0_3664,plain,
linorder(real),
c_0_2765,
[final] ).
cnf(c_0_3665,plain,
preorder(real),
c_0_2766,
[final] ).
cnf(c_0_3666,plain,
zero_neq_one(real),
c_0_2767,
[final] ).
cnf(c_0_3667,plain,
number_semiring(real),
c_0_2768,
[final] ).
cnf(c_0_3668,plain,
semiring_char_0(real),
c_0_2769,
[final] ).
cnf(c_0_3669,plain,
comm_semiring_1(real),
c_0_2770,
[final] ).
cnf(c_0_3670,plain,
linordered_idom(real),
c_0_2771,
[final] ).
cnf(c_0_3671,plain,
linordered_ring(real),
c_0_2772,
[final] ).
cnf(c_0_3672,plain,
comm_monoid_add(real),
c_0_2773,
[final] ).
cnf(c_0_3673,plain,
no_zero_divisors(real),
c_0_2774,
[final] ).
cnf(c_0_3674,plain,
ab_semigroup_add(real),
c_0_2775,
[final] ).
cnf(c_0_3675,plain,
dense_linorder(real),
c_0_2776,
[final] ).
cnf(c_0_3676,plain,
linordered_semidom(real),
c_0_2777,
[final] ).
cnf(c_0_3677,plain,
linordered_semiring(real),
c_0_2778,
[final] ).
cnf(c_0_3678,plain,
cancel_semigroup_add(real),
c_0_2779,
[final] ).
cnf(c_0_3679,plain,
linord581940658strict(real),
c_0_2780,
[final] ).
cnf(c_0_3680,plain,
ring_11004092258visors(real),
c_0_2781,
[final] ).
cnf(c_0_3681,plain,
cancel146912293up_add(real),
c_0_2782,
[final] ).
cnf(c_0_3682,plain,
linord219039673up_add(real),
c_0_2783,
[final] ).
cnf(c_0_3683,plain,
ordere216010020id_add(real),
c_0_2784,
[final] ).
cnf(c_0_3684,plain,
ordere779506340up_add(real),
c_0_2785,
[final] ).
cnf(c_0_3685,plain,
linord20386208strict(real),
c_0_2786,
[final] ).
cnf(c_0_3686,plain,
linord893533164strict(real),
c_0_2787,
[final] ).
cnf(c_0_3687,plain,
ordere236663937imp_le(real),
c_0_2788,
[final] ).
cnf(c_0_3688,plain,
ordere223160158up_add(real),
c_0_2789,
[final] ).
cnf(c_0_3689,plain,
semiri456707255roduct(real),
c_0_2790,
[final] ).
cnf(c_0_3690,plain,
ord(bool),
c_0_2791,
[final] ).
cnf(c_0_3691,plain,
order(bool),
c_0_2792,
[final] ).
cnf(c_0_3692,plain,
preorder(bool),
c_0_2793,
[final] ).
cnf(c_0_3693,plain,
one(nat),
c_0_2794,
[final] ).
cnf(c_0_3694,plain,
number(nat),
c_0_2795,
[final] ).
cnf(c_0_3695,plain,
zero(nat),
c_0_2796,
[final] ).
cnf(c_0_3696,plain,
power(nat),
c_0_2797,
[final] ).
cnf(c_0_3697,plain,
ord(nat),
c_0_2798,
[final] ).
cnf(c_0_3698,plain,
order(nat),
c_0_2799,
[final] ).
cnf(c_0_3699,plain,
mult_zero(nat),
c_0_2800,
[final] ).
cnf(c_0_3700,plain,
semiring_0(nat),
c_0_2801,
[final] ).
cnf(c_0_3701,plain,
semiring_1(nat),
c_0_2802,
[final] ).
cnf(c_0_3702,plain,
monoid_add(nat),
c_0_2803,
[final] ).
cnf(c_0_3703,plain,
monoid_mult(nat),
c_0_2804,
[final] ).
cnf(c_0_3704,plain,
linorder(nat),
c_0_2805,
[final] ).
cnf(c_0_3705,plain,
preorder(nat),
c_0_2806,
[final] ).
cnf(c_0_3706,plain,
zero_neq_one(nat),
c_0_2807,
[final] ).
cnf(c_0_3707,plain,
number_semiring(nat),
c_0_2808,
[final] ).
cnf(c_0_3708,plain,
semiring_char_0(nat),
c_0_2809,
[final] ).
cnf(c_0_3709,plain,
comm_semiring_1(nat),
c_0_2810,
[final] ).
cnf(c_0_3710,plain,
comm_monoid_add(nat),
c_0_2811,
[final] ).
cnf(c_0_3711,plain,
no_zero_divisors(nat),
c_0_2812,
[final] ).
cnf(c_0_3712,plain,
ab_semigroup_add(nat),
c_0_2813,
[final] ).
cnf(c_0_3713,plain,
linordered_semidom(nat),
c_0_2814,
[final] ).
cnf(c_0_3714,plain,
linordered_semiring(nat),
c_0_2815,
[final] ).
cnf(c_0_3715,plain,
cancel_semigroup_add(nat),
c_0_2816,
[final] ).
cnf(c_0_3716,plain,
cancel146912293up_add(nat),
c_0_2817,
[final] ).
cnf(c_0_3717,plain,
ordere216010020id_add(nat),
c_0_2818,
[final] ).
cnf(c_0_3718,plain,
ordere779506340up_add(nat),
c_0_2819,
[final] ).
cnf(c_0_3719,plain,
linord20386208strict(nat),
c_0_2820,
[final] ).
cnf(c_0_3720,plain,
linord893533164strict(nat),
c_0_2821,
[final] ).
cnf(c_0_3721,plain,
ordere236663937imp_le(nat),
c_0_2822,
[final] ).
cnf(c_0_3722,plain,
ordere223160158up_add(nat),
c_0_2823,
[final] ).
cnf(c_0_3723,plain,
semiri456707255roduct(nat),
c_0_2824,
[final] ).
cnf(c_0_3724,plain,
one(int),
c_0_2825,
[final] ).
cnf(c_0_3725,plain,
number(int),
c_0_2826,
[final] ).
cnf(c_0_3726,plain,
zero(int),
c_0_2827,
[final] ).
cnf(c_0_3727,plain,
power(int),
c_0_2828,
[final] ).
cnf(c_0_3728,plain,
ord(int),
c_0_2829,
[final] ).
cnf(c_0_3729,plain,
number_ring(int),
c_0_2830,
[final] ).
cnf(c_0_3730,plain,
ring_char_0(int),
c_0_2831,
[final] ).
cnf(c_0_3731,plain,
order(int),
c_0_2832,
[final] ).
cnf(c_0_3732,plain,
mult_zero(int),
c_0_2833,
[final] ).
cnf(c_0_3733,plain,
semiring_0(int),
c_0_2834,
[final] ).
cnf(c_0_3734,plain,
semiring_1(int),
c_0_2835,
[final] ).
cnf(c_0_3735,plain,
monoid_add(int),
c_0_2836,
[final] ).
cnf(c_0_3736,plain,
monoid_mult(int),
c_0_2837,
[final] ).
cnf(c_0_3737,plain,
linorder(int),
c_0_2838,
[final] ).
cnf(c_0_3738,plain,
preorder(int),
c_0_2839,
[final] ).
cnf(c_0_3739,plain,
zero_neq_one(int),
c_0_2840,
[final] ).
cnf(c_0_3740,plain,
number_semiring(int),
c_0_2841,
[final] ).
cnf(c_0_3741,plain,
semiring_char_0(int),
c_0_2842,
[final] ).
cnf(c_0_3742,plain,
comm_semiring_1(int),
c_0_2843,
[final] ).
cnf(c_0_3743,plain,
linordered_idom(int),
c_0_2844,
[final] ).
cnf(c_0_3744,plain,
linordered_ring(int),
c_0_2845,
[final] ).
cnf(c_0_3745,plain,
comm_monoid_add(int),
c_0_2846,
[final] ).
cnf(c_0_3746,plain,
no_zero_divisors(int),
c_0_2847,
[final] ).
cnf(c_0_3747,plain,
ab_semigroup_add(int),
c_0_2848,
[final] ).
cnf(c_0_3748,plain,
linordered_semidom(int),
c_0_2849,
[final] ).
cnf(c_0_3749,plain,
linordered_semiring(int),
c_0_2850,
[final] ).
cnf(c_0_3750,plain,
cancel_semigroup_add(int),
c_0_2851,
[final] ).
cnf(c_0_3751,plain,
linord581940658strict(int),
c_0_2852,
[final] ).
cnf(c_0_3752,plain,
ring_11004092258visors(int),
c_0_2853,
[final] ).
cnf(c_0_3753,plain,
cancel146912293up_add(int),
c_0_2854,
[final] ).
cnf(c_0_3754,plain,
linord219039673up_add(int),
c_0_2855,
[final] ).
cnf(c_0_3755,plain,
ordere216010020id_add(int),
c_0_2856,
[final] ).
cnf(c_0_3756,plain,
ordere779506340up_add(int),
c_0_2857,
[final] ).
cnf(c_0_3757,plain,
linord20386208strict(int),
c_0_2858,
[final] ).
cnf(c_0_3758,plain,
linord893533164strict(int),
c_0_2859,
[final] ).
cnf(c_0_3759,plain,
ordere236663937imp_le(int),
c_0_2860,
[final] ).
cnf(c_0_3760,plain,
ordere223160158up_add(int),
c_0_2861,
[final] ).
cnf(c_0_3761,plain,
semiri456707255roduct(int),
c_0_2862,
[final] ).
cnf(c_0_3762,plain,
zero_zero(int) = pls,
c_0_2863,
[final] ).
% End CNF derivation
% Generating one_way clauses for all literals in the CNF.
cnf(c_0_2865_0,axiom,
( ti(X1,X2) = zero_zero(X1)
| ~ linordered_idom(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,plus_plus(X1,hAPP(nat,X1,power_power(X1,X2),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,X1,power_power(X1,X3),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),zero_zero(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_2865]) ).
cnf(c_0_2865_1,axiom,
( ~ linordered_idom(X1)
| ti(X1,X2) = zero_zero(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,plus_plus(X1,hAPP(nat,X1,power_power(X1,X2),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,X1,power_power(X1,X3),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),zero_zero(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_2865]) ).
cnf(c_0_2865_2,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,plus_plus(X1,hAPP(nat,X1,power_power(X1,X2),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,X1,power_power(X1,X3),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),zero_zero(X1)))
| ~ linordered_idom(X1)
| ti(X1,X2) = zero_zero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2865]) ).
cnf(c_0_2866_0,axiom,
( ti(X1,X3) = zero_zero(X1)
| ~ linordered_idom(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,plus_plus(X1,hAPP(nat,X1,power_power(X1,X2),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,X1,power_power(X1,X3),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),zero_zero(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_2866]) ).
cnf(c_0_2866_1,axiom,
( ~ linordered_idom(X1)
| ti(X1,X3) = zero_zero(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,plus_plus(X1,hAPP(nat,X1,power_power(X1,X2),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,X1,power_power(X1,X3),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),zero_zero(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_2866]) ).
cnf(c_0_2866_2,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,plus_plus(X1,hAPP(nat,X1,power_power(X1,X2),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,X1,power_power(X1,X3),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),zero_zero(X1)))
| ~ linordered_idom(X1)
| ti(X1,X3) = zero_zero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2866]) ).
cnf(c_0_2867_0,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,plus_plus(X1,hAPP(nat,X1,power_power(X1,X2),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,X1,power_power(X1,X3),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),zero_zero(X1)))
| ~ linordered_idom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2867]) ).
cnf(c_0_2867_1,axiom,
( ~ linordered_idom(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,plus_plus(X1,hAPP(nat,X1,power_power(X1,X2),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,X1,power_power(X1,X3),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),zero_zero(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_2867]) ).
cnf(c_0_2868_0,axiom,
( hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),hAPP(X1,X2,X3,X6)),X5))
| ~ order(X1)
| ~ order(X2)
| ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),hAPP(X1,X2,X3,X4)),X5))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X6),X4))
| ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less_eq(X2),hAPP(X1,X2,X3,sk1_esk44_6(X1,X2,X6,X3,X4,X5))),hAPP(X1,X2,X3,sk1_esk43_6(X1,X2,X6,X3,X4,X5)))) ),
inference(literals_permutation,[status(thm)],[c_0_2868]) ).
cnf(c_0_2868_1,axiom,
( ~ order(X1)
| hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),hAPP(X1,X2,X3,X6)),X5))
| ~ order(X2)
| ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),hAPP(X1,X2,X3,X4)),X5))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X6),X4))
| ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less_eq(X2),hAPP(X1,X2,X3,sk1_esk44_6(X1,X2,X6,X3,X4,X5))),hAPP(X1,X2,X3,sk1_esk43_6(X1,X2,X6,X3,X4,X5)))) ),
inference(literals_permutation,[status(thm)],[c_0_2868]) ).
cnf(c_0_2868_2,axiom,
( ~ order(X2)
| ~ order(X1)
| hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),hAPP(X1,X2,X3,X6)),X5))
| ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),hAPP(X1,X2,X3,X4)),X5))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X6),X4))
| ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less_eq(X2),hAPP(X1,X2,X3,sk1_esk44_6(X1,X2,X6,X3,X4,X5))),hAPP(X1,X2,X3,sk1_esk43_6(X1,X2,X6,X3,X4,X5)))) ),
inference(literals_permutation,[status(thm)],[c_0_2868]) ).
cnf(c_0_2868_3,axiom,
( ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),hAPP(X1,X2,X3,X4)),X5))
| ~ order(X2)
| ~ order(X1)
| hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),hAPP(X1,X2,X3,X6)),X5))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X6),X4))
| ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less_eq(X2),hAPP(X1,X2,X3,sk1_esk44_6(X1,X2,X6,X3,X4,X5))),hAPP(X1,X2,X3,sk1_esk43_6(X1,X2,X6,X3,X4,X5)))) ),
inference(literals_permutation,[status(thm)],[c_0_2868]) ).
cnf(c_0_2868_4,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X6),X4))
| ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),hAPP(X1,X2,X3,X4)),X5))
| ~ order(X2)
| ~ order(X1)
| hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),hAPP(X1,X2,X3,X6)),X5))
| ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less_eq(X2),hAPP(X1,X2,X3,sk1_esk44_6(X1,X2,X6,X3,X4,X5))),hAPP(X1,X2,X3,sk1_esk43_6(X1,X2,X6,X3,X4,X5)))) ),
inference(literals_permutation,[status(thm)],[c_0_2868]) ).
cnf(c_0_2868_5,axiom,
( ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less_eq(X2),hAPP(X1,X2,X3,sk1_esk44_6(X1,X2,X6,X3,X4,X5))),hAPP(X1,X2,X3,sk1_esk43_6(X1,X2,X6,X3,X4,X5))))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X6),X4))
| ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),hAPP(X1,X2,X3,X4)),X5))
| ~ order(X2)
| ~ order(X1)
| hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),hAPP(X1,X2,X3,X6)),X5)) ),
inference(literals_permutation,[status(thm)],[c_0_2868]) ).
cnf(c_0_2869_0,axiom,
( hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),hAPP(X1,X2,X5,X3)),X6))
| ~ order(X1)
| ~ order(X2)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X4))
| ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),hAPP(X1,X2,X5,X4)),X6))
| ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less_eq(X2),hAPP(X1,X2,X5,sk1_esk39_6(X1,X2,X5,X6,X3,X4))),hAPP(X1,X2,X5,sk1_esk40_6(X1,X2,X5,X6,X3,X4)))) ),
inference(literals_permutation,[status(thm)],[c_0_2869]) ).
cnf(c_0_2869_1,axiom,
( ~ order(X1)
| hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),hAPP(X1,X2,X5,X3)),X6))
| ~ order(X2)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X4))
| ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),hAPP(X1,X2,X5,X4)),X6))
| ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less_eq(X2),hAPP(X1,X2,X5,sk1_esk39_6(X1,X2,X5,X6,X3,X4))),hAPP(X1,X2,X5,sk1_esk40_6(X1,X2,X5,X6,X3,X4)))) ),
inference(literals_permutation,[status(thm)],[c_0_2869]) ).
cnf(c_0_2869_2,axiom,
( ~ order(X2)
| ~ order(X1)
| hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),hAPP(X1,X2,X5,X3)),X6))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X4))
| ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),hAPP(X1,X2,X5,X4)),X6))
| ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less_eq(X2),hAPP(X1,X2,X5,sk1_esk39_6(X1,X2,X5,X6,X3,X4))),hAPP(X1,X2,X5,sk1_esk40_6(X1,X2,X5,X6,X3,X4)))) ),
inference(literals_permutation,[status(thm)],[c_0_2869]) ).
cnf(c_0_2869_3,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X4))
| ~ order(X2)
| ~ order(X1)
| hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),hAPP(X1,X2,X5,X3)),X6))
| ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),hAPP(X1,X2,X5,X4)),X6))
| ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less_eq(X2),hAPP(X1,X2,X5,sk1_esk39_6(X1,X2,X5,X6,X3,X4))),hAPP(X1,X2,X5,sk1_esk40_6(X1,X2,X5,X6,X3,X4)))) ),
inference(literals_permutation,[status(thm)],[c_0_2869]) ).
cnf(c_0_2869_4,axiom,
( ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),hAPP(X1,X2,X5,X4)),X6))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X4))
| ~ order(X2)
| ~ order(X1)
| hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),hAPP(X1,X2,X5,X3)),X6))
| ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less_eq(X2),hAPP(X1,X2,X5,sk1_esk39_6(X1,X2,X5,X6,X3,X4))),hAPP(X1,X2,X5,sk1_esk40_6(X1,X2,X5,X6,X3,X4)))) ),
inference(literals_permutation,[status(thm)],[c_0_2869]) ).
cnf(c_0_2869_5,axiom,
( ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less_eq(X2),hAPP(X1,X2,X5,sk1_esk39_6(X1,X2,X5,X6,X3,X4))),hAPP(X1,X2,X5,sk1_esk40_6(X1,X2,X5,X6,X3,X4))))
| ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),hAPP(X1,X2,X5,X4)),X6))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X4))
| ~ order(X2)
| ~ order(X1)
| hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),hAPP(X1,X2,X5,X3)),X6)) ),
inference(literals_permutation,[status(thm)],[c_0_2869]) ).
cnf(c_0_2870_0,axiom,
( hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),hAPP(X1,X2,X3,X6)),X5))
| ~ ord(X1)
| ~ order(X2)
| ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less_eq(X2),hAPP(X1,X2,X3,X4)),X5))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X6),X4))
| ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),hAPP(X1,X2,X3,sk1_esk38_6(X1,X2,X6,X3,X4,X5))),hAPP(X1,X2,X3,sk1_esk37_6(X1,X2,X6,X3,X4,X5)))) ),
inference(literals_permutation,[status(thm)],[c_0_2870]) ).
cnf(c_0_2870_1,axiom,
( ~ ord(X1)
| hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),hAPP(X1,X2,X3,X6)),X5))
| ~ order(X2)
| ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less_eq(X2),hAPP(X1,X2,X3,X4)),X5))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X6),X4))
| ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),hAPP(X1,X2,X3,sk1_esk38_6(X1,X2,X6,X3,X4,X5))),hAPP(X1,X2,X3,sk1_esk37_6(X1,X2,X6,X3,X4,X5)))) ),
inference(literals_permutation,[status(thm)],[c_0_2870]) ).
cnf(c_0_2870_2,axiom,
( ~ order(X2)
| ~ ord(X1)
| hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),hAPP(X1,X2,X3,X6)),X5))
| ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less_eq(X2),hAPP(X1,X2,X3,X4)),X5))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X6),X4))
| ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),hAPP(X1,X2,X3,sk1_esk38_6(X1,X2,X6,X3,X4,X5))),hAPP(X1,X2,X3,sk1_esk37_6(X1,X2,X6,X3,X4,X5)))) ),
inference(literals_permutation,[status(thm)],[c_0_2870]) ).
cnf(c_0_2870_3,axiom,
( ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less_eq(X2),hAPP(X1,X2,X3,X4)),X5))
| ~ order(X2)
| ~ ord(X1)
| hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),hAPP(X1,X2,X3,X6)),X5))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X6),X4))
| ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),hAPP(X1,X2,X3,sk1_esk38_6(X1,X2,X6,X3,X4,X5))),hAPP(X1,X2,X3,sk1_esk37_6(X1,X2,X6,X3,X4,X5)))) ),
inference(literals_permutation,[status(thm)],[c_0_2870]) ).
cnf(c_0_2870_4,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X6),X4))
| ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less_eq(X2),hAPP(X1,X2,X3,X4)),X5))
| ~ order(X2)
| ~ ord(X1)
| hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),hAPP(X1,X2,X3,X6)),X5))
| ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),hAPP(X1,X2,X3,sk1_esk38_6(X1,X2,X6,X3,X4,X5))),hAPP(X1,X2,X3,sk1_esk37_6(X1,X2,X6,X3,X4,X5)))) ),
inference(literals_permutation,[status(thm)],[c_0_2870]) ).
cnf(c_0_2870_5,axiom,
( ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),hAPP(X1,X2,X3,sk1_esk38_6(X1,X2,X6,X3,X4,X5))),hAPP(X1,X2,X3,sk1_esk37_6(X1,X2,X6,X3,X4,X5))))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X6),X4))
| ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less_eq(X2),hAPP(X1,X2,X3,X4)),X5))
| ~ order(X2)
| ~ ord(X1)
| hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),hAPP(X1,X2,X3,X6)),X5)) ),
inference(literals_permutation,[status(thm)],[c_0_2870]) ).
cnf(c_0_2871_0,axiom,
( hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),hAPP(X1,X2,X5,X3)),X6))
| ~ order(X1)
| ~ order(X2)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X4))
| ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less_eq(X2),hAPP(X1,X2,X5,X4)),X6))
| ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),hAPP(X1,X2,X5,sk1_esk34_6(X1,X2,X5,X6,X3,X4))),hAPP(X1,X2,X5,sk1_esk35_6(X1,X2,X5,X6,X3,X4)))) ),
inference(literals_permutation,[status(thm)],[c_0_2871]) ).
cnf(c_0_2871_1,axiom,
( ~ order(X1)
| hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),hAPP(X1,X2,X5,X3)),X6))
| ~ order(X2)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X4))
| ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less_eq(X2),hAPP(X1,X2,X5,X4)),X6))
| ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),hAPP(X1,X2,X5,sk1_esk34_6(X1,X2,X5,X6,X3,X4))),hAPP(X1,X2,X5,sk1_esk35_6(X1,X2,X5,X6,X3,X4)))) ),
inference(literals_permutation,[status(thm)],[c_0_2871]) ).
cnf(c_0_2871_2,axiom,
( ~ order(X2)
| ~ order(X1)
| hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),hAPP(X1,X2,X5,X3)),X6))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X4))
| ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less_eq(X2),hAPP(X1,X2,X5,X4)),X6))
| ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),hAPP(X1,X2,X5,sk1_esk34_6(X1,X2,X5,X6,X3,X4))),hAPP(X1,X2,X5,sk1_esk35_6(X1,X2,X5,X6,X3,X4)))) ),
inference(literals_permutation,[status(thm)],[c_0_2871]) ).
cnf(c_0_2871_3,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X4))
| ~ order(X2)
| ~ order(X1)
| hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),hAPP(X1,X2,X5,X3)),X6))
| ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less_eq(X2),hAPP(X1,X2,X5,X4)),X6))
| ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),hAPP(X1,X2,X5,sk1_esk34_6(X1,X2,X5,X6,X3,X4))),hAPP(X1,X2,X5,sk1_esk35_6(X1,X2,X5,X6,X3,X4)))) ),
inference(literals_permutation,[status(thm)],[c_0_2871]) ).
cnf(c_0_2871_4,axiom,
( ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less_eq(X2),hAPP(X1,X2,X5,X4)),X6))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X4))
| ~ order(X2)
| ~ order(X1)
| hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),hAPP(X1,X2,X5,X3)),X6))
| ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),hAPP(X1,X2,X5,sk1_esk34_6(X1,X2,X5,X6,X3,X4))),hAPP(X1,X2,X5,sk1_esk35_6(X1,X2,X5,X6,X3,X4)))) ),
inference(literals_permutation,[status(thm)],[c_0_2871]) ).
cnf(c_0_2871_5,axiom,
( ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),hAPP(X1,X2,X5,sk1_esk34_6(X1,X2,X5,X6,X3,X4))),hAPP(X1,X2,X5,sk1_esk35_6(X1,X2,X5,X6,X3,X4))))
| ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less_eq(X2),hAPP(X1,X2,X5,X4)),X6))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X4))
| ~ order(X2)
| ~ order(X1)
| hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),hAPP(X1,X2,X5,X3)),X6)) ),
inference(literals_permutation,[status(thm)],[c_0_2871]) ).
cnf(c_0_2872_0,axiom,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),hAPP(X2,X1,X4,X6)))
| ~ order(X1)
| ~ order(X2)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),hAPP(X2,X1,X4,X5)))
| ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),X5),X6))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X2,X1,X4,sk1_esk45_6(X1,X2,X6,X3,X4,X5))),hAPP(X2,X1,X4,sk1_esk46_6(X1,X2,X6,X3,X4,X5)))) ),
inference(literals_permutation,[status(thm)],[c_0_2872]) ).
cnf(c_0_2872_1,axiom,
( ~ order(X1)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),hAPP(X2,X1,X4,X6)))
| ~ order(X2)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),hAPP(X2,X1,X4,X5)))
| ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),X5),X6))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X2,X1,X4,sk1_esk45_6(X1,X2,X6,X3,X4,X5))),hAPP(X2,X1,X4,sk1_esk46_6(X1,X2,X6,X3,X4,X5)))) ),
inference(literals_permutation,[status(thm)],[c_0_2872]) ).
cnf(c_0_2872_2,axiom,
( ~ order(X2)
| ~ order(X1)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),hAPP(X2,X1,X4,X6)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),hAPP(X2,X1,X4,X5)))
| ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),X5),X6))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X2,X1,X4,sk1_esk45_6(X1,X2,X6,X3,X4,X5))),hAPP(X2,X1,X4,sk1_esk46_6(X1,X2,X6,X3,X4,X5)))) ),
inference(literals_permutation,[status(thm)],[c_0_2872]) ).
cnf(c_0_2872_3,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),hAPP(X2,X1,X4,X5)))
| ~ order(X2)
| ~ order(X1)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),hAPP(X2,X1,X4,X6)))
| ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),X5),X6))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X2,X1,X4,sk1_esk45_6(X1,X2,X6,X3,X4,X5))),hAPP(X2,X1,X4,sk1_esk46_6(X1,X2,X6,X3,X4,X5)))) ),
inference(literals_permutation,[status(thm)],[c_0_2872]) ).
cnf(c_0_2872_4,axiom,
( ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),X5),X6))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),hAPP(X2,X1,X4,X5)))
| ~ order(X2)
| ~ order(X1)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),hAPP(X2,X1,X4,X6)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X2,X1,X4,sk1_esk45_6(X1,X2,X6,X3,X4,X5))),hAPP(X2,X1,X4,sk1_esk46_6(X1,X2,X6,X3,X4,X5)))) ),
inference(literals_permutation,[status(thm)],[c_0_2872]) ).
cnf(c_0_2872_5,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X2,X1,X4,sk1_esk45_6(X1,X2,X6,X3,X4,X5))),hAPP(X2,X1,X4,sk1_esk46_6(X1,X2,X6,X3,X4,X5))))
| ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),X5),X6))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),hAPP(X2,X1,X4,X5)))
| ~ order(X2)
| ~ order(X1)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),hAPP(X2,X1,X4,X6))) ),
inference(literals_permutation,[status(thm)],[c_0_2872]) ).
cnf(c_0_2873_0,axiom,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),hAPP(X2,X1,X4,X6)))
| ~ order(X1)
| ~ order(X2)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),hAPP(X2,X1,X4,X5)))
| ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less_eq(X2),X5),X6))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X2,X1,X4,sk1_esk41_6(X1,X2,X6,X3,X4,X5))),hAPP(X2,X1,X4,sk1_esk42_6(X1,X2,X6,X3,X4,X5)))) ),
inference(literals_permutation,[status(thm)],[c_0_2873]) ).
cnf(c_0_2873_1,axiom,
( ~ order(X1)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),hAPP(X2,X1,X4,X6)))
| ~ order(X2)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),hAPP(X2,X1,X4,X5)))
| ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less_eq(X2),X5),X6))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X2,X1,X4,sk1_esk41_6(X1,X2,X6,X3,X4,X5))),hAPP(X2,X1,X4,sk1_esk42_6(X1,X2,X6,X3,X4,X5)))) ),
inference(literals_permutation,[status(thm)],[c_0_2873]) ).
cnf(c_0_2873_2,axiom,
( ~ order(X2)
| ~ order(X1)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),hAPP(X2,X1,X4,X6)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),hAPP(X2,X1,X4,X5)))
| ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less_eq(X2),X5),X6))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X2,X1,X4,sk1_esk41_6(X1,X2,X6,X3,X4,X5))),hAPP(X2,X1,X4,sk1_esk42_6(X1,X2,X6,X3,X4,X5)))) ),
inference(literals_permutation,[status(thm)],[c_0_2873]) ).
cnf(c_0_2873_3,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),hAPP(X2,X1,X4,X5)))
| ~ order(X2)
| ~ order(X1)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),hAPP(X2,X1,X4,X6)))
| ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less_eq(X2),X5),X6))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X2,X1,X4,sk1_esk41_6(X1,X2,X6,X3,X4,X5))),hAPP(X2,X1,X4,sk1_esk42_6(X1,X2,X6,X3,X4,X5)))) ),
inference(literals_permutation,[status(thm)],[c_0_2873]) ).
cnf(c_0_2873_4,axiom,
( ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less_eq(X2),X5),X6))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),hAPP(X2,X1,X4,X5)))
| ~ order(X2)
| ~ order(X1)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),hAPP(X2,X1,X4,X6)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X2,X1,X4,sk1_esk41_6(X1,X2,X6,X3,X4,X5))),hAPP(X2,X1,X4,sk1_esk42_6(X1,X2,X6,X3,X4,X5)))) ),
inference(literals_permutation,[status(thm)],[c_0_2873]) ).
cnf(c_0_2873_5,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X2,X1,X4,sk1_esk41_6(X1,X2,X6,X3,X4,X5))),hAPP(X2,X1,X4,sk1_esk42_6(X1,X2,X6,X3,X4,X5))))
| ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less_eq(X2),X5),X6))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),hAPP(X2,X1,X4,X5)))
| ~ order(X2)
| ~ order(X1)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),hAPP(X2,X1,X4,X6))) ),
inference(literals_permutation,[status(thm)],[c_0_2873]) ).
cnf(c_0_2874_0,axiom,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X5),hAPP(X2,X1,X6,X4)))
| ~ order(X1)
| ~ order(X2)
| ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less_eq(X2),X3),X4))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X5),hAPP(X2,X1,X6,X3)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X2,X1,X6,sk1_esk33_6(X1,X2,X5,X6,X3,X4))),hAPP(X2,X1,X6,sk1_esk32_6(X1,X2,X5,X6,X3,X4)))) ),
inference(literals_permutation,[status(thm)],[c_0_2874]) ).
cnf(c_0_2874_1,axiom,
( ~ order(X1)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X5),hAPP(X2,X1,X6,X4)))
| ~ order(X2)
| ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less_eq(X2),X3),X4))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X5),hAPP(X2,X1,X6,X3)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X2,X1,X6,sk1_esk33_6(X1,X2,X5,X6,X3,X4))),hAPP(X2,X1,X6,sk1_esk32_6(X1,X2,X5,X6,X3,X4)))) ),
inference(literals_permutation,[status(thm)],[c_0_2874]) ).
cnf(c_0_2874_2,axiom,
( ~ order(X2)
| ~ order(X1)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X5),hAPP(X2,X1,X6,X4)))
| ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less_eq(X2),X3),X4))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X5),hAPP(X2,X1,X6,X3)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X2,X1,X6,sk1_esk33_6(X1,X2,X5,X6,X3,X4))),hAPP(X2,X1,X6,sk1_esk32_6(X1,X2,X5,X6,X3,X4)))) ),
inference(literals_permutation,[status(thm)],[c_0_2874]) ).
cnf(c_0_2874_3,axiom,
( ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less_eq(X2),X3),X4))
| ~ order(X2)
| ~ order(X1)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X5),hAPP(X2,X1,X6,X4)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X5),hAPP(X2,X1,X6,X3)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X2,X1,X6,sk1_esk33_6(X1,X2,X5,X6,X3,X4))),hAPP(X2,X1,X6,sk1_esk32_6(X1,X2,X5,X6,X3,X4)))) ),
inference(literals_permutation,[status(thm)],[c_0_2874]) ).
cnf(c_0_2874_4,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X5),hAPP(X2,X1,X6,X3)))
| ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less_eq(X2),X3),X4))
| ~ order(X2)
| ~ order(X1)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X5),hAPP(X2,X1,X6,X4)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X2,X1,X6,sk1_esk33_6(X1,X2,X5,X6,X3,X4))),hAPP(X2,X1,X6,sk1_esk32_6(X1,X2,X5,X6,X3,X4)))) ),
inference(literals_permutation,[status(thm)],[c_0_2874]) ).
cnf(c_0_2874_5,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X2,X1,X6,sk1_esk33_6(X1,X2,X5,X6,X3,X4))),hAPP(X2,X1,X6,sk1_esk32_6(X1,X2,X5,X6,X3,X4))))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X5),hAPP(X2,X1,X6,X3)))
| ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less_eq(X2),X3),X4))
| ~ order(X2)
| ~ order(X1)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X5),hAPP(X2,X1,X6,X4))) ),
inference(literals_permutation,[status(thm)],[c_0_2874]) ).
cnf(c_0_2875_0,axiom,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X5),hAPP(X2,X1,X6,X4)))
| ~ order(X1)
| ~ order(X2)
| ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),X3),X4))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X5),hAPP(X2,X1,X6,X3)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X2,X1,X6,sk1_esk29_6(X1,X2,X5,X6,X3,X4))),hAPP(X2,X1,X6,sk1_esk28_6(X1,X2,X5,X6,X3,X4)))) ),
inference(literals_permutation,[status(thm)],[c_0_2875]) ).
cnf(c_0_2875_1,axiom,
( ~ order(X1)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X5),hAPP(X2,X1,X6,X4)))
| ~ order(X2)
| ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),X3),X4))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X5),hAPP(X2,X1,X6,X3)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X2,X1,X6,sk1_esk29_6(X1,X2,X5,X6,X3,X4))),hAPP(X2,X1,X6,sk1_esk28_6(X1,X2,X5,X6,X3,X4)))) ),
inference(literals_permutation,[status(thm)],[c_0_2875]) ).
cnf(c_0_2875_2,axiom,
( ~ order(X2)
| ~ order(X1)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X5),hAPP(X2,X1,X6,X4)))
| ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),X3),X4))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X5),hAPP(X2,X1,X6,X3)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X2,X1,X6,sk1_esk29_6(X1,X2,X5,X6,X3,X4))),hAPP(X2,X1,X6,sk1_esk28_6(X1,X2,X5,X6,X3,X4)))) ),
inference(literals_permutation,[status(thm)],[c_0_2875]) ).
cnf(c_0_2875_3,axiom,
( ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),X3),X4))
| ~ order(X2)
| ~ order(X1)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X5),hAPP(X2,X1,X6,X4)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X5),hAPP(X2,X1,X6,X3)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X2,X1,X6,sk1_esk29_6(X1,X2,X5,X6,X3,X4))),hAPP(X2,X1,X6,sk1_esk28_6(X1,X2,X5,X6,X3,X4)))) ),
inference(literals_permutation,[status(thm)],[c_0_2875]) ).
cnf(c_0_2875_4,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X5),hAPP(X2,X1,X6,X3)))
| ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),X3),X4))
| ~ order(X2)
| ~ order(X1)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X5),hAPP(X2,X1,X6,X4)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X2,X1,X6,sk1_esk29_6(X1,X2,X5,X6,X3,X4))),hAPP(X2,X1,X6,sk1_esk28_6(X1,X2,X5,X6,X3,X4)))) ),
inference(literals_permutation,[status(thm)],[c_0_2875]) ).
cnf(c_0_2875_5,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X2,X1,X6,sk1_esk29_6(X1,X2,X5,X6,X3,X4))),hAPP(X2,X1,X6,sk1_esk28_6(X1,X2,X5,X6,X3,X4))))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X5),hAPP(X2,X1,X6,X3)))
| ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),X3),X4))
| ~ order(X2)
| ~ order(X1)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X5),hAPP(X2,X1,X6,X4))) ),
inference(literals_permutation,[status(thm)],[c_0_2875]) ).
cnf(c_0_2877_0,axiom,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,plus_plus(X1,hAPP(nat,X1,power_power(X1,X2),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,X1,power_power(X1,X3),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),zero_zero(X1)))
| ~ linordered_idom(X1)
| ti(X1,X3) != zero_zero(X1)
| ti(X1,X2) != zero_zero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2877]) ).
cnf(c_0_2877_1,axiom,
( ~ linordered_idom(X1)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,plus_plus(X1,hAPP(nat,X1,power_power(X1,X2),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,X1,power_power(X1,X3),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),zero_zero(X1)))
| ti(X1,X3) != zero_zero(X1)
| ti(X1,X2) != zero_zero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2877]) ).
cnf(c_0_2877_2,axiom,
( ti(X1,X3) != zero_zero(X1)
| ~ linordered_idom(X1)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,plus_plus(X1,hAPP(nat,X1,power_power(X1,X2),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,X1,power_power(X1,X3),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),zero_zero(X1)))
| ti(X1,X2) != zero_zero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2877]) ).
cnf(c_0_2877_3,axiom,
( ti(X1,X2) != zero_zero(X1)
| ti(X1,X3) != zero_zero(X1)
| ~ linordered_idom(X1)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,plus_plus(X1,hAPP(nat,X1,power_power(X1,X2),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,X1,power_power(X1,X3),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),zero_zero(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_2877]) ).
cnf(c_0_2878_0,axiom,
( ~ linordered_idom(X1)
| ti(X1,X2) != zero_zero(X1)
| ti(X1,X3) != zero_zero(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),hAPP(X1,X1,plus_plus(X1,hAPP(nat,X1,power_power(X1,X3),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,X1,power_power(X1,X2),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))) ),
inference(literals_permutation,[status(thm)],[c_0_2878]) ).
cnf(c_0_2878_1,axiom,
( ti(X1,X2) != zero_zero(X1)
| ~ linordered_idom(X1)
| ti(X1,X3) != zero_zero(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),hAPP(X1,X1,plus_plus(X1,hAPP(nat,X1,power_power(X1,X3),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,X1,power_power(X1,X2),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))) ),
inference(literals_permutation,[status(thm)],[c_0_2878]) ).
cnf(c_0_2878_2,axiom,
( ti(X1,X3) != zero_zero(X1)
| ti(X1,X2) != zero_zero(X1)
| ~ linordered_idom(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),hAPP(X1,X1,plus_plus(X1,hAPP(nat,X1,power_power(X1,X3),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,X1,power_power(X1,X2),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))) ),
inference(literals_permutation,[status(thm)],[c_0_2878]) ).
cnf(c_0_2878_3,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),hAPP(X1,X1,plus_plus(X1,hAPP(nat,X1,power_power(X1,X3),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,X1,power_power(X1,X2),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))))
| ti(X1,X3) != zero_zero(X1)
| ti(X1,X2) != zero_zero(X1)
| ~ linordered_idom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2878]) ).
cnf(c_0_2879_0,axiom,
( hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),hAPP(X1,X2,X3,X6)),X5))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),sk1_esk44_6(X1,X2,X6,X3,X4,X5)),sk1_esk43_6(X1,X2,X6,X3,X4,X5)))
| ~ order(X1)
| ~ order(X2)
| ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),hAPP(X1,X2,X3,X4)),X5))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X6),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2879]) ).
cnf(c_0_2879_1,axiom,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),sk1_esk44_6(X1,X2,X6,X3,X4,X5)),sk1_esk43_6(X1,X2,X6,X3,X4,X5)))
| hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),hAPP(X1,X2,X3,X6)),X5))
| ~ order(X1)
| ~ order(X2)
| ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),hAPP(X1,X2,X3,X4)),X5))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X6),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2879]) ).
cnf(c_0_2879_2,axiom,
( ~ order(X1)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),sk1_esk44_6(X1,X2,X6,X3,X4,X5)),sk1_esk43_6(X1,X2,X6,X3,X4,X5)))
| hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),hAPP(X1,X2,X3,X6)),X5))
| ~ order(X2)
| ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),hAPP(X1,X2,X3,X4)),X5))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X6),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2879]) ).
cnf(c_0_2879_3,axiom,
( ~ order(X2)
| ~ order(X1)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),sk1_esk44_6(X1,X2,X6,X3,X4,X5)),sk1_esk43_6(X1,X2,X6,X3,X4,X5)))
| hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),hAPP(X1,X2,X3,X6)),X5))
| ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),hAPP(X1,X2,X3,X4)),X5))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X6),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2879]) ).
cnf(c_0_2879_4,axiom,
( ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),hAPP(X1,X2,X3,X4)),X5))
| ~ order(X2)
| ~ order(X1)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),sk1_esk44_6(X1,X2,X6,X3,X4,X5)),sk1_esk43_6(X1,X2,X6,X3,X4,X5)))
| hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),hAPP(X1,X2,X3,X6)),X5))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X6),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2879]) ).
cnf(c_0_2879_5,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X6),X4))
| ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),hAPP(X1,X2,X3,X4)),X5))
| ~ order(X2)
| ~ order(X1)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),sk1_esk44_6(X1,X2,X6,X3,X4,X5)),sk1_esk43_6(X1,X2,X6,X3,X4,X5)))
| hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),hAPP(X1,X2,X3,X6)),X5)) ),
inference(literals_permutation,[status(thm)],[c_0_2879]) ).
cnf(c_0_2880_0,axiom,
( hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),hAPP(X1,X2,X5,X3)),X6))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),sk1_esk39_6(X1,X2,X5,X6,X3,X4)),sk1_esk40_6(X1,X2,X5,X6,X3,X4)))
| ~ order(X1)
| ~ order(X2)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X4))
| ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),hAPP(X1,X2,X5,X4)),X6)) ),
inference(literals_permutation,[status(thm)],[c_0_2880]) ).
cnf(c_0_2880_1,axiom,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),sk1_esk39_6(X1,X2,X5,X6,X3,X4)),sk1_esk40_6(X1,X2,X5,X6,X3,X4)))
| hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),hAPP(X1,X2,X5,X3)),X6))
| ~ order(X1)
| ~ order(X2)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X4))
| ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),hAPP(X1,X2,X5,X4)),X6)) ),
inference(literals_permutation,[status(thm)],[c_0_2880]) ).
cnf(c_0_2880_2,axiom,
( ~ order(X1)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),sk1_esk39_6(X1,X2,X5,X6,X3,X4)),sk1_esk40_6(X1,X2,X5,X6,X3,X4)))
| hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),hAPP(X1,X2,X5,X3)),X6))
| ~ order(X2)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X4))
| ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),hAPP(X1,X2,X5,X4)),X6)) ),
inference(literals_permutation,[status(thm)],[c_0_2880]) ).
cnf(c_0_2880_3,axiom,
( ~ order(X2)
| ~ order(X1)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),sk1_esk39_6(X1,X2,X5,X6,X3,X4)),sk1_esk40_6(X1,X2,X5,X6,X3,X4)))
| hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),hAPP(X1,X2,X5,X3)),X6))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X4))
| ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),hAPP(X1,X2,X5,X4)),X6)) ),
inference(literals_permutation,[status(thm)],[c_0_2880]) ).
cnf(c_0_2880_4,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X4))
| ~ order(X2)
| ~ order(X1)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),sk1_esk39_6(X1,X2,X5,X6,X3,X4)),sk1_esk40_6(X1,X2,X5,X6,X3,X4)))
| hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),hAPP(X1,X2,X5,X3)),X6))
| ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),hAPP(X1,X2,X5,X4)),X6)) ),
inference(literals_permutation,[status(thm)],[c_0_2880]) ).
cnf(c_0_2880_5,axiom,
( ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),hAPP(X1,X2,X5,X4)),X6))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X4))
| ~ order(X2)
| ~ order(X1)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),sk1_esk39_6(X1,X2,X5,X6,X3,X4)),sk1_esk40_6(X1,X2,X5,X6,X3,X4)))
| hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),hAPP(X1,X2,X5,X3)),X6)) ),
inference(literals_permutation,[status(thm)],[c_0_2880]) ).
cnf(c_0_2881_0,axiom,
( hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),hAPP(X1,X2,X3,X6)),X5))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),sk1_esk38_6(X1,X2,X6,X3,X4,X5)),sk1_esk37_6(X1,X2,X6,X3,X4,X5)))
| ~ ord(X1)
| ~ order(X2)
| ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less_eq(X2),hAPP(X1,X2,X3,X4)),X5))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X6),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2881]) ).
cnf(c_0_2881_1,axiom,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),sk1_esk38_6(X1,X2,X6,X3,X4,X5)),sk1_esk37_6(X1,X2,X6,X3,X4,X5)))
| hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),hAPP(X1,X2,X3,X6)),X5))
| ~ ord(X1)
| ~ order(X2)
| ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less_eq(X2),hAPP(X1,X2,X3,X4)),X5))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X6),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2881]) ).
cnf(c_0_2881_2,axiom,
( ~ ord(X1)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),sk1_esk38_6(X1,X2,X6,X3,X4,X5)),sk1_esk37_6(X1,X2,X6,X3,X4,X5)))
| hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),hAPP(X1,X2,X3,X6)),X5))
| ~ order(X2)
| ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less_eq(X2),hAPP(X1,X2,X3,X4)),X5))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X6),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2881]) ).
cnf(c_0_2881_3,axiom,
( ~ order(X2)
| ~ ord(X1)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),sk1_esk38_6(X1,X2,X6,X3,X4,X5)),sk1_esk37_6(X1,X2,X6,X3,X4,X5)))
| hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),hAPP(X1,X2,X3,X6)),X5))
| ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less_eq(X2),hAPP(X1,X2,X3,X4)),X5))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X6),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2881]) ).
cnf(c_0_2881_4,axiom,
( ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less_eq(X2),hAPP(X1,X2,X3,X4)),X5))
| ~ order(X2)
| ~ ord(X1)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),sk1_esk38_6(X1,X2,X6,X3,X4,X5)),sk1_esk37_6(X1,X2,X6,X3,X4,X5)))
| hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),hAPP(X1,X2,X3,X6)),X5))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X6),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2881]) ).
cnf(c_0_2881_5,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X6),X4))
| ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less_eq(X2),hAPP(X1,X2,X3,X4)),X5))
| ~ order(X2)
| ~ ord(X1)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),sk1_esk38_6(X1,X2,X6,X3,X4,X5)),sk1_esk37_6(X1,X2,X6,X3,X4,X5)))
| hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),hAPP(X1,X2,X3,X6)),X5)) ),
inference(literals_permutation,[status(thm)],[c_0_2881]) ).
cnf(c_0_2882_0,axiom,
( hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),hAPP(X1,X2,X5,X3)),X6))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),sk1_esk34_6(X1,X2,X5,X6,X3,X4)),sk1_esk35_6(X1,X2,X5,X6,X3,X4)))
| ~ order(X1)
| ~ order(X2)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X4))
| ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less_eq(X2),hAPP(X1,X2,X5,X4)),X6)) ),
inference(literals_permutation,[status(thm)],[c_0_2882]) ).
cnf(c_0_2882_1,axiom,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),sk1_esk34_6(X1,X2,X5,X6,X3,X4)),sk1_esk35_6(X1,X2,X5,X6,X3,X4)))
| hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),hAPP(X1,X2,X5,X3)),X6))
| ~ order(X1)
| ~ order(X2)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X4))
| ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less_eq(X2),hAPP(X1,X2,X5,X4)),X6)) ),
inference(literals_permutation,[status(thm)],[c_0_2882]) ).
cnf(c_0_2882_2,axiom,
( ~ order(X1)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),sk1_esk34_6(X1,X2,X5,X6,X3,X4)),sk1_esk35_6(X1,X2,X5,X6,X3,X4)))
| hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),hAPP(X1,X2,X5,X3)),X6))
| ~ order(X2)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X4))
| ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less_eq(X2),hAPP(X1,X2,X5,X4)),X6)) ),
inference(literals_permutation,[status(thm)],[c_0_2882]) ).
cnf(c_0_2882_3,axiom,
( ~ order(X2)
| ~ order(X1)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),sk1_esk34_6(X1,X2,X5,X6,X3,X4)),sk1_esk35_6(X1,X2,X5,X6,X3,X4)))
| hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),hAPP(X1,X2,X5,X3)),X6))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X4))
| ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less_eq(X2),hAPP(X1,X2,X5,X4)),X6)) ),
inference(literals_permutation,[status(thm)],[c_0_2882]) ).
cnf(c_0_2882_4,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X4))
| ~ order(X2)
| ~ order(X1)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),sk1_esk34_6(X1,X2,X5,X6,X3,X4)),sk1_esk35_6(X1,X2,X5,X6,X3,X4)))
| hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),hAPP(X1,X2,X5,X3)),X6))
| ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less_eq(X2),hAPP(X1,X2,X5,X4)),X6)) ),
inference(literals_permutation,[status(thm)],[c_0_2882]) ).
cnf(c_0_2882_5,axiom,
( ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less_eq(X2),hAPP(X1,X2,X5,X4)),X6))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X4))
| ~ order(X2)
| ~ order(X1)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),sk1_esk34_6(X1,X2,X5,X6,X3,X4)),sk1_esk35_6(X1,X2,X5,X6,X3,X4)))
| hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),hAPP(X1,X2,X5,X3)),X6)) ),
inference(literals_permutation,[status(thm)],[c_0_2882]) ).
cnf(c_0_2883_0,axiom,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),hAPP(X2,X1,X4,X6)))
| hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),sk1_esk45_6(X1,X2,X6,X3,X4,X5)),sk1_esk46_6(X1,X2,X6,X3,X4,X5)))
| ~ order(X1)
| ~ order(X2)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),hAPP(X2,X1,X4,X5)))
| ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),X5),X6)) ),
inference(literals_permutation,[status(thm)],[c_0_2883]) ).
cnf(c_0_2883_1,axiom,
( hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),sk1_esk45_6(X1,X2,X6,X3,X4,X5)),sk1_esk46_6(X1,X2,X6,X3,X4,X5)))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),hAPP(X2,X1,X4,X6)))
| ~ order(X1)
| ~ order(X2)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),hAPP(X2,X1,X4,X5)))
| ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),X5),X6)) ),
inference(literals_permutation,[status(thm)],[c_0_2883]) ).
cnf(c_0_2883_2,axiom,
( ~ order(X1)
| hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),sk1_esk45_6(X1,X2,X6,X3,X4,X5)),sk1_esk46_6(X1,X2,X6,X3,X4,X5)))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),hAPP(X2,X1,X4,X6)))
| ~ order(X2)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),hAPP(X2,X1,X4,X5)))
| ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),X5),X6)) ),
inference(literals_permutation,[status(thm)],[c_0_2883]) ).
cnf(c_0_2883_3,axiom,
( ~ order(X2)
| ~ order(X1)
| hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),sk1_esk45_6(X1,X2,X6,X3,X4,X5)),sk1_esk46_6(X1,X2,X6,X3,X4,X5)))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),hAPP(X2,X1,X4,X6)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),hAPP(X2,X1,X4,X5)))
| ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),X5),X6)) ),
inference(literals_permutation,[status(thm)],[c_0_2883]) ).
cnf(c_0_2883_4,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),hAPP(X2,X1,X4,X5)))
| ~ order(X2)
| ~ order(X1)
| hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),sk1_esk45_6(X1,X2,X6,X3,X4,X5)),sk1_esk46_6(X1,X2,X6,X3,X4,X5)))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),hAPP(X2,X1,X4,X6)))
| ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),X5),X6)) ),
inference(literals_permutation,[status(thm)],[c_0_2883]) ).
cnf(c_0_2883_5,axiom,
( ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),X5),X6))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),hAPP(X2,X1,X4,X5)))
| ~ order(X2)
| ~ order(X1)
| hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),sk1_esk45_6(X1,X2,X6,X3,X4,X5)),sk1_esk46_6(X1,X2,X6,X3,X4,X5)))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),hAPP(X2,X1,X4,X6))) ),
inference(literals_permutation,[status(thm)],[c_0_2883]) ).
cnf(c_0_2884_0,axiom,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),hAPP(X2,X1,X4,X6)))
| hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less_eq(X2),sk1_esk41_6(X1,X2,X6,X3,X4,X5)),sk1_esk42_6(X1,X2,X6,X3,X4,X5)))
| ~ order(X1)
| ~ order(X2)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),hAPP(X2,X1,X4,X5)))
| ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less_eq(X2),X5),X6)) ),
inference(literals_permutation,[status(thm)],[c_0_2884]) ).
cnf(c_0_2884_1,axiom,
( hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less_eq(X2),sk1_esk41_6(X1,X2,X6,X3,X4,X5)),sk1_esk42_6(X1,X2,X6,X3,X4,X5)))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),hAPP(X2,X1,X4,X6)))
| ~ order(X1)
| ~ order(X2)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),hAPP(X2,X1,X4,X5)))
| ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less_eq(X2),X5),X6)) ),
inference(literals_permutation,[status(thm)],[c_0_2884]) ).
cnf(c_0_2884_2,axiom,
( ~ order(X1)
| hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less_eq(X2),sk1_esk41_6(X1,X2,X6,X3,X4,X5)),sk1_esk42_6(X1,X2,X6,X3,X4,X5)))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),hAPP(X2,X1,X4,X6)))
| ~ order(X2)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),hAPP(X2,X1,X4,X5)))
| ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less_eq(X2),X5),X6)) ),
inference(literals_permutation,[status(thm)],[c_0_2884]) ).
cnf(c_0_2884_3,axiom,
( ~ order(X2)
| ~ order(X1)
| hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less_eq(X2),sk1_esk41_6(X1,X2,X6,X3,X4,X5)),sk1_esk42_6(X1,X2,X6,X3,X4,X5)))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),hAPP(X2,X1,X4,X6)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),hAPP(X2,X1,X4,X5)))
| ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less_eq(X2),X5),X6)) ),
inference(literals_permutation,[status(thm)],[c_0_2884]) ).
cnf(c_0_2884_4,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),hAPP(X2,X1,X4,X5)))
| ~ order(X2)
| ~ order(X1)
| hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less_eq(X2),sk1_esk41_6(X1,X2,X6,X3,X4,X5)),sk1_esk42_6(X1,X2,X6,X3,X4,X5)))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),hAPP(X2,X1,X4,X6)))
| ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less_eq(X2),X5),X6)) ),
inference(literals_permutation,[status(thm)],[c_0_2884]) ).
cnf(c_0_2884_5,axiom,
( ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less_eq(X2),X5),X6))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),hAPP(X2,X1,X4,X5)))
| ~ order(X2)
| ~ order(X1)
| hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less_eq(X2),sk1_esk41_6(X1,X2,X6,X3,X4,X5)),sk1_esk42_6(X1,X2,X6,X3,X4,X5)))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),hAPP(X2,X1,X4,X6))) ),
inference(literals_permutation,[status(thm)],[c_0_2884]) ).
cnf(c_0_2885_0,axiom,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X5),hAPP(X2,X1,X6,X4)))
| hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less_eq(X2),sk1_esk33_6(X1,X2,X5,X6,X3,X4)),sk1_esk32_6(X1,X2,X5,X6,X3,X4)))
| ~ order(X1)
| ~ order(X2)
| ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less_eq(X2),X3),X4))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X5),hAPP(X2,X1,X6,X3))) ),
inference(literals_permutation,[status(thm)],[c_0_2885]) ).
cnf(c_0_2885_1,axiom,
( hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less_eq(X2),sk1_esk33_6(X1,X2,X5,X6,X3,X4)),sk1_esk32_6(X1,X2,X5,X6,X3,X4)))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X5),hAPP(X2,X1,X6,X4)))
| ~ order(X1)
| ~ order(X2)
| ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less_eq(X2),X3),X4))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X5),hAPP(X2,X1,X6,X3))) ),
inference(literals_permutation,[status(thm)],[c_0_2885]) ).
cnf(c_0_2885_2,axiom,
( ~ order(X1)
| hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less_eq(X2),sk1_esk33_6(X1,X2,X5,X6,X3,X4)),sk1_esk32_6(X1,X2,X5,X6,X3,X4)))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X5),hAPP(X2,X1,X6,X4)))
| ~ order(X2)
| ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less_eq(X2),X3),X4))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X5),hAPP(X2,X1,X6,X3))) ),
inference(literals_permutation,[status(thm)],[c_0_2885]) ).
cnf(c_0_2885_3,axiom,
( ~ order(X2)
| ~ order(X1)
| hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less_eq(X2),sk1_esk33_6(X1,X2,X5,X6,X3,X4)),sk1_esk32_6(X1,X2,X5,X6,X3,X4)))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X5),hAPP(X2,X1,X6,X4)))
| ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less_eq(X2),X3),X4))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X5),hAPP(X2,X1,X6,X3))) ),
inference(literals_permutation,[status(thm)],[c_0_2885]) ).
cnf(c_0_2885_4,axiom,
( ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less_eq(X2),X3),X4))
| ~ order(X2)
| ~ order(X1)
| hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less_eq(X2),sk1_esk33_6(X1,X2,X5,X6,X3,X4)),sk1_esk32_6(X1,X2,X5,X6,X3,X4)))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X5),hAPP(X2,X1,X6,X4)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X5),hAPP(X2,X1,X6,X3))) ),
inference(literals_permutation,[status(thm)],[c_0_2885]) ).
cnf(c_0_2885_5,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X5),hAPP(X2,X1,X6,X3)))
| ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less_eq(X2),X3),X4))
| ~ order(X2)
| ~ order(X1)
| hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less_eq(X2),sk1_esk33_6(X1,X2,X5,X6,X3,X4)),sk1_esk32_6(X1,X2,X5,X6,X3,X4)))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X5),hAPP(X2,X1,X6,X4))) ),
inference(literals_permutation,[status(thm)],[c_0_2885]) ).
cnf(c_0_2886_0,axiom,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X5),hAPP(X2,X1,X6,X4)))
| hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),sk1_esk29_6(X1,X2,X5,X6,X3,X4)),sk1_esk28_6(X1,X2,X5,X6,X3,X4)))
| ~ order(X1)
| ~ order(X2)
| ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),X3),X4))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X5),hAPP(X2,X1,X6,X3))) ),
inference(literals_permutation,[status(thm)],[c_0_2886]) ).
cnf(c_0_2886_1,axiom,
( hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),sk1_esk29_6(X1,X2,X5,X6,X3,X4)),sk1_esk28_6(X1,X2,X5,X6,X3,X4)))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X5),hAPP(X2,X1,X6,X4)))
| ~ order(X1)
| ~ order(X2)
| ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),X3),X4))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X5),hAPP(X2,X1,X6,X3))) ),
inference(literals_permutation,[status(thm)],[c_0_2886]) ).
cnf(c_0_2886_2,axiom,
( ~ order(X1)
| hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),sk1_esk29_6(X1,X2,X5,X6,X3,X4)),sk1_esk28_6(X1,X2,X5,X6,X3,X4)))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X5),hAPP(X2,X1,X6,X4)))
| ~ order(X2)
| ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),X3),X4))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X5),hAPP(X2,X1,X6,X3))) ),
inference(literals_permutation,[status(thm)],[c_0_2886]) ).
cnf(c_0_2886_3,axiom,
( ~ order(X2)
| ~ order(X1)
| hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),sk1_esk29_6(X1,X2,X5,X6,X3,X4)),sk1_esk28_6(X1,X2,X5,X6,X3,X4)))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X5),hAPP(X2,X1,X6,X4)))
| ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),X3),X4))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X5),hAPP(X2,X1,X6,X3))) ),
inference(literals_permutation,[status(thm)],[c_0_2886]) ).
cnf(c_0_2886_4,axiom,
( ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),X3),X4))
| ~ order(X2)
| ~ order(X1)
| hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),sk1_esk29_6(X1,X2,X5,X6,X3,X4)),sk1_esk28_6(X1,X2,X5,X6,X3,X4)))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X5),hAPP(X2,X1,X6,X4)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X5),hAPP(X2,X1,X6,X3))) ),
inference(literals_permutation,[status(thm)],[c_0_2886]) ).
cnf(c_0_2886_5,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X5),hAPP(X2,X1,X6,X3)))
| ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),X3),X4))
| ~ order(X2)
| ~ order(X1)
| hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),sk1_esk29_6(X1,X2,X5,X6,X3,X4)),sk1_esk28_6(X1,X2,X5,X6,X3,X4)))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X5),hAPP(X2,X1,X6,X4))) ),
inference(literals_permutation,[status(thm)],[c_0_2886]) ).
cnf(c_0_2887_0,axiom,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),hAPP(X1,X1,plus_plus(X1,hAPP(nat,X1,power_power(X1,X2),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,X1,power_power(X1,X3),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))))
| ti(X1,X2) = zero_zero(X1)
| ~ linordered_idom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2887]) ).
cnf(c_0_2887_1,axiom,
( ti(X1,X2) = zero_zero(X1)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),hAPP(X1,X1,plus_plus(X1,hAPP(nat,X1,power_power(X1,X2),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,X1,power_power(X1,X3),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))))
| ~ linordered_idom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2887]) ).
cnf(c_0_2887_2,axiom,
( ~ linordered_idom(X1)
| ti(X1,X2) = zero_zero(X1)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),hAPP(X1,X1,plus_plus(X1,hAPP(nat,X1,power_power(X1,X2),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,X1,power_power(X1,X3),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))) ),
inference(literals_permutation,[status(thm)],[c_0_2887]) ).
cnf(c_0_2888_0,axiom,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),hAPP(X1,X1,plus_plus(X1,hAPP(nat,X1,power_power(X1,X2),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,X1,power_power(X1,X3),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))))
| ti(X1,X3) = zero_zero(X1)
| ~ linordered_idom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2888]) ).
cnf(c_0_2888_1,axiom,
( ti(X1,X3) = zero_zero(X1)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),hAPP(X1,X1,plus_plus(X1,hAPP(nat,X1,power_power(X1,X2),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,X1,power_power(X1,X3),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))))
| ~ linordered_idom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2888]) ).
cnf(c_0_2888_2,axiom,
( ~ linordered_idom(X1)
| ti(X1,X3) = zero_zero(X1)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),hAPP(X1,X1,plus_plus(X1,hAPP(nat,X1,power_power(X1,X2),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,X1,power_power(X1,X3),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))) ),
inference(literals_permutation,[status(thm)],[c_0_2888]) ).
cnf(c_0_2889_0,axiom,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),hAPP(X1,X1,plus_plus(X1,hAPP(nat,X1,power_power(X1,X2),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,X1,power_power(X1,X3),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))))
| ~ linordered_idom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2889]) ).
cnf(c_0_2889_1,axiom,
( ~ linordered_idom(X1)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),hAPP(X1,X1,plus_plus(X1,hAPP(nat,X1,power_power(X1,X2),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,X1,power_power(X1,X3),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))) ),
inference(literals_permutation,[status(thm)],[c_0_2889]) ).
cnf(c_0_2890_0,axiom,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(nat,X1,power_power(X1,X2),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,X1,power_power(X1,X3),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))
| ~ linordered_semidom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2890]) ).
cnf(c_0_2890_1,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X3))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(nat,X1,power_power(X1,X2),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,X1,power_power(X1,X3),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))
| ~ linordered_semidom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2890]) ).
cnf(c_0_2890_2,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(nat,X1,power_power(X1,X2),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,X1,power_power(X1,X3),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X3))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| ~ linordered_semidom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2890]) ).
cnf(c_0_2890_3,axiom,
( ~ linordered_semidom(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(nat,X1,power_power(X1,X2),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,X1,power_power(X1,X3),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X3))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2890]) ).
cnf(c_0_2891_0,axiom,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(nat,X1,power_power(X1,X2),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,X1,power_power(X1,X3),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))
| ~ linordered_semidom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2891]) ).
cnf(c_0_2891_1,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X3))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(nat,X1,power_power(X1,X2),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,X1,power_power(X1,X3),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))
| ~ linordered_semidom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2891]) ).
cnf(c_0_2891_2,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(nat,X1,power_power(X1,X2),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,X1,power_power(X1,X3),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X3))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
| ~ linordered_semidom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2891]) ).
cnf(c_0_2891_3,axiom,
( ~ linordered_semidom(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(nat,X1,power_power(X1,X2),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,X1,power_power(X1,X3),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X3))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2891]) ).
cnf(c_0_2892_0,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,plus_plus(X1,hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X2)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X3),X3))),zero_zero(X1)))
| ~ linordered_ring(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2892]) ).
cnf(c_0_2892_1,axiom,
( ~ linordered_ring(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,plus_plus(X1,hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X2)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X3),X3))),zero_zero(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_2892]) ).
cnf(c_0_2893_0,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(nat,X1,power_power(X1,X2),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),zero_zero(X1)))
| ~ linordered_idom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2893]) ).
cnf(c_0_2893_1,axiom,
( ~ linordered_idom(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(nat,X1,power_power(X1,X2),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),zero_zero(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_2893]) ).
cnf(c_0_2894_0,axiom,
( ~ linord581940658strict(X1)
| ti(X1,X2) != zero_zero(X1)
| ti(X1,X3) != zero_zero(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),hAPP(X1,X1,plus_plus(X1,hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X3),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X2)))) ),
inference(literals_permutation,[status(thm)],[c_0_2894]) ).
cnf(c_0_2894_1,axiom,
( ti(X1,X2) != zero_zero(X1)
| ~ linord581940658strict(X1)
| ti(X1,X3) != zero_zero(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),hAPP(X1,X1,plus_plus(X1,hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X3),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X2)))) ),
inference(literals_permutation,[status(thm)],[c_0_2894]) ).
cnf(c_0_2894_2,axiom,
( ti(X1,X3) != zero_zero(X1)
| ti(X1,X2) != zero_zero(X1)
| ~ linord581940658strict(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),hAPP(X1,X1,plus_plus(X1,hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X3),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X2)))) ),
inference(literals_permutation,[status(thm)],[c_0_2894]) ).
cnf(c_0_2894_3,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),hAPP(X1,X1,plus_plus(X1,hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X3),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X2))))
| ti(X1,X3) != zero_zero(X1)
| ti(X1,X2) != zero_zero(X1)
| ~ linord581940658strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2894]) ).
cnf(c_0_2895_0,axiom,
( ti(X1,X2) = zero_zero(X1)
| ~ linordered_idom(X1)
| hAPP(X1,X1,plus_plus(X1,hAPP(nat,X1,power_power(X1,X2),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,X1,power_power(X1,X3),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) != zero_zero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2895]) ).
cnf(c_0_2895_1,axiom,
( ~ linordered_idom(X1)
| ti(X1,X2) = zero_zero(X1)
| hAPP(X1,X1,plus_plus(X1,hAPP(nat,X1,power_power(X1,X2),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,X1,power_power(X1,X3),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) != zero_zero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2895]) ).
cnf(c_0_2895_2,axiom,
( hAPP(X1,X1,plus_plus(X1,hAPP(nat,X1,power_power(X1,X2),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,X1,power_power(X1,X3),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) != zero_zero(X1)
| ~ linordered_idom(X1)
| ti(X1,X2) = zero_zero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2895]) ).
cnf(c_0_2896_0,axiom,
( ti(X1,X3) = zero_zero(X1)
| ~ linordered_idom(X1)
| hAPP(X1,X1,plus_plus(X1,hAPP(nat,X1,power_power(X1,X2),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,X1,power_power(X1,X3),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) != zero_zero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2896]) ).
cnf(c_0_2896_1,axiom,
( ~ linordered_idom(X1)
| ti(X1,X3) = zero_zero(X1)
| hAPP(X1,X1,plus_plus(X1,hAPP(nat,X1,power_power(X1,X2),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,X1,power_power(X1,X3),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) != zero_zero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2896]) ).
cnf(c_0_2896_2,axiom,
( hAPP(X1,X1,plus_plus(X1,hAPP(nat,X1,power_power(X1,X2),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,X1,power_power(X1,X3),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) != zero_zero(X1)
| ~ linordered_idom(X1)
| ti(X1,X3) = zero_zero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2896]) ).
cnf(c_0_2897_0,axiom,
( X1 = zero_zero(real)
| hAPP(real,real,plus_plus(real,hAPP(nat,real,power_power(real,X1),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,real,power_power(real,X2),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) != zero_zero(real) ),
inference(literals_permutation,[status(thm)],[c_0_2897]) ).
cnf(c_0_2897_1,axiom,
( hAPP(real,real,plus_plus(real,hAPP(nat,real,power_power(real,X1),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,real,power_power(real,X2),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) != zero_zero(real)
| X1 = zero_zero(real) ),
inference(literals_permutation,[status(thm)],[c_0_2897]) ).
cnf(c_0_2898_0,axiom,
( X2 = zero_zero(real)
| hAPP(real,real,plus_plus(real,hAPP(nat,real,power_power(real,X1),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,real,power_power(real,X2),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) != zero_zero(real) ),
inference(literals_permutation,[status(thm)],[c_0_2898]) ).
cnf(c_0_2898_1,axiom,
( hAPP(real,real,plus_plus(real,hAPP(nat,real,power_power(real,X1),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,real,power_power(real,X2),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) != zero_zero(real)
| X2 = zero_zero(real) ),
inference(literals_permutation,[status(thm)],[c_0_2898]) ).
cnf(c_0_2899_0,axiom,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(nat,X1,semiring_1_of_nat(X1),X2)),hAPP(nat,X1,power_power(X1,number_number_of(X1,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),X2)))
| ~ linordered_idom(X1)
| ~ number_ring(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2899]) ).
cnf(c_0_2899_1,axiom,
( ~ linordered_idom(X1)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(nat,X1,semiring_1_of_nat(X1),X2)),hAPP(nat,X1,power_power(X1,number_number_of(X1,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),X2)))
| ~ number_ring(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2899]) ).
cnf(c_0_2899_2,axiom,
( ~ number_ring(X1)
| ~ linordered_idom(X1)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(nat,X1,semiring_1_of_nat(X1),X2)),hAPP(nat,X1,power_power(X1,number_number_of(X1,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),X2))) ),
inference(literals_permutation,[status(thm)],[c_0_2899]) ).
cnf(c_0_2901_0,axiom,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,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(nat,fun(nat,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_2901]) ).
cnf(c_0_2901_1,axiom,
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,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(nat,fun(nat,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_2901]) ).
cnf(c_0_2903_0,axiom,
( ~ linordered_idom(X1)
| ti(X1,X2) != zero_zero(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),hAPP(nat,X1,power_power(X1,X2),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))) ),
inference(literals_permutation,[status(thm)],[c_0_2903]) ).
cnf(c_0_2903_1,axiom,
( ti(X1,X2) != zero_zero(X1)
| ~ linordered_idom(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),hAPP(nat,X1,power_power(X1,X2),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))) ),
inference(literals_permutation,[status(thm)],[c_0_2903]) ).
cnf(c_0_2903_2,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),hAPP(nat,X1,power_power(X1,X2),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))
| ti(X1,X2) != zero_zero(X1)
| ~ linordered_idom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2903]) ).
cnf(c_0_2904_0,axiom,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),hAPP(X1,X1,plus_plus(X1,hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X2)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X3),X3))))
| ti(X1,X2) = zero_zero(X1)
| ~ linord581940658strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2904]) ).
cnf(c_0_2904_1,axiom,
( ti(X1,X2) = zero_zero(X1)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),hAPP(X1,X1,plus_plus(X1,hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X2)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X3),X3))))
| ~ linord581940658strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2904]) ).
cnf(c_0_2904_2,axiom,
( ~ linord581940658strict(X1)
| ti(X1,X2) = zero_zero(X1)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),hAPP(X1,X1,plus_plus(X1,hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X2)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X3),X3)))) ),
inference(literals_permutation,[status(thm)],[c_0_2904]) ).
cnf(c_0_2905_0,axiom,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),hAPP(X1,X1,plus_plus(X1,hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X2)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X3),X3))))
| ti(X1,X3) = zero_zero(X1)
| ~ linord581940658strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2905]) ).
cnf(c_0_2905_1,axiom,
( ti(X1,X3) = zero_zero(X1)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),hAPP(X1,X1,plus_plus(X1,hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X2)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X3),X3))))
| ~ linord581940658strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2905]) ).
cnf(c_0_2905_2,axiom,
( ~ linord581940658strict(X1)
| ti(X1,X3) = zero_zero(X1)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),hAPP(X1,X1,plus_plus(X1,hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X2)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X3),X3)))) ),
inference(literals_permutation,[status(thm)],[c_0_2905]) ).
cnf(c_0_2906_0,axiom,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X4))
| ~ linord581940658strict(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X2))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X4))) ),
inference(literals_permutation,[status(thm)],[c_0_2906]) ).
cnf(c_0_2906_1,axiom,
( ~ linord581940658strict(X1)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X4))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X2))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X4))) ),
inference(literals_permutation,[status(thm)],[c_0_2906]) ).
cnf(c_0_2906_2,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X2))
| ~ linord581940658strict(X1)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X4))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X4))) ),
inference(literals_permutation,[status(thm)],[c_0_2906]) ).
cnf(c_0_2906_3,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X4)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X2))
| ~ linord581940658strict(X1)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2906]) ).
cnf(c_0_2907_0,axiom,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X4))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X4)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X3),X4)))
| ~ linordered_semiring(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2907]) ).
cnf(c_0_2907_1,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X4))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X4)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X3),X4)))
| ~ linordered_semiring(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2907]) ).
cnf(c_0_2907_2,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X4)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X3),X4)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X4))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| ~ linordered_semiring(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2907]) ).
cnf(c_0_2907_3,axiom,
( ~ linordered_semiring(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X4)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X3),X4)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X4))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2907]) ).
cnf(c_0_2908_0,axiom,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X4))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X4)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X3),X4)))
| ~ linord20386208strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2908]) ).
cnf(c_0_2908_1,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X4))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X4)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X3),X4)))
| ~ linord20386208strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2908]) ).
cnf(c_0_2908_2,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X4)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X3),X4)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X4))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| ~ linord20386208strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2908]) ).
cnf(c_0_2908_3,axiom,
( ~ linord20386208strict(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X4)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X3),X4)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X4))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2908]) ).
cnf(c_0_2909_0,axiom,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X4))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X2)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X3)))
| ~ linordered_semiring(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2909]) ).
cnf(c_0_2909_1,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X4))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X2)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X3)))
| ~ linordered_semiring(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2909]) ).
cnf(c_0_2909_2,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X2)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X3)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X4))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| ~ linordered_semiring(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2909]) ).
cnf(c_0_2909_3,axiom,
( ~ linordered_semiring(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X2)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X3)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X4))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2909]) ).
cnf(c_0_2910_0,axiom,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X4))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X2)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X3)))
| ~ linord20386208strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2910]) ).
cnf(c_0_2910_1,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X4))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X2)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X3)))
| ~ linord20386208strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2910]) ).
cnf(c_0_2910_2,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X2)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X3)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X4))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| ~ linord20386208strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2910]) ).
cnf(c_0_2910_3,axiom,
( ~ linord20386208strict(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X2)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X3)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X4))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2910]) ).
cnf(c_0_2911_0,axiom,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X4))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X4)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X3),X4)))
| ~ linord20386208strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2911]) ).
cnf(c_0_2911_1,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X4))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X4)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X3),X4)))
| ~ linord20386208strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2911]) ).
cnf(c_0_2911_2,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X4)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X3),X4)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X4))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
| ~ linord20386208strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2911]) ).
cnf(c_0_2911_3,axiom,
( ~ linord20386208strict(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X4)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X3),X4)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X4))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2911]) ).
cnf(c_0_2912_0,axiom,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X4))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X2)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X3)))
| ~ linord20386208strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2912]) ).
cnf(c_0_2912_1,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X4))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X2)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X3)))
| ~ linord20386208strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2912]) ).
cnf(c_0_2912_2,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X2)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X3)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X4))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
| ~ linord20386208strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2912]) ).
cnf(c_0_2912_3,axiom,
( ~ linord20386208strict(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X2)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X3)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X4))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2912]) ).
cnf(c_0_2913_0,axiom,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X4))
| ~ linord581940658strict(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),zero_zero(X1)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X4)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3))) ),
inference(literals_permutation,[status(thm)],[c_0_2913]) ).
cnf(c_0_2913_1,axiom,
( ~ linord581940658strict(X1)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X4))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),zero_zero(X1)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X4)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3))) ),
inference(literals_permutation,[status(thm)],[c_0_2913]) ).
cnf(c_0_2913_2,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),zero_zero(X1)))
| ~ linord581940658strict(X1)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X4))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X4)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3))) ),
inference(literals_permutation,[status(thm)],[c_0_2913]) ).
cnf(c_0_2913_3,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X4)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),zero_zero(X1)))
| ~ linord581940658strict(X1)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2913]) ).
cnf(c_0_2914_0,axiom,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X4))
| ~ linord581940658strict(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),zero_zero(X1)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X4)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3))) ),
inference(literals_permutation,[status(thm)],[c_0_2914]) ).
cnf(c_0_2914_1,axiom,
( ~ linord581940658strict(X1)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X4))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),zero_zero(X1)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X4)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3))) ),
inference(literals_permutation,[status(thm)],[c_0_2914]) ).
cnf(c_0_2914_2,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),zero_zero(X1)))
| ~ linord581940658strict(X1)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X4))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X4)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3))) ),
inference(literals_permutation,[status(thm)],[c_0_2914]) ).
cnf(c_0_2914_3,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X4)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),zero_zero(X1)))
| ~ linord581940658strict(X1)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2914]) ).
cnf(c_0_2915_0,axiom,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X5)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X4))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X5))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X4))
| ~ linord20386208strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2915]) ).
cnf(c_0_2915_1,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X3))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X5)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X4))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X5))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X4))
| ~ linord20386208strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2915]) ).
cnf(c_0_2915_2,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X4))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X3))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X5)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X5))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X4))
| ~ linord20386208strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2915]) ).
cnf(c_0_2915_3,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X5))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X4))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X3))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X5)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X4))
| ~ linord20386208strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2915]) ).
cnf(c_0_2915_4,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X4))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X5))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X4))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X3))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X5)))
| ~ linord20386208strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2915]) ).
cnf(c_0_2915_5,axiom,
( ~ linord20386208strict(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X4))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X5))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X4))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X3))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X5))) ),
inference(literals_permutation,[status(thm)],[c_0_2915]) ).
cnf(c_0_2916_0,axiom,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X5)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X2))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X5))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X4))
| ~ linord20386208strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2916]) ).
cnf(c_0_2916_1,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X3))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X5)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X2))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X5))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X4))
| ~ linord20386208strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2916]) ).
cnf(c_0_2916_2,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X2))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X3))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X5)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X5))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X4))
| ~ linord20386208strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2916]) ).
cnf(c_0_2916_3,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X5))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X2))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X3))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X5)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X4))
| ~ linord20386208strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2916]) ).
cnf(c_0_2916_4,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X4))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X5))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X2))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X3))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X5)))
| ~ linord20386208strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2916]) ).
cnf(c_0_2916_5,axiom,
( ~ linord20386208strict(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X4))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X5))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X2))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X3))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X5))) ),
inference(literals_permutation,[status(thm)],[c_0_2916]) ).
cnf(c_0_2917_0,axiom,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X5)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X2))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X5))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X4))
| ~ linord20386208strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2917]) ).
cnf(c_0_2917_1,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X3))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X5)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X2))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X5))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X4))
| ~ linord20386208strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2917]) ).
cnf(c_0_2917_2,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X2))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X3))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X5)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X5))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X4))
| ~ linord20386208strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2917]) ).
cnf(c_0_2917_3,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X5))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X2))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X3))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X5)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X4))
| ~ linord20386208strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2917]) ).
cnf(c_0_2917_4,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X4))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X5))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X2))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X3))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X5)))
| ~ linord20386208strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2917]) ).
cnf(c_0_2917_5,axiom,
( ~ linord20386208strict(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X4))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X5))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X2))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X3))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X5))) ),
inference(literals_permutation,[status(thm)],[c_0_2917]) ).
cnf(c_0_2918_0,axiom,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X5)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X2))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X5))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X4))
| ~ linord20386208strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2918]) ).
cnf(c_0_2918_1,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X3))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X5)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X2))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X5))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X4))
| ~ linord20386208strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2918]) ).
cnf(c_0_2918_2,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X2))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X3))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X5)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X5))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X4))
| ~ linord20386208strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2918]) ).
cnf(c_0_2918_3,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X5))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X2))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X3))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X5)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X4))
| ~ linord20386208strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2918]) ).
cnf(c_0_2918_4,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X4))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X5))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X2))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X3))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X5)))
| ~ linord20386208strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2918]) ).
cnf(c_0_2918_5,axiom,
( ~ linord20386208strict(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X4))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X5))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X2))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X3))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X5))) ),
inference(literals_permutation,[status(thm)],[c_0_2918]) ).
cnf(c_0_2919_0,axiom,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X1),zero_zero(int)))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,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_2919]) ).
cnf(c_0_2919_1,axiom,
( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,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(int,fun(int,bool),ord_less(int),X1),zero_zero(int))) ),
inference(literals_permutation,[status(thm)],[c_0_2919]) ).
cnf(c_0_2920_0,axiom,
( hAPP(X1,X1,plus_plus(X1,hAPP(nat,X1,power_power(X1,X2),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,X1,power_power(X1,X3),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) = zero_zero(X1)
| ~ linordered_idom(X1)
| ti(X1,X3) != zero_zero(X1)
| ti(X1,X2) != zero_zero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2920]) ).
cnf(c_0_2920_1,axiom,
( ~ linordered_idom(X1)
| hAPP(X1,X1,plus_plus(X1,hAPP(nat,X1,power_power(X1,X2),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,X1,power_power(X1,X3),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) = zero_zero(X1)
| ti(X1,X3) != zero_zero(X1)
| ti(X1,X2) != zero_zero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2920]) ).
cnf(c_0_2920_2,axiom,
( ti(X1,X3) != zero_zero(X1)
| ~ linordered_idom(X1)
| hAPP(X1,X1,plus_plus(X1,hAPP(nat,X1,power_power(X1,X2),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,X1,power_power(X1,X3),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) = zero_zero(X1)
| ti(X1,X2) != zero_zero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2920]) ).
cnf(c_0_2920_3,axiom,
( ti(X1,X2) != zero_zero(X1)
| ti(X1,X3) != zero_zero(X1)
| ~ linordered_idom(X1)
| hAPP(X1,X1,plus_plus(X1,hAPP(nat,X1,power_power(X1,X2),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,X1,power_power(X1,X3),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) = zero_zero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2920]) ).
cnf(c_0_2921_0,axiom,
( hAPP(real,real,plus_plus(real,hAPP(nat,real,power_power(real,X1),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,real,power_power(real,X2),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) = zero_zero(real)
| X2 != zero_zero(real)
| X1 != zero_zero(real) ),
inference(literals_permutation,[status(thm)],[c_0_2921]) ).
cnf(c_0_2921_1,axiom,
( X2 != zero_zero(real)
| hAPP(real,real,plus_plus(real,hAPP(nat,real,power_power(real,X1),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,real,power_power(real,X2),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) = zero_zero(real)
| X1 != zero_zero(real) ),
inference(literals_permutation,[status(thm)],[c_0_2921]) ).
cnf(c_0_2921_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,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,real,power_power(real,X2),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) = zero_zero(real) ),
inference(literals_permutation,[status(thm)],[c_0_2921]) ).
cnf(c_0_2922_0,axiom,
( hBOOL(hAPP(fun(X1,X2),bool,hAPP(fun(X1,X2),fun(fun(X1,X2),bool),ord_less_eq(fun(X1,X2)),X3),X4))
| ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less_eq(X2),hAPP(X1,X2,X3,sk1_esk25_4(X1,X2,X3,X4))),hAPP(X1,X2,X4,sk1_esk25_4(X1,X2,X3,X4))))
| ~ ord(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2922]) ).
cnf(c_0_2922_1,axiom,
( ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less_eq(X2),hAPP(X1,X2,X3,sk1_esk25_4(X1,X2,X3,X4))),hAPP(X1,X2,X4,sk1_esk25_4(X1,X2,X3,X4))))
| hBOOL(hAPP(fun(X1,X2),bool,hAPP(fun(X1,X2),fun(fun(X1,X2),bool),ord_less_eq(fun(X1,X2)),X3),X4))
| ~ ord(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2922]) ).
cnf(c_0_2922_2,axiom,
( ~ ord(X2)
| ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less_eq(X2),hAPP(X1,X2,X3,sk1_esk25_4(X1,X2,X3,X4))),hAPP(X1,X2,X4,sk1_esk25_4(X1,X2,X3,X4))))
| hBOOL(hAPP(fun(X1,X2),bool,hAPP(fun(X1,X2),fun(fun(X1,X2),bool),ord_less_eq(fun(X1,X2)),X3),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2922]) ).
cnf(c_0_2923_0,axiom,
( hBOOL(hAPP(fun(X2,X1),bool,hAPP(fun(X2,X1),fun(fun(X2,X1),bool),ord_less_eq(fun(X2,X1)),X3),X4))
| ~ ord(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X2,X1,X3,sk1_esk22_4(X2,X1,X3,X4))),hAPP(X2,X1,X4,sk1_esk22_4(X2,X1,X3,X4)))) ),
inference(literals_permutation,[status(thm)],[c_0_2923]) ).
cnf(c_0_2923_1,axiom,
( ~ ord(X1)
| hBOOL(hAPP(fun(X2,X1),bool,hAPP(fun(X2,X1),fun(fun(X2,X1),bool),ord_less_eq(fun(X2,X1)),X3),X4))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X2,X1,X3,sk1_esk22_4(X2,X1,X3,X4))),hAPP(X2,X1,X4,sk1_esk22_4(X2,X1,X3,X4)))) ),
inference(literals_permutation,[status(thm)],[c_0_2923]) ).
cnf(c_0_2923_2,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X2,X1,X3,sk1_esk22_4(X2,X1,X3,X4))),hAPP(X2,X1,X4,sk1_esk22_4(X2,X1,X3,X4))))
| ~ ord(X1)
| hBOOL(hAPP(fun(X2,X1),bool,hAPP(fun(X2,X1),fun(fun(X2,X1),bool),ord_less_eq(fun(X2,X1)),X3),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2923]) ).
cnf(c_0_2924_0,axiom,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,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(nat,fun(nat,bool),ord_less(nat),sk1_esk16_3(X2,X3,X1)),sk1_esk17_3(X2,X3,X1))) ),
inference(literals_permutation,[status(thm)],[c_0_2924]) ).
cnf(c_0_2924_1,axiom,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),sk1_esk16_3(X2,X3,X1)),sk1_esk17_3(X2,X3,X1)))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,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_2924]) ).
cnf(c_0_2925_0,axiom,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X3)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X4))
| ~ linord20386208strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2925]) ).
cnf(c_0_2925_1,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X3))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X3)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X4))
| ~ linord20386208strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2925]) ).
cnf(c_0_2925_2,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X4))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X3))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X3)))
| ~ linord20386208strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2925]) ).
cnf(c_0_2925_3,axiom,
( ~ linord20386208strict(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X4))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X3))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X3))) ),
inference(literals_permutation,[status(thm)],[c_0_2925]) ).
cnf(c_0_2926_0,axiom,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X4)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X2))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X4))
| ~ linord20386208strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2926]) ).
cnf(c_0_2926_1,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X2))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X4)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X4))
| ~ linord20386208strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2926]) ).
cnf(c_0_2926_2,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X4))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X2))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X4)))
| ~ linord20386208strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2926]) ).
cnf(c_0_2926_3,axiom,
( ~ linord20386208strict(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X4))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X2))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X4))) ),
inference(literals_permutation,[status(thm)],[c_0_2926]) ).
cnf(c_0_2927_0,axiom,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X4)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X2))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X4))
| ~ linord893533164strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2927]) ).
cnf(c_0_2927_1,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X2))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X4)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X4))
| ~ linord893533164strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2927]) ).
cnf(c_0_2927_2,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X4))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X2))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X4)))
| ~ linord893533164strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2927]) ).
cnf(c_0_2927_3,axiom,
( ~ linord893533164strict(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X4))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X2))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X4))) ),
inference(literals_permutation,[status(thm)],[c_0_2927]) ).
cnf(c_0_2928_0,axiom,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X4)))
| ~ linord581940658strict(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X2))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2928]) ).
cnf(c_0_2928_1,axiom,
( ~ linord581940658strict(X1)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X4)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X2))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2928]) ).
cnf(c_0_2928_2,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X2))
| ~ linord581940658strict(X1)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X4)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2928]) ).
cnf(c_0_2928_3,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X4))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X2))
| ~ linord581940658strict(X1)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X4))) ),
inference(literals_permutation,[status(thm)],[c_0_2928]) ).
cnf(c_0_2929_0,axiom,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X4)))
| ~ linord581940658strict(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),zero_zero(X1)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X4),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2929]) ).
cnf(c_0_2929_1,axiom,
( ~ linord581940658strict(X1)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X4)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),zero_zero(X1)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X4),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2929]) ).
cnf(c_0_2929_2,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),zero_zero(X1)))
| ~ linord581940658strict(X1)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X4)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X4),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2929]) ).
cnf(c_0_2929_3,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X4),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),zero_zero(X1)))
| ~ linord581940658strict(X1)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X4))) ),
inference(literals_permutation,[status(thm)],[c_0_2929]) ).
cnf(c_0_2930_0,axiom,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X3)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),zero_zero(X1)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X4),X2))
| ~ linord581940658strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2930]) ).
cnf(c_0_2930_1,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),zero_zero(X1)))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X3)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X4),X2))
| ~ linord581940658strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2930]) ).
cnf(c_0_2930_2,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X4),X2))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),zero_zero(X1)))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X3)))
| ~ linord581940658strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2930]) ).
cnf(c_0_2930_3,axiom,
( ~ linord581940658strict(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X4),X2))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),zero_zero(X1)))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X4),X3))) ),
inference(literals_permutation,[status(thm)],[c_0_2930]) ).
cnf(c_0_2931_0,axiom,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X4)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),zero_zero(X1)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X4),X3))
| ~ linord581940658strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2931]) ).
cnf(c_0_2931_1,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),zero_zero(X1)))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X4)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X4),X3))
| ~ linord581940658strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2931]) ).
cnf(c_0_2931_2,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X4),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),zero_zero(X1)))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X4)))
| ~ linord581940658strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2931]) ).
cnf(c_0_2931_3,axiom,
( ~ linord581940658strict(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X4),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),zero_zero(X1)))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X4))) ),
inference(literals_permutation,[status(thm)],[c_0_2931]) ).
cnf(c_0_2932_0,axiom,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X4)))
| ~ linord581940658strict(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),zero_zero(X1)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X4),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2932]) ).
cnf(c_0_2932_1,axiom,
( ~ linord581940658strict(X1)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X4)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),zero_zero(X1)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X4),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2932]) ).
cnf(c_0_2932_2,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),zero_zero(X1)))
| ~ linord581940658strict(X1)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X4)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X4),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2932]) ).
cnf(c_0_2932_3,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X4),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),zero_zero(X1)))
| ~ linord581940658strict(X1)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X4))) ),
inference(literals_permutation,[status(thm)],[c_0_2932]) ).
cnf(c_0_2933_0,axiom,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,X1,X2)),hAPP(nat,nat,X1,X3)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X2),X3))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,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_2933]) ).
cnf(c_0_2933_1,axiom,
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X2),X3))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,X1,X2)),hAPP(nat,nat,X1,X3)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,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_2933]) ).
cnf(c_0_2933_2,axiom,
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,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(nat,fun(nat,bool),ord_less_eq(nat),X2),X3))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,X1,X2)),hAPP(nat,nat,X1,X3))) ),
inference(literals_permutation,[status(thm)],[c_0_2933]) ).
cnf(c_0_2934_0,axiom,
( ti(X1,X2) = ti(X1,X3)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X2))
| hAPP(nat,X1,power_power(X1,X2),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) != hAPP(nat,X1,power_power(X1,X3),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))
| ~ linordered_semidom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2934]) ).
cnf(c_0_2934_1,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X3))
| ti(X1,X2) = ti(X1,X3)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X2))
| hAPP(nat,X1,power_power(X1,X2),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) != hAPP(nat,X1,power_power(X1,X3),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))
| ~ linordered_semidom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2934]) ).
cnf(c_0_2934_2,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X2))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X3))
| ti(X1,X2) = ti(X1,X3)
| hAPP(nat,X1,power_power(X1,X2),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) != hAPP(nat,X1,power_power(X1,X3),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))
| ~ linordered_semidom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2934]) ).
cnf(c_0_2934_3,axiom,
( hAPP(nat,X1,power_power(X1,X2),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) != hAPP(nat,X1,power_power(X1,X3),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X2))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X3))
| ti(X1,X2) = ti(X1,X3)
| ~ linordered_semidom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2934]) ).
cnf(c_0_2934_4,axiom,
( ~ linordered_semidom(X1)
| hAPP(nat,X1,power_power(X1,X2),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) != hAPP(nat,X1,power_power(X1,X3),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X2))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X3))
| ti(X1,X2) = ti(X1,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2934]) ).
cnf(c_0_2935_0,axiom,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,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(int,fun(int,bool),ord_less(int),X1),zero_zero(int))) ),
inference(literals_permutation,[status(thm)],[c_0_2935]) ).
cnf(c_0_2935_1,axiom,
( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X1),zero_zero(int)))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,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_2935]) ).
cnf(c_0_2936_0,axiom,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),hAPP(nat,X1,power_power(X1,X2),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))
| ti(X1,X2) = zero_zero(X1)
| ~ linordered_idom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2936]) ).
cnf(c_0_2936_1,axiom,
( ti(X1,X2) = zero_zero(X1)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),hAPP(nat,X1,power_power(X1,X2),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))
| ~ linordered_idom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2936]) ).
cnf(c_0_2936_2,axiom,
( ~ linordered_idom(X1)
| ti(X1,X2) = zero_zero(X1)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),hAPP(nat,X1,power_power(X1,X2),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))) ),
inference(literals_permutation,[status(thm)],[c_0_2936]) ).
cnf(c_0_2937_0,axiom,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),hAPP(nat,X1,power_power(X1,X2),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))
| ~ linordered_idom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2937]) ).
cnf(c_0_2937_1,axiom,
( ~ linordered_idom(X1)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),hAPP(nat,X1,power_power(X1,X2),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))) ),
inference(literals_permutation,[status(thm)],[c_0_2937]) ).
cnf(c_0_2939_0,axiom,
( X1 = one_one(int)
| X1 = zero_zero(int)
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X1),number_number_of(int,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2939]) ).
cnf(c_0_2939_1,axiom,
( X1 = zero_zero(int)
| X1 = one_one(int)
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X1),number_number_of(int,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2939]) ).
cnf(c_0_2939_2,axiom,
( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X1),number_number_of(int,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))
| X1 = zero_zero(int)
| X1 = one_one(int)
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2939]) ).
cnf(c_0_2939_3,axiom,
( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X1))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X1),number_number_of(int,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))
| X1 = zero_zero(int)
| X1 = one_one(int) ),
inference(literals_permutation,[status(thm)],[c_0_2939]) ).
cnf(c_0_2940_0,axiom,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),zero_zero(X1)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),zero_zero(X1)))
| ~ linord20386208strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2940]) ).
cnf(c_0_2940_1,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X3))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),zero_zero(X1)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),zero_zero(X1)))
| ~ linord20386208strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2940]) ).
cnf(c_0_2940_2,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),zero_zero(X1)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X3))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),zero_zero(X1)))
| ~ linord20386208strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2940]) ).
cnf(c_0_2940_3,axiom,
( ~ linord20386208strict(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),zero_zero(X1)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X3))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)),zero_zero(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_2940]) ).
cnf(c_0_2941_0,axiom,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(nat,X1,power_power(X1,X2),X3)),hAPP(nat,X1,power_power(X1,X4),X3)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X2))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X4))
| ~ linordered_semidom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2941]) ).
cnf(c_0_2941_1,axiom,
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X3))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(nat,X1,power_power(X1,X2),X3)),hAPP(nat,X1,power_power(X1,X4),X3)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X2))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X4))
| ~ linordered_semidom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2941]) ).
cnf(c_0_2941_2,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X2))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X3))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(nat,X1,power_power(X1,X2),X3)),hAPP(nat,X1,power_power(X1,X4),X3)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X4))
| ~ linordered_semidom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2941]) ).
cnf(c_0_2941_3,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X4))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X2))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X3))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(nat,X1,power_power(X1,X2),X3)),hAPP(nat,X1,power_power(X1,X4),X3)))
| ~ linordered_semidom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2941]) ).
cnf(c_0_2941_4,axiom,
( ~ linordered_semidom(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X4))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X2))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X3))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(nat,X1,power_power(X1,X2),X3)),hAPP(nat,X1,power_power(X1,X4),X3))) ),
inference(literals_permutation,[status(thm)],[c_0_2941]) ).
cnf(c_0_2942_0,axiom,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(nat,X1,power_power(X1,X2),X3)),hAPP(nat,X1,power_power(X1,X2),X4)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),one_one(X1)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X2))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X4),X3))
| ~ linordered_semidom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2942]) ).
cnf(c_0_2942_1,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),one_one(X1)))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(nat,X1,power_power(X1,X2),X3)),hAPP(nat,X1,power_power(X1,X2),X4)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X2))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X4),X3))
| ~ linordered_semidom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2942]) ).
cnf(c_0_2942_2,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X2))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),one_one(X1)))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(nat,X1,power_power(X1,X2),X3)),hAPP(nat,X1,power_power(X1,X2),X4)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X4),X3))
| ~ linordered_semidom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2942]) ).
cnf(c_0_2942_3,axiom,
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X4),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X2))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),one_one(X1)))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(nat,X1,power_power(X1,X2),X3)),hAPP(nat,X1,power_power(X1,X2),X4)))
| ~ linordered_semidom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2942]) ).
cnf(c_0_2942_4,axiom,
( ~ linordered_semidom(X1)
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X4),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X2))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),one_one(X1)))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(nat,X1,power_power(X1,X2),X3)),hAPP(nat,X1,power_power(X1,X2),X4))) ),
inference(literals_permutation,[status(thm)],[c_0_2942]) ).
cnf(c_0_2943_0,axiom,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(nat,X1,power_power(X1,X2),X3)),hAPP(nat,X1,power_power(X1,X2),X4)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),one_one(X1)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X2))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X4),X3))
| ~ linordered_semidom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2943]) ).
cnf(c_0_2943_1,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),one_one(X1)))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(nat,X1,power_power(X1,X2),X3)),hAPP(nat,X1,power_power(X1,X2),X4)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X2))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X4),X3))
| ~ linordered_semidom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2943]) ).
cnf(c_0_2943_2,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X2))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),one_one(X1)))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(nat,X1,power_power(X1,X2),X3)),hAPP(nat,X1,power_power(X1,X2),X4)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X4),X3))
| ~ linordered_semidom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2943]) ).
cnf(c_0_2943_3,axiom,
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X4),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X2))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),one_one(X1)))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(nat,X1,power_power(X1,X2),X3)),hAPP(nat,X1,power_power(X1,X2),X4)))
| ~ linordered_semidom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2943]) ).
cnf(c_0_2943_4,axiom,
( ~ linordered_semidom(X1)
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X4),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X2))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),one_one(X1)))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(nat,X1,power_power(X1,X2),X3)),hAPP(nat,X1,power_power(X1,X2),X4))) ),
inference(literals_permutation,[status(thm)],[c_0_2943]) ).
cnf(c_0_2944_0,axiom,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X2))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)))
| ~ linord20386208strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2944]) ).
cnf(c_0_2944_1,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X3))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X2))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)))
| ~ linord20386208strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2944]) ).
cnf(c_0_2944_2,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X3))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X2))
| ~ linord20386208strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2944]) ).
cnf(c_0_2944_3,axiom,
( ~ linord20386208strict(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X3))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2944]) ).
cnf(c_0_2945_0,axiom,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(nat,X1,power_power(X1,X2),X4)),hAPP(nat,X1,power_power(X1,X3),X4)))
| ~ linordered_semidom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2945]) ).
cnf(c_0_2945_1,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X3))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(nat,X1,power_power(X1,X2),X4)),hAPP(nat,X1,power_power(X1,X3),X4)))
| ~ linordered_semidom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2945]) ).
cnf(c_0_2945_2,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(nat,X1,power_power(X1,X2),X4)),hAPP(nat,X1,power_power(X1,X3),X4)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X3))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| ~ linordered_semidom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2945]) ).
cnf(c_0_2945_3,axiom,
( ~ linordered_semidom(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(nat,X1,power_power(X1,X2),X4)),hAPP(nat,X1,power_power(X1,X3),X4)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X3))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2945]) ).
cnf(c_0_2946_0,axiom,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2))
| ~ hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),hAPP(nat,X3,power_power(X3,X4),X1)),hAPP(nat,X3,power_power(X3,X4),X2)))
| ~ hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),one_one(X3)),X4))
| ~ linordered_semidom(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2946]) ).
cnf(c_0_2946_1,axiom,
( ~ hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),hAPP(nat,X3,power_power(X3,X4),X1)),hAPP(nat,X3,power_power(X3,X4),X2)))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2))
| ~ hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),one_one(X3)),X4))
| ~ linordered_semidom(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2946]) ).
cnf(c_0_2946_2,axiom,
( ~ hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),one_one(X3)),X4))
| ~ hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),hAPP(nat,X3,power_power(X3,X4),X1)),hAPP(nat,X3,power_power(X3,X4),X2)))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2))
| ~ linordered_semidom(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2946]) ).
cnf(c_0_2946_3,axiom,
( ~ linordered_semidom(X3)
| ~ hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),one_one(X3)),X4))
| ~ hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),hAPP(nat,X3,power_power(X3,X4),X1)),hAPP(nat,X3,power_power(X3,X4),X2)))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2946]) ).
cnf(c_0_2947_0,axiom,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X3),X4))
| ~ linordered_semidom(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),one_one(X1)),X2))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(nat,X1,power_power(X1,X2),X3)),hAPP(nat,X1,power_power(X1,X2),X4))) ),
inference(literals_permutation,[status(thm)],[c_0_2947]) ).
cnf(c_0_2947_1,axiom,
( ~ linordered_semidom(X1)
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X3),X4))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),one_one(X1)),X2))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(nat,X1,power_power(X1,X2),X3)),hAPP(nat,X1,power_power(X1,X2),X4))) ),
inference(literals_permutation,[status(thm)],[c_0_2947]) ).
cnf(c_0_2947_2,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),one_one(X1)),X2))
| ~ linordered_semidom(X1)
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X3),X4))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(nat,X1,power_power(X1,X2),X3)),hAPP(nat,X1,power_power(X1,X2),X4))) ),
inference(literals_permutation,[status(thm)],[c_0_2947]) ).
cnf(c_0_2947_3,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(nat,X1,power_power(X1,X2),X3)),hAPP(nat,X1,power_power(X1,X2),X4)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),one_one(X1)),X2))
| ~ linordered_semidom(X1)
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X3),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2947]) ).
cnf(c_0_2948_0,axiom,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2))
| ~ hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),hAPP(nat,X3,power_power(X3,X4),X1)),hAPP(nat,X3,power_power(X3,X4),X2)))
| ~ hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),one_one(X3)),X4))
| ~ linordered_semidom(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2948]) ).
cnf(c_0_2948_1,axiom,
( ~ hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),hAPP(nat,X3,power_power(X3,X4),X1)),hAPP(nat,X3,power_power(X3,X4),X2)))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2))
| ~ hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),one_one(X3)),X4))
| ~ linordered_semidom(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2948]) ).
cnf(c_0_2948_2,axiom,
( ~ hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),one_one(X3)),X4))
| ~ hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),hAPP(nat,X3,power_power(X3,X4),X1)),hAPP(nat,X3,power_power(X3,X4),X2)))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2))
| ~ linordered_semidom(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2948]) ).
cnf(c_0_2948_3,axiom,
( ~ linordered_semidom(X3)
| ~ hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),one_one(X3)),X4))
| ~ hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),hAPP(nat,X3,power_power(X3,X4),X1)),hAPP(nat,X3,power_power(X3,X4),X2)))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2948]) ).
cnf(c_0_2949_0,axiom,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X3),X4))
| ~ linordered_semidom(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),one_one(X1)),X2))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(nat,X1,power_power(X1,X2),X3)),hAPP(nat,X1,power_power(X1,X2),X4))) ),
inference(literals_permutation,[status(thm)],[c_0_2949]) ).
cnf(c_0_2949_1,axiom,
( ~ linordered_semidom(X1)
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X3),X4))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),one_one(X1)),X2))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(nat,X1,power_power(X1,X2),X3)),hAPP(nat,X1,power_power(X1,X2),X4))) ),
inference(literals_permutation,[status(thm)],[c_0_2949]) ).
cnf(c_0_2949_2,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),one_one(X1)),X2))
| ~ linordered_semidom(X1)
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X3),X4))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(nat,X1,power_power(X1,X2),X3)),hAPP(nat,X1,power_power(X1,X2),X4))) ),
inference(literals_permutation,[status(thm)],[c_0_2949]) ).
cnf(c_0_2949_3,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(nat,X1,power_power(X1,X2),X3)),hAPP(nat,X1,power_power(X1,X2),X4)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),one_one(X1)),X2))
| ~ linordered_semidom(X1)
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X3),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2949]) ).
cnf(c_0_2950_0,axiom,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(nat,X1,power_power(X1,X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),hAPP(nat,X1,power_power(X1,X2),X3))))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),one_one(X1)),X2))
| ~ linordered_semidom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2950]) ).
cnf(c_0_2950_1,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),one_one(X1)),X2))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(nat,X1,power_power(X1,X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),hAPP(nat,X1,power_power(X1,X2),X3))))
| ~ linordered_semidom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2950]) ).
cnf(c_0_2950_2,axiom,
( ~ linordered_semidom(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),one_one(X1)),X2))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(nat,X1,power_power(X1,X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),hAPP(nat,X1,power_power(X1,X2),X3)))) ),
inference(literals_permutation,[status(thm)],[c_0_2950]) ).
cnf(c_0_2951_0,axiom,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,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(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2951]) ).
cnf(c_0_2951_1,axiom,
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,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(nat,fun(nat,bool),ord_less(nat),X1),X2))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2951]) ).
cnf(c_0_2951_2,axiom,
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X3))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,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(nat,fun(nat,bool),ord_less(nat),X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2951]) ).
cnf(c_0_2952_0,axiom,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(nat,X1,power_power(X1,X2),X3)),hAPP(nat,X1,power_power(X1,X4),X3)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X2))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X4))
| ~ linordered_semidom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2952]) ).
cnf(c_0_2952_1,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X2))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(nat,X1,power_power(X1,X2),X3)),hAPP(nat,X1,power_power(X1,X4),X3)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X4))
| ~ linordered_semidom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2952]) ).
cnf(c_0_2952_2,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X4))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X2))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(nat,X1,power_power(X1,X2),X3)),hAPP(nat,X1,power_power(X1,X4),X3)))
| ~ linordered_semidom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2952]) ).
cnf(c_0_2952_3,axiom,
( ~ linordered_semidom(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X4))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X2))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(nat,X1,power_power(X1,X2),X3)),hAPP(nat,X1,power_power(X1,X4),X3))) ),
inference(literals_permutation,[status(thm)],[c_0_2952]) ).
cnf(c_0_2953_0,axiom,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),zero_zero(X1)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),zero_zero(X1)))
| ~ linord581940658strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2953]) ).
cnf(c_0_2953_1,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),zero_zero(X1)))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),zero_zero(X1)))
| ~ linord581940658strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2953]) ).
cnf(c_0_2953_2,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),zero_zero(X1)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),zero_zero(X1)))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3)))
| ~ linord581940658strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2953]) ).
cnf(c_0_2953_3,axiom,
( ~ linord581940658strict(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),zero_zero(X1)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),zero_zero(X1)))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),X3))) ),
inference(literals_permutation,[status(thm)],[c_0_2953]) ).
cnf(c_0_2954_0,axiom,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,plus_plus(X1,X2),X3)),hAPP(X1,X1,plus_plus(X1,X4),X5)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X5))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X4))
| ~ ordere223160158up_add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2954]) ).
cnf(c_0_2954_1,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X5))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,plus_plus(X1,X2),X3)),hAPP(X1,X1,plus_plus(X1,X4),X5)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X4))
| ~ ordere223160158up_add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2954]) ).
cnf(c_0_2954_2,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X4))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X5))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,plus_plus(X1,X2),X3)),hAPP(X1,X1,plus_plus(X1,X4),X5)))
| ~ ordere223160158up_add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2954]) ).
cnf(c_0_2954_3,axiom,
( ~ ordere223160158up_add(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X4))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X5))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,plus_plus(X1,X2),X3)),hAPP(X1,X1,plus_plus(X1,X4),X5))) ),
inference(literals_permutation,[status(thm)],[c_0_2954]) ).
cnf(c_0_2955_0,axiom,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,plus_plus(X1,X2),X3)),hAPP(X1,X1,plus_plus(X1,X4),X5)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X5))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X4))
| ~ ordere223160158up_add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2955]) ).
cnf(c_0_2955_1,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X5))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,plus_plus(X1,X2),X3)),hAPP(X1,X1,plus_plus(X1,X4),X5)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X4))
| ~ ordere223160158up_add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2955]) ).
cnf(c_0_2955_2,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X4))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X5))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,plus_plus(X1,X2),X3)),hAPP(X1,X1,plus_plus(X1,X4),X5)))
| ~ ordere223160158up_add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2955]) ).
cnf(c_0_2955_3,axiom,
( ~ ordere223160158up_add(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X4))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X5))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,plus_plus(X1,X2),X3)),hAPP(X1,X1,plus_plus(X1,X4),X5))) ),
inference(literals_permutation,[status(thm)],[c_0_2955]) ).
cnf(c_0_2956_0,axiom,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,plus_plus(X1,X2),X3)),hAPP(X1,X1,plus_plus(X1,X4),X5)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X5))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X4))
| ~ ordere779506340up_add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2956]) ).
cnf(c_0_2956_1,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X5))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,plus_plus(X1,X2),X3)),hAPP(X1,X1,plus_plus(X1,X4),X5)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X4))
| ~ ordere779506340up_add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2956]) ).
cnf(c_0_2956_2,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X4))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X5))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,plus_plus(X1,X2),X3)),hAPP(X1,X1,plus_plus(X1,X4),X5)))
| ~ ordere779506340up_add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2956]) ).
cnf(c_0_2956_3,axiom,
( ~ ordere779506340up_add(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X4))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X5))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,plus_plus(X1,X2),X3)),hAPP(X1,X1,plus_plus(X1,X4),X5))) ),
inference(literals_permutation,[status(thm)],[c_0_2956]) ).
cnf(c_0_2957_0,axiom,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,plus_plus(X1,X2),X3)),hAPP(X1,X1,plus_plus(X1,X4),X5)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X5))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X4))
| ~ ordere223160158up_add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2957]) ).
cnf(c_0_2957_1,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X5))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,plus_plus(X1,X2),X3)),hAPP(X1,X1,plus_plus(X1,X4),X5)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X4))
| ~ ordere223160158up_add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2957]) ).
cnf(c_0_2957_2,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X4))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X5))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,plus_plus(X1,X2),X3)),hAPP(X1,X1,plus_plus(X1,X4),X5)))
| ~ ordere223160158up_add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2957]) ).
cnf(c_0_2957_3,axiom,
( ~ ordere223160158up_add(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X4))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X5))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,plus_plus(X1,X2),X3)),hAPP(X1,X1,plus_plus(X1,X4),X5))) ),
inference(literals_permutation,[status(thm)],[c_0_2957]) ).
cnf(c_0_2958_0,axiom,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(nat,X1,power_power(X1,X2),X3)),hAPP(nat,X1,power_power(X1,X2),X4)))
| ~ linordered_semidom(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),one_one(X1)),X2))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X3),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2958]) ).
cnf(c_0_2958_1,axiom,
( ~ linordered_semidom(X1)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(nat,X1,power_power(X1,X2),X3)),hAPP(nat,X1,power_power(X1,X2),X4)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),one_one(X1)),X2))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X3),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2958]) ).
cnf(c_0_2958_2,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),one_one(X1)),X2))
| ~ linordered_semidom(X1)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(nat,X1,power_power(X1,X2),X3)),hAPP(nat,X1,power_power(X1,X2),X4)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X3),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2958]) ).
cnf(c_0_2958_3,axiom,
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X3),X4))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),one_one(X1)),X2))
| ~ linordered_semidom(X1)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(nat,X1,power_power(X1,X2),X3)),hAPP(nat,X1,power_power(X1,X2),X4))) ),
inference(literals_permutation,[status(thm)],[c_0_2958]) ).
cnf(c_0_2959_0,axiom,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(nat,X1,power_power(X1,X2),X3)),hAPP(nat,X1,power_power(X1,X2),X4)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),one_one(X1)),X2))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X3),X4))
| ~ linordered_semidom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2959]) ).
cnf(c_0_2959_1,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),one_one(X1)),X2))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(nat,X1,power_power(X1,X2),X3)),hAPP(nat,X1,power_power(X1,X2),X4)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X3),X4))
| ~ linordered_semidom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2959]) ).
cnf(c_0_2959_2,axiom,
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X3),X4))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),one_one(X1)),X2))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(nat,X1,power_power(X1,X2),X3)),hAPP(nat,X1,power_power(X1,X2),X4)))
| ~ linordered_semidom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2959]) ).
cnf(c_0_2959_3,axiom,
( ~ linordered_semidom(X1)
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X3),X4))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),one_one(X1)),X2))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(nat,X1,power_power(X1,X2),X3)),hAPP(nat,X1,power_power(X1,X2),X4))) ),
inference(literals_permutation,[status(thm)],[c_0_2959]) ).
cnf(c_0_2960_0,axiom,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(nat,X1,power_power(X1,X2),X3)),hAPP(nat,X1,power_power(X1,X2),X4)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),one_one(X1)),X2))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X3),X4))
| ~ linordered_semidom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2960]) ).
cnf(c_0_2960_1,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),one_one(X1)),X2))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(nat,X1,power_power(X1,X2),X3)),hAPP(nat,X1,power_power(X1,X2),X4)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X3),X4))
| ~ linordered_semidom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2960]) ).
cnf(c_0_2960_2,axiom,
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X3),X4))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),one_one(X1)),X2))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(nat,X1,power_power(X1,X2),X3)),hAPP(nat,X1,power_power(X1,X2),X4)))
| ~ linordered_semidom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2960]) ).
cnf(c_0_2960_3,axiom,
( ~ linordered_semidom(X1)
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X3),X4))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),one_one(X1)),X2))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(nat,X1,power_power(X1,X2),X3)),hAPP(nat,X1,power_power(X1,X2),X4))) ),
inference(literals_permutation,[status(thm)],[c_0_2960]) ).
cnf(c_0_2961_0,axiom,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(nat,X1,power_power(X1,X2),X3)),hAPP(nat,X1,power_power(X1,X2),X4)))
| ~ linordered_semidom(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),one_one(X1)),X2))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X3),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2961]) ).
cnf(c_0_2961_1,axiom,
( ~ linordered_semidom(X1)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(nat,X1,power_power(X1,X2),X3)),hAPP(nat,X1,power_power(X1,X2),X4)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),one_one(X1)),X2))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X3),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2961]) ).
cnf(c_0_2961_2,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),one_one(X1)),X2))
| ~ linordered_semidom(X1)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(nat,X1,power_power(X1,X2),X3)),hAPP(nat,X1,power_power(X1,X2),X4)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X3),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2961]) ).
cnf(c_0_2961_3,axiom,
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X3),X4))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),one_one(X1)),X2))
| ~ linordered_semidom(X1)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(nat,X1,power_power(X1,X2),X3)),hAPP(nat,X1,power_power(X1,X2),X4))) ),
inference(literals_permutation,[status(thm)],[c_0_2961]) ).
cnf(c_0_2962_0,axiom,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X4))
| ~ dense_linorder(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),sk1_esk27_4(X1,X4,X2,X3)),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2962]) ).
cnf(c_0_2962_1,axiom,
( ~ dense_linorder(X1)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X4))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),sk1_esk27_4(X1,X4,X2,X3)),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2962]) ).
cnf(c_0_2962_2,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| ~ dense_linorder(X1)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X4))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),sk1_esk27_4(X1,X4,X2,X3)),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2962]) ).
cnf(c_0_2962_3,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),sk1_esk27_4(X1,X4,X2,X3)),X4))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| ~ dense_linorder(X1)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2962]) ).
cnf(c_0_2963_0,axiom,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,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(nat,fun(nat,bool),ord_less_eq(nat),X2),X4))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2963]) ).
cnf(c_0_2963_1,axiom,
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X2),X4))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,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(nat,fun(nat,bool),ord_less_eq(nat),X1),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2963]) ).
cnf(c_0_2963_2,axiom,
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X3))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X2),X4))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,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_2963]) ).
cnf(c_0_2964_0,axiom,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,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(int,fun(int,bool),ord_less_eq(int),X2),X4))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X1),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2964]) ).
cnf(c_0_2964_1,axiom,
( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X2),X4))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,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(int,fun(int,bool),ord_less(int),X1),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2964]) ).
cnf(c_0_2964_2,axiom,
( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X1),X3))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X2),X4))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,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_2964]) ).
cnf(c_0_2965_0,axiom,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,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(nat,fun(nat,bool),ord_less(nat),X2),X4))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2965]) ).
cnf(c_0_2965_1,axiom,
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X2),X4))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,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(nat,fun(nat,bool),ord_less(nat),X1),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2965]) ).
cnf(c_0_2965_2,axiom,
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X3))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X2),X4))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,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_2965]) ).
cnf(c_0_2966_0,axiom,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),one_one(X1)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),hAPP(nat,X1,power_power(X1,X2),X3))))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),one_one(X1)),X2))
| ~ linordered_semidom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2966]) ).
cnf(c_0_2966_1,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),one_one(X1)),X2))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),one_one(X1)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),hAPP(nat,X1,power_power(X1,X2),X3))))
| ~ linordered_semidom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2966]) ).
cnf(c_0_2966_2,axiom,
( ~ linordered_semidom(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),one_one(X1)),X2))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),one_one(X1)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),times_times(X1),X2),hAPP(nat,X1,power_power(X1,X2),X3)))) ),
inference(literals_permutation,[status(thm)],[c_0_2966]) ).
cnf(c_0_2967_0,axiom,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,plus_plus(X1,X4),X2)),hAPP(X1,X1,plus_plus(X1,X4),X3)))
| ~ ordere236663937imp_le(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2967]) ).
cnf(c_0_2967_1,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,plus_plus(X1,X4),X2)),hAPP(X1,X1,plus_plus(X1,X4),X3)))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
| ~ ordere236663937imp_le(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2967]) ).
cnf(c_0_2967_2,axiom,
( ~ ordere236663937imp_le(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,plus_plus(X1,X4),X2)),hAPP(X1,X1,plus_plus(X1,X4),X3)))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2967]) ).
cnf(c_0_2968_0,axiom,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,plus_plus(X1,X2),X4)),hAPP(X1,X1,plus_plus(X1,X3),X4)))
| ~ ordere236663937imp_le(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2968]) ).
cnf(c_0_2968_1,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,plus_plus(X1,X2),X4)),hAPP(X1,X1,plus_plus(X1,X3),X4)))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
| ~ ordere236663937imp_le(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2968]) ).
cnf(c_0_2968_2,axiom,
( ~ ordere236663937imp_le(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,plus_plus(X1,X2),X4)),hAPP(X1,X1,plus_plus(X1,X3),X4)))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2968]) ).
cnf(c_0_2969_0,axiom,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
| ~ ordere236663937imp_le(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,plus_plus(X1,X4),X2)),hAPP(X1,X1,plus_plus(X1,X4),X3))) ),
inference(literals_permutation,[status(thm)],[c_0_2969]) ).
cnf(c_0_2969_1,axiom,
( ~ ordere236663937imp_le(X1)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,plus_plus(X1,X4),X2)),hAPP(X1,X1,plus_plus(X1,X4),X3))) ),
inference(literals_permutation,[status(thm)],[c_0_2969]) ).
cnf(c_0_2969_2,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,plus_plus(X1,X4),X2)),hAPP(X1,X1,plus_plus(X1,X4),X3)))
| ~ ordere236663937imp_le(X1)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2969]) ).
cnf(c_0_2970_0,axiom,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
| ~ ordere236663937imp_le(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,plus_plus(X1,X2),X4)),hAPP(X1,X1,plus_plus(X1,X3),X4))) ),
inference(literals_permutation,[status(thm)],[c_0_2970]) ).
cnf(c_0_2970_1,axiom,
( ~ ordere236663937imp_le(X1)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,plus_plus(X1,X2),X4)),hAPP(X1,X1,plus_plus(X1,X3),X4))) ),
inference(literals_permutation,[status(thm)],[c_0_2970]) ).
cnf(c_0_2970_2,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,plus_plus(X1,X2),X4)),hAPP(X1,X1,plus_plus(X1,X3),X4)))
| ~ ordere236663937imp_le(X1)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2970]) ).
cnf(c_0_2971_0,axiom,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| ~ ordere236663937imp_le(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,plus_plus(X1,X2),X4)),hAPP(X1,X1,plus_plus(X1,X3),X4))) ),
inference(literals_permutation,[status(thm)],[c_0_2971]) ).
cnf(c_0_2971_1,axiom,
( ~ ordere236663937imp_le(X1)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,plus_plus(X1,X2),X4)),hAPP(X1,X1,plus_plus(X1,X3),X4))) ),
inference(literals_permutation,[status(thm)],[c_0_2971]) ).
cnf(c_0_2971_2,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,plus_plus(X1,X2),X4)),hAPP(X1,X1,plus_plus(X1,X3),X4)))
| ~ ordere236663937imp_le(X1)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2971]) ).
cnf(c_0_2972_0,axiom,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| ~ ordere236663937imp_le(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,plus_plus(X1,X4),X2)),hAPP(X1,X1,plus_plus(X1,X4),X3))) ),
inference(literals_permutation,[status(thm)],[c_0_2972]) ).
cnf(c_0_2972_1,axiom,
( ~ ordere236663937imp_le(X1)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,plus_plus(X1,X4),X2)),hAPP(X1,X1,plus_plus(X1,X4),X3))) ),
inference(literals_permutation,[status(thm)],[c_0_2972]) ).
cnf(c_0_2972_2,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,plus_plus(X1,X4),X2)),hAPP(X1,X1,plus_plus(X1,X4),X3)))
| ~ ordere236663937imp_le(X1)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2972]) ).
cnf(c_0_2973_0,axiom,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,plus_plus(X1,X2),X4)),hAPP(X1,X1,plus_plus(X1,X3),X4)))
| ~ ordere236663937imp_le(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2973]) ).
cnf(c_0_2973_1,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,plus_plus(X1,X2),X4)),hAPP(X1,X1,plus_plus(X1,X3),X4)))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| ~ ordere236663937imp_le(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2973]) ).
cnf(c_0_2973_2,axiom,
( ~ ordere236663937imp_le(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,plus_plus(X1,X2),X4)),hAPP(X1,X1,plus_plus(X1,X3),X4)))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2973]) ).
cnf(c_0_2974_0,axiom,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,plus_plus(X1,X4),X2)),hAPP(X1,X1,plus_plus(X1,X4),X3)))
| ~ ordere236663937imp_le(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2974]) ).
cnf(c_0_2974_1,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,plus_plus(X1,X4),X2)),hAPP(X1,X1,plus_plus(X1,X4),X3)))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| ~ ordere236663937imp_le(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2974]) ).
cnf(c_0_2974_2,axiom,
( ~ ordere236663937imp_le(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,plus_plus(X1,X4),X2)),hAPP(X1,X1,plus_plus(X1,X4),X3)))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2974]) ).
cnf(c_0_2975_0,axiom,
( hBOOL(hAPP(int,bool,X3,X2))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,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_2975]) ).
cnf(c_0_2975_1,axiom,
( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,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_2975]) ).
cnf(c_0_2975_2,axiom,
( ~ hBOOL(hAPP(int,bool,X3,hAPP(int,int,plus_plus(int,X1),one_one(int))))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,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_2975]) ).
cnf(c_0_2975_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(int,fun(int,bool),ord_less(int),X1),X2))
| hBOOL(hAPP(int,bool,X3,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2975]) ).
cnf(c_0_2977_0,axiom,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,X1,X2)),hAPP(nat,nat,X1,X3)))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),sk1_esk20_3(X2,X3,X1)),sk1_esk21_3(X2,X3,X1)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2977]) ).
cnf(c_0_2977_1,axiom,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),sk1_esk20_3(X2,X3,X1)),sk1_esk21_3(X2,X3,X1)))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,X1,X2)),hAPP(nat,nat,X1,X3)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2977]) ).
cnf(c_0_2977_2,axiom,
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X2),X3))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),sk1_esk20_3(X2,X3,X1)),sk1_esk21_3(X2,X3,X1)))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,X1,X2)),hAPP(nat,nat,X1,X3))) ),
inference(literals_permutation,[status(thm)],[c_0_2977]) ).
cnf(c_0_2978_0,axiom,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,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_2978]) ).
cnf(c_0_2978_1,axiom,
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,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(nat,fun(nat,bool),ord_less_eq(nat),X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2978]) ).
cnf(c_0_2979_0,axiom,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,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_2979]) ).
cnf(c_0_2979_1,axiom,
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,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(nat,fun(nat,bool),ord_less(nat),X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2979]) ).
cnf(c_0_2980_0,axiom,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X1,X2),X3))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X1,X2),X3))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X1,X2),X3))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X1,X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2980]) ).
cnf(c_0_2980_1,axiom,
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X1,X2),X3))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X1,X2),X3))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X1,X2),X3))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X1,X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2980]) ).
cnf(c_0_2980_2,axiom,
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X1,X2),X3))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X1,X2),X3))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X1,X2),X3))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X1,X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2980]) ).
cnf(c_0_2980_3,axiom,
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X1,X2),X3))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X1,X2),X3))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X1,X2),X3))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X1,X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2980]) ).
cnf(c_0_2981_0,axiom,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,plus_plus(X1,X2),X3)),zero_zero(X1)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),zero_zero(X1)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),zero_zero(X1)))
| ~ ordere216010020id_add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2981]) ).
cnf(c_0_2981_1,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),zero_zero(X1)))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,plus_plus(X1,X2),X3)),zero_zero(X1)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),zero_zero(X1)))
| ~ ordere216010020id_add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2981]) ).
cnf(c_0_2981_2,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),zero_zero(X1)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),zero_zero(X1)))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,plus_plus(X1,X2),X3)),zero_zero(X1)))
| ~ ordere216010020id_add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2981]) ).
cnf(c_0_2981_3,axiom,
( ~ ordere216010020id_add(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),zero_zero(X1)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),zero_zero(X1)))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,plus_plus(X1,X2),X3)),zero_zero(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_2981]) ).
cnf(c_0_2982_0,axiom,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,plus_plus(X1,X2),X3)),zero_zero(X1)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),zero_zero(X1)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),zero_zero(X1)))
| ~ ordere216010020id_add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2982]) ).
cnf(c_0_2982_1,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),zero_zero(X1)))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,plus_plus(X1,X2),X3)),zero_zero(X1)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),zero_zero(X1)))
| ~ ordere216010020id_add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2982]) ).
cnf(c_0_2982_2,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),zero_zero(X1)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),zero_zero(X1)))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,plus_plus(X1,X2),X3)),zero_zero(X1)))
| ~ ordere216010020id_add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2982]) ).
cnf(c_0_2982_3,axiom,
( ~ ordere216010020id_add(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),zero_zero(X1)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),zero_zero(X1)))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,plus_plus(X1,X2),X3)),zero_zero(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_2982]) ).
cnf(c_0_2983_0,axiom,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,plus_plus(X1,X2),X3)),zero_zero(X1)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),zero_zero(X1)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),zero_zero(X1)))
| ~ ordere216010020id_add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2983]) ).
cnf(c_0_2983_1,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),zero_zero(X1)))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,plus_plus(X1,X2),X3)),zero_zero(X1)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),zero_zero(X1)))
| ~ ordere216010020id_add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2983]) ).
cnf(c_0_2983_2,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),zero_zero(X1)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),zero_zero(X1)))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,plus_plus(X1,X2),X3)),zero_zero(X1)))
| ~ ordere216010020id_add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2983]) ).
cnf(c_0_2983_3,axiom,
( ~ ordere216010020id_add(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),zero_zero(X1)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),zero_zero(X1)))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,plus_plus(X1,X2),X3)),zero_zero(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_2983]) ).
cnf(c_0_2984_0,axiom,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,plus_plus(X1,X2),X3)),zero_zero(X1)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),zero_zero(X1)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),zero_zero(X1)))
| ~ ordere216010020id_add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2984]) ).
cnf(c_0_2984_1,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),zero_zero(X1)))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,plus_plus(X1,X2),X3)),zero_zero(X1)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),zero_zero(X1)))
| ~ ordere216010020id_add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2984]) ).
cnf(c_0_2984_2,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),zero_zero(X1)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),zero_zero(X1)))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,plus_plus(X1,X2),X3)),zero_zero(X1)))
| ~ ordere216010020id_add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2984]) ).
cnf(c_0_2984_3,axiom,
( ~ ordere216010020id_add(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),zero_zero(X1)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),zero_zero(X1)))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,plus_plus(X1,X2),X3)),zero_zero(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_2984]) ).
cnf(c_0_2985_0,axiom,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X2),X3))
| ~ linordered_semidom(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(nat,X1,semiring_1_of_nat(X1),X2)),hAPP(nat,X1,semiring_1_of_nat(X1),X3))) ),
inference(literals_permutation,[status(thm)],[c_0_2985]) ).
cnf(c_0_2985_1,axiom,
( ~ linordered_semidom(X1)
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X2),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(nat,X1,semiring_1_of_nat(X1),X2)),hAPP(nat,X1,semiring_1_of_nat(X1),X3))) ),
inference(literals_permutation,[status(thm)],[c_0_2985]) ).
cnf(c_0_2985_2,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(nat,X1,semiring_1_of_nat(X1),X2)),hAPP(nat,X1,semiring_1_of_nat(X1),X3)))
| ~ linordered_semidom(X1)
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2985]) ).
cnf(c_0_2986_0,axiom,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2))
| ~ hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),hAPP(nat,X3,semiring_1_of_nat(X3),X1)),hAPP(nat,X3,semiring_1_of_nat(X3),X2)))
| ~ linordered_semidom(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2986]) ).
cnf(c_0_2986_1,axiom,
( ~ hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),hAPP(nat,X3,semiring_1_of_nat(X3),X1)),hAPP(nat,X3,semiring_1_of_nat(X3),X2)))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2))
| ~ linordered_semidom(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2986]) ).
cnf(c_0_2986_2,axiom,
( ~ linordered_semidom(X3)
| ~ hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),hAPP(nat,X3,semiring_1_of_nat(X3),X1)),hAPP(nat,X3,semiring_1_of_nat(X3),X2)))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2986]) ).
cnf(c_0_2987_0,axiom,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X2),X3))
| ~ linordered_semidom(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(nat,X1,semiring_1_of_nat(X1),X2)),hAPP(nat,X1,semiring_1_of_nat(X1),X3))) ),
inference(literals_permutation,[status(thm)],[c_0_2987]) ).
cnf(c_0_2987_1,axiom,
( ~ linordered_semidom(X1)
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X2),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(nat,X1,semiring_1_of_nat(X1),X2)),hAPP(nat,X1,semiring_1_of_nat(X1),X3))) ),
inference(literals_permutation,[status(thm)],[c_0_2987]) ).
cnf(c_0_2987_2,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(nat,X1,semiring_1_of_nat(X1),X2)),hAPP(nat,X1,semiring_1_of_nat(X1),X3)))
| ~ linordered_semidom(X1)
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2987]) ).
cnf(c_0_2988_0,axiom,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(nat,int,semiring_1_of_nat(int),X1)),hAPP(nat,int,semiring_1_of_nat(int),X2))) ),
inference(literals_permutation,[status(thm)],[c_0_2988]) ).
cnf(c_0_2988_1,axiom,
( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(nat,int,semiring_1_of_nat(int),X1)),hAPP(nat,int,semiring_1_of_nat(int),X2)))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2988]) ).
cnf(c_0_2989_0,axiom,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(nat,int,semiring_1_of_nat(int),X1)),hAPP(nat,int,semiring_1_of_nat(int),X2))) ),
inference(literals_permutation,[status(thm)],[c_0_2989]) ).
cnf(c_0_2989_1,axiom,
( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(nat,int,semiring_1_of_nat(int),X1)),hAPP(nat,int,semiring_1_of_nat(int),X2)))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2989]) ).
cnf(c_0_2990_0,axiom,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(nat,int,semiring_1_of_nat(int),X1)),hAPP(nat,int,semiring_1_of_nat(int),X2))) ),
inference(literals_permutation,[status(thm)],[c_0_2990]) ).
cnf(c_0_2990_1,axiom,
( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(nat,int,semiring_1_of_nat(int),X1)),hAPP(nat,int,semiring_1_of_nat(int),X2)))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2990]) ).
cnf(c_0_2991_0,axiom,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(nat,int,semiring_1_of_nat(int),X1)),hAPP(nat,int,semiring_1_of_nat(int),X2))) ),
inference(literals_permutation,[status(thm)],[c_0_2991]) ).
cnf(c_0_2991_1,axiom,
( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(nat,int,semiring_1_of_nat(int),X1)),hAPP(nat,int,semiring_1_of_nat(int),X2)))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2991]) ).
cnf(c_0_2992_0,axiom,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X1),X2))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,bit1,X1)),hAPP(int,int,bit0,X2))) ),
inference(literals_permutation,[status(thm)],[c_0_2992]) ).
cnf(c_0_2992_1,axiom,
( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,bit1,X1)),hAPP(int,int,bit0,X2)))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2992]) ).
cnf(c_0_2993_0,axiom,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X1),X2))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,bit1,X1)),hAPP(int,int,bit0,X2))) ),
inference(literals_permutation,[status(thm)],[c_0_2993]) ).
cnf(c_0_2993_1,axiom,
( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,bit1,X1)),hAPP(int,int,bit0,X2)))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2993]) ).
cnf(c_0_2994_0,axiom,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X1),X2))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit0,X1)),hAPP(int,int,bit1,X2))) ),
inference(literals_permutation,[status(thm)],[c_0_2994]) ).
cnf(c_0_2994_1,axiom,
( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit0,X1)),hAPP(int,int,bit1,X2)))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2994]) ).
cnf(c_0_2995_0,axiom,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X1),X2))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit0,X1)),hAPP(int,int,bit1,X2))) ),
inference(literals_permutation,[status(thm)],[c_0_2995]) ).
cnf(c_0_2995_1,axiom,
( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit0,X1)),hAPP(int,int,bit1,X2)))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2995]) ).
cnf(c_0_2996_0,axiom,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X1),X2))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,bit0,X1)),hAPP(int,int,bit1,X2))) ),
inference(literals_permutation,[status(thm)],[c_0_2996]) ).
cnf(c_0_2996_1,axiom,
( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,bit0,X1)),hAPP(int,int,bit1,X2)))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2996]) ).
cnf(c_0_2997_0,axiom,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X1),X2))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,bit0,X1)),hAPP(int,int,bit1,X2))) ),
inference(literals_permutation,[status(thm)],[c_0_2997]) ).
cnf(c_0_2997_1,axiom,
( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,bit0,X1)),hAPP(int,int,bit1,X2)))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2997]) ).
cnf(c_0_2998_0,axiom,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X1),X2))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,bit0,X1)),hAPP(int,int,bit0,X2))) ),
inference(literals_permutation,[status(thm)],[c_0_2998]) ).
cnf(c_0_2998_1,axiom,
( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,bit0,X1)),hAPP(int,int,bit0,X2)))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2998]) ).
cnf(c_0_2999_0,axiom,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X1),X2))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,bit0,X1)),hAPP(int,int,bit0,X2))) ),
inference(literals_permutation,[status(thm)],[c_0_2999]) ).
cnf(c_0_2999_1,axiom,
( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,bit0,X1)),hAPP(int,int,bit0,X2)))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2999]) ).
cnf(c_0_3000_0,axiom,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X1),X2))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,bit1,X1)),hAPP(int,int,bit1,X2))) ),
inference(literals_permutation,[status(thm)],[c_0_3000]) ).
cnf(c_0_3000_1,axiom,
( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,bit1,X1)),hAPP(int,int,bit1,X2)))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3000]) ).
cnf(c_0_3001_0,axiom,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X1),X2))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,bit1,X1)),hAPP(int,int,bit1,X2))) ),
inference(literals_permutation,[status(thm)],[c_0_3001]) ).
cnf(c_0_3001_1,axiom,
( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,bit1,X1)),hAPP(int,int,bit1,X2)))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3001]) ).
cnf(c_0_3002_0,axiom,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X1),X2))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit1,X1)),hAPP(int,int,bit0,X2))) ),
inference(literals_permutation,[status(thm)],[c_0_3002]) ).
cnf(c_0_3002_1,axiom,
( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit1,X1)),hAPP(int,int,bit0,X2)))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3002]) ).
cnf(c_0_3003_0,axiom,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X1),X2))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit1,X1)),hAPP(int,int,bit0,X2))) ),
inference(literals_permutation,[status(thm)],[c_0_3003]) ).
cnf(c_0_3003_1,axiom,
( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit1,X1)),hAPP(int,int,bit0,X2)))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3003]) ).
cnf(c_0_3004_0,axiom,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X1),X2))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit0,X1)),hAPP(int,int,bit0,X2))) ),
inference(literals_permutation,[status(thm)],[c_0_3004]) ).
cnf(c_0_3004_1,axiom,
( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit0,X1)),hAPP(int,int,bit0,X2)))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3004]) ).
cnf(c_0_3005_0,axiom,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X1),X2))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit0,X1)),hAPP(int,int,bit0,X2))) ),
inference(literals_permutation,[status(thm)],[c_0_3005]) ).
cnf(c_0_3005_1,axiom,
( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit0,X1)),hAPP(int,int,bit0,X2)))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3005]) ).
cnf(c_0_3006_0,axiom,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X1),X2))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit1,X1)),hAPP(int,int,bit1,X2))) ),
inference(literals_permutation,[status(thm)],[c_0_3006]) ).
cnf(c_0_3006_1,axiom,
( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit1,X1)),hAPP(int,int,bit1,X2)))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3006]) ).
cnf(c_0_3007_0,axiom,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X1),X2))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit1,X1)),hAPP(int,int,bit1,X2))) ),
inference(literals_permutation,[status(thm)],[c_0_3007]) ).
cnf(c_0_3007_1,axiom,
( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit1,X1)),hAPP(int,int,bit1,X2)))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3007]) ).
cnf(c_0_3008_0,axiom,
( ti(X1,X2) = ti(X1,X3)
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X4))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X2))
| hAPP(nat,X1,power_power(X1,X2),X4) != hAPP(nat,X1,power_power(X1,X3),X4)
| ~ linordered_semidom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3008]) ).
cnf(c_0_3008_1,axiom,
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X4))
| ti(X1,X2) = ti(X1,X3)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X2))
| hAPP(nat,X1,power_power(X1,X2),X4) != hAPP(nat,X1,power_power(X1,X3),X4)
| ~ linordered_semidom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3008]) ).
cnf(c_0_3008_2,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X3))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X4))
| ti(X1,X2) = ti(X1,X3)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X2))
| hAPP(nat,X1,power_power(X1,X2),X4) != hAPP(nat,X1,power_power(X1,X3),X4)
| ~ linordered_semidom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3008]) ).
cnf(c_0_3008_3,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X2))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X3))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X4))
| ti(X1,X2) = ti(X1,X3)
| hAPP(nat,X1,power_power(X1,X2),X4) != hAPP(nat,X1,power_power(X1,X3),X4)
| ~ linordered_semidom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3008]) ).
cnf(c_0_3008_4,axiom,
( hAPP(nat,X1,power_power(X1,X2),X4) != hAPP(nat,X1,power_power(X1,X3),X4)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X2))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X3))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X4))
| ti(X1,X2) = ti(X1,X3)
| ~ linordered_semidom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3008]) ).
cnf(c_0_3008_5,axiom,
( ~ linordered_semidom(X1)
| hAPP(nat,X1,power_power(X1,X2),X4) != hAPP(nat,X1,power_power(X1,X3),X4)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X2))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X3))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X4))
| ti(X1,X2) = ti(X1,X3) ),
inference(literals_permutation,[status(thm)],[c_0_3008]) ).
cnf(c_0_3009_0,axiom,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X3,X2),X1))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X3,X2),X1))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X3,X2),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_3009]) ).
cnf(c_0_3009_1,axiom,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X3,X2),X1))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X3,X2),X1))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X3,X2),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_3009]) ).
cnf(c_0_3009_2,axiom,
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X3,X2),X1))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X3,X2),X1))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X3,X2),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_3009]) ).
cnf(c_0_3009_3,axiom,
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X3,X2),X1))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X3,X2),X1))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X3,X2),X1))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3009]) ).
cnf(c_0_3010_0,axiom,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X1,X2),X3))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X2),X3))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X1,X2),X3))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X1,X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3010]) ).
cnf(c_0_3010_1,axiom,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X2),X3))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X1,X2),X3))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X1,X2),X3))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X1,X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3010]) ).
cnf(c_0_3010_2,axiom,
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X1,X2),X3))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X2),X3))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X1,X2),X3))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X1,X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3010]) ).
cnf(c_0_3010_3,axiom,
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X1,X2),X3))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X1,X2),X3))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X2),X3))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X1,X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3010]) ).
cnf(c_0_3011_0,axiom,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X2,X1,X3,X4)),hAPP(X2,X1,X5,X4)))
| ~ ord(X1)
| ~ hBOOL(hAPP(fun(X2,X1),bool,hAPP(fun(X2,X1),fun(fun(X2,X1),bool),ord_less_eq(fun(X2,X1)),X3),X5)) ),
inference(literals_permutation,[status(thm)],[c_0_3011]) ).
cnf(c_0_3011_1,axiom,
( ~ ord(X1)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X2,X1,X3,X4)),hAPP(X2,X1,X5,X4)))
| ~ hBOOL(hAPP(fun(X2,X1),bool,hAPP(fun(X2,X1),fun(fun(X2,X1),bool),ord_less_eq(fun(X2,X1)),X3),X5)) ),
inference(literals_permutation,[status(thm)],[c_0_3011]) ).
cnf(c_0_3011_2,axiom,
( ~ hBOOL(hAPP(fun(X2,X1),bool,hAPP(fun(X2,X1),fun(fun(X2,X1),bool),ord_less_eq(fun(X2,X1)),X3),X5))
| ~ ord(X1)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X2,X1,X3,X4)),hAPP(X2,X1,X5,X4))) ),
inference(literals_permutation,[status(thm)],[c_0_3011]) ).
cnf(c_0_3012_0,axiom,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X2,X1,X3,X4)),hAPP(X2,X1,X5,X4)))
| ~ hBOOL(hAPP(fun(X2,X1),bool,hAPP(fun(X2,X1),fun(fun(X2,X1),bool),ord_less_eq(fun(X2,X1)),X3),X5))
| ~ ord(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3012]) ).
cnf(c_0_3012_1,axiom,
( ~ hBOOL(hAPP(fun(X2,X1),bool,hAPP(fun(X2,X1),fun(fun(X2,X1),bool),ord_less_eq(fun(X2,X1)),X3),X5))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X2,X1,X3,X4)),hAPP(X2,X1,X5,X4)))
| ~ ord(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3012]) ).
cnf(c_0_3012_2,axiom,
( ~ ord(X1)
| ~ hBOOL(hAPP(fun(X2,X1),bool,hAPP(fun(X2,X1),fun(fun(X2,X1),bool),ord_less_eq(fun(X2,X1)),X3),X5))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X2,X1,X3,X4)),hAPP(X2,X1,X5,X4))) ),
inference(literals_permutation,[status(thm)],[c_0_3012]) ).
cnf(c_0_3013_0,axiom,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X2,X1,X3,X4)),hAPP(X2,X1,X5,X4)))
| ~ hBOOL(hAPP(fun(X2,X1),bool,hAPP(fun(X2,X1),fun(fun(X2,X1),bool),ord_less_eq(fun(X2,X1)),X3),X5))
| ~ ord(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3013]) ).
cnf(c_0_3013_1,axiom,
( ~ hBOOL(hAPP(fun(X2,X1),bool,hAPP(fun(X2,X1),fun(fun(X2,X1),bool),ord_less_eq(fun(X2,X1)),X3),X5))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X2,X1,X3,X4)),hAPP(X2,X1,X5,X4)))
| ~ ord(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3013]) ).
cnf(c_0_3013_2,axiom,
( ~ ord(X1)
| ~ hBOOL(hAPP(fun(X2,X1),bool,hAPP(fun(X2,X1),fun(fun(X2,X1),bool),ord_less_eq(fun(X2,X1)),X3),X5))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X2,X1,X3,X4)),hAPP(X2,X1,X5,X4))) ),
inference(literals_permutation,[status(thm)],[c_0_3013]) ).
cnf(c_0_3014_0,axiom,
( X3 = sk1_esk4_2(X2,X1)
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X1))
| ~ hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X2))
| hAPP(nat,real,power_power(real,X3),X1) != X2
| ~ hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3014]) ).
cnf(c_0_3014_1,axiom,
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X1))
| X3 = sk1_esk4_2(X2,X1)
| ~ hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X2))
| hAPP(nat,real,power_power(real,X3),X1) != X2
| ~ hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3014]) ).
cnf(c_0_3014_2,axiom,
( ~ hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X2))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,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(real,fun(real,bool),ord_less(real),zero_zero(real)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3014]) ).
cnf(c_0_3014_3,axiom,
( hAPP(nat,real,power_power(real,X3),X1) != X2
| ~ hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X2))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X1))
| X3 = sk1_esk4_2(X2,X1)
| ~ hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3014]) ).
cnf(c_0_3014_4,axiom,
( ~ hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X3))
| hAPP(nat,real,power_power(real,X3),X1) != X2
| ~ hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X2))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X1))
| X3 = sk1_esk4_2(X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_3014]) ).
cnf(c_0_3015_0,axiom,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),hAPP(X1,X1,plus_plus(X1,X2),X3)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X2))
| ~ ordere216010020id_add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3015]) ).
cnf(c_0_3015_1,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X3))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),hAPP(X1,X1,plus_plus(X1,X2),X3)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X2))
| ~ ordere216010020id_add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3015]) ).
cnf(c_0_3015_2,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X2))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X3))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),hAPP(X1,X1,plus_plus(X1,X2),X3)))
| ~ ordere216010020id_add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3015]) ).
cnf(c_0_3015_3,axiom,
( ~ ordere216010020id_add(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X2))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X3))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),hAPP(X1,X1,plus_plus(X1,X2),X3))) ),
inference(literals_permutation,[status(thm)],[c_0_3015]) ).
cnf(c_0_3016_0,axiom,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),hAPP(X1,X1,plus_plus(X1,X2),X3)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X2))
| ~ ordere216010020id_add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3016]) ).
cnf(c_0_3016_1,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X3))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),hAPP(X1,X1,plus_plus(X1,X2),X3)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X2))
| ~ ordere216010020id_add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3016]) ).
cnf(c_0_3016_2,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X2))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X3))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),hAPP(X1,X1,plus_plus(X1,X2),X3)))
| ~ ordere216010020id_add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3016]) ).
cnf(c_0_3016_3,axiom,
( ~ ordere216010020id_add(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X2))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X3))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),hAPP(X1,X1,plus_plus(X1,X2),X3))) ),
inference(literals_permutation,[status(thm)],[c_0_3016]) ).
cnf(c_0_3017_0,axiom,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),hAPP(X1,X1,plus_plus(X1,X2),X3)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X2))
| ~ ordere216010020id_add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3017]) ).
cnf(c_0_3017_1,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X3))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),hAPP(X1,X1,plus_plus(X1,X2),X3)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X2))
| ~ ordere216010020id_add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3017]) ).
cnf(c_0_3017_2,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X2))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X3))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),hAPP(X1,X1,plus_plus(X1,X2),X3)))
| ~ ordere216010020id_add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3017]) ).
cnf(c_0_3017_3,axiom,
( ~ ordere216010020id_add(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X2))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X3))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),hAPP(X1,X1,plus_plus(X1,X2),X3))) ),
inference(literals_permutation,[status(thm)],[c_0_3017]) ).
cnf(c_0_3018_0,axiom,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),hAPP(X1,X1,plus_plus(X1,X2),X3)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X2))
| ~ ordere216010020id_add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3018]) ).
cnf(c_0_3018_1,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X3))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),hAPP(X1,X1,plus_plus(X1,X2),X3)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X2))
| ~ ordere216010020id_add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3018]) ).
cnf(c_0_3018_2,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X2))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X3))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),hAPP(X1,X1,plus_plus(X1,X2),X3)))
| ~ ordere216010020id_add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3018]) ).
cnf(c_0_3018_3,axiom,
( ~ ordere216010020id_add(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X2))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X3))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),hAPP(X1,X1,plus_plus(X1,X2),X3))) ),
inference(literals_permutation,[status(thm)],[c_0_3018]) ).
cnf(c_0_3019_0,axiom,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),hAPP(X1,X1,plus_plus(X1,X3),X4)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X4))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X3))
| ~ ordere216010020id_add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3019]) ).
cnf(c_0_3019_1,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X4))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),hAPP(X1,X1,plus_plus(X1,X3),X4)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X3))
| ~ ordere216010020id_add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3019]) ).
cnf(c_0_3019_2,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X4))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),hAPP(X1,X1,plus_plus(X1,X3),X4)))
| ~ ordere216010020id_add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3019]) ).
cnf(c_0_3019_3,axiom,
( ~ ordere216010020id_add(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X4))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),hAPP(X1,X1,plus_plus(X1,X3),X4))) ),
inference(literals_permutation,[status(thm)],[c_0_3019]) ).
cnf(c_0_3020_0,axiom,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),hAPP(X1,X1,plus_plus(X1,X3),X4)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X4))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X3))
| ~ ordere216010020id_add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3020]) ).
cnf(c_0_3020_1,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X4))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),hAPP(X1,X1,plus_plus(X1,X3),X4)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X3))
| ~ ordere216010020id_add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3020]) ).
cnf(c_0_3020_2,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X4))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),hAPP(X1,X1,plus_plus(X1,X3),X4)))
| ~ ordere216010020id_add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3020]) ).
cnf(c_0_3020_3,axiom,
( ~ ordere216010020id_add(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X4))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),hAPP(X1,X1,plus_plus(X1,X3),X4))) ),
inference(literals_permutation,[status(thm)],[c_0_3020]) ).
cnf(c_0_3021_0,axiom,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),hAPP(X1,X1,plus_plus(X1,X3),X4)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X4))
| ~ ordere216010020id_add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3021]) ).
cnf(c_0_3021_1,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),hAPP(X1,X1,plus_plus(X1,X3),X4)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X4))
| ~ ordere216010020id_add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3021]) ).
cnf(c_0_3021_2,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X4))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),hAPP(X1,X1,plus_plus(X1,X3),X4)))
| ~ ordere216010020id_add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3021]) ).
cnf(c_0_3021_3,axiom,
( ~ ordere216010020id_add(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X4))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),hAPP(X1,X1,plus_plus(X1,X3),X4))) ),
inference(literals_permutation,[status(thm)],[c_0_3021]) ).
cnf(c_0_3022_0,axiom,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),hAPP(X1,X1,plus_plus(X1,X3),X4)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X4))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X3))
| ~ ordere216010020id_add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3022]) ).
cnf(c_0_3022_1,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X4))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),hAPP(X1,X1,plus_plus(X1,X3),X4)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X3))
| ~ ordere216010020id_add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3022]) ).
cnf(c_0_3022_2,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X4))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),hAPP(X1,X1,plus_plus(X1,X3),X4)))
| ~ ordere216010020id_add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3022]) ).
cnf(c_0_3022_3,axiom,
( ~ ordere216010020id_add(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X4))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),hAPP(X1,X1,plus_plus(X1,X3),X4))) ),
inference(literals_permutation,[status(thm)],[c_0_3022]) ).
cnf(c_0_3023_0,axiom,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),hAPP(X1,X1,plus_plus(X1,X3),X4)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X4))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X3))
| ~ linordered_semidom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3023]) ).
cnf(c_0_3023_1,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X4))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),hAPP(X1,X1,plus_plus(X1,X3),X4)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X3))
| ~ linordered_semidom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3023]) ).
cnf(c_0_3023_2,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X4))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),hAPP(X1,X1,plus_plus(X1,X3),X4)))
| ~ linordered_semidom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3023]) ).
cnf(c_0_3023_3,axiom,
( ~ linordered_semidom(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X4))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),hAPP(X1,X1,plus_plus(X1,X3),X4))) ),
inference(literals_permutation,[status(thm)],[c_0_3023]) ).
cnf(c_0_3024_0,axiom,
( hBOOL(hAPP(fun(X2,X1),bool,hAPP(fun(X2,X1),fun(fun(X2,X1),bool),ord_less(fun(X2,X1)),X3),X4))
| hBOOL(hAPP(fun(X2,X1),bool,hAPP(fun(X2,X1),fun(fun(X2,X1),bool),ord_less_eq(fun(X2,X1)),X4),X3))
| ~ ord(X1)
| ~ hBOOL(hAPP(fun(X2,X1),bool,hAPP(fun(X2,X1),fun(fun(X2,X1),bool),ord_less_eq(fun(X2,X1)),X3),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_3024]) ).
cnf(c_0_3024_1,axiom,
( hBOOL(hAPP(fun(X2,X1),bool,hAPP(fun(X2,X1),fun(fun(X2,X1),bool),ord_less_eq(fun(X2,X1)),X4),X3))
| hBOOL(hAPP(fun(X2,X1),bool,hAPP(fun(X2,X1),fun(fun(X2,X1),bool),ord_less(fun(X2,X1)),X3),X4))
| ~ ord(X1)
| ~ hBOOL(hAPP(fun(X2,X1),bool,hAPP(fun(X2,X1),fun(fun(X2,X1),bool),ord_less_eq(fun(X2,X1)),X3),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_3024]) ).
cnf(c_0_3024_2,axiom,
( ~ ord(X1)
| hBOOL(hAPP(fun(X2,X1),bool,hAPP(fun(X2,X1),fun(fun(X2,X1),bool),ord_less_eq(fun(X2,X1)),X4),X3))
| hBOOL(hAPP(fun(X2,X1),bool,hAPP(fun(X2,X1),fun(fun(X2,X1),bool),ord_less(fun(X2,X1)),X3),X4))
| ~ hBOOL(hAPP(fun(X2,X1),bool,hAPP(fun(X2,X1),fun(fun(X2,X1),bool),ord_less_eq(fun(X2,X1)),X3),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_3024]) ).
cnf(c_0_3024_3,axiom,
( ~ hBOOL(hAPP(fun(X2,X1),bool,hAPP(fun(X2,X1),fun(fun(X2,X1),bool),ord_less_eq(fun(X2,X1)),X3),X4))
| ~ ord(X1)
| hBOOL(hAPP(fun(X2,X1),bool,hAPP(fun(X2,X1),fun(fun(X2,X1),bool),ord_less_eq(fun(X2,X1)),X4),X3))
| hBOOL(hAPP(fun(X2,X1),bool,hAPP(fun(X2,X1),fun(fun(X2,X1),bool),ord_less(fun(X2,X1)),X3),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_3024]) ).
cnf(c_0_3025_0,axiom,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),one_one(X1)),hAPP(nat,X1,power_power(X1,X2),X3)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),one_one(X1)),X2))
| ~ linordered_semidom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3025]) ).
cnf(c_0_3025_1,axiom,
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X3))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),one_one(X1)),hAPP(nat,X1,power_power(X1,X2),X3)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),one_one(X1)),X2))
| ~ linordered_semidom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3025]) ).
cnf(c_0_3025_2,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),one_one(X1)),X2))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X3))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),one_one(X1)),hAPP(nat,X1,power_power(X1,X2),X3)))
| ~ linordered_semidom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3025]) ).
cnf(c_0_3025_3,axiom,
( ~ linordered_semidom(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),one_one(X1)),X2))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X3))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),one_one(X1)),hAPP(nat,X1,power_power(X1,X2),X3))) ),
inference(literals_permutation,[status(thm)],[c_0_3025]) ).
cnf(c_0_3026_0,axiom,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X4))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),sk1_esk27_4(X1,X4,X2,X3)),X3))
| ~ dense_linorder(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3026]) ).
cnf(c_0_3026_1,axiom,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),sk1_esk27_4(X1,X4,X2,X3)),X3))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X4))
| ~ dense_linorder(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3026]) ).
cnf(c_0_3026_2,axiom,
( ~ dense_linorder(X1)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),sk1_esk27_4(X1,X4,X2,X3)),X3))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X4))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3026]) ).
cnf(c_0_3026_3,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| ~ dense_linorder(X1)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),sk1_esk27_4(X1,X4,X2,X3)),X3))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_3026]) ).
cnf(c_0_3027_0,axiom,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,plus_plus(int,X1),X2)))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X2))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_3027]) ).
cnf(c_0_3027_1,axiom,
( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X2))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,plus_plus(int,X1),X2)))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_3027]) ).
cnf(c_0_3027_2,axiom,
( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X1))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X2))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,plus_plus(int,X1),X2))) ),
inference(literals_permutation,[status(thm)],[c_0_3027]) ).
cnf(c_0_3028_0,axiom,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),zero_zero(X1)))
| ~ linord219039673up_add(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,plus_plus(X1,X2),X2)),zero_zero(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_3028]) ).
cnf(c_0_3028_1,axiom,
( ~ linord219039673up_add(X1)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),zero_zero(X1)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,plus_plus(X1,X2),X2)),zero_zero(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_3028]) ).
cnf(c_0_3028_2,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,plus_plus(X1,X2),X2)),zero_zero(X1)))
| ~ linord219039673up_add(X1)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),zero_zero(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_3028]) ).
cnf(c_0_3029_0,axiom,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),zero_zero(X1)))
| ~ linord219039673up_add(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,plus_plus(X1,X2),X2)),zero_zero(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_3029]) ).
cnf(c_0_3029_1,axiom,
( ~ linord219039673up_add(X1)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),zero_zero(X1)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,plus_plus(X1,X2),X2)),zero_zero(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_3029]) ).
cnf(c_0_3029_2,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,plus_plus(X1,X2),X2)),zero_zero(X1)))
| ~ linord219039673up_add(X1)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),zero_zero(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_3029]) ).
cnf(c_0_3030_0,axiom,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),zero_zero(X1)))
| ~ linordered_idom(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,plus_plus(X1,X2),X2)),zero_zero(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_3030]) ).
cnf(c_0_3030_1,axiom,
( ~ linordered_idom(X1)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),zero_zero(X1)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,plus_plus(X1,X2),X2)),zero_zero(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_3030]) ).
cnf(c_0_3030_2,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,plus_plus(X1,X2),X2)),zero_zero(X1)))
| ~ linordered_idom(X1)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),zero_zero(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_3030]) ).
cnf(c_0_3031_0,axiom,
( hBOOL(hAPP(int,bool,X3,X2))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,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_3031]) ).
cnf(c_0_3031_1,axiom,
( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,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_3031]) ).
cnf(c_0_3031_2,axiom,
( ~ hBOOL(hAPP(int,bool,X3,X1))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,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_3031]) ).
cnf(c_0_3031_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(int,fun(int,bool),ord_less_eq(int),X1),X2))
| hBOOL(hAPP(int,bool,X3,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3031]) ).
cnf(c_0_3032_0,axiom,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X1),X2))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,plus_plus(int,X1),one_one(int))),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3032]) ).
cnf(c_0_3032_1,axiom,
( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,plus_plus(int,X1),one_one(int))),X2))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3032]) ).
cnf(c_0_3036_0,axiom,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,plus_plus(X1,X2),X3)),hAPP(X1,X1,plus_plus(X1,X2),X4)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X4))
| ~ ordere779506340up_add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3036]) ).
cnf(c_0_3036_1,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X4))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,plus_plus(X1,X2),X3)),hAPP(X1,X1,plus_plus(X1,X2),X4)))
| ~ ordere779506340up_add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3036]) ).
cnf(c_0_3036_2,axiom,
( ~ ordere779506340up_add(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X4))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,plus_plus(X1,X2),X3)),hAPP(X1,X1,plus_plus(X1,X2),X4))) ),
inference(literals_permutation,[status(thm)],[c_0_3036]) ).
cnf(c_0_3037_0,axiom,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,plus_plus(X1,X2),X3)),hAPP(X1,X1,plus_plus(X1,X4),X3)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X4))
| ~ ordere779506340up_add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3037]) ).
cnf(c_0_3037_1,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X4))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,plus_plus(X1,X2),X3)),hAPP(X1,X1,plus_plus(X1,X4),X3)))
| ~ ordere779506340up_add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3037]) ).
cnf(c_0_3037_2,axiom,
( ~ ordere779506340up_add(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X4))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,plus_plus(X1,X2),X3)),hAPP(X1,X1,plus_plus(X1,X4),X3))) ),
inference(literals_permutation,[status(thm)],[c_0_3037]) ).
cnf(c_0_3038_0,axiom,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,plus_plus(X1,X2),X3)),hAPP(X1,X1,plus_plus(X1,X2),X4)))
| ~ ordere236663937imp_le(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_3038]) ).
cnf(c_0_3038_1,axiom,
( ~ ordere236663937imp_le(X1)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,plus_plus(X1,X2),X3)),hAPP(X1,X1,plus_plus(X1,X2),X4)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_3038]) ).
cnf(c_0_3038_2,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X4))
| ~ ordere236663937imp_le(X1)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,plus_plus(X1,X2),X3)),hAPP(X1,X1,plus_plus(X1,X2),X4))) ),
inference(literals_permutation,[status(thm)],[c_0_3038]) ).
cnf(c_0_3039_0,axiom,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,plus_plus(X1,X2),X3)),hAPP(X1,X1,plus_plus(X1,X4),X3)))
| ~ ordere236663937imp_le(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_3039]) ).
cnf(c_0_3039_1,axiom,
( ~ ordere236663937imp_le(X1)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,plus_plus(X1,X2),X3)),hAPP(X1,X1,plus_plus(X1,X4),X3)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_3039]) ).
cnf(c_0_3039_2,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X4))
| ~ ordere236663937imp_le(X1)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,plus_plus(X1,X2),X3)),hAPP(X1,X1,plus_plus(X1,X4),X3))) ),
inference(literals_permutation,[status(thm)],[c_0_3039]) ).
cnf(c_0_3040_0,axiom,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,plus_plus(X1,X2),X3)),hAPP(X1,X1,plus_plus(X1,X4),X3)))
| ~ ordere236663937imp_le(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_3040]) ).
cnf(c_0_3040_1,axiom,
( ~ ordere236663937imp_le(X1)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,plus_plus(X1,X2),X3)),hAPP(X1,X1,plus_plus(X1,X4),X3)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_3040]) ).
cnf(c_0_3040_2,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X4))
| ~ ordere236663937imp_le(X1)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,plus_plus(X1,X2),X3)),hAPP(X1,X1,plus_plus(X1,X4),X3))) ),
inference(literals_permutation,[status(thm)],[c_0_3040]) ).
cnf(c_0_3041_0,axiom,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,plus_plus(X1,X2),X3)),hAPP(X1,X1,plus_plus(X1,X2),X4)))
| ~ ordere236663937imp_le(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_3041]) ).
cnf(c_0_3041_1,axiom,
( ~ ordere236663937imp_le(X1)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,plus_plus(X1,X2),X3)),hAPP(X1,X1,plus_plus(X1,X2),X4)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_3041]) ).
cnf(c_0_3041_2,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X4))
| ~ ordere236663937imp_le(X1)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,plus_plus(X1,X2),X3)),hAPP(X1,X1,plus_plus(X1,X2),X4))) ),
inference(literals_permutation,[status(thm)],[c_0_3041]) ).
cnf(c_0_3042_0,axiom,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,plus_plus(X1,X2),X3)),hAPP(X1,X1,plus_plus(X1,X4),X3)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X4))
| ~ ordere223160158up_add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3042]) ).
cnf(c_0_3042_1,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X4))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,plus_plus(X1,X2),X3)),hAPP(X1,X1,plus_plus(X1,X4),X3)))
| ~ ordere223160158up_add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3042]) ).
cnf(c_0_3042_2,axiom,
( ~ ordere223160158up_add(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X4))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,plus_plus(X1,X2),X3)),hAPP(X1,X1,plus_plus(X1,X4),X3))) ),
inference(literals_permutation,[status(thm)],[c_0_3042]) ).
cnf(c_0_3043_0,axiom,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,plus_plus(X1,X2),X3)),hAPP(X1,X1,plus_plus(X1,X2),X4)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X4))
| ~ ordere223160158up_add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3043]) ).
cnf(c_0_3043_1,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X4))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,plus_plus(X1,X2),X3)),hAPP(X1,X1,plus_plus(X1,X2),X4)))
| ~ ordere223160158up_add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3043]) ).
cnf(c_0_3043_2,axiom,
( ~ ordere223160158up_add(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X4))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,plus_plus(X1,X2),X3)),hAPP(X1,X1,plus_plus(X1,X2),X4))) ),
inference(literals_permutation,[status(thm)],[c_0_3043]) ).
cnf(c_0_3044_0,axiom,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X3))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,plus_plus(nat,X1),X2)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3044]) ).
cnf(c_0_3044_1,axiom,
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,plus_plus(nat,X1),X2)),X3))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3044]) ).
cnf(c_0_3045_0,axiom,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X2),X3))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,plus_plus(nat,X1),X2)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3045]) ).
cnf(c_0_3045_1,axiom,
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,plus_plus(nat,X1),X2)),X3))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3045]) ).
cnf(c_0_3046_0,axiom,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,plus_plus(nat,X1),X3)),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3046]) ).
cnf(c_0_3046_1,axiom,
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,plus_plus(nat,X1),X3)),X2))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3046]) ).
cnf(c_0_3047_0,axiom,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,plus_plus(nat,X3),X1)),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3047]) ).
cnf(c_0_3047_1,axiom,
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,plus_plus(nat,X3),X1)),X2))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3047]) ).
cnf(c_0_3048_0,axiom,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,plus_plus(nat,X1),X3)),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3048]) ).
cnf(c_0_3048_1,axiom,
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,plus_plus(nat,X1),X3)),X2))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3048]) ).
cnf(c_0_3049_0,axiom,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X1))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X2))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,plus_plus(nat,X2),X1))) ),
inference(literals_permutation,[status(thm)],[c_0_3049]) ).
cnf(c_0_3049_1,axiom,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X2))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X1))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,plus_plus(nat,X2),X1))) ),
inference(literals_permutation,[status(thm)],[c_0_3049]) ).
cnf(c_0_3049_2,axiom,
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,plus_plus(nat,X2),X1)))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X2))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_3049]) ).
cnf(c_0_3050_0,axiom,
( hBOOL(hAPP(real,bool,hAPP(real,fun(real,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(real,fun(real,bool),ord_less_eq(real),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3050]) ).
cnf(c_0_3050_1,axiom,
( ~ hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X2),X3))
| hBOOL(hAPP(real,bool,hAPP(real,fun(real,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_3050]) ).
cnf(c_0_3051_0,axiom,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,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(nat,fun(nat,bool),ord_less_eq(nat),X1),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3051]) ).
cnf(c_0_3051_1,axiom,
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X3))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,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_3051]) ).
cnf(c_0_3052_0,axiom,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,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(nat,fun(nat,bool),ord_less_eq(nat),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3052]) ).
cnf(c_0_3052_1,axiom,
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X2),X3))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,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_3052]) ).
cnf(c_0_3053_0,axiom,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,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(int,fun(int,bool),ord_less_eq(int),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3053]) ).
cnf(c_0_3053_1,axiom,
( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X2),X3))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,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_3053]) ).
cnf(c_0_3054_0,axiom,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,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(nat,fun(nat,bool),ord_less(nat),X1),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3054]) ).
cnf(c_0_3054_1,axiom,
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X3))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,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_3054]) ).
cnf(c_0_3055_0,axiom,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,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(nat,fun(nat,bool),ord_less(nat),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3055]) ).
cnf(c_0_3055_1,axiom,
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X2),X3))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,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_3055]) ).
cnf(c_0_3056_0,axiom,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,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(int,fun(int,bool),ord_less(int),X1),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3056]) ).
cnf(c_0_3056_1,axiom,
( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X1),X3))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,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_3056]) ).
cnf(c_0_3057_0,axiom,
( hBOOL(hAPP(int,bool,X3,X2))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X1),sk1_esk1_3(X3,X1,X2)))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,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_3057]) ).
cnf(c_0_3057_1,axiom,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X1),sk1_esk1_3(X3,X1,X2)))
| hBOOL(hAPP(int,bool,X3,X2))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,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_3057]) ).
cnf(c_0_3057_2,axiom,
( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X1),X2))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,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_3057]) ).
cnf(c_0_3057_3,axiom,
( ~ hBOOL(hAPP(int,bool,X3,hAPP(int,int,plus_plus(int,X1),one_one(int))))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X1),X2))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X1),sk1_esk1_3(X3,X1,X2)))
| hBOOL(hAPP(int,bool,X3,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3057]) ).
cnf(c_0_3058_0,axiom,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),one_one(X1)),number_number_of(X1,X2)))
| ~ linordered_idom(X1)
| ~ number_ring(X1)
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,bit1,pls)),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3058]) ).
cnf(c_0_3058_1,axiom,
( ~ linordered_idom(X1)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),one_one(X1)),number_number_of(X1,X2)))
| ~ number_ring(X1)
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,bit1,pls)),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3058]) ).
cnf(c_0_3058_2,axiom,
( ~ number_ring(X1)
| ~ linordered_idom(X1)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),one_one(X1)),number_number_of(X1,X2)))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,bit1,pls)),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3058]) ).
cnf(c_0_3058_3,axiom,
( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,bit1,pls)),X2))
| ~ number_ring(X1)
| ~ linordered_idom(X1)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),one_one(X1)),number_number_of(X1,X2))) ),
inference(literals_permutation,[status(thm)],[c_0_3058]) ).
cnf(c_0_3059_0,axiom,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),one_one(X1)),number_number_of(X1,X2)))
| ~ linordered_idom(X1)
| ~ number_ring(X1)
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit1,pls)),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3059]) ).
cnf(c_0_3059_1,axiom,
( ~ linordered_idom(X1)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),one_one(X1)),number_number_of(X1,X2)))
| ~ number_ring(X1)
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit1,pls)),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3059]) ).
cnf(c_0_3059_2,axiom,
( ~ number_ring(X1)
| ~ linordered_idom(X1)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),one_one(X1)),number_number_of(X1,X2)))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit1,pls)),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3059]) ).
cnf(c_0_3059_3,axiom,
( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit1,pls)),X2))
| ~ number_ring(X1)
| ~ linordered_idom(X1)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),one_one(X1)),number_number_of(X1,X2))) ),
inference(literals_permutation,[status(thm)],[c_0_3059]) ).
cnf(c_0_3061_0,axiom,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X3,X2),X1))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X2),X1))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X3,X2),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_3061]) ).
cnf(c_0_3061_1,axiom,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X3,X2),X1))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X2),X1))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X3,X2),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_3061]) ).
cnf(c_0_3061_2,axiom,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X2),X1))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X3,X2),X1))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X3,X2),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_3061]) ).
cnf(c_0_3061_3,axiom,
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X3,X2),X1))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X2),X1))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X3,X2),X1))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3061]) ).
cnf(c_0_3062_0,axiom,
( hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X1),one_one(real)))
| ~ hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,sqrt,X1)),one_one(real))) ),
inference(literals_permutation,[status(thm)],[c_0_3062]) ).
cnf(c_0_3062_1,axiom,
( ~ hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,sqrt,X1)),one_one(real)))
| hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X1),one_one(real))) ),
inference(literals_permutation,[status(thm)],[c_0_3062]) ).
cnf(c_0_3063_0,axiom,
( hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X1),zero_zero(real)))
| ~ hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,sqrt,X1)),zero_zero(real))) ),
inference(literals_permutation,[status(thm)],[c_0_3063]) ).
cnf(c_0_3063_1,axiom,
( ~ hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,sqrt,X1)),zero_zero(real)))
| hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X1),zero_zero(real))) ),
inference(literals_permutation,[status(thm)],[c_0_3063]) ).
cnf(c_0_3064_0,axiom,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X1),zero_zero(int)))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit0,X1)),zero_zero(int))) ),
inference(literals_permutation,[status(thm)],[c_0_3064]) ).
cnf(c_0_3064_1,axiom,
( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit0,X1)),zero_zero(int)))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X1),zero_zero(int))) ),
inference(literals_permutation,[status(thm)],[c_0_3064]) ).
cnf(c_0_3065_0,axiom,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X1),zero_zero(int)))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit1,X1)),zero_zero(int))) ),
inference(literals_permutation,[status(thm)],[c_0_3065]) ).
cnf(c_0_3065_1,axiom,
( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit1,X1)),zero_zero(int)))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X1),zero_zero(int))) ),
inference(literals_permutation,[status(thm)],[c_0_3065]) ).
cnf(c_0_3066_0,axiom,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(nat,X1,semiring_1_of_nat(X1),X2)),hAPP(nat,X1,semiring_1_of_nat(X1),X3)))
| ~ linordered_semidom(X1)
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3066]) ).
cnf(c_0_3066_1,axiom,
( ~ linordered_semidom(X1)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(nat,X1,semiring_1_of_nat(X1),X2)),hAPP(nat,X1,semiring_1_of_nat(X1),X3)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3066]) ).
cnf(c_0_3066_2,axiom,
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X2),X3))
| ~ linordered_semidom(X1)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(nat,X1,semiring_1_of_nat(X1),X2)),hAPP(nat,X1,semiring_1_of_nat(X1),X3))) ),
inference(literals_permutation,[status(thm)],[c_0_3066]) ).
cnf(c_0_3067_0,axiom,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(nat,X1,semiring_1_of_nat(X1),X2)),hAPP(nat,X1,semiring_1_of_nat(X1),X3)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X2),X3))
| ~ linordered_semidom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3067]) ).
cnf(c_0_3067_1,axiom,
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X2),X3))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(nat,X1,semiring_1_of_nat(X1),X2)),hAPP(nat,X1,semiring_1_of_nat(X1),X3)))
| ~ linordered_semidom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3067]) ).
cnf(c_0_3067_2,axiom,
( ~ linordered_semidom(X1)
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X2),X3))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(nat,X1,semiring_1_of_nat(X1),X2)),hAPP(nat,X1,semiring_1_of_nat(X1),X3))) ),
inference(literals_permutation,[status(thm)],[c_0_3067]) ).
cnf(c_0_3068_0,axiom,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(nat,X1,semiring_1_of_nat(X1),X2)),hAPP(nat,X1,semiring_1_of_nat(X1),X3)))
| ~ linordered_semidom(X1)
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3068]) ).
cnf(c_0_3068_1,axiom,
( ~ linordered_semidom(X1)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(nat,X1,semiring_1_of_nat(X1),X2)),hAPP(nat,X1,semiring_1_of_nat(X1),X3)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3068]) ).
cnf(c_0_3068_2,axiom,
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X2),X3))
| ~ linordered_semidom(X1)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(nat,X1,semiring_1_of_nat(X1),X2)),hAPP(nat,X1,semiring_1_of_nat(X1),X3))) ),
inference(literals_permutation,[status(thm)],[c_0_3068]) ).
cnf(c_0_3069_0,axiom,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X1),pls))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,bit1,X1)),pls)) ),
inference(literals_permutation,[status(thm)],[c_0_3069]) ).
cnf(c_0_3069_1,axiom,
( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,bit1,X1)),pls))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X1),pls)) ),
inference(literals_permutation,[status(thm)],[c_0_3069]) ).
cnf(c_0_3070_0,axiom,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X1),pls))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,bit0,X1)),pls)) ),
inference(literals_permutation,[status(thm)],[c_0_3070]) ).
cnf(c_0_3070_1,axiom,
( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,bit0,X1)),pls))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X1),pls)) ),
inference(literals_permutation,[status(thm)],[c_0_3070]) ).
cnf(c_0_3071_0,axiom,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X1),pls))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit0,X1)),pls)) ),
inference(literals_permutation,[status(thm)],[c_0_3071]) ).
cnf(c_0_3071_1,axiom,
( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit0,X1)),pls))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X1),pls)) ),
inference(literals_permutation,[status(thm)],[c_0_3071]) ).
cnf(c_0_3072_0,axiom,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X1),pls))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit1,X1)),pls)) ),
inference(literals_permutation,[status(thm)],[c_0_3072]) ).
cnf(c_0_3072_1,axiom,
( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit1,X1)),pls))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X1),pls)) ),
inference(literals_permutation,[status(thm)],[c_0_3072]) ).
cnf(c_0_3073_0,axiom,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(nat,int,semiring_1_of_nat(int),X1)),hAPP(nat,int,semiring_1_of_nat(int),X2)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3073]) ).
cnf(c_0_3073_1,axiom,
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(nat,int,semiring_1_of_nat(int),X1)),hAPP(nat,int,semiring_1_of_nat(int),X2))) ),
inference(literals_permutation,[status(thm)],[c_0_3073]) ).
cnf(c_0_3074_0,axiom,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(nat,int,semiring_1_of_nat(int),X1)),hAPP(nat,int,semiring_1_of_nat(int),X2)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3074]) ).
cnf(c_0_3074_1,axiom,
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(nat,int,semiring_1_of_nat(int),X1)),hAPP(nat,int,semiring_1_of_nat(int),X2))) ),
inference(literals_permutation,[status(thm)],[c_0_3074]) ).
cnf(c_0_3075_0,axiom,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(nat,int,semiring_1_of_nat(int),X1)),hAPP(nat,int,semiring_1_of_nat(int),X2)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3075]) ).
cnf(c_0_3075_1,axiom,
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(nat,int,semiring_1_of_nat(int),X1)),hAPP(nat,int,semiring_1_of_nat(int),X2))) ),
inference(literals_permutation,[status(thm)],[c_0_3075]) ).
cnf(c_0_3076_0,axiom,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(nat,int,semiring_1_of_nat(int),X1)),hAPP(nat,int,semiring_1_of_nat(int),X2)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3076]) ).
cnf(c_0_3076_1,axiom,
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(nat,int,semiring_1_of_nat(int),X1)),hAPP(nat,int,semiring_1_of_nat(int),X2))) ),
inference(literals_permutation,[status(thm)],[c_0_3076]) ).
cnf(c_0_3077_0,axiom,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,bit1,X1)),hAPP(int,int,bit0,X2)))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3077]) ).
cnf(c_0_3077_1,axiom,
( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X1),X2))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,bit1,X1)),hAPP(int,int,bit0,X2))) ),
inference(literals_permutation,[status(thm)],[c_0_3077]) ).
cnf(c_0_3078_0,axiom,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,bit1,X1)),hAPP(int,int,bit0,X2)))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3078]) ).
cnf(c_0_3078_1,axiom,
( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X1),X2))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,bit1,X1)),hAPP(int,int,bit0,X2))) ),
inference(literals_permutation,[status(thm)],[c_0_3078]) ).
cnf(c_0_3079_0,axiom,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit0,X1)),hAPP(int,int,bit1,X2)))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3079]) ).
cnf(c_0_3079_1,axiom,
( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X1),X2))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit0,X1)),hAPP(int,int,bit1,X2))) ),
inference(literals_permutation,[status(thm)],[c_0_3079]) ).
cnf(c_0_3080_0,axiom,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit0,X1)),hAPP(int,int,bit1,X2)))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3080]) ).
cnf(c_0_3080_1,axiom,
( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X1),X2))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit0,X1)),hAPP(int,int,bit1,X2))) ),
inference(literals_permutation,[status(thm)],[c_0_3080]) ).
cnf(c_0_3081_0,axiom,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,bit0,X1)),hAPP(int,int,bit1,X2)))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3081]) ).
cnf(c_0_3081_1,axiom,
( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X1),X2))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,bit0,X1)),hAPP(int,int,bit1,X2))) ),
inference(literals_permutation,[status(thm)],[c_0_3081]) ).
cnf(c_0_3082_0,axiom,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,bit0,X1)),hAPP(int,int,bit1,X2)))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3082]) ).
cnf(c_0_3082_1,axiom,
( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X1),X2))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,bit0,X1)),hAPP(int,int,bit1,X2))) ),
inference(literals_permutation,[status(thm)],[c_0_3082]) ).
cnf(c_0_3083_0,axiom,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,bit0,X1)),hAPP(int,int,bit0,X2)))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3083]) ).
cnf(c_0_3083_1,axiom,
( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X1),X2))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,bit0,X1)),hAPP(int,int,bit0,X2))) ),
inference(literals_permutation,[status(thm)],[c_0_3083]) ).
cnf(c_0_3084_0,axiom,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,bit0,X1)),hAPP(int,int,bit0,X2)))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3084]) ).
cnf(c_0_3084_1,axiom,
( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X1),X2))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,bit0,X1)),hAPP(int,int,bit0,X2))) ),
inference(literals_permutation,[status(thm)],[c_0_3084]) ).
cnf(c_0_3085_0,axiom,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,bit1,X1)),hAPP(int,int,bit1,X2)))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3085]) ).
cnf(c_0_3085_1,axiom,
( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X1),X2))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,bit1,X1)),hAPP(int,int,bit1,X2))) ),
inference(literals_permutation,[status(thm)],[c_0_3085]) ).
cnf(c_0_3086_0,axiom,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,bit1,X1)),hAPP(int,int,bit1,X2)))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3086]) ).
cnf(c_0_3086_1,axiom,
( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X1),X2))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,bit1,X1)),hAPP(int,int,bit1,X2))) ),
inference(literals_permutation,[status(thm)],[c_0_3086]) ).
cnf(c_0_3087_0,axiom,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit1,X1)),hAPP(int,int,bit0,X2)))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3087]) ).
cnf(c_0_3087_1,axiom,
( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X1),X2))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit1,X1)),hAPP(int,int,bit0,X2))) ),
inference(literals_permutation,[status(thm)],[c_0_3087]) ).
cnf(c_0_3088_0,axiom,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit1,X1)),hAPP(int,int,bit0,X2)))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3088]) ).
cnf(c_0_3088_1,axiom,
( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X1),X2))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit1,X1)),hAPP(int,int,bit0,X2))) ),
inference(literals_permutation,[status(thm)],[c_0_3088]) ).
cnf(c_0_3089_0,axiom,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit0,X1)),hAPP(int,int,bit0,X2)))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3089]) ).
cnf(c_0_3089_1,axiom,
( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X1),X2))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit0,X1)),hAPP(int,int,bit0,X2))) ),
inference(literals_permutation,[status(thm)],[c_0_3089]) ).
cnf(c_0_3090_0,axiom,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit0,X1)),hAPP(int,int,bit0,X2)))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3090]) ).
cnf(c_0_3090_1,axiom,
( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X1),X2))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit0,X1)),hAPP(int,int,bit0,X2))) ),
inference(literals_permutation,[status(thm)],[c_0_3090]) ).
cnf(c_0_3091_0,axiom,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit1,X1)),hAPP(int,int,bit1,X2)))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3091]) ).
cnf(c_0_3091_1,axiom,
( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X1),X2))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit1,X1)),hAPP(int,int,bit1,X2))) ),
inference(literals_permutation,[status(thm)],[c_0_3091]) ).
cnf(c_0_3092_0,axiom,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit1,X1)),hAPP(int,int,bit1,X2)))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3092]) ).
cnf(c_0_3092_1,axiom,
( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X1),X2))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit1,X1)),hAPP(int,int,bit1,X2))) ),
inference(literals_permutation,[status(thm)],[c_0_3092]) ).
cnf(c_0_3093_0,axiom,
( ~ ord(X1)
| ~ hBOOL(hAPP(fun(X2,X1),bool,hAPP(fun(X2,X1),fun(fun(X2,X1),bool),ord_less(fun(X2,X1)),X3),X4))
| ~ hBOOL(hAPP(fun(X2,X1),bool,hAPP(fun(X2,X1),fun(fun(X2,X1),bool),ord_less_eq(fun(X2,X1)),X4),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3093]) ).
cnf(c_0_3093_1,axiom,
( ~ hBOOL(hAPP(fun(X2,X1),bool,hAPP(fun(X2,X1),fun(fun(X2,X1),bool),ord_less(fun(X2,X1)),X3),X4))
| ~ ord(X1)
| ~ hBOOL(hAPP(fun(X2,X1),bool,hAPP(fun(X2,X1),fun(fun(X2,X1),bool),ord_less_eq(fun(X2,X1)),X4),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3093]) ).
cnf(c_0_3093_2,axiom,
( ~ hBOOL(hAPP(fun(X2,X1),bool,hAPP(fun(X2,X1),fun(fun(X2,X1),bool),ord_less_eq(fun(X2,X1)),X4),X3))
| ~ hBOOL(hAPP(fun(X2,X1),bool,hAPP(fun(X2,X1),fun(fun(X2,X1),bool),ord_less(fun(X2,X1)),X3),X4))
| ~ ord(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3093]) ).
cnf(c_0_3094_0,axiom,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X4))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),sk1_esk27_4(X1,X4,X2,X3)))
| ~ dense_linorder(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3094]) ).
cnf(c_0_3094_1,axiom,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),sk1_esk27_4(X1,X4,X2,X3)))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X4))
| ~ dense_linorder(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3094]) ).
cnf(c_0_3094_2,axiom,
( ~ dense_linorder(X1)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),sk1_esk27_4(X1,X4,X2,X3)))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X4))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3094]) ).
cnf(c_0_3094_3,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| ~ dense_linorder(X1)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),sk1_esk27_4(X1,X4,X2,X3)))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_3094]) ).
cnf(c_0_3095_0,axiom,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),X2))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),number_number_of(nat,X1)),number_number_of(nat,X2)))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3095]) ).
cnf(c_0_3095_1,axiom,
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),number_number_of(nat,X1)),number_number_of(nat,X2)))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),X2))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3095]) ).
cnf(c_0_3095_2,axiom,
( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X1),X2))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),number_number_of(nat,X1)),number_number_of(nat,X2)))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3095]) ).
cnf(c_0_3096_0,axiom,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X4))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X4),X3))
| ~ order(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3096]) ).
cnf(c_0_3096_1,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X4))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X4),X3))
| ~ order(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3096]) ).
cnf(c_0_3096_2,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X4),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X4))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| ~ order(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3096]) ).
cnf(c_0_3096_3,axiom,
( ~ order(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X4),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X4))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3096]) ).
cnf(c_0_3097_0,axiom,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X4),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X4))
| ~ preorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3097]) ).
cnf(c_0_3097_1,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X4),X3))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X4))
| ~ preorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3097]) ).
cnf(c_0_3097_2,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X4))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X4),X3))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| ~ preorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3097]) ).
cnf(c_0_3097_3,axiom,
( ~ preorder(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X4))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X4),X3))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3097]) ).
cnf(c_0_3098_0,axiom,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X4))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X4),X3))
| ~ order(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3098]) ).
cnf(c_0_3098_1,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X4))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X4),X3))
| ~ order(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3098]) ).
cnf(c_0_3098_2,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X4),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X4))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| ~ order(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3098]) ).
cnf(c_0_3098_3,axiom,
( ~ order(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X4),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X4))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3098]) ).
cnf(c_0_3099_0,axiom,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X4),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X4))
| ~ preorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3099]) ).
cnf(c_0_3099_1,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X4),X3))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X4))
| ~ preorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3099]) ).
cnf(c_0_3099_2,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X4))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X4),X3))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| ~ preorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3099]) ).
cnf(c_0_3099_3,axiom,
( ~ preorder(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X4))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X4),X3))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3099]) ).
cnf(c_0_3100_0,axiom,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X4),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X4))
| ~ preorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3100]) ).
cnf(c_0_3100_1,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X4),X3))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X4))
| ~ preorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3100]) ).
cnf(c_0_3100_2,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X4))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X4),X3))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| ~ preorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3100]) ).
cnf(c_0_3100_3,axiom,
( ~ preorder(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X4))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X4),X3))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3100]) ).
cnf(c_0_3101_0,axiom,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X4))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X4),X3))
| ~ order(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3101]) ).
cnf(c_0_3101_1,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X4))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X4),X3))
| ~ order(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3101]) ).
cnf(c_0_3101_2,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X4),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X4))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| ~ order(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3101]) ).
cnf(c_0_3101_3,axiom,
( ~ order(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X4),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X4))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3101]) ).
cnf(c_0_3102_0,axiom,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X4),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X4))
| ~ preorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3102]) ).
cnf(c_0_3102_1,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X4),X3))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X4))
| ~ preorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3102]) ).
cnf(c_0_3102_2,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X4))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X4),X3))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
| ~ preorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3102]) ).
cnf(c_0_3102_3,axiom,
( ~ preorder(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X4))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X4),X3))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3102]) ).
cnf(c_0_3103_0,axiom,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X4))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X4),X3))
| ~ order(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3103]) ).
cnf(c_0_3103_1,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X4))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X4),X3))
| ~ order(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3103]) ).
cnf(c_0_3103_2,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X4),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X4))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
| ~ order(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3103]) ).
cnf(c_0_3103_3,axiom,
( ~ order(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X4),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X4))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3103]) ).
cnf(c_0_3104_0,axiom,
( hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),sk1_esk23_2(X2,X1)),X1))
| ~ hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X1))
| ~ hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3104]) ).
cnf(c_0_3104_1,axiom,
( ~ hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X1))
| hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),sk1_esk23_2(X2,X1)),X1))
| ~ hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3104]) ).
cnf(c_0_3104_2,axiom,
( ~ hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X2))
| ~ hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X1))
| hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),sk1_esk23_2(X2,X1)),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_3104]) ).
cnf(c_0_3105_0,axiom,
( hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),sk1_esk23_2(X2,X1)),X2))
| ~ hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X1))
| ~ hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3105]) ).
cnf(c_0_3105_1,axiom,
( ~ hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X1))
| hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),sk1_esk23_2(X2,X1)),X2))
| ~ hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3105]) ).
cnf(c_0_3105_2,axiom,
( ~ hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X2))
| ~ hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X1))
| hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),sk1_esk23_2(X2,X1)),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3105]) ).
cnf(c_0_3106_0,axiom,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),number_number_of(nat,X1)),number_number_of(nat,X2)))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X1),X2))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3106]) ).
cnf(c_0_3106_1,axiom,
( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X1),X2))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),number_number_of(nat,X1)),number_number_of(nat,X2)))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3106]) ).
cnf(c_0_3106_2,axiom,
( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),X2))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X1),X2))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),number_number_of(nat,X1)),number_number_of(nat,X2))) ),
inference(literals_permutation,[status(thm)],[c_0_3106]) ).
cnf(c_0_3107_0,axiom,
( hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),sk1_esk23_2(X2,X1)))
| ~ hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X1))
| ~ hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3107]) ).
cnf(c_0_3107_1,axiom,
( ~ hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X1))
| hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),sk1_esk23_2(X2,X1)))
| ~ hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3107]) ).
cnf(c_0_3107_2,axiom,
( ~ hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X2))
| ~ hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X1))
| hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),sk1_esk23_2(X2,X1))) ),
inference(literals_permutation,[status(thm)],[c_0_3107]) ).
cnf(c_0_3108_0,axiom,
( hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),sk1_esk5_2(X2,X1)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X1))
| ~ hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3108]) ).
cnf(c_0_3108_1,axiom,
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X1))
| hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),sk1_esk5_2(X2,X1)))
| ~ hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3108]) ).
cnf(c_0_3108_2,axiom,
( ~ hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X2))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X1))
| hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),sk1_esk5_2(X2,X1))) ),
inference(literals_permutation,[status(thm)],[c_0_3108]) ).
cnf(c_0_3109_0,axiom,
( hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),sk1_esk4_2(X2,X1)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X1))
| ~ hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3109]) ).
cnf(c_0_3109_1,axiom,
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X1))
| hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),sk1_esk4_2(X2,X1)))
| ~ hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3109]) ).
cnf(c_0_3109_2,axiom,
( ~ hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X2))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X1))
| hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),sk1_esk4_2(X2,X1))) ),
inference(literals_permutation,[status(thm)],[c_0_3109]) ).
cnf(c_0_3110_0,axiom,
( hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X1),X2))
| ~ hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X3),X2))
| ~ hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X1),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3110]) ).
cnf(c_0_3110_1,axiom,
( ~ hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X3),X2))
| hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X1),X2))
| ~ hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X1),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3110]) ).
cnf(c_0_3110_2,axiom,
( ~ hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X1),X3))
| ~ hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X3),X2))
| hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3110]) ).
cnf(c_0_3111_0,axiom,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X3),X2))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3111]) ).
cnf(c_0_3111_1,axiom,
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X3),X2))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3111]) ).
cnf(c_0_3111_2,axiom,
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X3))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X3),X2))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3111]) ).
cnf(c_0_3112_0,axiom,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X1),X2))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X3),X2))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X1),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3112]) ).
cnf(c_0_3112_1,axiom,
( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X3),X2))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X1),X2))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X1),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3112]) ).
cnf(c_0_3112_2,axiom,
( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X1),X3))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X3),X2))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3112]) ).
cnf(c_0_3113_0,axiom,
( X3 = X2
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X1,X2),X3))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X1,X2),X3))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X1,X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3113]) ).
cnf(c_0_3113_1,axiom,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X1,X2),X3))
| X3 = X2
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X1,X2),X3))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X1,X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3113]) ).
cnf(c_0_3113_2,axiom,
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X1,X2),X3))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X1,X2),X3))
| X3 = X2
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X1,X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3113]) ).
cnf(c_0_3113_3,axiom,
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X1,X2),X3))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X1,X2),X3))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X1,X2),X3))
| X3 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_3113]) ).
cnf(c_0_3114_0,axiom,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,plus_plus(X1,X2),X2)),zero_zero(X1)))
| ~ linord219039673up_add(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),zero_zero(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_3114]) ).
cnf(c_0_3114_1,axiom,
( ~ linord219039673up_add(X1)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,plus_plus(X1,X2),X2)),zero_zero(X1)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),zero_zero(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_3114]) ).
cnf(c_0_3114_2,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),zero_zero(X1)))
| ~ linord219039673up_add(X1)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,plus_plus(X1,X2),X2)),zero_zero(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_3114]) ).
cnf(c_0_3115_0,axiom,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,plus_plus(X1,X2),X2)),zero_zero(X1)))
| ~ linord219039673up_add(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),zero_zero(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_3115]) ).
cnf(c_0_3115_1,axiom,
( ~ linord219039673up_add(X1)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,plus_plus(X1,X2),X2)),zero_zero(X1)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),zero_zero(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_3115]) ).
cnf(c_0_3115_2,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),zero_zero(X1)))
| ~ linord219039673up_add(X1)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,plus_plus(X1,X2),X2)),zero_zero(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_3115]) ).
cnf(c_0_3116_0,axiom,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,plus_plus(X1,X2),X2)),zero_zero(X1)))
| ~ linordered_idom(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),zero_zero(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_3116]) ).
cnf(c_0_3116_1,axiom,
( ~ linordered_idom(X1)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,plus_plus(X1,X2),X2)),zero_zero(X1)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),zero_zero(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_3116]) ).
cnf(c_0_3116_2,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),zero_zero(X1)))
| ~ linordered_idom(X1)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,plus_plus(X1,X2),X2)),zero_zero(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_3116]) ).
cnf(c_0_3117_0,axiom,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,plus_plus(int,X1),one_one(int))),X2))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3117]) ).
cnf(c_0_3117_1,axiom,
( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X1),X2))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,plus_plus(int,X1),one_one(int))),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3117]) ).
cnf(c_0_3118_0,axiom,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,plus_plus(int,X1),one_one(int))),X2))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3118]) ).
cnf(c_0_3118_1,axiom,
( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X1),X2))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,plus_plus(int,X1),one_one(int))),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3118]) ).
cnf(c_0_3119_0,axiom,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,bit1,pls)),X2))
| ~ linordered_idom(X1)
| ~ number_ring(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),one_one(X1)),number_number_of(X1,X2))) ),
inference(literals_permutation,[status(thm)],[c_0_3119]) ).
cnf(c_0_3119_1,axiom,
( ~ linordered_idom(X1)
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,bit1,pls)),X2))
| ~ number_ring(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),one_one(X1)),number_number_of(X1,X2))) ),
inference(literals_permutation,[status(thm)],[c_0_3119]) ).
cnf(c_0_3119_2,axiom,
( ~ number_ring(X1)
| ~ linordered_idom(X1)
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,bit1,pls)),X2))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),one_one(X1)),number_number_of(X1,X2))) ),
inference(literals_permutation,[status(thm)],[c_0_3119]) ).
cnf(c_0_3119_3,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),one_one(X1)),number_number_of(X1,X2)))
| ~ number_ring(X1)
| ~ linordered_idom(X1)
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,bit1,pls)),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3119]) ).
cnf(c_0_3120_0,axiom,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit1,pls)),X2))
| ~ linordered_idom(X1)
| ~ number_ring(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),one_one(X1)),number_number_of(X1,X2))) ),
inference(literals_permutation,[status(thm)],[c_0_3120]) ).
cnf(c_0_3120_1,axiom,
( ~ linordered_idom(X1)
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit1,pls)),X2))
| ~ number_ring(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),one_one(X1)),number_number_of(X1,X2))) ),
inference(literals_permutation,[status(thm)],[c_0_3120]) ).
cnf(c_0_3120_2,axiom,
( ~ number_ring(X1)
| ~ linordered_idom(X1)
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit1,pls)),X2))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),one_one(X1)),number_number_of(X1,X2))) ),
inference(literals_permutation,[status(thm)],[c_0_3120]) ).
cnf(c_0_3120_3,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),one_one(X1)),number_number_of(X1,X2)))
| ~ number_ring(X1)
| ~ linordered_idom(X1)
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit1,pls)),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3120]) ).
cnf(c_0_3121_0,axiom,
( hBOOL(hAPP(int,bool,X3,X2))
| hBOOL(hAPP(int,bool,X3,sk1_esk1_3(X3,X1,X2)))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,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_3121]) ).
cnf(c_0_3121_1,axiom,
( hBOOL(hAPP(int,bool,X3,sk1_esk1_3(X3,X1,X2)))
| hBOOL(hAPP(int,bool,X3,X2))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,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_3121]) ).
cnf(c_0_3121_2,axiom,
( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,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_3121]) ).
cnf(c_0_3121_3,axiom,
( ~ hBOOL(hAPP(int,bool,X3,hAPP(int,int,plus_plus(int,X1),one_one(int))))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,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_3121]) ).
cnf(c_0_3122_0,axiom,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),number_number_of(int,hAPP(int,int,bit0,X1))))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),number_number_of(int,X1))) ),
inference(literals_permutation,[status(thm)],[c_0_3122]) ).
cnf(c_0_3122_1,axiom,
( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),number_number_of(int,X1)))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),number_number_of(int,hAPP(int,int,bit0,X1)))) ),
inference(literals_permutation,[status(thm)],[c_0_3122]) ).
cnf(c_0_3123_0,axiom,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),number_number_of(int,hAPP(int,int,bit1,X1))))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),number_number_of(int,X1))) ),
inference(literals_permutation,[status(thm)],[c_0_3123]) ).
cnf(c_0_3123_1,axiom,
( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),number_number_of(int,X1)))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),number_number_of(int,hAPP(int,int,bit1,X1)))) ),
inference(literals_permutation,[status(thm)],[c_0_3123]) ).
cnf(c_0_3124_0,axiom,
( hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,sqrt,X1)),one_one(real)))
| ~ hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X1),one_one(real))) ),
inference(literals_permutation,[status(thm)],[c_0_3124]) ).
cnf(c_0_3124_1,axiom,
( ~ hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X1),one_one(real)))
| hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,sqrt,X1)),one_one(real))) ),
inference(literals_permutation,[status(thm)],[c_0_3124]) ).
cnf(c_0_3125_0,axiom,
( hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,sqrt,X1)),zero_zero(real)))
| ~ hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X1),zero_zero(real))) ),
inference(literals_permutation,[status(thm)],[c_0_3125]) ).
cnf(c_0_3125_1,axiom,
( ~ hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X1),zero_zero(real)))
| hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,sqrt,X1)),zero_zero(real))) ),
inference(literals_permutation,[status(thm)],[c_0_3125]) ).
cnf(c_0_3126_0,axiom,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit0,X1)),zero_zero(int)))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X1),zero_zero(int))) ),
inference(literals_permutation,[status(thm)],[c_0_3126]) ).
cnf(c_0_3126_1,axiom,
( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X1),zero_zero(int)))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit0,X1)),zero_zero(int))) ),
inference(literals_permutation,[status(thm)],[c_0_3126]) ).
cnf(c_0_3127_0,axiom,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit1,X1)),zero_zero(int)))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X1),zero_zero(int))) ),
inference(literals_permutation,[status(thm)],[c_0_3127]) ).
cnf(c_0_3127_1,axiom,
( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X1),zero_zero(int)))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit1,X1)),zero_zero(int))) ),
inference(literals_permutation,[status(thm)],[c_0_3127]) ).
cnf(c_0_3128_0,axiom,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,bit1,X1)),pls))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X1),pls)) ),
inference(literals_permutation,[status(thm)],[c_0_3128]) ).
cnf(c_0_3128_1,axiom,
( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X1),pls))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,bit1,X1)),pls)) ),
inference(literals_permutation,[status(thm)],[c_0_3128]) ).
cnf(c_0_3129_0,axiom,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,bit0,X1)),pls))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X1),pls)) ),
inference(literals_permutation,[status(thm)],[c_0_3129]) ).
cnf(c_0_3129_1,axiom,
( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X1),pls))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,bit0,X1)),pls)) ),
inference(literals_permutation,[status(thm)],[c_0_3129]) ).
cnf(c_0_3130_0,axiom,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit0,X1)),pls))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X1),pls)) ),
inference(literals_permutation,[status(thm)],[c_0_3130]) ).
cnf(c_0_3130_1,axiom,
( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X1),pls))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit0,X1)),pls)) ),
inference(literals_permutation,[status(thm)],[c_0_3130]) ).
cnf(c_0_3131_0,axiom,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit1,X1)),pls))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X1),pls)) ),
inference(literals_permutation,[status(thm)],[c_0_3131]) ).
cnf(c_0_3131_1,axiom,
( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X1),pls))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit1,X1)),pls)) ),
inference(literals_permutation,[status(thm)],[c_0_3131]) ).
cnf(c_0_3132_0,axiom,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X2))
| ~ linord219039673up_add(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),hAPP(X1,X1,plus_plus(X1,X2),X2))) ),
inference(literals_permutation,[status(thm)],[c_0_3132]) ).
cnf(c_0_3132_1,axiom,
( ~ linord219039673up_add(X1)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X2))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),hAPP(X1,X1,plus_plus(X1,X2),X2))) ),
inference(literals_permutation,[status(thm)],[c_0_3132]) ).
cnf(c_0_3132_2,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),hAPP(X1,X1,plus_plus(X1,X2),X2)))
| ~ linord219039673up_add(X1)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3132]) ).
cnf(c_0_3133_0,axiom,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X2))
| ~ linord219039673up_add(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),hAPP(X1,X1,plus_plus(X1,X2),X2))) ),
inference(literals_permutation,[status(thm)],[c_0_3133]) ).
cnf(c_0_3133_1,axiom,
( ~ linord219039673up_add(X1)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X2))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),hAPP(X1,X1,plus_plus(X1,X2),X2))) ),
inference(literals_permutation,[status(thm)],[c_0_3133]) ).
cnf(c_0_3133_2,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),hAPP(X1,X1,plus_plus(X1,X2),X2)))
| ~ linord219039673up_add(X1)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3133]) ).
cnf(c_0_3134_0,axiom,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X1))
| number_number_of(nat,X2) = zero_zero(nat)
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,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_3134]) ).
cnf(c_0_3134_1,axiom,
( number_number_of(nat,X2) = zero_zero(nat)
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X1))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,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_3134]) ).
cnf(c_0_3134_2,axiom,
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,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(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_3134]) ).
cnf(c_0_3137_0,axiom,
( hAPP(X1,X1,plus_plus(X1,number_number_of(X1,X2)),number_number_of(X1,X3)) = number_number_of(X1,hAPP(int,int,plus_plus(int,X2),X3))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),X3))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),X2))
| ~ number_semiring(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3137]) ).
cnf(c_0_3137_1,axiom,
( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),X3))
| hAPP(X1,X1,plus_plus(X1,number_number_of(X1,X2)),number_number_of(X1,X3)) = number_number_of(X1,hAPP(int,int,plus_plus(int,X2),X3))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),X2))
| ~ number_semiring(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3137]) ).
cnf(c_0_3137_2,axiom,
( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),X2))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),X3))
| hAPP(X1,X1,plus_plus(X1,number_number_of(X1,X2)),number_number_of(X1,X3)) = number_number_of(X1,hAPP(int,int,plus_plus(int,X2),X3))
| ~ number_semiring(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3137]) ).
cnf(c_0_3137_3,axiom,
( ~ number_semiring(X1)
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),X2))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),X3))
| hAPP(X1,X1,plus_plus(X1,number_number_of(X1,X2)),number_number_of(X1,X3)) = number_number_of(X1,hAPP(int,int,plus_plus(int,X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3137]) ).
cnf(c_0_3138_0,axiom,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X1),pls))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X1),X2))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),number_number_of(nat,X1)),number_number_of(nat,X2))) ),
inference(literals_permutation,[status(thm)],[c_0_3138]) ).
cnf(c_0_3138_1,axiom,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X1),X2))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X1),pls))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),number_number_of(nat,X1)),number_number_of(nat,X2))) ),
inference(literals_permutation,[status(thm)],[c_0_3138]) ).
cnf(c_0_3138_2,axiom,
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),number_number_of(nat,X1)),number_number_of(nat,X2)))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X1),X2))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X1),pls)) ),
inference(literals_permutation,[status(thm)],[c_0_3138]) ).
cnf(c_0_3139_0,axiom,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X1))
| X2 = zero_zero(nat)
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,power_power(nat,X1),X2))) ),
inference(literals_permutation,[status(thm)],[c_0_3139]) ).
cnf(c_0_3139_1,axiom,
( X2 = zero_zero(nat)
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X1))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,power_power(nat,X1),X2))) ),
inference(literals_permutation,[status(thm)],[c_0_3139]) ).
cnf(c_0_3139_2,axiom,
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,power_power(nat,X1),X2)))
| X2 = zero_zero(nat)
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_3139]) ).
cnf(c_0_3140_0,axiom,
( X1 = zero_zero(nat)
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X2))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,power_power(nat,X2),X1))) ),
inference(literals_permutation,[status(thm)],[c_0_3140]) ).
cnf(c_0_3140_1,axiom,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X2))
| X1 = zero_zero(nat)
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,power_power(nat,X2),X1))) ),
inference(literals_permutation,[status(thm)],[c_0_3140]) ).
cnf(c_0_3140_2,axiom,
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,power_power(nat,X2),X1)))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X2))
| X1 = zero_zero(nat) ),
inference(literals_permutation,[status(thm)],[c_0_3140]) ).
cnf(c_0_3141_0,axiom,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),number_number_of(nat,X1)),number_number_of(nat,X2)))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X1),X2))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3141]) ).
cnf(c_0_3141_1,axiom,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X1),X2))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),number_number_of(nat,X1)),number_number_of(nat,X2)))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3141]) ).
cnf(c_0_3141_2,axiom,
( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X1),X2))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X1),X2))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),number_number_of(nat,X1)),number_number_of(nat,X2))) ),
inference(literals_permutation,[status(thm)],[c_0_3141]) ).
cnf(c_0_3142_0,axiom,
( X1 = X2
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X1),X2))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X1),hAPP(int,int,plus_plus(int,X2),one_one(int)))) ),
inference(literals_permutation,[status(thm)],[c_0_3142]) ).
cnf(c_0_3142_1,axiom,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X1),X2))
| X1 = X2
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X1),hAPP(int,int,plus_plus(int,X2),one_one(int)))) ),
inference(literals_permutation,[status(thm)],[c_0_3142]) ).
cnf(c_0_3142_2,axiom,
( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X1),hAPP(int,int,plus_plus(int,X2),one_one(int))))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X1),X2))
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_3142]) ).
cnf(c_0_3143_0,axiom,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X1),X2))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X1),hAPP(int,int,plus_plus(int,X2),one_one(int)))) ),
inference(literals_permutation,[status(thm)],[c_0_3143]) ).
cnf(c_0_3143_1,axiom,
( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X1),hAPP(int,int,plus_plus(int,X2),one_one(int))))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3143]) ).
cnf(c_0_3144_0,axiom,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X2))
| ~ preorder(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3144]) ).
cnf(c_0_3144_1,axiom,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X2))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| ~ preorder(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3144]) ).
cnf(c_0_3144_2,axiom,
( ~ preorder(X1)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X2))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3144]) ).
cnf(c_0_3144_3,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
| ~ preorder(X1)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X2))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3144]) ).
cnf(c_0_3145_0,axiom,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X2))
| ~ linordered_semidom(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),hAPP(nat,X1,semiring_1_of_nat(X1),X2))) ),
inference(literals_permutation,[status(thm)],[c_0_3145]) ).
cnf(c_0_3145_1,axiom,
( ~ linordered_semidom(X1)
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X2))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),hAPP(nat,X1,semiring_1_of_nat(X1),X2))) ),
inference(literals_permutation,[status(thm)],[c_0_3145]) ).
cnf(c_0_3145_2,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),hAPP(nat,X1,semiring_1_of_nat(X1),X2)))
| ~ linordered_semidom(X1)
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3145]) ).
cnf(c_0_3146_0,axiom,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),number_number_of(X1,X2)),one_one(X1)))
| ~ linordered_idom(X1)
| ~ number_ring(X1)
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X2),hAPP(int,int,bit1,pls))) ),
inference(literals_permutation,[status(thm)],[c_0_3146]) ).
cnf(c_0_3146_1,axiom,
( ~ linordered_idom(X1)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),number_number_of(X1,X2)),one_one(X1)))
| ~ number_ring(X1)
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X2),hAPP(int,int,bit1,pls))) ),
inference(literals_permutation,[status(thm)],[c_0_3146]) ).
cnf(c_0_3146_2,axiom,
( ~ number_ring(X1)
| ~ linordered_idom(X1)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),number_number_of(X1,X2)),one_one(X1)))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X2),hAPP(int,int,bit1,pls))) ),
inference(literals_permutation,[status(thm)],[c_0_3146]) ).
cnf(c_0_3146_3,axiom,
( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X2),hAPP(int,int,bit1,pls)))
| ~ number_ring(X1)
| ~ linordered_idom(X1)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),number_number_of(X1,X2)),one_one(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_3146]) ).
cnf(c_0_3147_0,axiom,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),number_number_of(X1,X2)),one_one(X1)))
| ~ linordered_idom(X1)
| ~ number_ring(X1)
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X2),hAPP(int,int,bit1,pls))) ),
inference(literals_permutation,[status(thm)],[c_0_3147]) ).
cnf(c_0_3147_1,axiom,
( ~ linordered_idom(X1)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),number_number_of(X1,X2)),one_one(X1)))
| ~ number_ring(X1)
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X2),hAPP(int,int,bit1,pls))) ),
inference(literals_permutation,[status(thm)],[c_0_3147]) ).
cnf(c_0_3147_2,axiom,
( ~ number_ring(X1)
| ~ linordered_idom(X1)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),number_number_of(X1,X2)),one_one(X1)))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X2),hAPP(int,int,bit1,pls))) ),
inference(literals_permutation,[status(thm)],[c_0_3147]) ).
cnf(c_0_3147_3,axiom,
( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X2),hAPP(int,int,bit1,pls)))
| ~ number_ring(X1)
| ~ linordered_idom(X1)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),number_number_of(X1,X2)),one_one(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_3147]) ).
cnf(c_0_3148_0,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(nat,X1,semiring_1_of_nat(X1),X2)),zero_zero(X1)))
| ~ linordered_semidom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3148]) ).
cnf(c_0_3148_1,axiom,
( ~ linordered_semidom(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(nat,X1,semiring_1_of_nat(X1),X2)),zero_zero(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_3148]) ).
cnf(c_0_3149_0,axiom,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X1))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X1))
| ~ hBOOL(X2)
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_3149]) ).
cnf(c_0_3149_1,axiom,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X1))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X1))
| ~ hBOOL(X2)
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_3149]) ).
cnf(c_0_3149_2,axiom,
( ~ hBOOL(X2)
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X1))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X1))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_3149]) ).
cnf(c_0_3149_3,axiom,
( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X1))
| ~ hBOOL(X2)
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X1))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_3149]) ).
cnf(c_0_3150_0,axiom,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X1))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X1))
| ~ hBOOL(X2)
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_3150]) ).
cnf(c_0_3150_1,axiom,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X1))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X1))
| ~ hBOOL(X2)
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_3150]) ).
cnf(c_0_3150_2,axiom,
( ~ hBOOL(X2)
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X1))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X1))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_3150]) ).
cnf(c_0_3150_3,axiom,
( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X1))
| ~ hBOOL(X2)
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X1))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_3150]) ).
cnf(c_0_3151_0,axiom,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X1))
| hBOOL(X2)
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X1))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_3151]) ).
cnf(c_0_3151_1,axiom,
( hBOOL(X2)
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X1))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X1))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_3151]) ).
cnf(c_0_3151_2,axiom,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X1))
| hBOOL(X2)
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X1))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_3151]) ).
cnf(c_0_3151_3,axiom,
( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X1))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X1))
| hBOOL(X2)
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_3151]) ).
cnf(c_0_3152_0,axiom,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X1))
| hBOOL(X2)
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X1))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_3152]) ).
cnf(c_0_3152_1,axiom,
( hBOOL(X2)
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X1))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X1))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_3152]) ).
cnf(c_0_3152_2,axiom,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X1))
| hBOOL(X2)
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X1))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_3152]) ).
cnf(c_0_3152_3,axiom,
( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X1))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X1))
| hBOOL(X2)
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_3152]) ).
cnf(c_0_3153_0,axiom,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X1))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(nat,int,semiring_1_of_nat(int),X1))) ),
inference(literals_permutation,[status(thm)],[c_0_3153]) ).
cnf(c_0_3153_1,axiom,
( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(nat,int,semiring_1_of_nat(int),X1)))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_3153]) ).
cnf(c_0_3154_0,axiom,
( hBOOL(hAPP(fun(X2,X1),bool,hAPP(fun(X2,X1),fun(fun(X2,X1),bool),ord_less_eq(fun(X2,X1)),X3),X4))
| ~ ord(X1)
| ~ hBOOL(hAPP(fun(X2,X1),bool,hAPP(fun(X2,X1),fun(fun(X2,X1),bool),ord_less(fun(X2,X1)),X3),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_3154]) ).
cnf(c_0_3154_1,axiom,
( ~ ord(X1)
| hBOOL(hAPP(fun(X2,X1),bool,hAPP(fun(X2,X1),fun(fun(X2,X1),bool),ord_less_eq(fun(X2,X1)),X3),X4))
| ~ hBOOL(hAPP(fun(X2,X1),bool,hAPP(fun(X2,X1),fun(fun(X2,X1),bool),ord_less(fun(X2,X1)),X3),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_3154]) ).
cnf(c_0_3154_2,axiom,
( ~ hBOOL(hAPP(fun(X2,X1),bool,hAPP(fun(X2,X1),fun(fun(X2,X1),bool),ord_less(fun(X2,X1)),X3),X4))
| ~ ord(X1)
| hBOOL(hAPP(fun(X2,X1),bool,hAPP(fun(X2,X1),fun(fun(X2,X1),bool),ord_less_eq(fun(X2,X1)),X3),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_3154]) ).
cnf(c_0_3155_0,axiom,
( hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),one_one(real)),X1))
| ~ hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),one_one(real)),hAPP(real,real,sqrt,X1))) ),
inference(literals_permutation,[status(thm)],[c_0_3155]) ).
cnf(c_0_3155_1,axiom,
( ~ hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),one_one(real)),hAPP(real,real,sqrt,X1)))
| hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),one_one(real)),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_3155]) ).
cnf(c_0_3156_0,axiom,
( hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X1))
| ~ hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(real,real,sqrt,X1))) ),
inference(literals_permutation,[status(thm)],[c_0_3156]) ).
cnf(c_0_3156_1,axiom,
( ~ hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(real,real,sqrt,X1)))
| hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_3156]) ).
cnf(c_0_3157_0,axiom,
( X1 = zero_zero(nat)
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(nat,int,semiring_1_of_nat(int),X1)),zero_zero(int))) ),
inference(literals_permutation,[status(thm)],[c_0_3157]) ).
cnf(c_0_3157_1,axiom,
( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(nat,int,semiring_1_of_nat(int),X1)),zero_zero(int)))
| X1 = zero_zero(nat) ),
inference(literals_permutation,[status(thm)],[c_0_3157]) ).
cnf(c_0_3159_0,axiom,
( ti(X1,X2) = zero_zero(X1)
| ~ ordere216010020id_add(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X2))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X3))
| hAPP(X1,X1,plus_plus(X1,X2),X3) != zero_zero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3159]) ).
cnf(c_0_3159_1,axiom,
( ~ ordere216010020id_add(X1)
| ti(X1,X2) = zero_zero(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X2))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X3))
| hAPP(X1,X1,plus_plus(X1,X2),X3) != zero_zero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3159]) ).
cnf(c_0_3159_2,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X2))
| ~ ordere216010020id_add(X1)
| ti(X1,X2) = zero_zero(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X3))
| hAPP(X1,X1,plus_plus(X1,X2),X3) != zero_zero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3159]) ).
cnf(c_0_3159_3,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X2))
| ~ ordere216010020id_add(X1)
| ti(X1,X2) = zero_zero(X1)
| hAPP(X1,X1,plus_plus(X1,X2),X3) != zero_zero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3159]) ).
cnf(c_0_3159_4,axiom,
( hAPP(X1,X1,plus_plus(X1,X2),X3) != zero_zero(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X2))
| ~ ordere216010020id_add(X1)
| ti(X1,X2) = zero_zero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3159]) ).
cnf(c_0_3160_0,axiom,
( ti(X1,X3) = zero_zero(X1)
| ~ ordere216010020id_add(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X2))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X3))
| hAPP(X1,X1,plus_plus(X1,X2),X3) != zero_zero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3160]) ).
cnf(c_0_3160_1,axiom,
( ~ ordere216010020id_add(X1)
| ti(X1,X3) = zero_zero(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X2))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X3))
| hAPP(X1,X1,plus_plus(X1,X2),X3) != zero_zero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3160]) ).
cnf(c_0_3160_2,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X2))
| ~ ordere216010020id_add(X1)
| ti(X1,X3) = zero_zero(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X3))
| hAPP(X1,X1,plus_plus(X1,X2),X3) != zero_zero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3160]) ).
cnf(c_0_3160_3,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X2))
| ~ ordere216010020id_add(X1)
| ti(X1,X3) = zero_zero(X1)
| hAPP(X1,X1,plus_plus(X1,X2),X3) != zero_zero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3160]) ).
cnf(c_0_3160_4,axiom,
( hAPP(X1,X1,plus_plus(X1,X2),X3) != zero_zero(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X2))
| ~ ordere216010020id_add(X1)
| ti(X1,X3) = zero_zero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3160]) ).
cnf(c_0_3161_0,axiom,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2))
| X1 = X2
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X3,X2),X1))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X3,X2),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_3161]) ).
cnf(c_0_3161_1,axiom,
( X1 = X2
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X3,X2),X1))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X3,X2),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_3161]) ).
cnf(c_0_3161_2,axiom,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X3,X2),X1))
| X1 = X2
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X3,X2),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_3161]) ).
cnf(c_0_3161_3,axiom,
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X3,X2),X1))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X3,X2),X1))
| X1 = X2
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3161]) ).
cnf(c_0_3162_0,axiom,
( X3 = X2
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X1,X2),X3))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X2),X3))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X1,X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3162]) ).
cnf(c_0_3162_1,axiom,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X1,X2),X3))
| X3 = X2
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X2),X3))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X1,X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3162]) ).
cnf(c_0_3162_2,axiom,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X2),X3))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X1,X2),X3))
| X3 = X2
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X1,X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3162]) ).
cnf(c_0_3162_3,axiom,
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X1,X2),X3))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X2),X3))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X1,X2),X3))
| X3 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_3162]) ).
cnf(c_0_3163_0,axiom,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),X1))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),hAPP(int,int,bit1,X1))) ),
inference(literals_permutation,[status(thm)],[c_0_3163]) ).
cnf(c_0_3163_1,axiom,
( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),hAPP(int,int,bit1,X1)))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_3163]) ).
cnf(c_0_3164_0,axiom,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),X1))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),hAPP(int,int,bit0,X1))) ),
inference(literals_permutation,[status(thm)],[c_0_3164]) ).
cnf(c_0_3164_1,axiom,
( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),hAPP(int,int,bit0,X1)))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_3164]) ).
cnf(c_0_3165_0,axiom,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),X1))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),hAPP(int,int,bit1,X1))) ),
inference(literals_permutation,[status(thm)],[c_0_3165]) ).
cnf(c_0_3165_1,axiom,
( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),hAPP(int,int,bit1,X1)))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_3165]) ).
cnf(c_0_3166_0,axiom,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),X1))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),hAPP(int,int,bit0,X1))) ),
inference(literals_permutation,[status(thm)],[c_0_3166]) ).
cnf(c_0_3166_1,axiom,
( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),hAPP(int,int,bit0,X1)))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_3166]) ).
cnf(c_0_3167_0,axiom,
( ~ linorder(X1)
| ~ number(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),number_number_of(X1,X2)),number_number_of(X1,X3)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),number_number_of(X1,X3)),number_number_of(X1,X2))) ),
inference(literals_permutation,[status(thm)],[c_0_3167]) ).
cnf(c_0_3167_1,axiom,
( ~ number(X1)
| ~ linorder(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),number_number_of(X1,X2)),number_number_of(X1,X3)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),number_number_of(X1,X3)),number_number_of(X1,X2))) ),
inference(literals_permutation,[status(thm)],[c_0_3167]) ).
cnf(c_0_3167_2,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),number_number_of(X1,X2)),number_number_of(X1,X3)))
| ~ number(X1)
| ~ linorder(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),number_number_of(X1,X3)),number_number_of(X1,X2))) ),
inference(literals_permutation,[status(thm)],[c_0_3167]) ).
cnf(c_0_3167_3,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),number_number_of(X1,X3)),number_number_of(X1,X2)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),number_number_of(X1,X2)),number_number_of(X1,X3)))
| ~ number(X1)
| ~ linorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3167]) ).
cnf(c_0_3168_0,axiom,
( hBOOL(hAPP(int,bool,X3,X2))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X1),sk1_esk18_3(X3,X1,X2)))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X1),X2))
| ~ hBOOL(hAPP(int,bool,X3,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_3168]) ).
cnf(c_0_3168_1,axiom,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X1),sk1_esk18_3(X3,X1,X2)))
| hBOOL(hAPP(int,bool,X3,X2))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X1),X2))
| ~ hBOOL(hAPP(int,bool,X3,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_3168]) ).
cnf(c_0_3168_2,axiom,
( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X1),X2))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,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_3168]) ).
cnf(c_0_3168_3,axiom,
( ~ hBOOL(hAPP(int,bool,X3,X1))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X1),X2))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,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_3168]) ).
cnf(c_0_3169_0,axiom,
( hAPP(X1,X1,plus_plus(X1,X2),X3) = zero_zero(X1)
| ~ ordere216010020id_add(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X2))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X3))
| ti(X1,X3) != zero_zero(X1)
| ti(X1,X2) != zero_zero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3169]) ).
cnf(c_0_3169_1,axiom,
( ~ ordere216010020id_add(X1)
| hAPP(X1,X1,plus_plus(X1,X2),X3) = zero_zero(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X2))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X3))
| ti(X1,X3) != zero_zero(X1)
| ti(X1,X2) != zero_zero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3169]) ).
cnf(c_0_3169_2,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X2))
| ~ ordere216010020id_add(X1)
| hAPP(X1,X1,plus_plus(X1,X2),X3) = zero_zero(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X3))
| ti(X1,X3) != zero_zero(X1)
| ti(X1,X2) != zero_zero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3169]) ).
cnf(c_0_3169_3,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X2))
| ~ ordere216010020id_add(X1)
| hAPP(X1,X1,plus_plus(X1,X2),X3) = zero_zero(X1)
| ti(X1,X3) != zero_zero(X1)
| ti(X1,X2) != zero_zero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3169]) ).
cnf(c_0_3169_4,axiom,
( ti(X1,X3) != zero_zero(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X2))
| ~ ordere216010020id_add(X1)
| hAPP(X1,X1,plus_plus(X1,X2),X3) = zero_zero(X1)
| ti(X1,X2) != zero_zero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3169]) ).
cnf(c_0_3169_5,axiom,
( ti(X1,X2) != zero_zero(X1)
| ti(X1,X3) != zero_zero(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X2))
| ~ ordere216010020id_add(X1)
| hAPP(X1,X1,plus_plus(X1,X2),X3) = zero_zero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3169]) ).
cnf(c_0_3170_0,axiom,
( hBOOL(hAPP(int,bool,X1,X2))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X2))
| ~ hBOOL(hAPP(int,bool,X1,hAPP(nat,int,semiring_1_of_nat(int),sk1_esk9_1(X1)))) ),
inference(literals_permutation,[status(thm)],[c_0_3170]) ).
cnf(c_0_3170_1,axiom,
( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X2))
| hBOOL(hAPP(int,bool,X1,X2))
| ~ hBOOL(hAPP(int,bool,X1,hAPP(nat,int,semiring_1_of_nat(int),sk1_esk9_1(X1)))) ),
inference(literals_permutation,[status(thm)],[c_0_3170]) ).
cnf(c_0_3170_2,axiom,
( ~ hBOOL(hAPP(int,bool,X1,hAPP(nat,int,semiring_1_of_nat(int),sk1_esk9_1(X1))))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X2))
| hBOOL(hAPP(int,bool,X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3170]) ).
cnf(c_0_3171_0,axiom,
( hAPP(nat,real,power_power(real,sk1_esk5_2(X2,X1)),X1) = X2
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X1))
| ~ hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3171]) ).
cnf(c_0_3171_1,axiom,
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,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(real,fun(real,bool),ord_less(real),zero_zero(real)),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3171]) ).
cnf(c_0_3171_2,axiom,
( ~ hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X2))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,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_3171]) ).
cnf(c_0_3172_0,axiom,
( hAPP(nat,real,power_power(real,sk1_esk4_2(X2,X1)),X1) = X2
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X1))
| ~ hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3172]) ).
cnf(c_0_3172_1,axiom,
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,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(real,fun(real,bool),ord_less(real),zero_zero(real)),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3172]) ).
cnf(c_0_3172_2,axiom,
( ~ hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X2))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,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_3172]) ).
cnf(c_0_3173_0,axiom,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),hAPP(X1,X1,plus_plus(X1,X2),X2)))
| ~ linord219039673up_add(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3173]) ).
cnf(c_0_3173_1,axiom,
( ~ linord219039673up_add(X1)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),hAPP(X1,X1,plus_plus(X1,X2),X2)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3173]) ).
cnf(c_0_3173_2,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X2))
| ~ linord219039673up_add(X1)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),hAPP(X1,X1,plus_plus(X1,X2),X2))) ),
inference(literals_permutation,[status(thm)],[c_0_3173]) ).
cnf(c_0_3174_0,axiom,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),hAPP(X1,X1,plus_plus(X1,X2),X2)))
| ~ linord219039673up_add(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3174]) ).
cnf(c_0_3174_1,axiom,
( ~ linord219039673up_add(X1)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),hAPP(X1,X1,plus_plus(X1,X2),X2)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3174]) ).
cnf(c_0_3174_2,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X2))
| ~ linord219039673up_add(X1)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),hAPP(X1,X1,plus_plus(X1,X2),X2))) ),
inference(literals_permutation,[status(thm)],[c_0_3174]) ).
cnf(c_0_3175_0,axiom,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),one_one(X1)),hAPP(nat,X1,power_power(X1,X2),X3)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),one_one(X1)),X2))
| ~ linordered_semidom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3175]) ).
cnf(c_0_3175_1,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),one_one(X1)),X2))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),one_one(X1)),hAPP(nat,X1,power_power(X1,X2),X3)))
| ~ linordered_semidom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3175]) ).
cnf(c_0_3175_2,axiom,
( ~ linordered_semidom(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),one_one(X1)),X2))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),one_one(X1)),hAPP(nat,X1,power_power(X1,X2),X3))) ),
inference(literals_permutation,[status(thm)],[c_0_3175]) ).
cnf(c_0_3176_0,axiom,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),hAPP(nat,X1,power_power(X1,X2),X3)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X2))
| ~ linordered_semidom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3176]) ).
cnf(c_0_3176_1,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X2))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),hAPP(nat,X1,power_power(X1,X2),X3)))
| ~ linordered_semidom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3176]) ).
cnf(c_0_3176_2,axiom,
( ~ linordered_semidom(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X2))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),hAPP(nat,X1,power_power(X1,X2),X3))) ),
inference(literals_permutation,[status(thm)],[c_0_3176]) ).
cnf(c_0_3177_0,axiom,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),hAPP(nat,X1,power_power(X1,X2),X3)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X2))
| ~ linordered_semidom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3177]) ).
cnf(c_0_3177_1,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X2))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),hAPP(nat,X1,power_power(X1,X2),X3)))
| ~ linordered_semidom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3177]) ).
cnf(c_0_3177_2,axiom,
( ~ linordered_semidom(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X2))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),hAPP(nat,X1,power_power(X1,X2),X3))) ),
inference(literals_permutation,[status(thm)],[c_0_3177]) ).
cnf(c_0_3178_0,axiom,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X2),hAPP(int,int,bit1,pls)))
| ~ linordered_idom(X1)
| ~ number_ring(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),number_number_of(X1,X2)),one_one(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_3178]) ).
cnf(c_0_3178_1,axiom,
( ~ linordered_idom(X1)
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X2),hAPP(int,int,bit1,pls)))
| ~ number_ring(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),number_number_of(X1,X2)),one_one(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_3178]) ).
cnf(c_0_3178_2,axiom,
( ~ number_ring(X1)
| ~ linordered_idom(X1)
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X2),hAPP(int,int,bit1,pls)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),number_number_of(X1,X2)),one_one(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_3178]) ).
cnf(c_0_3178_3,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),number_number_of(X1,X2)),one_one(X1)))
| ~ number_ring(X1)
| ~ linordered_idom(X1)
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X2),hAPP(int,int,bit1,pls))) ),
inference(literals_permutation,[status(thm)],[c_0_3178]) ).
cnf(c_0_3179_0,axiom,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X2),hAPP(int,int,bit1,pls)))
| ~ linordered_idom(X1)
| ~ number_ring(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),number_number_of(X1,X2)),one_one(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_3179]) ).
cnf(c_0_3179_1,axiom,
( ~ linordered_idom(X1)
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X2),hAPP(int,int,bit1,pls)))
| ~ number_ring(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),number_number_of(X1,X2)),one_one(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_3179]) ).
cnf(c_0_3179_2,axiom,
( ~ number_ring(X1)
| ~ linordered_idom(X1)
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X2),hAPP(int,int,bit1,pls)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),number_number_of(X1,X2)),one_one(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_3179]) ).
cnf(c_0_3179_3,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),number_number_of(X1,X2)),one_one(X1)))
| ~ number_ring(X1)
| ~ linordered_idom(X1)
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X2),hAPP(int,int,bit1,pls))) ),
inference(literals_permutation,[status(thm)],[c_0_3179]) ).
cnf(c_0_3180_0,axiom,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,power_power(nat,X1),number_number_of(nat,X2))))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_3180]) ).
cnf(c_0_3180_1,axiom,
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X1))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,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_3180]) ).
cnf(c_0_3181_0,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),sk1_esk26_2(X1,X3)),X2))
| ~ linorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3181]) ).
cnf(c_0_3181_1,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),sk1_esk26_2(X1,X3)),X2))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
| ~ linorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3181]) ).
cnf(c_0_3181_2,axiom,
( ~ linorder(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),sk1_esk26_2(X1,X3)),X2))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3181]) ).
cnf(c_0_3182_0,axiom,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(int,int,plus_plus(int,one_one(int)),X1)))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_3182]) ).
cnf(c_0_3182_1,axiom,
( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X1))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(int,int,plus_plus(int,one_one(int)),X1))) ),
inference(literals_permutation,[status(thm)],[c_0_3182]) ).
cnf(c_0_3183_0,axiom,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(nat,int,power_power(int,X1),X2)))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_3183]) ).
cnf(c_0_3183_1,axiom,
( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X1))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(nat,int,power_power(int,X1),X2))) ),
inference(literals_permutation,[status(thm)],[c_0_3183]) ).
cnf(c_0_3184_0,axiom,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,power_power(nat,X1),X2)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_3184]) ).
cnf(c_0_3184_1,axiom,
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X1))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,power_power(nat,X1),X2))) ),
inference(literals_permutation,[status(thm)],[c_0_3184]) ).
cnf(c_0_3185_0,axiom,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,plus_plus(nat,X1),X2)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_3185]) ).
cnf(c_0_3185_1,axiom,
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X1))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,plus_plus(nat,X1),X2))) ),
inference(literals_permutation,[status(thm)],[c_0_3185]) ).
cnf(c_0_3186_0,axiom,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,plus_plus(nat,X1),X2)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3186]) ).
cnf(c_0_3186_1,axiom,
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X2))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,plus_plus(nat,X1),X2))) ),
inference(literals_permutation,[status(thm)],[c_0_3186]) ).
cnf(c_0_3187_0,axiom,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,power_power(nat,X1),X2)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_3187]) ).
cnf(c_0_3187_1,axiom,
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X1))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,power_power(nat,X1),X2))) ),
inference(literals_permutation,[status(thm)],[c_0_3187]) ).
cnf(c_0_3188_0,axiom,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),hAPP(nat,X1,semiring_1_of_nat(X1),X2)))
| ~ linordered_semidom(X1)
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3188]) ).
cnf(c_0_3188_1,axiom,
( ~ linordered_semidom(X1)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),hAPP(nat,X1,semiring_1_of_nat(X1),X2)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3188]) ).
cnf(c_0_3188_2,axiom,
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X2))
| ~ linordered_semidom(X1)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),hAPP(nat,X1,semiring_1_of_nat(X1),X2))) ),
inference(literals_permutation,[status(thm)],[c_0_3188]) ).
cnf(c_0_3189_0,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),sk1_esk36_2(X1,X2)))
| ~ linorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3189]) ).
cnf(c_0_3189_1,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),sk1_esk36_2(X1,X2)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
| ~ linorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3189]) ).
cnf(c_0_3189_2,axiom,
( ~ linorder(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),sk1_esk36_2(X1,X2)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3189]) ).
cnf(c_0_3190_0,axiom,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X1),hAPP(int,int,plus_plus(int,X2),one_one(int))))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3190]) ).
cnf(c_0_3190_1,axiom,
( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X1),X2))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X1),hAPP(int,int,plus_plus(int,X2),one_one(int)))) ),
inference(literals_permutation,[status(thm)],[c_0_3190]) ).
cnf(c_0_3191_0,axiom,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X1),hAPP(int,int,plus_plus(int,X2),one_one(int))))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3191]) ).
cnf(c_0_3191_1,axiom,
( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X1),X2))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X1),hAPP(int,int,plus_plus(int,X2),one_one(int)))) ),
inference(literals_permutation,[status(thm)],[c_0_3191]) ).
cnf(c_0_3192_0,axiom,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),hAPP(nat,nat,plus_plus(nat,X2),X3)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3192]) ).
cnf(c_0_3192_1,axiom,
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X3))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),hAPP(nat,nat,plus_plus(nat,X2),X3))) ),
inference(literals_permutation,[status(thm)],[c_0_3192]) ).
cnf(c_0_3193_0,axiom,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),hAPP(nat,nat,plus_plus(nat,X2),X3)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3193]) ).
cnf(c_0_3193_1,axiom,
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),hAPP(nat,nat,plus_plus(nat,X2),X3))) ),
inference(literals_permutation,[status(thm)],[c_0_3193]) ).
cnf(c_0_3194_0,axiom,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),hAPP(nat,nat,plus_plus(nat,X2),X3)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3194]) ).
cnf(c_0_3194_1,axiom,
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X3))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),hAPP(nat,nat,plus_plus(nat,X2),X3))) ),
inference(literals_permutation,[status(thm)],[c_0_3194]) ).
cnf(c_0_3195_0,axiom,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),hAPP(nat,nat,plus_plus(nat,X2),X3)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3195]) ).
cnf(c_0_3195_1,axiom,
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),hAPP(nat,nat,plus_plus(nat,X2),X3))) ),
inference(literals_permutation,[status(thm)],[c_0_3195]) ).
cnf(c_0_3196_0,axiom,
( ~ linorder(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| ti(X1,X2) != ti(X1,X3) ),
inference(literals_permutation,[status(thm)],[c_0_3196]) ).
cnf(c_0_3196_1,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
| ~ linorder(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| ti(X1,X2) != ti(X1,X3) ),
inference(literals_permutation,[status(thm)],[c_0_3196]) ).
cnf(c_0_3196_2,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
| ~ linorder(X1)
| ti(X1,X2) != ti(X1,X3) ),
inference(literals_permutation,[status(thm)],[c_0_3196]) ).
cnf(c_0_3196_3,axiom,
( ti(X1,X2) != ti(X1,X3)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
| ~ linorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3196]) ).
cnf(c_0_3197_0,axiom,
( ti(X1,X2) = ti(X1,X3)
| ~ order(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X2))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3197]) ).
cnf(c_0_3197_1,axiom,
( ~ order(X1)
| ti(X1,X2) = ti(X1,X3)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X2))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3197]) ).
cnf(c_0_3197_2,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X2))
| ~ order(X1)
| ti(X1,X2) = ti(X1,X3)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3197]) ).
cnf(c_0_3197_3,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X2))
| ~ order(X1)
| ti(X1,X2) = ti(X1,X3) ),
inference(literals_permutation,[status(thm)],[c_0_3197]) ).
cnf(c_0_3198_0,axiom,
( ti(X1,X3) = ti(X1,X2)
| ~ order(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3198]) ).
cnf(c_0_3198_1,axiom,
( ~ order(X1)
| ti(X1,X3) = ti(X1,X2)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3198]) ).
cnf(c_0_3198_2,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
| ~ order(X1)
| ti(X1,X3) = ti(X1,X2)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3198]) ).
cnf(c_0_3198_3,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X2))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
| ~ order(X1)
| ti(X1,X3) = ti(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_3198]) ).
cnf(c_0_3199_0,axiom,
( ti(X1,X2) = ti(X1,X3)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X2))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
| ~ order(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3199]) ).
cnf(c_0_3199_1,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X2))
| ti(X1,X2) = ti(X1,X3)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
| ~ order(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3199]) ).
cnf(c_0_3199_2,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X2))
| ti(X1,X2) = ti(X1,X3)
| ~ order(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3199]) ).
cnf(c_0_3199_3,axiom,
( ~ order(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X2))
| ti(X1,X2) = ti(X1,X3) ),
inference(literals_permutation,[status(thm)],[c_0_3199]) ).
cnf(c_0_3200_0,axiom,
( ti(X1,X2) = ti(X1,X3)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X2))
| ~ order(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3200]) ).
cnf(c_0_3200_1,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
| ti(X1,X2) = ti(X1,X3)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X2))
| ~ order(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3200]) ).
cnf(c_0_3200_2,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X2))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
| ti(X1,X2) = ti(X1,X3)
| ~ order(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3200]) ).
cnf(c_0_3200_3,axiom,
( ~ order(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X2))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
| ti(X1,X2) = ti(X1,X3) ),
inference(literals_permutation,[status(thm)],[c_0_3200]) ).
cnf(c_0_3201_0,axiom,
( ti(X1,X2) = zero_zero(X1)
| ~ ring_11004092258visors(X1)
| hAPP(nat,X1,power_power(X1,X2),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) != zero_zero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3201]) ).
cnf(c_0_3201_1,axiom,
( ~ ring_11004092258visors(X1)
| ti(X1,X2) = zero_zero(X1)
| hAPP(nat,X1,power_power(X1,X2),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) != zero_zero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3201]) ).
cnf(c_0_3201_2,axiom,
( hAPP(nat,X1,power_power(X1,X2),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) != zero_zero(X1)
| ~ ring_11004092258visors(X1)
| ti(X1,X2) = zero_zero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3201]) ).
cnf(c_0_3202_0,axiom,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(nat,int,semiring_1_of_nat(int),X1)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_3202]) ).
cnf(c_0_3202_1,axiom,
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X1))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(nat,int,semiring_1_of_nat(int),X1))) ),
inference(literals_permutation,[status(thm)],[c_0_3202]) ).
cnf(c_0_3203_0,axiom,
( hBOOL(X1)
| ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),X3),X4))
| ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),X4),X3))
| ~ preorder(X2) ),
inference(literals_permutation,[status(thm)],[c_0_3203]) ).
cnf(c_0_3203_1,axiom,
( ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),X3),X4))
| hBOOL(X1)
| ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),X4),X3))
| ~ preorder(X2) ),
inference(literals_permutation,[status(thm)],[c_0_3203]) ).
cnf(c_0_3203_2,axiom,
( ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),X4),X3))
| ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),X3),X4))
| hBOOL(X1)
| ~ preorder(X2) ),
inference(literals_permutation,[status(thm)],[c_0_3203]) ).
cnf(c_0_3203_3,axiom,
( ~ preorder(X2)
| ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),X4),X3))
| ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),X3),X4))
| hBOOL(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3203]) ).
cnf(c_0_3204_0,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X2))
| ~ linorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3204]) ).
cnf(c_0_3204_1,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X2))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| ~ linorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3204]) ).
cnf(c_0_3204_2,axiom,
( ~ linorder(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X2))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3204]) ).
cnf(c_0_3205_0,axiom,
( ~ preorder(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3205]) ).
cnf(c_0_3205_1,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| ~ preorder(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3205]) ).
cnf(c_0_3205_2,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X2))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| ~ preorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3205]) ).
cnf(c_0_3206_0,axiom,
( ~ linorder(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3206]) ).
cnf(c_0_3206_1,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
| ~ linorder(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3206]) ).
cnf(c_0_3206_2,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X2))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
| ~ linorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3206]) ).
cnf(c_0_3207_0,axiom,
( ~ linorder(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3207]) ).
cnf(c_0_3207_1,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| ~ linorder(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3207]) ).
cnf(c_0_3207_2,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X2))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| ~ linorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3207]) ).
cnf(c_0_3208_0,axiom,
( ~ linorder(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3208]) ).
cnf(c_0_3208_1,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| ~ linorder(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3208]) ).
cnf(c_0_3208_2,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X2))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| ~ linorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3208]) ).
cnf(c_0_3209_0,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X2))
| ~ preorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3209]) ).
cnf(c_0_3209_1,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X2))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| ~ preorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3209]) ).
cnf(c_0_3209_2,axiom,
( ~ preorder(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X2))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3209]) ).
cnf(c_0_3210_0,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X2))
| ~ preorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3210]) ).
cnf(c_0_3210_1,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X2))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| ~ preorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3210]) ).
cnf(c_0_3210_2,axiom,
( ~ preorder(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X2))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3210]) ).
cnf(c_0_3211_0,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X2))
| ~ preorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3211]) ).
cnf(c_0_3211_1,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X2))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| ~ preorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3211]) ).
cnf(c_0_3211_2,axiom,
( ~ preorder(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X2))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3211]) ).
cnf(c_0_3212_0,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X2))
| ~ order(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3212]) ).
cnf(c_0_3212_1,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X2))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| ~ order(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3212]) ).
cnf(c_0_3212_2,axiom,
( ~ order(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X2))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3212]) ).
cnf(c_0_3213_0,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X2))
| ~ preorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3213]) ).
cnf(c_0_3213_1,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X2))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| ~ preorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3213]) ).
cnf(c_0_3213_2,axiom,
( ~ preorder(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X2))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3213]) ).
cnf(c_0_3214_0,axiom,
( hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),one_one(real)),hAPP(real,real,sqrt,X1)))
| ~ hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),one_one(real)),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_3214]) ).
cnf(c_0_3214_1,axiom,
( ~ hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),one_one(real)),X1))
| hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),one_one(real)),hAPP(real,real,sqrt,X1))) ),
inference(literals_permutation,[status(thm)],[c_0_3214]) ).
cnf(c_0_3215_0,axiom,
( hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(real,real,sqrt,X1)))
| ~ hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_3215]) ).
cnf(c_0_3215_1,axiom,
( ~ hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X1))
| hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(real,real,sqrt,X1))) ),
inference(literals_permutation,[status(thm)],[c_0_3215]) ).
cnf(c_0_3216_0,axiom,
( hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(real,real,sqrt,X1)))
| ~ hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_3216]) ).
cnf(c_0_3216_1,axiom,
( ~ hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X1))
| hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(real,real,sqrt,X1))) ),
inference(literals_permutation,[status(thm)],[c_0_3216]) ).
cnf(c_0_3217_0,axiom,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),hAPP(int,int,bit1,X1)))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_3217]) ).
cnf(c_0_3217_1,axiom,
( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),X1))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),hAPP(int,int,bit1,X1))) ),
inference(literals_permutation,[status(thm)],[c_0_3217]) ).
cnf(c_0_3218_0,axiom,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),hAPP(int,int,bit0,X1)))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_3218]) ).
cnf(c_0_3218_1,axiom,
( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),X1))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),hAPP(int,int,bit0,X1))) ),
inference(literals_permutation,[status(thm)],[c_0_3218]) ).
cnf(c_0_3219_0,axiom,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),hAPP(int,int,bit1,X1)))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_3219]) ).
cnf(c_0_3219_1,axiom,
( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),X1))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),hAPP(int,int,bit1,X1))) ),
inference(literals_permutation,[status(thm)],[c_0_3219]) ).
cnf(c_0_3220_0,axiom,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),hAPP(int,int,bit0,X1)))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_3220]) ).
cnf(c_0_3220_1,axiom,
( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),X1))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),hAPP(int,int,bit0,X1))) ),
inference(literals_permutation,[status(thm)],[c_0_3220]) ).
cnf(c_0_3221_0,axiom,
( X1 = X2
| ~ hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X2),X1))
| ~ hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3221]) ).
cnf(c_0_3221_1,axiom,
( ~ hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X2),X1))
| X1 = X2
| ~ hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3221]) ).
cnf(c_0_3221_2,axiom,
( ~ hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X1),X2))
| ~ hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X2),X1))
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_3221]) ).
cnf(c_0_3222_0,axiom,
( X1 = X2
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X2),X1))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3222]) ).
cnf(c_0_3222_1,axiom,
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X2),X1))
| X1 = X2
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3222]) ).
cnf(c_0_3222_2,axiom,
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X2),X1))
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_3222]) ).
cnf(c_0_3223_0,axiom,
( X1 = X2
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X2),X1))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3223]) ).
cnf(c_0_3223_1,axiom,
( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X2),X1))
| X1 = X2
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3223]) ).
cnf(c_0_3223_2,axiom,
( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X1),X2))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X2),X1))
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_3223]) ).
cnf(c_0_3224_0,axiom,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,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(nat,fun(nat,bool),ord_less(nat),X4),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3224]) ).
cnf(c_0_3224_1,axiom,
( hAPP(nat,nat,plus_plus(nat,X1),X3) != hAPP(nat,nat,plus_plus(nat,X4),X2)
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X4),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3224]) ).
cnf(c_0_3224_2,axiom,
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,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(nat,fun(nat,bool),ord_less(nat),X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3224]) ).
cnf(c_0_3225_0,axiom,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
| ~ dense_linorder(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),sk1_esk24_3(X1,X3,X2)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3225]) ).
cnf(c_0_3225_1,axiom,
( ~ dense_linorder(X1)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),sk1_esk24_3(X1,X3,X2)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3225]) ).
cnf(c_0_3225_2,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),sk1_esk24_3(X1,X3,X2)),X3))
| ~ dense_linorder(X1)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3225]) ).
cnf(c_0_3226_0,axiom,
( hBOOL(hAPP(int,bool,X1,hAPP(nat,int,semiring_1_of_nat(int),sk1_esk6_1(X1))))
| ~ hBOOL(hAPP(int,bool,X1,X2))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3226]) ).
cnf(c_0_3226_1,axiom,
( ~ hBOOL(hAPP(int,bool,X1,X2))
| hBOOL(hAPP(int,bool,X1,hAPP(nat,int,semiring_1_of_nat(int),sk1_esk6_1(X1))))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3226]) ).
cnf(c_0_3226_2,axiom,
( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X2))
| ~ hBOOL(hAPP(int,bool,X1,X2))
| hBOOL(hAPP(int,bool,X1,hAPP(nat,int,semiring_1_of_nat(int),sk1_esk6_1(X1)))) ),
inference(literals_permutation,[status(thm)],[c_0_3226]) ).
cnf(c_0_3227_0,axiom,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2))
| X1 = X2
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X3,X2),X1))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X2),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_3227]) ).
cnf(c_0_3227_1,axiom,
( X1 = X2
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X3,X2),X1))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X2),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_3227]) ).
cnf(c_0_3227_2,axiom,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X3,X2),X1))
| X1 = X2
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X2),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_3227]) ).
cnf(c_0_3227_3,axiom,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X2),X1))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X3,X2),X1))
| X1 = X2
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3227]) ).
cnf(c_0_3232_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(nat,fun(nat,bool),ord_less(nat),X3),sk1_esk19_2(X2,X1))) ),
inference(literals_permutation,[status(thm)],[c_0_3232]) ).
cnf(c_0_3232_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(nat,fun(nat,bool),ord_less(nat),X3),sk1_esk19_2(X2,X1))) ),
inference(literals_permutation,[status(thm)],[c_0_3232]) ).
cnf(c_0_3232_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(nat,fun(nat,bool),ord_less(nat),X3),sk1_esk19_2(X2,X1))) ),
inference(literals_permutation,[status(thm)],[c_0_3232]) ).
cnf(c_0_3232_3,axiom,
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,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_3232]) ).
cnf(c_0_3233_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(nat,fun(nat,bool),ord_less_eq(nat),X3),sk1_esk14_2(X2,X1))) ),
inference(literals_permutation,[status(thm)],[c_0_3233]) ).
cnf(c_0_3233_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(nat,fun(nat,bool),ord_less_eq(nat),X3),sk1_esk14_2(X2,X1))) ),
inference(literals_permutation,[status(thm)],[c_0_3233]) ).
cnf(c_0_3233_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(nat,fun(nat,bool),ord_less_eq(nat),X3),sk1_esk14_2(X2,X1))) ),
inference(literals_permutation,[status(thm)],[c_0_3233]) ).
cnf(c_0_3233_3,axiom,
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,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_3233]) ).
cnf(c_0_3234_0,axiom,
( hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),hAPP(bool,fun(nat,fun(nat,nat)),if(nat),X2),X1),X3)) = hAPP(nat,int,semiring_1_of_nat(int),X1)
| ~ hBOOL(X2) ),
inference(literals_permutation,[status(thm)],[c_0_3234]) ).
cnf(c_0_3234_1,axiom,
( ~ hBOOL(X2)
| hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),hAPP(bool,fun(nat,fun(nat,nat)),if(nat),X2),X1),X3)) = hAPP(nat,int,semiring_1_of_nat(int),X1) ),
inference(literals_permutation,[status(thm)],[c_0_3234]) ).
cnf(c_0_3235_0,axiom,
( hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),hAPP(bool,fun(nat,fun(nat,nat)),if(nat),X2),X3),X1)) = hAPP(nat,int,semiring_1_of_nat(int),X1)
| hBOOL(X2) ),
inference(literals_permutation,[status(thm)],[c_0_3235]) ).
cnf(c_0_3235_1,axiom,
( hBOOL(X2)
| hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),hAPP(bool,fun(nat,fun(nat,nat)),if(nat),X2),X3),X1)) = hAPP(nat,int,semiring_1_of_nat(int),X1) ),
inference(literals_permutation,[status(thm)],[c_0_3235]) ).
cnf(c_0_3236_0,axiom,
( hBOOL(hAPP(int,bool,X3,X2))
| hBOOL(hAPP(int,bool,X3,sk1_esk18_3(X3,X1,X2)))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X1),X2))
| ~ hBOOL(hAPP(int,bool,X3,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_3236]) ).
cnf(c_0_3236_1,axiom,
( hBOOL(hAPP(int,bool,X3,sk1_esk18_3(X3,X1,X2)))
| hBOOL(hAPP(int,bool,X3,X2))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X1),X2))
| ~ hBOOL(hAPP(int,bool,X3,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_3236]) ).
cnf(c_0_3236_2,axiom,
( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,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_3236]) ).
cnf(c_0_3236_3,axiom,
( ~ hBOOL(hAPP(int,bool,X3,X1))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,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_3236]) ).
cnf(c_0_3237_0,axiom,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,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(int,fun(int,bool),ord_less(int),X2),pls)) ),
inference(literals_permutation,[status(thm)],[c_0_3237]) ).
cnf(c_0_3237_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(int,fun(int,bool),ord_less(int),X1),pls))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X2),pls)) ),
inference(literals_permutation,[status(thm)],[c_0_3237]) ).
cnf(c_0_3237_2,axiom,
( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,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(int,fun(int,bool),ord_less(int),X1),pls)) ),
inference(literals_permutation,[status(thm)],[c_0_3237]) ).
cnf(c_0_3238_0,axiom,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X2),X3))
| ~ linordered_idom(X1)
| ~ number_ring(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),number_number_of(X1,X2)),number_number_of(X1,X3))) ),
inference(literals_permutation,[status(thm)],[c_0_3238]) ).
cnf(c_0_3238_1,axiom,
( ~ linordered_idom(X1)
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X2),X3))
| ~ number_ring(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),number_number_of(X1,X2)),number_number_of(X1,X3))) ),
inference(literals_permutation,[status(thm)],[c_0_3238]) ).
cnf(c_0_3238_2,axiom,
( ~ number_ring(X1)
| ~ linordered_idom(X1)
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X2),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),number_number_of(X1,X2)),number_number_of(X1,X3))) ),
inference(literals_permutation,[status(thm)],[c_0_3238]) ).
cnf(c_0_3238_3,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),number_number_of(X1,X2)),number_number_of(X1,X3)))
| ~ number_ring(X1)
| ~ linordered_idom(X1)
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3238]) ).
cnf(c_0_3239_0,axiom,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X2),X3))
| ~ linordered_idom(X1)
| ~ number_ring(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),number_number_of(X1,X2)),number_number_of(X1,X3))) ),
inference(literals_permutation,[status(thm)],[c_0_3239]) ).
cnf(c_0_3239_1,axiom,
( ~ linordered_idom(X1)
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X2),X3))
| ~ number_ring(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),number_number_of(X1,X2)),number_number_of(X1,X3))) ),
inference(literals_permutation,[status(thm)],[c_0_3239]) ).
cnf(c_0_3239_2,axiom,
( ~ number_ring(X1)
| ~ linordered_idom(X1)
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X2),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),number_number_of(X1,X2)),number_number_of(X1,X3))) ),
inference(literals_permutation,[status(thm)],[c_0_3239]) ).
cnf(c_0_3239_3,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),number_number_of(X1,X2)),number_number_of(X1,X3)))
| ~ number_ring(X1)
| ~ linordered_idom(X1)
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3239]) ).
cnf(c_0_3240_0,axiom,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),sk1_esk31_2(X1,X2)),X3))
| ~ linorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3240]) ).
cnf(c_0_3240_1,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),sk1_esk31_2(X1,X2)),X3))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
| ~ linorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3240]) ).
cnf(c_0_3240_2,axiom,
( ~ linorder(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),sk1_esk31_2(X1,X2)),X3))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3240]) ).
cnf(c_0_3241_0,axiom,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X2),pls))
| ~ linordered_idom(X1)
| ~ number_ring(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),number_number_of(X1,X2)),zero_zero(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_3241]) ).
cnf(c_0_3241_1,axiom,
( ~ linordered_idom(X1)
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X2),pls))
| ~ number_ring(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),number_number_of(X1,X2)),zero_zero(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_3241]) ).
cnf(c_0_3241_2,axiom,
( ~ number_ring(X1)
| ~ linordered_idom(X1)
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X2),pls))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),number_number_of(X1,X2)),zero_zero(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_3241]) ).
cnf(c_0_3241_3,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),number_number_of(X1,X2)),zero_zero(X1)))
| ~ number_ring(X1)
| ~ linordered_idom(X1)
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X2),pls)) ),
inference(literals_permutation,[status(thm)],[c_0_3241]) ).
cnf(c_0_3242_0,axiom,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X2),pls))
| ~ linordered_idom(X1)
| ~ number_ring(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),number_number_of(X1,X2)),zero_zero(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_3242]) ).
cnf(c_0_3242_1,axiom,
( ~ linordered_idom(X1)
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X2),pls))
| ~ number_ring(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),number_number_of(X1,X2)),zero_zero(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_3242]) ).
cnf(c_0_3242_2,axiom,
( ~ number_ring(X1)
| ~ linordered_idom(X1)
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X2),pls))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),number_number_of(X1,X2)),zero_zero(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_3242]) ).
cnf(c_0_3242_3,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),number_number_of(X1,X2)),zero_zero(X1)))
| ~ number_ring(X1)
| ~ linordered_idom(X1)
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X2),pls)) ),
inference(literals_permutation,[status(thm)],[c_0_3242]) ).
cnf(c_0_3243_0,axiom,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X1),X2))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),number_number_of(int,X1)),number_number_of(int,X2))) ),
inference(literals_permutation,[status(thm)],[c_0_3243]) ).
cnf(c_0_3243_1,axiom,
( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),number_number_of(int,X1)),number_number_of(int,X2)))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3243]) ).
cnf(c_0_3244_0,axiom,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X1),X2))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),number_number_of(nat,X1)),number_number_of(nat,X2))) ),
inference(literals_permutation,[status(thm)],[c_0_3244]) ).
cnf(c_0_3244_1,axiom,
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),number_number_of(nat,X1)),number_number_of(nat,X2)))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3244]) ).
cnf(c_0_3245_0,axiom,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X1),X2))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),number_number_of(int,X1)),number_number_of(int,X2))) ),
inference(literals_permutation,[status(thm)],[c_0_3245]) ).
cnf(c_0_3245_1,axiom,
( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),number_number_of(int,X1)),number_number_of(int,X2)))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3245]) ).
cnf(c_0_3246_0,axiom,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),number_number_of(X1,X2)),number_number_of(X1,X3)))
| ~ linordered_idom(X1)
| ~ number_ring(X1)
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3246]) ).
cnf(c_0_3246_1,axiom,
( ~ linordered_idom(X1)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),number_number_of(X1,X2)),number_number_of(X1,X3)))
| ~ number_ring(X1)
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3246]) ).
cnf(c_0_3246_2,axiom,
( ~ number_ring(X1)
| ~ linordered_idom(X1)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),number_number_of(X1,X2)),number_number_of(X1,X3)))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3246]) ).
cnf(c_0_3246_3,axiom,
( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X2),X3))
| ~ number_ring(X1)
| ~ linordered_idom(X1)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),number_number_of(X1,X2)),number_number_of(X1,X3))) ),
inference(literals_permutation,[status(thm)],[c_0_3246]) ).
cnf(c_0_3247_0,axiom,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),number_number_of(X1,X2)),number_number_of(X1,X3)))
| ~ linordered_idom(X1)
| ~ number_ring(X1)
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3247]) ).
cnf(c_0_3247_1,axiom,
( ~ linordered_idom(X1)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),number_number_of(X1,X2)),number_number_of(X1,X3)))
| ~ number_ring(X1)
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3247]) ).
cnf(c_0_3247_2,axiom,
( ~ number_ring(X1)
| ~ linordered_idom(X1)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),number_number_of(X1,X2)),number_number_of(X1,X3)))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3247]) ).
cnf(c_0_3247_3,axiom,
( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X2),X3))
| ~ number_ring(X1)
| ~ linordered_idom(X1)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),number_number_of(X1,X2)),number_number_of(X1,X3))) ),
inference(literals_permutation,[status(thm)],[c_0_3247]) ).
cnf(c_0_3248_0,axiom,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),X2))
| ~ linordered_idom(X1)
| ~ number_ring(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),number_number_of(X1,X2))) ),
inference(literals_permutation,[status(thm)],[c_0_3248]) ).
cnf(c_0_3248_1,axiom,
( ~ linordered_idom(X1)
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),X2))
| ~ number_ring(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),number_number_of(X1,X2))) ),
inference(literals_permutation,[status(thm)],[c_0_3248]) ).
cnf(c_0_3248_2,axiom,
( ~ number_ring(X1)
| ~ linordered_idom(X1)
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),X2))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),number_number_of(X1,X2))) ),
inference(literals_permutation,[status(thm)],[c_0_3248]) ).
cnf(c_0_3248_3,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),number_number_of(X1,X2)))
| ~ number_ring(X1)
| ~ linordered_idom(X1)
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3248]) ).
cnf(c_0_3249_0,axiom,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),X2))
| ~ linordered_idom(X1)
| ~ number_ring(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),number_number_of(X1,X2))) ),
inference(literals_permutation,[status(thm)],[c_0_3249]) ).
cnf(c_0_3249_1,axiom,
( ~ linordered_idom(X1)
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),X2))
| ~ number_ring(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),number_number_of(X1,X2))) ),
inference(literals_permutation,[status(thm)],[c_0_3249]) ).
cnf(c_0_3249_2,axiom,
( ~ number_ring(X1)
| ~ linordered_idom(X1)
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),X2))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),number_number_of(X1,X2))) ),
inference(literals_permutation,[status(thm)],[c_0_3249]) ).
cnf(c_0_3249_3,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),number_number_of(X1,X2)))
| ~ number_ring(X1)
| ~ linordered_idom(X1)
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3249]) ).
cnf(c_0_3250_0,axiom,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),sk1_esk30_2(X1,X3)))
| ~ linorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3250]) ).
cnf(c_0_3250_1,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),sk1_esk30_2(X1,X3)))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
| ~ linorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3250]) ).
cnf(c_0_3250_2,axiom,
( ~ linorder(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),sk1_esk30_2(X1,X3)))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3250]) ).
cnf(c_0_3251_0,axiom,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),number_number_of(X1,X2)),zero_zero(X1)))
| ~ linordered_idom(X1)
| ~ number_ring(X1)
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X2),pls)) ),
inference(literals_permutation,[status(thm)],[c_0_3251]) ).
cnf(c_0_3251_1,axiom,
( ~ linordered_idom(X1)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),number_number_of(X1,X2)),zero_zero(X1)))
| ~ number_ring(X1)
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X2),pls)) ),
inference(literals_permutation,[status(thm)],[c_0_3251]) ).
cnf(c_0_3251_2,axiom,
( ~ number_ring(X1)
| ~ linordered_idom(X1)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),number_number_of(X1,X2)),zero_zero(X1)))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X2),pls)) ),
inference(literals_permutation,[status(thm)],[c_0_3251]) ).
cnf(c_0_3251_3,axiom,
( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X2),pls))
| ~ number_ring(X1)
| ~ linordered_idom(X1)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),number_number_of(X1,X2)),zero_zero(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_3251]) ).
cnf(c_0_3252_0,axiom,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),number_number_of(X1,X2)),zero_zero(X1)))
| ~ linordered_idom(X1)
| ~ number_ring(X1)
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X2),pls)) ),
inference(literals_permutation,[status(thm)],[c_0_3252]) ).
cnf(c_0_3252_1,axiom,
( ~ linordered_idom(X1)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),number_number_of(X1,X2)),zero_zero(X1)))
| ~ number_ring(X1)
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X2),pls)) ),
inference(literals_permutation,[status(thm)],[c_0_3252]) ).
cnf(c_0_3252_2,axiom,
( ~ number_ring(X1)
| ~ linordered_idom(X1)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),number_number_of(X1,X2)),zero_zero(X1)))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X2),pls)) ),
inference(literals_permutation,[status(thm)],[c_0_3252]) ).
cnf(c_0_3252_3,axiom,
( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X2),pls))
| ~ number_ring(X1)
| ~ linordered_idom(X1)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),number_number_of(X1,X2)),zero_zero(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_3252]) ).
cnf(c_0_3253_0,axiom,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| ~ linorder(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X2))
| ti(X1,X3) != ti(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_3253]) ).
cnf(c_0_3253_1,axiom,
( ~ linorder(X1)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X2))
| ti(X1,X3) != ti(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_3253]) ).
cnf(c_0_3253_2,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X2))
| ~ linorder(X1)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| ti(X1,X3) != ti(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_3253]) ).
cnf(c_0_3253_3,axiom,
( ti(X1,X3) != ti(X1,X2)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X2))
| ~ linorder(X1)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3253]) ).
cnf(c_0_3254_0,axiom,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X4))
| ti(X1,X3) != ti(X1,X4)
| ~ order(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3254]) ).
cnf(c_0_3254_1,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X4))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| ti(X1,X3) != ti(X1,X4)
| ~ order(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3254]) ).
cnf(c_0_3254_2,axiom,
( ti(X1,X3) != ti(X1,X4)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X4))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| ~ order(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3254]) ).
cnf(c_0_3254_3,axiom,
( ~ order(X1)
| ti(X1,X3) != ti(X1,X4)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X4))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3254]) ).
cnf(c_0_3255_0,axiom,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| ti(X1,X4) != ti(X1,X2)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X4),X3))
| ~ order(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3255]) ).
cnf(c_0_3255_1,axiom,
( ti(X1,X4) != ti(X1,X2)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X4),X3))
| ~ order(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3255]) ).
cnf(c_0_3255_2,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X4),X3))
| ti(X1,X4) != ti(X1,X2)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| ~ order(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3255]) ).
cnf(c_0_3255_3,axiom,
( ~ order(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X4),X3))
| ti(X1,X4) != ti(X1,X2)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3255]) ).
cnf(c_0_3256_0,axiom,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X2))
| ~ order(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
| ti(X1,X3) != ti(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_3256]) ).
cnf(c_0_3256_1,axiom,
( ~ order(X1)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X2))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
| ti(X1,X3) != ti(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_3256]) ).
cnf(c_0_3256_2,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
| ~ order(X1)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X2))
| ti(X1,X3) != ti(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_3256]) ).
cnf(c_0_3256_3,axiom,
( ti(X1,X3) != ti(X1,X2)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
| ~ order(X1)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3256]) ).
cnf(c_0_3257_0,axiom,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X4))
| ti(X1,X3) != ti(X1,X4)
| ~ order(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3257]) ).
cnf(c_0_3257_1,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X4))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
| ti(X1,X3) != ti(X1,X4)
| ~ order(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3257]) ).
cnf(c_0_3257_2,axiom,
( ti(X1,X3) != ti(X1,X4)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X4))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
| ~ order(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3257]) ).
cnf(c_0_3257_3,axiom,
( ~ order(X1)
| ti(X1,X3) != ti(X1,X4)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X4))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3257]) ).
cnf(c_0_3258_0,axiom,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
| ti(X1,X4) != ti(X1,X2)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X4),X3))
| ~ order(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3258]) ).
cnf(c_0_3258_1,axiom,
( ti(X1,X4) != ti(X1,X2)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X4),X3))
| ~ order(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3258]) ).
cnf(c_0_3258_2,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X4),X3))
| ti(X1,X4) != ti(X1,X2)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
| ~ order(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3258]) ).
cnf(c_0_3258_3,axiom,
( ~ order(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X4),X3))
| ti(X1,X4) != ti(X1,X2)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3258]) ).
cnf(c_0_3259_0,axiom,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),number_number_of(nat,X1)),number_number_of(nat,X2)))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3259]) ).
cnf(c_0_3259_1,axiom,
( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X1),X2))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),number_number_of(nat,X1)),number_number_of(nat,X2))) ),
inference(literals_permutation,[status(thm)],[c_0_3259]) ).
cnf(c_0_3260_0,axiom,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),number_number_of(int,X1)),number_number_of(int,X2)))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3260]) ).
cnf(c_0_3260_1,axiom,
( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X1),X2))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),number_number_of(int,X1)),number_number_of(int,X2))) ),
inference(literals_permutation,[status(thm)],[c_0_3260]) ).
cnf(c_0_3261_0,axiom,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),number_number_of(int,X1)),number_number_of(int,X2)))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3261]) ).
cnf(c_0_3261_1,axiom,
( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X1),X2))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),number_number_of(int,X1)),number_number_of(int,X2))) ),
inference(literals_permutation,[status(thm)],[c_0_3261]) ).
cnf(c_0_3262_0,axiom,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),number_number_of(nat,X1)),number_number_of(nat,X2)))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X1),pls)) ),
inference(literals_permutation,[status(thm)],[c_0_3262]) ).
cnf(c_0_3262_1,axiom,
( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X1),pls))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),number_number_of(nat,X1)),number_number_of(nat,X2))) ),
inference(literals_permutation,[status(thm)],[c_0_3262]) ).
cnf(c_0_3263_0,axiom,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| ti(X1,X3) = ti(X1,X2)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
| ~ order(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3263]) ).
cnf(c_0_3263_1,axiom,
( ti(X1,X3) = ti(X1,X2)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
| ~ order(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3263]) ).
cnf(c_0_3263_2,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
| ti(X1,X3) = ti(X1,X2)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| ~ order(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3263]) ).
cnf(c_0_3263_3,axiom,
( ~ order(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
| ti(X1,X3) = ti(X1,X2)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3263]) ).
cnf(c_0_3264_0,axiom,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| ti(X1,X2) = ti(X1,X3)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
| ~ order(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3264]) ).
cnf(c_0_3264_1,axiom,
( ti(X1,X2) = ti(X1,X3)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
| ~ order(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3264]) ).
cnf(c_0_3264_2,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
| ti(X1,X2) = ti(X1,X3)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| ~ order(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3264]) ).
cnf(c_0_3264_3,axiom,
( ~ order(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
| ti(X1,X2) = ti(X1,X3)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3264]) ).
cnf(c_0_3265_0,axiom,
( ti(X1,X2) = ti(X1,X3)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
| ~ order(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3265]) ).
cnf(c_0_3265_1,axiom,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| ti(X1,X2) = ti(X1,X3)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
| ~ order(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3265]) ).
cnf(c_0_3265_2,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| ti(X1,X2) = ti(X1,X3)
| ~ order(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3265]) ).
cnf(c_0_3265_3,axiom,
( ~ order(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| ti(X1,X2) = ti(X1,X3) ),
inference(literals_permutation,[status(thm)],[c_0_3265]) ).
cnf(c_0_3266_0,axiom,
( ti(X1,X2) = ti(X1,X3)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| ~ linorder(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3266]) ).
cnf(c_0_3266_1,axiom,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| ti(X1,X2) = ti(X1,X3)
| ~ linorder(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3266]) ).
cnf(c_0_3266_2,axiom,
( ~ linorder(X1)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| ti(X1,X2) = ti(X1,X3)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3266]) ).
cnf(c_0_3266_3,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
| ~ linorder(X1)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| ti(X1,X2) = ti(X1,X3) ),
inference(literals_permutation,[status(thm)],[c_0_3266]) ).
cnf(c_0_3267_0,axiom,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| ti(X1,X3) = ti(X1,X2)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
| ~ order(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3267]) ).
cnf(c_0_3267_1,axiom,
( ti(X1,X3) = ti(X1,X2)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
| ~ order(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3267]) ).
cnf(c_0_3267_2,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
| ti(X1,X3) = ti(X1,X2)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| ~ order(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3267]) ).
cnf(c_0_3267_3,axiom,
( ~ order(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
| ti(X1,X3) = ti(X1,X2)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3267]) ).
cnf(c_0_3268_0,axiom,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| ti(X1,X2) = ti(X1,X3)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
| ~ order(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3268]) ).
cnf(c_0_3268_1,axiom,
( ti(X1,X2) = ti(X1,X3)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
| ~ order(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3268]) ).
cnf(c_0_3268_2,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
| ti(X1,X2) = ti(X1,X3)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| ~ order(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3268]) ).
cnf(c_0_3268_3,axiom,
( ~ order(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
| ti(X1,X2) = ti(X1,X3)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3268]) ).
cnf(c_0_3269_0,axiom,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| ti(X1,X2) = ti(X1,X3)
| ~ linorder(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3269]) ).
cnf(c_0_3269_1,axiom,
( ti(X1,X2) = ti(X1,X3)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| ~ linorder(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3269]) ).
cnf(c_0_3269_2,axiom,
( ~ linorder(X1)
| ti(X1,X2) = ti(X1,X3)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3269]) ).
cnf(c_0_3269_3,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
| ~ linorder(X1)
| ti(X1,X2) = ti(X1,X3)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3269]) ).
cnf(c_0_3270_0,axiom,
( ti(X1,X2) = ti(X1,X3)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| ~ order(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3270]) ).
cnf(c_0_3270_1,axiom,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| ti(X1,X2) = ti(X1,X3)
| ~ order(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3270]) ).
cnf(c_0_3270_2,axiom,
( ~ order(X1)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| ti(X1,X2) = ti(X1,X3)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3270]) ).
cnf(c_0_3270_3,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
| ~ order(X1)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| ti(X1,X2) = ti(X1,X3) ),
inference(literals_permutation,[status(thm)],[c_0_3270]) ).
cnf(c_0_3271_0,axiom,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| ti(X1,X2) = ti(X1,X3)
| ~ order(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3271]) ).
cnf(c_0_3271_1,axiom,
( ti(X1,X2) = ti(X1,X3)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| ~ order(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3271]) ).
cnf(c_0_3271_2,axiom,
( ~ order(X1)
| ti(X1,X2) = ti(X1,X3)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3271]) ).
cnf(c_0_3271_3,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
| ~ order(X1)
| ti(X1,X2) = ti(X1,X3)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3271]) ).
cnf(c_0_3272_0,axiom,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),number_number_of(X1,X2)))
| ~ linordered_idom(X1)
| ~ number_ring(X1)
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3272]) ).
cnf(c_0_3272_1,axiom,
( ~ linordered_idom(X1)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),number_number_of(X1,X2)))
| ~ number_ring(X1)
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3272]) ).
cnf(c_0_3272_2,axiom,
( ~ number_ring(X1)
| ~ linordered_idom(X1)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),number_number_of(X1,X2)))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3272]) ).
cnf(c_0_3272_3,axiom,
( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),X2))
| ~ number_ring(X1)
| ~ linordered_idom(X1)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),number_number_of(X1,X2))) ),
inference(literals_permutation,[status(thm)],[c_0_3272]) ).
cnf(c_0_3273_0,axiom,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),number_number_of(X1,X2)))
| ~ linordered_idom(X1)
| ~ number_ring(X1)
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3273]) ).
cnf(c_0_3273_1,axiom,
( ~ linordered_idom(X1)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),number_number_of(X1,X2)))
| ~ number_ring(X1)
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3273]) ).
cnf(c_0_3273_2,axiom,
( ~ number_ring(X1)
| ~ linordered_idom(X1)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),number_number_of(X1,X2)))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3273]) ).
cnf(c_0_3273_3,axiom,
( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),X2))
| ~ number_ring(X1)
| ~ linordered_idom(X1)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),number_number_of(X1,X2))) ),
inference(literals_permutation,[status(thm)],[c_0_3273]) ).
cnf(c_0_3274_0,axiom,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X4),X3))
| X2 != X4
| ~ ord(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3274]) ).
cnf(c_0_3274_1,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X4),X3))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| X2 != X4
| ~ ord(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3274]) ).
cnf(c_0_3274_2,axiom,
( X2 != X4
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X4),X3))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| ~ ord(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3274]) ).
cnf(c_0_3274_3,axiom,
( ~ ord(X1)
| X2 != X4
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X4),X3))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3274]) ).
cnf(c_0_3275_0,axiom,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| X4 != X3
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X4))
| ~ ord(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3275]) ).
cnf(c_0_3275_1,axiom,
( X4 != X3
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X4))
| ~ ord(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3275]) ).
cnf(c_0_3275_2,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X4))
| X4 != X3
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| ~ ord(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3275]) ).
cnf(c_0_3275_3,axiom,
( ~ ord(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X4))
| X4 != X3
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3275]) ).
cnf(c_0_3276_0,axiom,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X4),X3))
| X2 != X4
| ~ ord(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3276]) ).
cnf(c_0_3276_1,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X4),X3))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
| X2 != X4
| ~ ord(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3276]) ).
cnf(c_0_3276_2,axiom,
( X2 != X4
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X4),X3))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
| ~ ord(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3276]) ).
cnf(c_0_3276_3,axiom,
( ~ ord(X1)
| X2 != X4
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X4),X3))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3276]) ).
cnf(c_0_3277_0,axiom,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
| X4 != X3
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X4))
| ~ ord(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3277]) ).
cnf(c_0_3277_1,axiom,
( X4 != X3
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X4))
| ~ ord(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3277]) ).
cnf(c_0_3277_2,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X4))
| X4 != X3
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
| ~ ord(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3277]) ).
cnf(c_0_3277_3,axiom,
( ~ ord(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X4))
| X4 != X3
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3277]) ).
cnf(c_0_3278_0,axiom,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| ~ preorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3278]) ).
cnf(c_0_3278_1,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
| ~ preorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3278]) ).
cnf(c_0_3278_2,axiom,
( ~ preorder(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3278]) ).
cnf(c_0_3279_0,axiom,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
| ~ order(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3279]) ).
cnf(c_0_3279_1,axiom,
( ~ order(X1)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3279]) ).
cnf(c_0_3279_2,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| ~ order(X1)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3279]) ).
cnf(c_0_3280_0,axiom,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
| ~ preorder(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3280]) ).
cnf(c_0_3280_1,axiom,
( ~ preorder(X1)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3280]) ).
cnf(c_0_3280_2,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| ~ preorder(X1)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3280]) ).
cnf(c_0_3281_0,axiom,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
| ~ order(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3281]) ).
cnf(c_0_3281_1,axiom,
( ~ order(X1)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3281]) ).
cnf(c_0_3281_2,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| ~ order(X1)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3281]) ).
cnf(c_0_3282_0,axiom,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),X1))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),number_number_of(nat,X1))) ),
inference(literals_permutation,[status(thm)],[c_0_3282]) ).
cnf(c_0_3282_1,axiom,
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),number_number_of(nat,X1)))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_3282]) ).
cnf(c_0_3283_0,axiom,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),sk1_esk3_2(X1,X2)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3283]) ).
cnf(c_0_3283_1,axiom,
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),sk1_esk3_2(X1,X2))) ),
inference(literals_permutation,[status(thm)],[c_0_3283]) ).
cnf(c_0_3284_0,axiom,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X3))
| ~ hBOOL(X1)
| ~ hBOOL(X2)
| ~ hBOOL(X2)
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3284]) ).
cnf(c_0_3284_1,axiom,
( ~ hBOOL(X1)
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X3))
| ~ hBOOL(X2)
| ~ hBOOL(X2)
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3284]) ).
cnf(c_0_3284_2,axiom,
( ~ hBOOL(X2)
| ~ hBOOL(X1)
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X3))
| ~ hBOOL(X2)
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3284]) ).
cnf(c_0_3284_3,axiom,
( ~ hBOOL(X2)
| ~ hBOOL(X2)
| ~ hBOOL(X1)
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X3))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3284]) ).
cnf(c_0_3284_4,axiom,
( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X3))
| ~ hBOOL(X2)
| ~ hBOOL(X2)
| ~ hBOOL(X1)
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3284]) ).
cnf(c_0_3285_0,axiom,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X3))
| ~ hBOOL(X1)
| ~ hBOOL(X2)
| ~ hBOOL(X1)
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3285]) ).
cnf(c_0_3285_1,axiom,
( ~ hBOOL(X1)
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X3))
| ~ hBOOL(X2)
| ~ hBOOL(X1)
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3285]) ).
cnf(c_0_3285_2,axiom,
( ~ hBOOL(X2)
| ~ hBOOL(X1)
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X3))
| ~ hBOOL(X1)
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3285]) ).
cnf(c_0_3285_3,axiom,
( ~ hBOOL(X1)
| ~ hBOOL(X2)
| ~ hBOOL(X1)
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X3))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3285]) ).
cnf(c_0_3285_4,axiom,
( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X3))
| ~ hBOOL(X1)
| ~ hBOOL(X2)
| ~ hBOOL(X1)
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3285]) ).
cnf(c_0_3286_0,axiom,
( hBOOL(X1)
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X3))
| ~ hBOOL(X1)
| ~ hBOOL(X2)
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3286]) ).
cnf(c_0_3286_1,axiom,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X3))
| hBOOL(X1)
| ~ hBOOL(X1)
| ~ hBOOL(X2)
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3286]) ).
cnf(c_0_3286_2,axiom,
( ~ hBOOL(X1)
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X3))
| hBOOL(X1)
| ~ hBOOL(X2)
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3286]) ).
cnf(c_0_3286_3,axiom,
( ~ hBOOL(X2)
| ~ hBOOL(X1)
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X3))
| hBOOL(X1)
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3286]) ).
cnf(c_0_3286_4,axiom,
( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X3))
| ~ hBOOL(X2)
| ~ hBOOL(X1)
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X3))
| hBOOL(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3286]) ).
cnf(c_0_3287_0,axiom,
( hBOOL(X2)
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X3))
| ~ hBOOL(X1)
| ~ hBOOL(X2)
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3287]) ).
cnf(c_0_3287_1,axiom,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X3))
| hBOOL(X2)
| ~ hBOOL(X1)
| ~ hBOOL(X2)
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3287]) ).
cnf(c_0_3287_2,axiom,
( ~ hBOOL(X1)
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X3))
| hBOOL(X2)
| ~ hBOOL(X2)
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3287]) ).
cnf(c_0_3287_3,axiom,
( ~ hBOOL(X2)
| ~ hBOOL(X1)
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X3))
| hBOOL(X2)
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3287]) ).
cnf(c_0_3287_4,axiom,
( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X3))
| ~ hBOOL(X2)
| ~ hBOOL(X1)
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X3))
| hBOOL(X2) ),
inference(literals_permutation,[status(thm)],[c_0_3287]) ).
cnf(c_0_3288_0,axiom,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),number_number_of(nat,X1)))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_3288]) ).
cnf(c_0_3288_1,axiom,
( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),X1))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),number_number_of(nat,X1))) ),
inference(literals_permutation,[status(thm)],[c_0_3288]) ).
cnf(c_0_3289_0,axiom,
( hBOOL(X1)
| hBOOL(X2)
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X3))
| ~ hBOOL(X2)
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3289]) ).
cnf(c_0_3289_1,axiom,
( hBOOL(X2)
| hBOOL(X1)
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X3))
| ~ hBOOL(X2)
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3289]) ).
cnf(c_0_3289_2,axiom,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X3))
| hBOOL(X2)
| hBOOL(X1)
| ~ hBOOL(X2)
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3289]) ).
cnf(c_0_3289_3,axiom,
( ~ hBOOL(X2)
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X3))
| hBOOL(X2)
| hBOOL(X1)
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3289]) ).
cnf(c_0_3289_4,axiom,
( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X3))
| ~ hBOOL(X2)
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X3))
| hBOOL(X2)
| hBOOL(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3289]) ).
cnf(c_0_3290_0,axiom,
( hBOOL(X1)
| hBOOL(X2)
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X3))
| ~ hBOOL(X1)
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3290]) ).
cnf(c_0_3290_1,axiom,
( hBOOL(X2)
| hBOOL(X1)
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X3))
| ~ hBOOL(X1)
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3290]) ).
cnf(c_0_3290_2,axiom,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X3))
| hBOOL(X2)
| hBOOL(X1)
| ~ hBOOL(X1)
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3290]) ).
cnf(c_0_3290_3,axiom,
( ~ hBOOL(X1)
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X3))
| hBOOL(X2)
| hBOOL(X1)
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3290]) ).
cnf(c_0_3290_4,axiom,
( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X3))
| ~ hBOOL(X1)
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X3))
| hBOOL(X2)
| hBOOL(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3290]) ).
cnf(c_0_3291_0,axiom,
( hBOOL(X1)
| hBOOL(X2)
| hBOOL(X1)
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X3))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3291]) ).
cnf(c_0_3291_1,axiom,
( hBOOL(X2)
| hBOOL(X1)
| hBOOL(X1)
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X3))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3291]) ).
cnf(c_0_3291_2,axiom,
( hBOOL(X1)
| hBOOL(X2)
| hBOOL(X1)
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X3))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3291]) ).
cnf(c_0_3291_3,axiom,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X3))
| hBOOL(X1)
| hBOOL(X2)
| hBOOL(X1)
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3291]) ).
cnf(c_0_3291_4,axiom,
( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X3))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X3))
| hBOOL(X1)
| hBOOL(X2)
| hBOOL(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3291]) ).
cnf(c_0_3292_0,axiom,
( hBOOL(X1)
| hBOOL(X2)
| hBOOL(X2)
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X3))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3292]) ).
cnf(c_0_3292_1,axiom,
( hBOOL(X2)
| hBOOL(X1)
| hBOOL(X2)
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X3))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3292]) ).
cnf(c_0_3292_2,axiom,
( hBOOL(X2)
| hBOOL(X2)
| hBOOL(X1)
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X3))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3292]) ).
cnf(c_0_3292_3,axiom,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X3))
| hBOOL(X2)
| hBOOL(X2)
| hBOOL(X1)
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3292]) ).
cnf(c_0_3292_4,axiom,
( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X3))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X3))
| hBOOL(X2)
| hBOOL(X2)
| hBOOL(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3292]) ).
cnf(c_0_3293_0,axiom,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),sk1_esk2_1(X1)))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_3293]) ).
cnf(c_0_3293_1,axiom,
( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),X1))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),sk1_esk2_1(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_3293]) ).
cnf(c_0_3294_0,axiom,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X1))
| hBOOL(X2)
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X1))
| ~ hBOOL(X3) ),
inference(literals_permutation,[status(thm)],[c_0_3294]) ).
cnf(c_0_3294_1,axiom,
( hBOOL(X2)
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X1))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X1))
| ~ hBOOL(X3) ),
inference(literals_permutation,[status(thm)],[c_0_3294]) ).
cnf(c_0_3294_2,axiom,
( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X1))
| hBOOL(X2)
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X1))
| ~ hBOOL(X3) ),
inference(literals_permutation,[status(thm)],[c_0_3294]) ).
cnf(c_0_3294_3,axiom,
( ~ hBOOL(X3)
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X1))
| hBOOL(X2)
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_3294]) ).
cnf(c_0_3295_0,axiom,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X1))
| hBOOL(X2)
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X1))
| ~ hBOOL(X3) ),
inference(literals_permutation,[status(thm)],[c_0_3295]) ).
cnf(c_0_3295_1,axiom,
( hBOOL(X2)
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X1))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X1))
| ~ hBOOL(X3) ),
inference(literals_permutation,[status(thm)],[c_0_3295]) ).
cnf(c_0_3295_2,axiom,
( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X1))
| hBOOL(X2)
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X1))
| ~ hBOOL(X3) ),
inference(literals_permutation,[status(thm)],[c_0_3295]) ).
cnf(c_0_3295_3,axiom,
( ~ hBOOL(X3)
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X1))
| hBOOL(X2)
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_3295]) ).
cnf(c_0_3296_0,axiom,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X1))
| hBOOL(X3)
| ~ hBOOL(X2)
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_3296]) ).
cnf(c_0_3296_1,axiom,
( hBOOL(X3)
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X1))
| ~ hBOOL(X2)
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_3296]) ).
cnf(c_0_3296_2,axiom,
( ~ hBOOL(X2)
| hBOOL(X3)
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X1))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_3296]) ).
cnf(c_0_3296_3,axiom,
( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X1))
| ~ hBOOL(X2)
| hBOOL(X3)
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_3296]) ).
cnf(c_0_3297_0,axiom,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X1))
| hBOOL(X3)
| ~ hBOOL(X2)
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_3297]) ).
cnf(c_0_3297_1,axiom,
( hBOOL(X3)
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X1))
| ~ hBOOL(X2)
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_3297]) ).
cnf(c_0_3297_2,axiom,
( ~ hBOOL(X2)
| hBOOL(X3)
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X1))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_3297]) ).
cnf(c_0_3297_3,axiom,
( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X1))
| ~ hBOOL(X2)
| hBOOL(X3)
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_3297]) ).
cnf(c_0_3298_0,axiom,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),X1))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),one_one(int)),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_3298]) ).
cnf(c_0_3298_1,axiom,
( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),one_one(int)),X1))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_3298]) ).
cnf(c_0_3299_0,axiom,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),one_one(int)),X1))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_3299]) ).
cnf(c_0_3299_1,axiom,
( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),X1))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),one_one(int)),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_3299]) ).
cnf(c_0_3300_0,axiom,
( hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X1),X2))
| X1 = X2
| ~ hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3300]) ).
cnf(c_0_3300_1,axiom,
( X1 = X2
| hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X1),X2))
| ~ hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3300]) ).
cnf(c_0_3300_2,axiom,
( ~ hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X1),X2))
| X1 = X2
| hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3300]) ).
cnf(c_0_3301_0,axiom,
( X1 = X2
| hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X1),X2))
| ~ hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3301]) ).
cnf(c_0_3301_1,axiom,
( hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X1),X2))
| X1 = X2
| ~ hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3301]) ).
cnf(c_0_3301_2,axiom,
( ~ hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X1),X2))
| hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X1),X2))
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_3301]) ).
cnf(c_0_3302_0,axiom,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2))
| X1 = X2
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3302]) ).
cnf(c_0_3302_1,axiom,
( X1 = X2
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3302]) ).
cnf(c_0_3302_2,axiom,
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2))
| X1 = X2
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3302]) ).
cnf(c_0_3303_0,axiom,
( X1 = X2
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3303]) ).
cnf(c_0_3303_1,axiom,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2))
| X1 = X2
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3303]) ).
cnf(c_0_3303_2,axiom,
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2))
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_3303]) ).
cnf(c_0_3304_0,axiom,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2))
| X1 = X2
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3304]) ).
cnf(c_0_3304_1,axiom,
( X1 = X2
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3304]) ).
cnf(c_0_3304_2,axiom,
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2))
| X1 = X2
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3304]) ).
cnf(c_0_3305_0,axiom,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X1),X2))
| X1 = X2
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3305]) ).
cnf(c_0_3305_1,axiom,
( X1 = X2
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X1),X2))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3305]) ).
cnf(c_0_3305_2,axiom,
( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X1),X2))
| X1 = X2
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3305]) ).
cnf(c_0_3306_0,axiom,
( hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X1),X2))
| ~ hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3306]) ).
cnf(c_0_3306_1,axiom,
( ~ hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X1),X2))
| hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3306]) ).
cnf(c_0_3307_0,axiom,
( hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X1),X2))
| ~ hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3307]) ).
cnf(c_0_3307_1,axiom,
( ~ hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X1),X2))
| hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3307]) ).
cnf(c_0_3308_0,axiom,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3308]) ).
cnf(c_0_3308_1,axiom,
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,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(nat,fun(nat,bool),ord_less_eq(nat),X1),X2))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3309]) ).
cnf(c_0_3309_1,axiom,
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3309]) ).
cnf(c_0_3310_0,axiom,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3310]) ).
cnf(c_0_3310_1,axiom,
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3310]) ).
cnf(c_0_3311_0,axiom,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3311]) ).
cnf(c_0_3311_1,axiom,
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3311]) ).
cnf(c_0_3312_0,axiom,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X1),X2))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3312]) ).
cnf(c_0_3312_1,axiom,
( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X1),X2))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3312]) ).
cnf(c_0_3313_0,axiom,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,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(int,fun(int,bool),ord_less(int),X2),pls)) ),
inference(literals_permutation,[status(thm)],[c_0_3313]) ).
cnf(c_0_3313_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(int,fun(int,bool),ord_less(int),X1),pls))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X2),pls)) ),
inference(literals_permutation,[status(thm)],[c_0_3313]) ).
cnf(c_0_3313_2,axiom,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,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(int,fun(int,bool),ord_less(int),X1),pls)) ),
inference(literals_permutation,[status(thm)],[c_0_3313]) ).
cnf(c_0_3314_0,axiom,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),sk1_esk7_1(X1)))
| ~ hBOOL(hAPP(int,bool,X1,hAPP(nat,int,semiring_1_of_nat(int),X2))) ),
inference(literals_permutation,[status(thm)],[c_0_3314]) ).
cnf(c_0_3314_1,axiom,
( ~ hBOOL(hAPP(int,bool,X1,hAPP(nat,int,semiring_1_of_nat(int),X2)))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),sk1_esk7_1(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_3314]) ).
cnf(c_0_3315_0,axiom,
( hAPP(X1,X1,plus_plus(X1,hAPP(X1,X1,plus_plus(X1,X2),X3)),hAPP(X1,X1,plus_plus(X1,X4),X5)) = hAPP(X1,X1,plus_plus(X1,hAPP(X1,X1,plus_plus(X1,X2),X4)),hAPP(X1,X1,plus_plus(X1,X3),X5))
| ~ comm_semiring_1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3315]) ).
cnf(c_0_3315_1,axiom,
( ~ comm_semiring_1(X1)
| hAPP(X1,X1,plus_plus(X1,hAPP(X1,X1,plus_plus(X1,X2),X3)),hAPP(X1,X1,plus_plus(X1,X4),X5)) = hAPP(X1,X1,plus_plus(X1,hAPP(X1,X1,plus_plus(X1,X2),X4)),hAPP(X1,X1,plus_plus(X1,X3),X5)) ),
inference(literals_permutation,[status(thm)],[c_0_3315]) ).
cnf(c_0_3316_0,axiom,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),sk1_esk24_3(X1,X3,X2)),X2))
| ~ dense_linorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3316]) ).
cnf(c_0_3316_1,axiom,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),sk1_esk24_3(X1,X3,X2)),X2))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
| ~ dense_linorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3316]) ).
cnf(c_0_3316_2,axiom,
( ~ dense_linorder(X1)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),sk1_esk24_3(X1,X3,X2)),X2))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3316]) ).
cnf(c_0_3317_0,axiom,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(nat,int,semiring_1_of_nat(int),X1)),zero_zero(int)))
| X1 != zero_zero(nat) ),
inference(literals_permutation,[status(thm)],[c_0_3317]) ).
cnf(c_0_3317_1,axiom,
( X1 != zero_zero(nat)
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(nat,int,semiring_1_of_nat(int),X1)),zero_zero(int))) ),
inference(literals_permutation,[status(thm)],[c_0_3317]) ).
cnf(c_0_3318_0,axiom,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),number_number_of(X1,X2)),number_number_of(X1,X3)))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),number_number_of(X1,X3)),number_number_of(X1,X2)))
| ~ linorder(X1)
| ~ number(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3318]) ).
cnf(c_0_3318_1,axiom,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),number_number_of(X1,X3)),number_number_of(X1,X2)))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),number_number_of(X1,X2)),number_number_of(X1,X3)))
| ~ linorder(X1)
| ~ number(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3318]) ).
cnf(c_0_3318_2,axiom,
( ~ linorder(X1)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),number_number_of(X1,X3)),number_number_of(X1,X2)))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),number_number_of(X1,X2)),number_number_of(X1,X3)))
| ~ number(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3318]) ).
cnf(c_0_3318_3,axiom,
( ~ number(X1)
| ~ linorder(X1)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),number_number_of(X1,X3)),number_number_of(X1,X2)))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),number_number_of(X1,X2)),number_number_of(X1,X3))) ),
inference(literals_permutation,[status(thm)],[c_0_3318]) ).
cnf(c_0_3320_0,axiom,
( hAPP(X1,X1,plus_plus(X1,number_number_of(X1,X2)),hAPP(X1,X1,plus_plus(X1,number_number_of(X1,X3)),X4)) = hAPP(X1,X1,plus_plus(X1,number_number_of(X1,hAPP(int,int,plus_plus(int,X2),X3))),X4)
| ~ number_ring(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3320]) ).
cnf(c_0_3320_1,axiom,
( ~ number_ring(X1)
| hAPP(X1,X1,plus_plus(X1,number_number_of(X1,X2)),hAPP(X1,X1,plus_plus(X1,number_number_of(X1,X3)),X4)) = hAPP(X1,X1,plus_plus(X1,number_number_of(X1,hAPP(int,int,plus_plus(int,X2),X3))),X4) ),
inference(literals_permutation,[status(thm)],[c_0_3320]) ).
cnf(c_0_3321_0,axiom,
( X3 = X4
| ~ linordered_semidom(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),one_one(X1)),X2))
| hAPP(nat,X1,power_power(X1,X2),X3) != hAPP(nat,X1,power_power(X1,X2),X4) ),
inference(literals_permutation,[status(thm)],[c_0_3321]) ).
cnf(c_0_3321_1,axiom,
( ~ linordered_semidom(X1)
| X3 = X4
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),one_one(X1)),X2))
| hAPP(nat,X1,power_power(X1,X2),X3) != hAPP(nat,X1,power_power(X1,X2),X4) ),
inference(literals_permutation,[status(thm)],[c_0_3321]) ).
cnf(c_0_3321_2,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),one_one(X1)),X2))
| ~ linordered_semidom(X1)
| X3 = X4
| hAPP(nat,X1,power_power(X1,X2),X3) != hAPP(nat,X1,power_power(X1,X2),X4) ),
inference(literals_permutation,[status(thm)],[c_0_3321]) ).
cnf(c_0_3321_3,axiom,
( hAPP(nat,X1,power_power(X1,X2),X3) != hAPP(nat,X1,power_power(X1,X2),X4)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),one_one(X1)),X2))
| ~ linordered_semidom(X1)
| X3 = X4 ),
inference(literals_permutation,[status(thm)],[c_0_3321]) ).
cnf(c_0_3322_0,axiom,
( hAPP(X1,X1,plus_plus(X1,number_number_of(X1,X2)),one_one(X1)) = number_number_of(X1,hAPP(int,int,succ,X2))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),X2))
| ~ number_semiring(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3322]) ).
cnf(c_0_3322_1,axiom,
( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),X2))
| hAPP(X1,X1,plus_plus(X1,number_number_of(X1,X2)),one_one(X1)) = number_number_of(X1,hAPP(int,int,succ,X2))
| ~ number_semiring(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3322]) ).
cnf(c_0_3322_2,axiom,
( ~ number_semiring(X1)
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),X2))
| hAPP(X1,X1,plus_plus(X1,number_number_of(X1,X2)),one_one(X1)) = number_number_of(X1,hAPP(int,int,succ,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3322]) ).
cnf(c_0_3323_0,axiom,
( hAPP(int,int,plus_plus(int,X2),hAPP(nat,int,semiring_1_of_nat(int),sk1_esk10_2(X2,X1))) = X1
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X2),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_3323]) ).
cnf(c_0_3323_1,axiom,
( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X2),X1))
| hAPP(int,int,plus_plus(int,X2),hAPP(nat,int,semiring_1_of_nat(int),sk1_esk10_2(X2,X1))) = X1 ),
inference(literals_permutation,[status(thm)],[c_0_3323]) ).
cnf(c_0_3324_0,axiom,
( hAPP(X1,X1,plus_plus(X1,one_one(X1)),number_number_of(X1,X2)) = number_number_of(X1,hAPP(int,int,succ,X2))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),X2))
| ~ number_semiring(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3324]) ).
cnf(c_0_3324_1,axiom,
( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),X2))
| hAPP(X1,X1,plus_plus(X1,one_one(X1)),number_number_of(X1,X2)) = number_number_of(X1,hAPP(int,int,succ,X2))
| ~ number_semiring(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3324]) ).
cnf(c_0_3324_2,axiom,
( ~ number_semiring(X1)
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),X2))
| hAPP(X1,X1,plus_plus(X1,one_one(X1)),number_number_of(X1,X2)) = number_number_of(X1,hAPP(int,int,succ,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3324]) ).
cnf(c_0_3325_0,axiom,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
| ~ linorder(X1)
| ti(X1,X2) != ti(X1,X3) ),
inference(literals_permutation,[status(thm)],[c_0_3325]) ).
cnf(c_0_3325_1,axiom,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| ~ linorder(X1)
| ti(X1,X2) != ti(X1,X3) ),
inference(literals_permutation,[status(thm)],[c_0_3325]) ).
cnf(c_0_3325_2,axiom,
( ~ linorder(X1)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| ti(X1,X2) != ti(X1,X3) ),
inference(literals_permutation,[status(thm)],[c_0_3325]) ).
cnf(c_0_3325_3,axiom,
( ti(X1,X2) != ti(X1,X3)
| ~ linorder(X1)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3325]) ).
cnf(c_0_3326_0,axiom,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X2))
| ti(X1,X3) = ti(X1,X2)
| ~ linorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3326]) ).
cnf(c_0_3326_1,axiom,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X2))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| ti(X1,X3) = ti(X1,X2)
| ~ linorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3326]) ).
cnf(c_0_3326_2,axiom,
( ti(X1,X3) = ti(X1,X2)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X2))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| ~ linorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3326]) ).
cnf(c_0_3326_3,axiom,
( ~ linorder(X1)
| ti(X1,X3) = ti(X1,X2)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X2))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3326]) ).
cnf(c_0_3327_0,axiom,
( ti(X1,X2) = ti(X1,X3)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X2))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| ~ linorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3327]) ).
cnf(c_0_3327_1,axiom,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X2))
| ti(X1,X2) = ti(X1,X3)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| ~ linorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3327]) ).
cnf(c_0_3327_2,axiom,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X2))
| ti(X1,X2) = ti(X1,X3)
| ~ linorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3327]) ).
cnf(c_0_3327_3,axiom,
( ~ linorder(X1)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X2))
| ti(X1,X2) = ti(X1,X3) ),
inference(literals_permutation,[status(thm)],[c_0_3327]) ).
cnf(c_0_3328_0,axiom,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| ti(X1,X3) = ti(X1,X2)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X2))
| ~ linorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3328]) ).
cnf(c_0_3328_1,axiom,
( ti(X1,X3) = ti(X1,X2)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X2))
| ~ linorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3328]) ).
cnf(c_0_3328_2,axiom,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X2))
| ti(X1,X3) = ti(X1,X2)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| ~ linorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3328]) ).
cnf(c_0_3328_3,axiom,
( ~ linorder(X1)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X2))
| ti(X1,X3) = ti(X1,X2)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3328]) ).
cnf(c_0_3329_0,axiom,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| ti(X1,X3) = ti(X1,X2)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X2))
| ~ linorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3329]) ).
cnf(c_0_3329_1,axiom,
( ti(X1,X3) = ti(X1,X2)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X2))
| ~ linorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3329]) ).
cnf(c_0_3329_2,axiom,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X2))
| ti(X1,X3) = ti(X1,X2)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| ~ linorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3329]) ).
cnf(c_0_3329_3,axiom,
( ~ linorder(X1)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X2))
| ti(X1,X3) = ti(X1,X2)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3329]) ).
cnf(c_0_3330_0,axiom,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X2))
| ti(X1,X3) = ti(X1,X2)
| ~ linorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3330]) ).
cnf(c_0_3330_1,axiom,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X2))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| ti(X1,X3) = ti(X1,X2)
| ~ linorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3330]) ).
cnf(c_0_3330_2,axiom,
( ti(X1,X3) = ti(X1,X2)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X2))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| ~ linorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3330]) ).
cnf(c_0_3330_3,axiom,
( ~ linorder(X1)
| ti(X1,X3) = ti(X1,X2)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X2))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3330]) ).
cnf(c_0_3331_0,axiom,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| ti(X1,X3) = ti(X1,X2)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X2))
| ~ linorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3331]) ).
cnf(c_0_3331_1,axiom,
( ti(X1,X3) = ti(X1,X2)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X2))
| ~ linorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3331]) ).
cnf(c_0_3331_2,axiom,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X2))
| ti(X1,X3) = ti(X1,X2)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| ~ linorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3331]) ).
cnf(c_0_3331_3,axiom,
( ~ linorder(X1)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X2))
| ti(X1,X3) = ti(X1,X2)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3331]) ).
cnf(c_0_3332_0,axiom,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X2))
| ti(X1,X3) = ti(X1,X2)
| ~ linordered_idom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3332]) ).
cnf(c_0_3332_1,axiom,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X2))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| ti(X1,X3) = ti(X1,X2)
| ~ linordered_idom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3332]) ).
cnf(c_0_3332_2,axiom,
( ti(X1,X3) = ti(X1,X2)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X2))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| ~ linordered_idom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3332]) ).
cnf(c_0_3332_3,axiom,
( ~ linordered_idom(X1)
| ti(X1,X3) = ti(X1,X2)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X2))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3332]) ).
cnf(c_0_3333_0,axiom,
( hAPP(nat,X1,power_power(X1,X2),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) = zero_zero(X1)
| ~ ring_11004092258visors(X1)
| ti(X1,X2) != zero_zero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3333]) ).
cnf(c_0_3333_1,axiom,
( ~ ring_11004092258visors(X1)
| hAPP(nat,X1,power_power(X1,X2),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) = zero_zero(X1)
| ti(X1,X2) != zero_zero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3333]) ).
cnf(c_0_3333_2,axiom,
( ti(X1,X2) != zero_zero(X1)
| ~ ring_11004092258visors(X1)
| hAPP(nat,X1,power_power(X1,X2),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) = zero_zero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3333]) ).
cnf(c_0_3334_0,axiom,
( hAPP(nat,X1,power_power(X1,zero_zero(X1)),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) = zero_zero(X1)
| ~ semiring_1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3334]) ).
cnf(c_0_3334_1,axiom,
( ~ semiring_1(X1)
| hAPP(nat,X1,power_power(X1,zero_zero(X1)),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) = zero_zero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3334]) ).
cnf(c_0_3335_0,axiom,
( hAPP(nat,X1,power_power(X1,one_one(X1)),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) = one_one(X1)
| ~ semiring_1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3335]) ).
cnf(c_0_3335_1,axiom,
( ~ semiring_1(X1)
| hAPP(nat,X1,power_power(X1,one_one(X1)),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) = one_one(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3335]) ).
cnf(c_0_3336_0,axiom,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X2))
| ~ linorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3336]) ).
cnf(c_0_3336_1,axiom,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X2))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| ~ linorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3336]) ).
cnf(c_0_3336_2,axiom,
( ~ linorder(X1)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X2))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3336]) ).
cnf(c_0_3337_0,axiom,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X2))
| ~ linorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3337]) ).
cnf(c_0_3337_1,axiom,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X2))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
| ~ linorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3337]) ).
cnf(c_0_3337_2,axiom,
( ~ linorder(X1)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X2))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3337]) ).
cnf(c_0_3338_0,axiom,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X2))
| ~ linorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3338]) ).
cnf(c_0_3338_1,axiom,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X2))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| ~ linorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3338]) ).
cnf(c_0_3338_2,axiom,
( ~ linorder(X1)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X2))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3338]) ).
cnf(c_0_3339_0,axiom,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X2))
| ~ linorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3339]) ).
cnf(c_0_3339_1,axiom,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X2))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| ~ linorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3339]) ).
cnf(c_0_3339_2,axiom,
( ~ linorder(X1)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X2))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3339]) ).
cnf(c_0_3340_0,axiom,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X2))
| ~ linorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3340]) ).
cnf(c_0_3340_1,axiom,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X2))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
| ~ linorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3340]) ).
cnf(c_0_3340_2,axiom,
( ~ linorder(X1)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X2))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3340]) ).
cnf(c_0_3341_0,axiom,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X2))
| ~ linorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3341]) ).
cnf(c_0_3341_1,axiom,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X2))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
| ~ linorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3341]) ).
cnf(c_0_3341_2,axiom,
( ~ linorder(X1)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X2))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3341]) ).
cnf(c_0_3342_0,axiom,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X2))
| ~ linorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3342]) ).
cnf(c_0_3342_1,axiom,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X2))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
| ~ linorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3342]) ).
cnf(c_0_3342_2,axiom,
( ~ linorder(X1)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X2))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3342]) ).
cnf(c_0_3343_0,axiom,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X2),X1))
| X2 = X1 ),
inference(literals_permutation,[status(thm)],[c_0_3343]) ).
cnf(c_0_3343_1,axiom,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X2),X1))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2))
| X2 = X1 ),
inference(literals_permutation,[status(thm)],[c_0_3343]) ).
cnf(c_0_3343_2,axiom,
( X2 = X1
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X2),X1))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3343]) ).
cnf(c_0_3344_0,axiom,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X2),X1))
| X2 = X1 ),
inference(literals_permutation,[status(thm)],[c_0_3344]) ).
cnf(c_0_3344_1,axiom,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X2),X1))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2))
| X2 = X1 ),
inference(literals_permutation,[status(thm)],[c_0_3344]) ).
cnf(c_0_3344_2,axiom,
( X2 = X1
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X2),X1))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3344]) ).
cnf(c_0_3345_0,axiom,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X1),X2))
| X2 = X1
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X2),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_3345]) ).
cnf(c_0_3345_1,axiom,
( X2 = X1
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X1),X2))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X2),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_3345]) ).
cnf(c_0_3345_2,axiom,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X2),X1))
| X2 = X1
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3345]) ).
cnf(c_0_3346_0,axiom,
( hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X1),X2))
| hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X2),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_3346]) ).
cnf(c_0_3346_1,axiom,
( hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X2),X1))
| hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3346]) ).
cnf(c_0_3347_0,axiom,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X2),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_3347]) ).
cnf(c_0_3347_1,axiom,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X2),X1))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3347]) ).
cnf(c_0_3348_0,axiom,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X1),X2))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X2),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_3348]) ).
cnf(c_0_3348_1,axiom,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X2),X1))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3348]) ).
cnf(c_0_3349_0,axiom,
( hAPP(nat,X1,power_power(X1,X2),X3) = hAPP(nat,X1,power_power(X1,X2),X4)
| ~ linordered_semidom(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),one_one(X1)),X2))
| X3 != X4 ),
inference(literals_permutation,[status(thm)],[c_0_3349]) ).
cnf(c_0_3349_1,axiom,
( ~ linordered_semidom(X1)
| hAPP(nat,X1,power_power(X1,X2),X3) = hAPP(nat,X1,power_power(X1,X2),X4)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),one_one(X1)),X2))
| X3 != X4 ),
inference(literals_permutation,[status(thm)],[c_0_3349]) ).
cnf(c_0_3349_2,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),one_one(X1)),X2))
| ~ linordered_semidom(X1)
| hAPP(nat,X1,power_power(X1,X2),X3) = hAPP(nat,X1,power_power(X1,X2),X4)
| X3 != X4 ),
inference(literals_permutation,[status(thm)],[c_0_3349]) ).
cnf(c_0_3349_3,axiom,
( X3 != X4
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),one_one(X1)),X2))
| ~ linordered_semidom(X1)
| hAPP(nat,X1,power_power(X1,X2),X3) = hAPP(nat,X1,power_power(X1,X2),X4) ),
inference(literals_permutation,[status(thm)],[c_0_3349]) ).
cnf(c_0_3350_0,axiom,
( hBOOL(hAPP(int,bool,X1,hAPP(nat,int,semiring_1_of_nat(int),X2)))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),sk1_esk8_1(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_3350]) ).
cnf(c_0_3350_1,axiom,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),sk1_esk8_1(X1)))
| hBOOL(hAPP(int,bool,X1,hAPP(nat,int,semiring_1_of_nat(int),X2))) ),
inference(literals_permutation,[status(thm)],[c_0_3350]) ).
cnf(c_0_3351_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_3351]) ).
cnf(c_0_3351_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_3351]) ).
cnf(c_0_3351_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_3351]) ).
cnf(c_0_3352_0,axiom,
( hBOOL(hAPP(nat,bool,X1,zero_zero(nat)))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),sk1_esk19_2(X2,X1)),X2))
| ~ hBOOL(hAPP(nat,bool,X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3352]) ).
cnf(c_0_3352_1,axiom,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,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_3352]) ).
cnf(c_0_3352_2,axiom,
( ~ hBOOL(hAPP(nat,bool,X1,X2))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,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_3352]) ).
cnf(c_0_3353_0,axiom,
( hBOOL(hAPP(nat,bool,X1,zero_zero(nat)))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),sk1_esk14_2(X2,X1)),X2))
| ~ hBOOL(hAPP(nat,bool,X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3353]) ).
cnf(c_0_3353_1,axiom,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,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_3353]) ).
cnf(c_0_3353_2,axiom,
( ~ hBOOL(hAPP(nat,bool,X1,X2))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,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_3353]) ).
cnf(c_0_3354_0,axiom,
( hAPP(real,real,sqrt,X1) != zero_zero(real)
| ~ hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_3354]) ).
cnf(c_0_3354_1,axiom,
( ~ hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X1))
| hAPP(real,real,sqrt,X1) != zero_zero(real) ),
inference(literals_permutation,[status(thm)],[c_0_3354]) ).
cnf(c_0_3355_0,axiom,
( hAPP(nat,X1,semiring_1_of_nat(X1),number_number_of(nat,X2)) = number_number_of(X1,X2)
| ~ number_ring(X1)
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),number_number_of(int,X2))) ),
inference(literals_permutation,[status(thm)],[c_0_3355]) ).
cnf(c_0_3355_1,axiom,
( ~ number_ring(X1)
| hAPP(nat,X1,semiring_1_of_nat(X1),number_number_of(nat,X2)) = number_number_of(X1,X2)
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),number_number_of(int,X2))) ),
inference(literals_permutation,[status(thm)],[c_0_3355]) ).
cnf(c_0_3355_2,axiom,
( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),number_number_of(int,X2)))
| ~ number_ring(X1)
| hAPP(nat,X1,semiring_1_of_nat(X1),number_number_of(nat,X2)) = number_number_of(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_3355]) ).
cnf(c_0_3356_0,axiom,
( hBOOL(hAPP(int,bool,X1,sk1_esk7_1(X1)))
| ~ hBOOL(hAPP(int,bool,X1,hAPP(nat,int,semiring_1_of_nat(int),X2))) ),
inference(literals_permutation,[status(thm)],[c_0_3356]) ).
cnf(c_0_3356_1,axiom,
( ~ hBOOL(hAPP(int,bool,X1,hAPP(nat,int,semiring_1_of_nat(int),X2)))
| hBOOL(hAPP(int,bool,X1,sk1_esk7_1(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_3356]) ).
cnf(c_0_3357_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(int,fun(int,bool),ord_less(int),X1),pls)) ),
inference(literals_permutation,[status(thm)],[c_0_3357]) ).
cnf(c_0_3357_1,axiom,
( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,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_3357]) ).
cnf(c_0_3358_0,axiom,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),hAPP(X1,X1,plus_plus(X1,one_one(X1)),one_one(X1))))
| ~ linordered_semidom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3358]) ).
cnf(c_0_3358_1,axiom,
( ~ linordered_semidom(X1)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),hAPP(X1,X1,plus_plus(X1,one_one(X1)),one_one(X1)))) ),
inference(literals_permutation,[status(thm)],[c_0_3358]) ).
cnf(c_0_3359_0,axiom,
( hAPP(X1,X1,plus_plus(X1,one_one(X1)),number_number_of(X1,X2)) = number_number_of(X1,hAPP(int,int,plus_plus(int,hAPP(int,int,bit1,pls)),X2))
| ~ number_ring(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3359]) ).
cnf(c_0_3359_1,axiom,
( ~ number_ring(X1)
| hAPP(X1,X1,plus_plus(X1,one_one(X1)),number_number_of(X1,X2)) = number_number_of(X1,hAPP(int,int,plus_plus(int,hAPP(int,int,bit1,pls)),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3359]) ).
cnf(c_0_3360_0,axiom,
( hAPP(nat,nat,plus_plus(nat,number_number_of(nat,X1)),one_one(nat)) = one_one(nat)
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X1),pls)) ),
inference(literals_permutation,[status(thm)],[c_0_3360]) ).
cnf(c_0_3360_1,axiom,
( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,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_3360]) ).
cnf(c_0_3361_0,axiom,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X1),X2))
| X2 != hAPP(int,int,plus_plus(int,X1),hAPP(nat,int,semiring_1_of_nat(int),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3361]) ).
cnf(c_0_3361_1,axiom,
( X2 != hAPP(int,int,plus_plus(int,X1),hAPP(nat,int,semiring_1_of_nat(int),X3))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3361]) ).
cnf(c_0_3362_0,axiom,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,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_3362]) ).
cnf(c_0_3362_1,axiom,
( number_number_of(nat,X2) != zero_zero(nat)
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,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_3362]) ).
cnf(c_0_3363_0,axiom,
( hAPP(nat,nat,plus_plus(nat,X2),sk1_esk13_2(X2,X1)) = X1
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X2),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_3363]) ).
cnf(c_0_3363_1,axiom,
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,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_3363]) ).
cnf(c_0_3364_0,axiom,
( hAPP(nat,nat,plus_plus(nat,X1),sk1_esk3_2(X1,X2)) = X2
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3364]) ).
cnf(c_0_3364_1,axiom,
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,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_3364]) ).
cnf(c_0_3365_0,axiom,
( hAPP(nat,nat,plus_plus(nat,one_one(nat)),number_number_of(nat,X1)) = one_one(nat)
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X1),pls)) ),
inference(literals_permutation,[status(thm)],[c_0_3365]) ).
cnf(c_0_3365_1,axiom,
( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,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_3365]) ).
cnf(c_0_3366_0,axiom,
( hAPP(X1,X1,plus_plus(X1,hAPP(X1,X1,plus_plus(X1,X2),X3)),X4) = hAPP(X1,X1,plus_plus(X1,hAPP(X1,X1,plus_plus(X1,X2),X4)),X3)
| ~ comm_semiring_1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3366]) ).
cnf(c_0_3366_1,axiom,
( ~ comm_semiring_1(X1)
| hAPP(X1,X1,plus_plus(X1,hAPP(X1,X1,plus_plus(X1,X2),X3)),X4) = hAPP(X1,X1,plus_plus(X1,hAPP(X1,X1,plus_plus(X1,X2),X4)),X3) ),
inference(literals_permutation,[status(thm)],[c_0_3366]) ).
cnf(c_0_3367_0,axiom,
( hAPP(nat,int,semiring_1_of_nat(int),sk1_esk15_1(X1)) = X1
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_3367]) ).
cnf(c_0_3367_1,axiom,
( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X1))
| hAPP(nat,int,semiring_1_of_nat(int),sk1_esk15_1(X1)) = X1 ),
inference(literals_permutation,[status(thm)],[c_0_3367]) ).
cnf(c_0_3368_0,axiom,
( hAPP(nat,int,semiring_1_of_nat(int),sk1_esk12_1(X1)) = X1
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_3368]) ).
cnf(c_0_3368_1,axiom,
( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X1))
| hAPP(nat,int,semiring_1_of_nat(int),sk1_esk12_1(X1)) = X1 ),
inference(literals_permutation,[status(thm)],[c_0_3368]) ).
cnf(c_0_3369_0,axiom,
( hAPP(nat,int,semiring_1_of_nat(int),sk1_esk11_1(X1)) = X1
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_3369]) ).
cnf(c_0_3369_1,axiom,
( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X1))
| hAPP(nat,int,semiring_1_of_nat(int),sk1_esk11_1(X1)) = X1 ),
inference(literals_permutation,[status(thm)],[c_0_3369]) ).
cnf(c_0_3370_0,axiom,
( hAPP(nat,int,semiring_1_of_nat(int),sk1_esk2_1(X1)) = X1
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_3370]) ).
cnf(c_0_3370_1,axiom,
( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),X1))
| hAPP(nat,int,semiring_1_of_nat(int),sk1_esk2_1(X1)) = X1 ),
inference(literals_permutation,[status(thm)],[c_0_3370]) ).
cnf(c_0_3371_0,axiom,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),hAPP(X1,X1,plus_plus(X1,X2),one_one(X1))))
| ~ linordered_semidom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3371]) ).
cnf(c_0_3371_1,axiom,
( ~ linordered_semidom(X1)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),hAPP(X1,X1,plus_plus(X1,X2),one_one(X1)))) ),
inference(literals_permutation,[status(thm)],[c_0_3371]) ).
cnf(c_0_3372_0,axiom,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,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_3372]) ).
cnf(c_0_3372_1,axiom,
( X2 != zero_zero(nat)
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,power_power(nat,X1),X2))) ),
inference(literals_permutation,[status(thm)],[c_0_3372]) ).
cnf(c_0_3373_0,axiom,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,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_3373]) ).
cnf(c_0_3373_1,axiom,
( X2 != zero_zero(nat)
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,power_power(nat,X1),X2))) ),
inference(literals_permutation,[status(thm)],[c_0_3373]) ).
cnf(c_0_3374_0,axiom,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X1),hAPP(int,int,plus_plus(int,X2),one_one(int))))
| X1 != X2 ),
inference(literals_permutation,[status(thm)],[c_0_3374]) ).
cnf(c_0_3374_1,axiom,
( X1 != X2
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X1),hAPP(int,int,plus_plus(int,X2),one_one(int)))) ),
inference(literals_permutation,[status(thm)],[c_0_3374]) ).
cnf(c_0_3375_0,axiom,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),hAPP(nat,X1,semiring_1_of_nat(X1),X2)))
| ~ linordered_semidom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3375]) ).
cnf(c_0_3375_1,axiom,
( ~ linordered_semidom(X1)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),hAPP(nat,X1,semiring_1_of_nat(X1),X2))) ),
inference(literals_permutation,[status(thm)],[c_0_3375]) ).
cnf(c_0_3376_0,axiom,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),hAPP(nat,X1,semiring_1_of_nat(X1),X2)))
| ~ linordered_semidom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3376]) ).
cnf(c_0_3376_1,axiom,
( ~ linordered_semidom(X1)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),hAPP(nat,X1,semiring_1_of_nat(X1),X2))) ),
inference(literals_permutation,[status(thm)],[c_0_3376]) ).
cnf(c_0_3379_0,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),one_one(X1)),zero_zero(X1)))
| ~ linordered_semidom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3379]) ).
cnf(c_0_3379_1,axiom,
( ~ linordered_semidom(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),one_one(X1)),zero_zero(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_3379]) ).
cnf(c_0_3380_0,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),one_one(X1)),zero_zero(X1)))
| ~ linordered_semidom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3380]) ).
cnf(c_0_3380_1,axiom,
( ~ linordered_semidom(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),one_one(X1)),zero_zero(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_3380]) ).
cnf(c_0_3381_0,axiom,
( hAPP(X1,X1,plus_plus(X1,hAPP(nat,X1,semiring_1_of_nat(X1),X2)),hAPP(nat,X1,semiring_1_of_nat(X1),X3)) = hAPP(nat,X1,semiring_1_of_nat(X1),hAPP(nat,nat,plus_plus(nat,X2),X3))
| ~ semiring_1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3381]) ).
cnf(c_0_3381_1,axiom,
( ~ semiring_1(X1)
| hAPP(X1,X1,plus_plus(X1,hAPP(nat,X1,semiring_1_of_nat(X1),X2)),hAPP(nat,X1,semiring_1_of_nat(X1),X3)) = hAPP(nat,X1,semiring_1_of_nat(X1),hAPP(nat,nat,plus_plus(nat,X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3381]) ).
cnf(c_0_3384_0,axiom,
( ~ order(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| ti(X1,X2) != ti(X1,X3) ),
inference(literals_permutation,[status(thm)],[c_0_3384]) ).
cnf(c_0_3384_1,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| ~ order(X1)
| ti(X1,X2) != ti(X1,X3) ),
inference(literals_permutation,[status(thm)],[c_0_3384]) ).
cnf(c_0_3384_2,axiom,
( ti(X1,X2) != ti(X1,X3)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| ~ order(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3384]) ).
cnf(c_0_3385_0,axiom,
( ~ linorder(X1)
| ti(X1,X2) != ti(X1,X3)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3385]) ).
cnf(c_0_3385_1,axiom,
( ti(X1,X2) != ti(X1,X3)
| ~ linorder(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3385]) ).
cnf(c_0_3385_2,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| ti(X1,X2) != ti(X1,X3)
| ~ linorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3385]) ).
cnf(c_0_3386_0,axiom,
( ~ linorder(X1)
| ti(X1,X2) != ti(X1,X3)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3386]) ).
cnf(c_0_3386_1,axiom,
( ti(X1,X2) != ti(X1,X3)
| ~ linorder(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3386]) ).
cnf(c_0_3386_2,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X2))
| ti(X1,X2) != ti(X1,X3)
| ~ linorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3386]) ).
cnf(c_0_3387_0,axiom,
( ~ linorder(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| ti(X1,X2) != ti(X1,X3) ),
inference(literals_permutation,[status(thm)],[c_0_3387]) ).
cnf(c_0_3387_1,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| ~ linorder(X1)
| ti(X1,X2) != ti(X1,X3) ),
inference(literals_permutation,[status(thm)],[c_0_3387]) ).
cnf(c_0_3387_2,axiom,
( ti(X1,X2) != ti(X1,X3)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| ~ linorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3387]) ).
cnf(c_0_3388_0,axiom,
( ti(X1,X2) != ti(X1,X3)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| ~ order(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3388]) ).
cnf(c_0_3388_1,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| ti(X1,X2) != ti(X1,X3)
| ~ order(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3388]) ).
cnf(c_0_3388_2,axiom,
( ~ order(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| ti(X1,X2) != ti(X1,X3) ),
inference(literals_permutation,[status(thm)],[c_0_3388]) ).
cnf(c_0_3389_0,axiom,
( ti(X1,X2) != ti(X1,X3)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| ~ order(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3389]) ).
cnf(c_0_3389_1,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| ti(X1,X2) != ti(X1,X3)
| ~ order(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3389]) ).
cnf(c_0_3389_2,axiom,
( ~ order(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| ti(X1,X2) != ti(X1,X3) ),
inference(literals_permutation,[status(thm)],[c_0_3389]) ).
cnf(c_0_3390_0,axiom,
( ti(X1,X2) != ti(X1,X3)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X2))
| ~ order(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3390]) ).
cnf(c_0_3390_1,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X2))
| ti(X1,X2) != ti(X1,X3)
| ~ order(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3390]) ).
cnf(c_0_3390_2,axiom,
( ~ order(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X2))
| ti(X1,X2) != ti(X1,X3) ),
inference(literals_permutation,[status(thm)],[c_0_3390]) ).
cnf(c_0_3393_0,axiom,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X2))
| ~ preorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3393]) ).
cnf(c_0_3393_1,axiom,
( ~ preorder(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3393]) ).
cnf(c_0_3394_0,axiom,
( hBOOL(X1)
| ~ hBOOL(X1)
| ~ hBOOL(X2)
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X3))
| ~ hBOOL(X2) ),
inference(literals_permutation,[status(thm)],[c_0_3394]) ).
cnf(c_0_3394_1,axiom,
( ~ hBOOL(X1)
| hBOOL(X1)
| ~ hBOOL(X2)
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X3))
| ~ hBOOL(X2) ),
inference(literals_permutation,[status(thm)],[c_0_3394]) ).
cnf(c_0_3394_2,axiom,
( ~ hBOOL(X2)
| ~ hBOOL(X1)
| hBOOL(X1)
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X3))
| ~ hBOOL(X2) ),
inference(literals_permutation,[status(thm)],[c_0_3394]) ).
cnf(c_0_3394_3,axiom,
( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X3))
| ~ hBOOL(X2)
| ~ hBOOL(X1)
| hBOOL(X1)
| ~ hBOOL(X2) ),
inference(literals_permutation,[status(thm)],[c_0_3394]) ).
cnf(c_0_3394_4,axiom,
( ~ hBOOL(X2)
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X3))
| ~ hBOOL(X2)
| ~ hBOOL(X1)
| hBOOL(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3394]) ).
cnf(c_0_3395_0,axiom,
( hBOOL(X2)
| ~ hBOOL(X1)
| ~ hBOOL(X2)
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X3))
| ~ hBOOL(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3395]) ).
cnf(c_0_3395_1,axiom,
( ~ hBOOL(X1)
| hBOOL(X2)
| ~ hBOOL(X2)
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X3))
| ~ hBOOL(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3395]) ).
cnf(c_0_3395_2,axiom,
( ~ hBOOL(X2)
| ~ hBOOL(X1)
| hBOOL(X2)
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X3))
| ~ hBOOL(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3395]) ).
cnf(c_0_3395_3,axiom,
( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X3))
| ~ hBOOL(X2)
| ~ hBOOL(X1)
| hBOOL(X2)
| ~ hBOOL(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3395]) ).
cnf(c_0_3395_4,axiom,
( ~ hBOOL(X1)
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X3))
| ~ hBOOL(X2)
| ~ hBOOL(X1)
| hBOOL(X2) ),
inference(literals_permutation,[status(thm)],[c_0_3395]) ).
cnf(c_0_3396_0,axiom,
( hBOOL(X1)
| ~ hBOOL(X1)
| ~ hBOOL(X2)
| ~ hBOOL(X2)
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3396]) ).
cnf(c_0_3396_1,axiom,
( ~ hBOOL(X1)
| hBOOL(X1)
| ~ hBOOL(X2)
| ~ hBOOL(X2)
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3396]) ).
cnf(c_0_3396_2,axiom,
( ~ hBOOL(X2)
| ~ hBOOL(X1)
| hBOOL(X1)
| ~ hBOOL(X2)
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3396]) ).
cnf(c_0_3396_3,axiom,
( ~ hBOOL(X2)
| ~ hBOOL(X2)
| ~ hBOOL(X1)
| hBOOL(X1)
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3396]) ).
cnf(c_0_3396_4,axiom,
( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X3))
| ~ hBOOL(X2)
| ~ hBOOL(X2)
| ~ hBOOL(X1)
| hBOOL(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3396]) ).
cnf(c_0_3397_0,axiom,
( hBOOL(X2)
| ~ hBOOL(X1)
| ~ hBOOL(X2)
| ~ hBOOL(X1)
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3397]) ).
cnf(c_0_3397_1,axiom,
( ~ hBOOL(X1)
| hBOOL(X2)
| ~ hBOOL(X2)
| ~ hBOOL(X1)
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3397]) ).
cnf(c_0_3397_2,axiom,
( ~ hBOOL(X2)
| ~ hBOOL(X1)
| hBOOL(X2)
| ~ hBOOL(X1)
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3397]) ).
cnf(c_0_3397_3,axiom,
( ~ hBOOL(X1)
| ~ hBOOL(X2)
| ~ hBOOL(X1)
| hBOOL(X2)
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3397]) ).
cnf(c_0_3397_4,axiom,
( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X3))
| ~ hBOOL(X1)
| ~ hBOOL(X2)
| ~ hBOOL(X1)
| hBOOL(X2) ),
inference(literals_permutation,[status(thm)],[c_0_3397]) ).
cnf(c_0_3398_0,axiom,
( hBOOL(X1)
| hBOOL(X2)
| hBOOL(X1)
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X3))
| ~ hBOOL(X2) ),
inference(literals_permutation,[status(thm)],[c_0_3398]) ).
cnf(c_0_3398_1,axiom,
( hBOOL(X2)
| hBOOL(X1)
| hBOOL(X1)
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X3))
| ~ hBOOL(X2) ),
inference(literals_permutation,[status(thm)],[c_0_3398]) ).
cnf(c_0_3398_2,axiom,
( hBOOL(X1)
| hBOOL(X2)
| hBOOL(X1)
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X3))
| ~ hBOOL(X2) ),
inference(literals_permutation,[status(thm)],[c_0_3398]) ).
cnf(c_0_3398_3,axiom,
( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X3))
| hBOOL(X1)
| hBOOL(X2)
| hBOOL(X1)
| ~ hBOOL(X2) ),
inference(literals_permutation,[status(thm)],[c_0_3398]) ).
cnf(c_0_3398_4,axiom,
( ~ hBOOL(X2)
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X3))
| hBOOL(X1)
| hBOOL(X2)
| hBOOL(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3398]) ).
cnf(c_0_3399_0,axiom,
( hBOOL(X1)
| hBOOL(X2)
| hBOOL(X2)
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X3))
| ~ hBOOL(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3399]) ).
cnf(c_0_3399_1,axiom,
( hBOOL(X2)
| hBOOL(X1)
| hBOOL(X2)
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X3))
| ~ hBOOL(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3399]) ).
cnf(c_0_3399_2,axiom,
( hBOOL(X2)
| hBOOL(X2)
| hBOOL(X1)
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X3))
| ~ hBOOL(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3399]) ).
cnf(c_0_3399_3,axiom,
( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X3))
| hBOOL(X2)
| hBOOL(X2)
| hBOOL(X1)
| ~ hBOOL(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3399]) ).
cnf(c_0_3399_4,axiom,
( ~ hBOOL(X1)
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X3))
| hBOOL(X2)
| hBOOL(X2)
| hBOOL(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3399]) ).
cnf(c_0_3400_0,axiom,
( hBOOL(X1)
| hBOOL(X2)
| hBOOL(X1)
| ~ hBOOL(X2)
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3400]) ).
cnf(c_0_3400_1,axiom,
( hBOOL(X2)
| hBOOL(X1)
| hBOOL(X1)
| ~ hBOOL(X2)
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3400]) ).
cnf(c_0_3400_2,axiom,
( hBOOL(X1)
| hBOOL(X2)
| hBOOL(X1)
| ~ hBOOL(X2)
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3400]) ).
cnf(c_0_3400_3,axiom,
( ~ hBOOL(X2)
| hBOOL(X1)
| hBOOL(X2)
| hBOOL(X1)
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3400]) ).
cnf(c_0_3400_4,axiom,
( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X3))
| ~ hBOOL(X2)
| hBOOL(X1)
| hBOOL(X2)
| hBOOL(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3400]) ).
cnf(c_0_3401_0,axiom,
( hBOOL(X1)
| hBOOL(X2)
| hBOOL(X2)
| ~ hBOOL(X1)
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3401]) ).
cnf(c_0_3401_1,axiom,
( hBOOL(X2)
| hBOOL(X1)
| hBOOL(X2)
| ~ hBOOL(X1)
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3401]) ).
cnf(c_0_3401_2,axiom,
( hBOOL(X2)
| hBOOL(X2)
| hBOOL(X1)
| ~ hBOOL(X1)
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3401]) ).
cnf(c_0_3401_3,axiom,
( ~ hBOOL(X1)
| hBOOL(X2)
| hBOOL(X2)
| hBOOL(X1)
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3401]) ).
cnf(c_0_3401_4,axiom,
( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X3))
| ~ hBOOL(X1)
| hBOOL(X2)
| hBOOL(X2)
| hBOOL(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3401]) ).
cnf(c_0_3405_0,axiom,
( X1 != zero_zero(nat)
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_3405]) ).
cnf(c_0_3405_1,axiom,
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X1))
| X1 != zero_zero(nat) ),
inference(literals_permutation,[status(thm)],[c_0_3405]) ).
cnf(c_0_3406_0,axiom,
( X1 = zero_zero(nat)
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),zero_zero(nat))) ),
inference(literals_permutation,[status(thm)],[c_0_3406]) ).
cnf(c_0_3406_1,axiom,
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),zero_zero(nat)))
| X1 = zero_zero(nat) ),
inference(literals_permutation,[status(thm)],[c_0_3406]) ).
cnf(c_0_3407_0,axiom,
( number_number_of(nat,X1) = zero_zero(nat)
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X1),pls)) ),
inference(literals_permutation,[status(thm)],[c_0_3407]) ).
cnf(c_0_3407_1,axiom,
( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X1),pls))
| number_number_of(nat,X1) = zero_zero(nat) ),
inference(literals_permutation,[status(thm)],[c_0_3407]) ).
cnf(c_0_3408_0,axiom,
( number_number_of(nat,X1) = zero_zero(nat)
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X1),pls)) ),
inference(literals_permutation,[status(thm)],[c_0_3408]) ).
cnf(c_0_3408_1,axiom,
( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X1),pls))
| number_number_of(nat,X1) = zero_zero(nat) ),
inference(literals_permutation,[status(thm)],[c_0_3408]) ).
cnf(c_0_3412_0,axiom,
( X1 != zero_zero(nat)
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X2),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_3412]) ).
cnf(c_0_3412_1,axiom,
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X2),X1))
| X1 != zero_zero(nat) ),
inference(literals_permutation,[status(thm)],[c_0_3412]) ).
cnf(c_0_3413_0,axiom,
( ~ hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X1),X2))
| X1 != X2 ),
inference(literals_permutation,[status(thm)],[c_0_3413]) ).
cnf(c_0_3413_1,axiom,
( X1 != X2
| ~ hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3413]) ).
cnf(c_0_3414_0,axiom,
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2))
| X1 != X2 ),
inference(literals_permutation,[status(thm)],[c_0_3414]) ).
cnf(c_0_3414_1,axiom,
( X1 != X2
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3414]) ).
cnf(c_0_3415_0,axiom,
( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X1),X2))
| X1 != X2 ),
inference(literals_permutation,[status(thm)],[c_0_3415]) ).
cnf(c_0_3415_1,axiom,
( X1 != X2
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3415]) ).
cnf(c_0_3416_0,axiom,
( X1 != X2
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3416]) ).
cnf(c_0_3416_1,axiom,
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2))
| X1 != X2 ),
inference(literals_permutation,[status(thm)],[c_0_3416]) ).
cnf(c_0_3417_0,axiom,
( X1 != X2
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X2),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_3417]) ).
cnf(c_0_3417_1,axiom,
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X2),X1))
| X1 != X2 ),
inference(literals_permutation,[status(thm)],[c_0_3417]) ).
cnf(c_0_3418_0,axiom,
( X1 != X2
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3418]) ).
cnf(c_0_3418_1,axiom,
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2))
| X1 != X2 ),
inference(literals_permutation,[status(thm)],[c_0_3418]) ).
cnf(c_0_3419_0,axiom,
( X1 != X2
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X2),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_3419]) ).
cnf(c_0_3419_1,axiom,
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X2),X1))
| X1 != X2 ),
inference(literals_permutation,[status(thm)],[c_0_3419]) ).
cnf(c_0_3424_0,axiom,
( hAPP(nat,nat,plus_plus(nat,number_number_of(nat,X1)),one_one(nat)) = number_number_of(nat,hAPP(int,int,succ,X1))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X1),pls)) ),
inference(literals_permutation,[status(thm)],[c_0_3424]) ).
cnf(c_0_3424_1,axiom,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X1),pls))
| hAPP(nat,nat,plus_plus(nat,number_number_of(nat,X1)),one_one(nat)) = number_number_of(nat,hAPP(int,int,succ,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_3424]) ).
cnf(c_0_3425_0,axiom,
( hAPP(nat,nat,plus_plus(nat,one_one(nat)),number_number_of(nat,X1)) = number_number_of(nat,hAPP(int,int,succ,X1))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X1),pls)) ),
inference(literals_permutation,[status(thm)],[c_0_3425]) ).
cnf(c_0_3425_1,axiom,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X1),pls))
| hAPP(nat,nat,plus_plus(nat,one_one(nat)),number_number_of(nat,X1)) = number_number_of(nat,hAPP(int,int,succ,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_3425]) ).
cnf(c_0_3426_0,axiom,
( hBOOL(hAPP(int,bool,X1,hAPP(nat,int,semiring_1_of_nat(int),X2)))
| ~ hBOOL(hAPP(int,bool,X1,sk1_esk8_1(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_3426]) ).
cnf(c_0_3426_1,axiom,
( ~ hBOOL(hAPP(int,bool,X1,sk1_esk8_1(X1)))
| hBOOL(hAPP(int,bool,X1,hAPP(nat,int,semiring_1_of_nat(int),X2))) ),
inference(literals_permutation,[status(thm)],[c_0_3426]) ).
cnf(c_0_3427_0,axiom,
( hAPP(X1,X1,plus_plus(X1,hAPP(X1,X1,plus_plus(X1,X2),X3)),X4) = hAPP(X1,X1,plus_plus(X1,X2),hAPP(X1,X1,plus_plus(X1,X3),X4))
| ~ comm_semiring_1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3427]) ).
cnf(c_0_3427_1,axiom,
( ~ comm_semiring_1(X1)
| hAPP(X1,X1,plus_plus(X1,hAPP(X1,X1,plus_plus(X1,X2),X3)),X4) = hAPP(X1,X1,plus_plus(X1,X2),hAPP(X1,X1,plus_plus(X1,X3),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_3427]) ).
cnf(c_0_3428_0,axiom,
( hAPP(X1,X1,plus_plus(X1,hAPP(X1,X1,plus_plus(X1,X2),X3)),X4) = hAPP(X1,X1,plus_plus(X1,X2),hAPP(X1,X1,plus_plus(X1,X3),X4))
| ~ comm_semiring_1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3428]) ).
cnf(c_0_3428_1,axiom,
( ~ comm_semiring_1(X1)
| hAPP(X1,X1,plus_plus(X1,hAPP(X1,X1,plus_plus(X1,X2),X3)),X4) = hAPP(X1,X1,plus_plus(X1,X2),hAPP(X1,X1,plus_plus(X1,X3),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_3428]) ).
cnf(c_0_3429_0,axiom,
( hAPP(X1,X1,plus_plus(X1,hAPP(X1,X1,plus_plus(X1,X2),X3)),X4) = hAPP(X1,X1,plus_plus(X1,X2),hAPP(X1,X1,plus_plus(X1,X3),X4))
| ~ ab_semigroup_add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3429]) ).
cnf(c_0_3429_1,axiom,
( ~ ab_semigroup_add(X1)
| hAPP(X1,X1,plus_plus(X1,hAPP(X1,X1,plus_plus(X1,X2),X3)),X4) = hAPP(X1,X1,plus_plus(X1,X2),hAPP(X1,X1,plus_plus(X1,X3),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_3429]) ).
cnf(c_0_3435_0,axiom,
( hAPP(nat,X1,power_power(X1,hAPP(nat,X1,semiring_1_of_nat(X1),X2)),X3) = hAPP(nat,X1,semiring_1_of_nat(X1),hAPP(nat,nat,power_power(nat,X2),X3))
| ~ semiring_1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3435]) ).
cnf(c_0_3435_1,axiom,
( ~ semiring_1(X1)
| hAPP(nat,X1,power_power(X1,hAPP(nat,X1,semiring_1_of_nat(X1),X2)),X3) = hAPP(nat,X1,semiring_1_of_nat(X1),hAPP(nat,nat,power_power(nat,X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3435]) ).
cnf(c_0_3436_0,axiom,
( hAPP(X1,X1,plus_plus(X1,hAPP(X1,X1,plus_plus(X1,one_one(X1)),number_number_of(X1,X2))),number_number_of(X1,X2)) = number_number_of(X1,hAPP(int,int,bit1,X2))
| ~ number_ring(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3436]) ).
cnf(c_0_3436_1,axiom,
( ~ number_ring(X1)
| hAPP(X1,X1,plus_plus(X1,hAPP(X1,X1,plus_plus(X1,one_one(X1)),number_number_of(X1,X2))),number_number_of(X1,X2)) = number_number_of(X1,hAPP(int,int,bit1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3436]) ).
cnf(c_0_3437_0,axiom,
( hAPP(X1,X1,plus_plus(X1,hAPP(X1,X1,plus_plus(X1,zero_zero(X1)),number_number_of(X1,X2))),number_number_of(X1,X2)) = number_number_of(X1,hAPP(int,int,bit0,X2))
| ~ number_ring(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3437]) ).
cnf(c_0_3437_1,axiom,
( ~ number_ring(X1)
| hAPP(X1,X1,plus_plus(X1,hAPP(X1,X1,plus_plus(X1,zero_zero(X1)),number_number_of(X1,X2))),number_number_of(X1,X2)) = number_number_of(X1,hAPP(int,int,bit0,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3437]) ).
cnf(c_0_3441_0,axiom,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2))
| X2 != hAPP(nat,nat,plus_plus(nat,X1),X3) ),
inference(literals_permutation,[status(thm)],[c_0_3441]) ).
cnf(c_0_3441_1,axiom,
( X2 != hAPP(nat,nat,plus_plus(nat,X1),X3)
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3441]) ).
cnf(c_0_3442_0,axiom,
( hAPP(nat,X1,semiring_1_of_nat(X1),number_number_of(nat,X2)) = zero_zero(X1)
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),number_number_of(int,X2)))
| ~ number_ring(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3442]) ).
cnf(c_0_3442_1,axiom,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),number_number_of(int,X2)))
| hAPP(nat,X1,semiring_1_of_nat(X1),number_number_of(nat,X2)) = zero_zero(X1)
| ~ number_ring(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3442]) ).
cnf(c_0_3442_2,axiom,
( ~ number_ring(X1)
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),number_number_of(int,X2)))
| hAPP(nat,X1,semiring_1_of_nat(X1),number_number_of(nat,X2)) = zero_zero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3442]) ).
cnf(c_0_3443_0,axiom,
( hAPP(X1,X1,plus_plus(X1,number_number_of(X1,X2)),one_one(X1)) = number_number_of(X1,hAPP(int,int,plus_plus(int,X2),hAPP(int,int,bit1,pls)))
| ~ number_ring(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3443]) ).
cnf(c_0_3443_1,axiom,
( ~ number_ring(X1)
| hAPP(X1,X1,plus_plus(X1,number_number_of(X1,X2)),one_one(X1)) = number_number_of(X1,hAPP(int,int,plus_plus(int,X2),hAPP(int,int,bit1,pls))) ),
inference(literals_permutation,[status(thm)],[c_0_3443]) ).
cnf(c_0_3444_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_3444]) ).
cnf(c_0_3444_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_3444]) ).
cnf(c_0_3444_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_3444]) ).
cnf(c_0_3445_0,axiom,
( hAPP(X1,X1,plus_plus(X1,one_one(X1)),one_one(X1)) = number_number_of(X1,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))
| ~ number_semiring(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3445]) ).
cnf(c_0_3445_1,axiom,
( ~ number_semiring(X1)
| hAPP(X1,X1,plus_plus(X1,one_one(X1)),one_one(X1)) = number_number_of(X1,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))) ),
inference(literals_permutation,[status(thm)],[c_0_3445]) ).
cnf(c_0_3446_0,axiom,
( hAPP(X1,X1,plus_plus(X1,one_one(X1)),one_one(X1)) = number_number_of(X1,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))
| ~ number_ring(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3446]) ).
cnf(c_0_3446_1,axiom,
( ~ number_ring(X1)
| hAPP(X1,X1,plus_plus(X1,one_one(X1)),one_one(X1)) = number_number_of(X1,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))) ),
inference(literals_permutation,[status(thm)],[c_0_3446]) ).
cnf(c_0_3448_0,axiom,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
| ~ order(X1)
| ti(X1,X2) != ti(X1,X3) ),
inference(literals_permutation,[status(thm)],[c_0_3448]) ).
cnf(c_0_3448_1,axiom,
( ~ order(X1)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
| ti(X1,X2) != ti(X1,X3) ),
inference(literals_permutation,[status(thm)],[c_0_3448]) ).
cnf(c_0_3448_2,axiom,
( ti(X1,X2) != ti(X1,X3)
| ~ order(X1)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3448]) ).
cnf(c_0_3449_0,axiom,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
| ~ order(X1)
| ti(X1,X2) != ti(X1,X3) ),
inference(literals_permutation,[status(thm)],[c_0_3449]) ).
cnf(c_0_3449_1,axiom,
( ~ order(X1)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
| ti(X1,X2) != ti(X1,X3) ),
inference(literals_permutation,[status(thm)],[c_0_3449]) ).
cnf(c_0_3449_2,axiom,
( ti(X1,X2) != ti(X1,X3)
| ~ order(X1)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3449]) ).
cnf(c_0_3450_0,axiom,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X2))
| ~ order(X1)
| ti(X1,X2) != ti(X1,X3) ),
inference(literals_permutation,[status(thm)],[c_0_3450]) ).
cnf(c_0_3450_1,axiom,
( ~ order(X1)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X2))
| ti(X1,X2) != ti(X1,X3) ),
inference(literals_permutation,[status(thm)],[c_0_3450]) ).
cnf(c_0_3450_2,axiom,
( ti(X1,X2) != ti(X1,X3)
| ~ order(X1)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3450]) ).
cnf(c_0_3451_0,axiom,
( hAPP(X1,X1,plus_plus(X1,X2),hAPP(X1,X1,plus_plus(X1,X3),X4)) = hAPP(X1,X1,plus_plus(X1,X3),hAPP(X1,X1,plus_plus(X1,X2),X4))
| ~ comm_semiring_1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3451]) ).
cnf(c_0_3451_1,axiom,
( ~ comm_semiring_1(X1)
| hAPP(X1,X1,plus_plus(X1,X2),hAPP(X1,X1,plus_plus(X1,X3),X4)) = hAPP(X1,X1,plus_plus(X1,X3),hAPP(X1,X1,plus_plus(X1,X2),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_3451]) ).
cnf(c_0_3452_0,axiom,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),one_one(X1)))
| ~ linordered_semidom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3452]) ).
cnf(c_0_3452_1,axiom,
( ~ linordered_semidom(X1)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),one_one(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_3452]) ).
cnf(c_0_3453_0,axiom,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),one_one(X1)))
| ~ linordered_semidom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3453]) ).
cnf(c_0_3453_1,axiom,
( ~ linordered_semidom(X1)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),one_one(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_3453]) ).
cnf(c_0_3455_0,axiom,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
| X2 != X3
| ~ preorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3455]) ).
cnf(c_0_3455_1,axiom,
( X2 != X3
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
| ~ preorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3455]) ).
cnf(c_0_3455_2,axiom,
( ~ preorder(X1)
| X2 != X3
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3455]) ).
cnf(c_0_3456_0,axiom,
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X2))
| ~ preorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3456]) ).
cnf(c_0_3456_1,axiom,
( ~ preorder(X1)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3456]) ).
cnf(c_0_3460_0,axiom,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X1),pls))
| number_number_of(nat,X1) != zero_zero(nat) ),
inference(literals_permutation,[status(thm)],[c_0_3460]) ).
cnf(c_0_3460_1,axiom,
( number_number_of(nat,X1) != zero_zero(nat)
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X1),pls)) ),
inference(literals_permutation,[status(thm)],[c_0_3460]) ).
cnf(c_0_3461_0,axiom,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X1),pls))
| number_number_of(nat,X1) != zero_zero(nat) ),
inference(literals_permutation,[status(thm)],[c_0_3461]) ).
cnf(c_0_3461_1,axiom,
( number_number_of(nat,X1) != zero_zero(nat)
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X1),pls)) ),
inference(literals_permutation,[status(thm)],[c_0_3461]) ).
cnf(c_0_3465_0,axiom,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X1))
| X1 = zero_zero(nat) ),
inference(literals_permutation,[status(thm)],[c_0_3465]) ).
cnf(c_0_3465_1,axiom,
( X1 = zero_zero(nat)
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_3465]) ).
cnf(c_0_3466_0,axiom,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X1))
| X1 = zero_zero(nat) ),
inference(literals_permutation,[status(thm)],[c_0_3466]) ).
cnf(c_0_3466_1,axiom,
( X1 = zero_zero(nat)
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_3466]) ).
cnf(c_0_3469_0,axiom,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),zero_zero(nat)))
| X1 != zero_zero(nat) ),
inference(literals_permutation,[status(thm)],[c_0_3469]) ).
cnf(c_0_3469_1,axiom,
( X1 != zero_zero(nat)
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),zero_zero(nat))) ),
inference(literals_permutation,[status(thm)],[c_0_3469]) ).
cnf(c_0_3474_0,axiom,
( hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X1),X2))
| X1 != X2 ),
inference(literals_permutation,[status(thm)],[c_0_3474]) ).
cnf(c_0_3474_1,axiom,
( X1 != X2
| hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3474]) ).
cnf(c_0_3475_0,axiom,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2))
| X1 != X2 ),
inference(literals_permutation,[status(thm)],[c_0_3475]) ).
cnf(c_0_3475_1,axiom,
( X1 != X2
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3475]) ).
cnf(c_0_3476_0,axiom,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2))
| X1 != X2 ),
inference(literals_permutation,[status(thm)],[c_0_3476]) ).
cnf(c_0_3476_1,axiom,
( X1 != X2
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3476]) ).
cnf(c_0_3477_0,axiom,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2))
| X1 != X2 ),
inference(literals_permutation,[status(thm)],[c_0_3477]) ).
cnf(c_0_3477_1,axiom,
( X1 != X2
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3477]) ).
cnf(c_0_3486_0,axiom,
( hAPP(X1,X1,plus_plus(X1,number_number_of(X1,X2)),number_number_of(X1,X3)) = number_number_of(X1,hAPP(int,int,plus_plus(int,X2),X3))
| ~ number_ring(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3486]) ).
cnf(c_0_3486_1,axiom,
( ~ number_ring(X1)
| hAPP(X1,X1,plus_plus(X1,number_number_of(X1,X2)),number_number_of(X1,X3)) = number_number_of(X1,hAPP(int,int,plus_plus(int,X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3486]) ).
cnf(c_0_3487_0,axiom,
( hAPP(X1,X1,plus_plus(X1,number_number_of(X1,X2)),number_number_of(X1,X3)) = number_number_of(X1,hAPP(int,int,plus_plus(int,X2),X3))
| ~ number_ring(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3487]) ).
cnf(c_0_3487_1,axiom,
( ~ number_ring(X1)
| hAPP(X1,X1,plus_plus(X1,number_number_of(X1,X2)),number_number_of(X1,X3)) = number_number_of(X1,hAPP(int,int,plus_plus(int,X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3487]) ).
cnf(c_0_3488_0,axiom,
( ti(X1,X2) = ti(X1,X3)
| ~ cancel_semigroup_add(X1)
| hAPP(X1,X1,plus_plus(X1,X4),X2) != hAPP(X1,X1,plus_plus(X1,X4),X3) ),
inference(literals_permutation,[status(thm)],[c_0_3488]) ).
cnf(c_0_3488_1,axiom,
( ~ cancel_semigroup_add(X1)
| ti(X1,X2) = ti(X1,X3)
| hAPP(X1,X1,plus_plus(X1,X4),X2) != hAPP(X1,X1,plus_plus(X1,X4),X3) ),
inference(literals_permutation,[status(thm)],[c_0_3488]) ).
cnf(c_0_3488_2,axiom,
( hAPP(X1,X1,plus_plus(X1,X4),X2) != hAPP(X1,X1,plus_plus(X1,X4),X3)
| ~ cancel_semigroup_add(X1)
| ti(X1,X2) = ti(X1,X3) ),
inference(literals_permutation,[status(thm)],[c_0_3488]) ).
cnf(c_0_3489_0,axiom,
( ti(X1,X2) = ti(X1,X3)
| ~ cancel_semigroup_add(X1)
| hAPP(X1,X1,plus_plus(X1,X2),X4) != hAPP(X1,X1,plus_plus(X1,X3),X4) ),
inference(literals_permutation,[status(thm)],[c_0_3489]) ).
cnf(c_0_3489_1,axiom,
( ~ cancel_semigroup_add(X1)
| ti(X1,X2) = ti(X1,X3)
| hAPP(X1,X1,plus_plus(X1,X2),X4) != hAPP(X1,X1,plus_plus(X1,X3),X4) ),
inference(literals_permutation,[status(thm)],[c_0_3489]) ).
cnf(c_0_3489_2,axiom,
( hAPP(X1,X1,plus_plus(X1,X2),X4) != hAPP(X1,X1,plus_plus(X1,X3),X4)
| ~ cancel_semigroup_add(X1)
| ti(X1,X2) = ti(X1,X3) ),
inference(literals_permutation,[status(thm)],[c_0_3489]) ).
cnf(c_0_3490_0,axiom,
( ti(X1,X2) = ti(X1,X3)
| hAPP(X1,X1,plus_plus(X1,X4),X2) != hAPP(X1,X1,plus_plus(X1,X4),X3)
| ~ cancel_semigroup_add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3490]) ).
cnf(c_0_3490_1,axiom,
( hAPP(X1,X1,plus_plus(X1,X4),X2) != hAPP(X1,X1,plus_plus(X1,X4),X3)
| ti(X1,X2) = ti(X1,X3)
| ~ cancel_semigroup_add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3490]) ).
cnf(c_0_3490_2,axiom,
( ~ cancel_semigroup_add(X1)
| hAPP(X1,X1,plus_plus(X1,X4),X2) != hAPP(X1,X1,plus_plus(X1,X4),X3)
| ti(X1,X2) = ti(X1,X3) ),
inference(literals_permutation,[status(thm)],[c_0_3490]) ).
cnf(c_0_3491_0,axiom,
( ti(X1,X2) = ti(X1,X3)
| hAPP(X1,X1,plus_plus(X1,X4),X2) != hAPP(X1,X1,plus_plus(X1,X4),X3)
| ~ cancel146912293up_add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3491]) ).
cnf(c_0_3491_1,axiom,
( hAPP(X1,X1,plus_plus(X1,X4),X2) != hAPP(X1,X1,plus_plus(X1,X4),X3)
| ti(X1,X2) = ti(X1,X3)
| ~ cancel146912293up_add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3491]) ).
cnf(c_0_3491_2,axiom,
( ~ cancel146912293up_add(X1)
| hAPP(X1,X1,plus_plus(X1,X4),X2) != hAPP(X1,X1,plus_plus(X1,X4),X3)
| ti(X1,X2) = ti(X1,X3) ),
inference(literals_permutation,[status(thm)],[c_0_3491]) ).
cnf(c_0_3492_0,axiom,
( ti(X1,X2) = ti(X1,X3)
| hAPP(X1,X1,plus_plus(X1,X2),X4) != hAPP(X1,X1,plus_plus(X1,X3),X4)
| ~ cancel_semigroup_add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3492]) ).
cnf(c_0_3492_1,axiom,
( hAPP(X1,X1,plus_plus(X1,X2),X4) != hAPP(X1,X1,plus_plus(X1,X3),X4)
| ti(X1,X2) = ti(X1,X3)
| ~ cancel_semigroup_add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3492]) ).
cnf(c_0_3492_2,axiom,
( ~ cancel_semigroup_add(X1)
| hAPP(X1,X1,plus_plus(X1,X2),X4) != hAPP(X1,X1,plus_plus(X1,X3),X4)
| ti(X1,X2) = ti(X1,X3) ),
inference(literals_permutation,[status(thm)],[c_0_3492]) ).
cnf(c_0_3495_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_3495]) ).
cnf(c_0_3495_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_3495]) ).
cnf(c_0_3496_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_3496]) ).
cnf(c_0_3496_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_3496]) ).
cnf(c_0_3497_0,axiom,
( hAPP(X1,X1,plus_plus(X1,one_one(X1)),number_number_of(X1,X2)) = number_number_of(X1,hAPP(int,int,succ,X2))
| ~ number_ring(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3497]) ).
cnf(c_0_3497_1,axiom,
( ~ number_ring(X1)
| hAPP(X1,X1,plus_plus(X1,one_one(X1)),number_number_of(X1,X2)) = number_number_of(X1,hAPP(int,int,succ,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3497]) ).
cnf(c_0_3498_0,axiom,
( X2 = X3
| ~ semiring_char_0(X1)
| hAPP(nat,X1,semiring_1_of_nat(X1),X2) != hAPP(nat,X1,semiring_1_of_nat(X1),X3) ),
inference(literals_permutation,[status(thm)],[c_0_3498]) ).
cnf(c_0_3498_1,axiom,
( ~ semiring_char_0(X1)
| X2 = X3
| hAPP(nat,X1,semiring_1_of_nat(X1),X2) != hAPP(nat,X1,semiring_1_of_nat(X1),X3) ),
inference(literals_permutation,[status(thm)],[c_0_3498]) ).
cnf(c_0_3498_2,axiom,
( hAPP(nat,X1,semiring_1_of_nat(X1),X2) != hAPP(nat,X1,semiring_1_of_nat(X1),X3)
| ~ semiring_char_0(X1)
| X2 = X3 ),
inference(literals_permutation,[status(thm)],[c_0_3498]) ).
cnf(c_0_3499_0,axiom,
( X1 = X2
| hAPP(nat,int,semiring_1_of_nat(int),X1) != hAPP(nat,int,semiring_1_of_nat(int),X2) ),
inference(literals_permutation,[status(thm)],[c_0_3499]) ).
cnf(c_0_3499_1,axiom,
( hAPP(nat,int,semiring_1_of_nat(int),X1) != hAPP(nat,int,semiring_1_of_nat(int),X2)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_3499]) ).
cnf(c_0_3500_0,axiom,
( X1 = X2
| hAPP(nat,int,semiring_1_of_nat(int),X1) != hAPP(nat,int,semiring_1_of_nat(int),X2) ),
inference(literals_permutation,[status(thm)],[c_0_3500]) ).
cnf(c_0_3500_1,axiom,
( hAPP(nat,int,semiring_1_of_nat(int),X1) != hAPP(nat,int,semiring_1_of_nat(int),X2)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_3500]) ).
cnf(c_0_3501_0,axiom,
( number_number_of(X1,hAPP(nat,int,semiring_1_of_nat(int),X2)) = hAPP(nat,X1,semiring_1_of_nat(X1),X2)
| ~ number_semiring(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3501]) ).
cnf(c_0_3501_1,axiom,
( ~ number_semiring(X1)
| number_number_of(X1,hAPP(nat,int,semiring_1_of_nat(int),X2)) = hAPP(nat,X1,semiring_1_of_nat(X1),X2) ),
inference(literals_permutation,[status(thm)],[c_0_3501]) ).
cnf(c_0_3502_0,axiom,
( X1 = X2
| hAPP(int,int,bit0,X1) != hAPP(int,int,bit0,X2) ),
inference(literals_permutation,[status(thm)],[c_0_3502]) ).
cnf(c_0_3502_1,axiom,
( hAPP(int,int,bit0,X1) != hAPP(int,int,bit0,X2)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_3502]) ).
cnf(c_0_3503_0,axiom,
( X1 = X2
| hAPP(int,int,bit1,X1) != hAPP(int,int,bit1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_3503]) ).
cnf(c_0_3503_1,axiom,
( hAPP(int,int,bit1,X1) != hAPP(int,int,bit1,X2)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_3503]) ).
cnf(c_0_3506_0,axiom,
( ti(X1,hAPP(X2,X1,X3,X4)) = hAPP(X2,X1,X3,X4)
| ~ ord(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3506]) ).
cnf(c_0_3506_1,axiom,
( ~ ord(X1)
| ti(X1,hAPP(X2,X1,X3,X4)) = hAPP(X2,X1,X3,X4) ),
inference(literals_permutation,[status(thm)],[c_0_3506]) ).
cnf(c_0_3507_0,axiom,
( ti(X1,hAPP(nat,X1,X2,X3)) = hAPP(nat,X1,X2,X3)
| ~ power(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3507]) ).
cnf(c_0_3507_1,axiom,
( ~ power(X1)
| ti(X1,hAPP(nat,X1,X2,X3)) = hAPP(nat,X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_3507]) ).
cnf(c_0_3511_0,axiom,
( hAPP(X1,X1,plus_plus(X1,X2),X3) = hAPP(X1,X1,plus_plus(X1,X2),X4)
| ~ cancel_semigroup_add(X1)
| ti(X1,X3) != ti(X1,X4) ),
inference(literals_permutation,[status(thm)],[c_0_3511]) ).
cnf(c_0_3511_1,axiom,
( ~ cancel_semigroup_add(X1)
| hAPP(X1,X1,plus_plus(X1,X2),X3) = hAPP(X1,X1,plus_plus(X1,X2),X4)
| ti(X1,X3) != ti(X1,X4) ),
inference(literals_permutation,[status(thm)],[c_0_3511]) ).
cnf(c_0_3511_2,axiom,
( ti(X1,X3) != ti(X1,X4)
| ~ cancel_semigroup_add(X1)
| hAPP(X1,X1,plus_plus(X1,X2),X3) = hAPP(X1,X1,plus_plus(X1,X2),X4) ),
inference(literals_permutation,[status(thm)],[c_0_3511]) ).
cnf(c_0_3512_0,axiom,
( hAPP(X1,X1,plus_plus(X1,X2),X3) = hAPP(X1,X1,plus_plus(X1,X4),X3)
| ~ cancel_semigroup_add(X1)
| ti(X1,X2) != ti(X1,X4) ),
inference(literals_permutation,[status(thm)],[c_0_3512]) ).
cnf(c_0_3512_1,axiom,
( ~ cancel_semigroup_add(X1)
| hAPP(X1,X1,plus_plus(X1,X2),X3) = hAPP(X1,X1,plus_plus(X1,X4),X3)
| ti(X1,X2) != ti(X1,X4) ),
inference(literals_permutation,[status(thm)],[c_0_3512]) ).
cnf(c_0_3512_2,axiom,
( ti(X1,X2) != ti(X1,X4)
| ~ cancel_semigroup_add(X1)
| hAPP(X1,X1,plus_plus(X1,X2),X3) = hAPP(X1,X1,plus_plus(X1,X4),X3) ),
inference(literals_permutation,[status(thm)],[c_0_3512]) ).
cnf(c_0_3513_0,axiom,
( hAPP(X1,X2,ti(fun(X1,X2),X3),X4) = hAPP(X1,X2,X3,X4)
| ~ ord(X2) ),
inference(literals_permutation,[status(thm)],[c_0_3513]) ).
cnf(c_0_3513_1,axiom,
( ~ ord(X2)
| hAPP(X1,X2,ti(fun(X1,X2),X3),X4) = hAPP(X1,X2,X3,X4) ),
inference(literals_permutation,[status(thm)],[c_0_3513]) ).
cnf(c_0_3516_0,axiom,
( hAPP(nat,X1,ti(fun(nat,X1),X2),X3) = hAPP(nat,X1,X2,X3)
| ~ power(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3516]) ).
cnf(c_0_3516_1,axiom,
( ~ power(X1)
| hAPP(nat,X1,ti(fun(nat,X1),X2),X3) = hAPP(nat,X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_3516]) ).
cnf(c_0_3517_0,axiom,
( hAPP(X1,X1,plus_plus(X1,X2),X3) = hAPP(X1,X1,plus_plus(X1,X3),X2)
| ~ comm_semiring_1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3517]) ).
cnf(c_0_3517_1,axiom,
( ~ comm_semiring_1(X1)
| hAPP(X1,X1,plus_plus(X1,X2),X3) = hAPP(X1,X1,plus_plus(X1,X3),X2) ),
inference(literals_permutation,[status(thm)],[c_0_3517]) ).
cnf(c_0_3518_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_3518]) ).
cnf(c_0_3518_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_3518]) ).
cnf(c_0_3519_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_3519]) ).
cnf(c_0_3519_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_3519]) ).
cnf(c_0_3522_0,axiom,
( hAPP(X1,X2,X3,ti(X1,X4)) = hAPP(X1,X2,X3,X4)
| ~ ord(X2) ),
inference(literals_permutation,[status(thm)],[c_0_3522]) ).
cnf(c_0_3522_1,axiom,
( ~ ord(X2)
| hAPP(X1,X2,X3,ti(X1,X4)) = hAPP(X1,X2,X3,X4) ),
inference(literals_permutation,[status(thm)],[c_0_3522]) ).
cnf(c_0_3523_0,axiom,
( ~ zero_neq_one(X1)
| ~ no_zero_divisors(X1)
| ~ mult_zero(X1)
| ~ power(X1)
| hAPP(nat,X1,power_power(X1,X2),number_number_of(nat,X3)) != zero_zero(X1)
| number_number_of(nat,X3) != zero_zero(nat) ),
inference(literals_permutation,[status(thm)],[c_0_3523]) ).
cnf(c_0_3523_1,axiom,
( ~ no_zero_divisors(X1)
| ~ zero_neq_one(X1)
| ~ mult_zero(X1)
| ~ power(X1)
| hAPP(nat,X1,power_power(X1,X2),number_number_of(nat,X3)) != zero_zero(X1)
| number_number_of(nat,X3) != zero_zero(nat) ),
inference(literals_permutation,[status(thm)],[c_0_3523]) ).
cnf(c_0_3523_2,axiom,
( ~ mult_zero(X1)
| ~ no_zero_divisors(X1)
| ~ zero_neq_one(X1)
| ~ power(X1)
| hAPP(nat,X1,power_power(X1,X2),number_number_of(nat,X3)) != zero_zero(X1)
| number_number_of(nat,X3) != zero_zero(nat) ),
inference(literals_permutation,[status(thm)],[c_0_3523]) ).
cnf(c_0_3523_3,axiom,
( ~ power(X1)
| ~ mult_zero(X1)
| ~ no_zero_divisors(X1)
| ~ zero_neq_one(X1)
| hAPP(nat,X1,power_power(X1,X2),number_number_of(nat,X3)) != zero_zero(X1)
| number_number_of(nat,X3) != zero_zero(nat) ),
inference(literals_permutation,[status(thm)],[c_0_3523]) ).
cnf(c_0_3523_4,axiom,
( hAPP(nat,X1,power_power(X1,X2),number_number_of(nat,X3)) != zero_zero(X1)
| ~ power(X1)
| ~ mult_zero(X1)
| ~ no_zero_divisors(X1)
| ~ zero_neq_one(X1)
| number_number_of(nat,X3) != zero_zero(nat) ),
inference(literals_permutation,[status(thm)],[c_0_3523]) ).
cnf(c_0_3523_5,axiom,
( number_number_of(nat,X3) != zero_zero(nat)
| hAPP(nat,X1,power_power(X1,X2),number_number_of(nat,X3)) != zero_zero(X1)
| ~ power(X1)
| ~ mult_zero(X1)
| ~ no_zero_divisors(X1)
| ~ zero_neq_one(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3523]) ).
cnf(c_0_3524_0,axiom,
( hAPP(nat,X1,X2,ti(nat,X3)) = hAPP(nat,X1,X2,X3)
| ~ power(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3524]) ).
cnf(c_0_3524_1,axiom,
( ~ power(X1)
| hAPP(nat,X1,X2,ti(nat,X3)) = hAPP(nat,X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_3524]) ).
cnf(c_0_3526_0,axiom,
( ti(X1,X2) = zero_zero(X1)
| ~ zero_neq_one(X1)
| ~ no_zero_divisors(X1)
| ~ mult_zero(X1)
| ~ power(X1)
| hAPP(nat,X1,power_power(X1,X2),number_number_of(nat,X3)) != zero_zero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3526]) ).
cnf(c_0_3526_1,axiom,
( ~ zero_neq_one(X1)
| ti(X1,X2) = zero_zero(X1)
| ~ no_zero_divisors(X1)
| ~ mult_zero(X1)
| ~ power(X1)
| hAPP(nat,X1,power_power(X1,X2),number_number_of(nat,X3)) != zero_zero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3526]) ).
cnf(c_0_3526_2,axiom,
( ~ no_zero_divisors(X1)
| ~ zero_neq_one(X1)
| ti(X1,X2) = zero_zero(X1)
| ~ mult_zero(X1)
| ~ power(X1)
| hAPP(nat,X1,power_power(X1,X2),number_number_of(nat,X3)) != zero_zero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3526]) ).
cnf(c_0_3526_3,axiom,
( ~ mult_zero(X1)
| ~ no_zero_divisors(X1)
| ~ zero_neq_one(X1)
| ti(X1,X2) = zero_zero(X1)
| ~ power(X1)
| hAPP(nat,X1,power_power(X1,X2),number_number_of(nat,X3)) != zero_zero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3526]) ).
cnf(c_0_3526_4,axiom,
( ~ power(X1)
| ~ mult_zero(X1)
| ~ no_zero_divisors(X1)
| ~ zero_neq_one(X1)
| ti(X1,X2) = zero_zero(X1)
| hAPP(nat,X1,power_power(X1,X2),number_number_of(nat,X3)) != zero_zero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3526]) ).
cnf(c_0_3526_5,axiom,
( hAPP(nat,X1,power_power(X1,X2),number_number_of(nat,X3)) != zero_zero(X1)
| ~ power(X1)
| ~ mult_zero(X1)
| ~ no_zero_divisors(X1)
| ~ zero_neq_one(X1)
| ti(X1,X2) = zero_zero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3526]) ).
cnf(c_0_3527_0,axiom,
( hAPP(nat,X1,semiring_1_of_nat(X1),X2) = hAPP(nat,X1,semiring_1_of_nat(X1),X3)
| ~ semiring_char_0(X1)
| X2 != X3 ),
inference(literals_permutation,[status(thm)],[c_0_3527]) ).
cnf(c_0_3527_1,axiom,
( ~ semiring_char_0(X1)
| hAPP(nat,X1,semiring_1_of_nat(X1),X2) = hAPP(nat,X1,semiring_1_of_nat(X1),X3)
| X2 != X3 ),
inference(literals_permutation,[status(thm)],[c_0_3527]) ).
cnf(c_0_3527_2,axiom,
( X2 != X3
| ~ semiring_char_0(X1)
| hAPP(nat,X1,semiring_1_of_nat(X1),X2) = hAPP(nat,X1,semiring_1_of_nat(X1),X3) ),
inference(literals_permutation,[status(thm)],[c_0_3527]) ).
cnf(c_0_3530_0,axiom,
( number_number_of(X1,hAPP(int,int,bit1,pls)) = one_one(X1)
| ~ number_semiring(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3530]) ).
cnf(c_0_3530_1,axiom,
( ~ number_semiring(X1)
| number_number_of(X1,hAPP(int,int,bit1,pls)) = one_one(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3530]) ).
cnf(c_0_3531_0,axiom,
( number_number_of(X1,hAPP(int,int,bit1,pls)) = one_one(X1)
| ~ number_ring(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3531]) ).
cnf(c_0_3531_1,axiom,
( ~ number_ring(X1)
| number_number_of(X1,hAPP(int,int,bit1,pls)) = one_one(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3531]) ).
cnf(c_0_3532_0,axiom,
( number_number_of(X1,hAPP(int,int,bit1,pls)) = one_one(X1)
| ~ number_ring(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3532]) ).
cnf(c_0_3532_1,axiom,
( ~ number_ring(X1)
| number_number_of(X1,hAPP(int,int,bit1,pls)) = one_one(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3532]) ).
cnf(c_0_3533_0,axiom,
( hAPP(nat,int,semiring_1_of_nat(int),X1) = hAPP(nat,int,semiring_1_of_nat(int),X2)
| X1 != X2 ),
inference(literals_permutation,[status(thm)],[c_0_3533]) ).
cnf(c_0_3533_1,axiom,
( X1 != X2
| hAPP(nat,int,semiring_1_of_nat(int),X1) = hAPP(nat,int,semiring_1_of_nat(int),X2) ),
inference(literals_permutation,[status(thm)],[c_0_3533]) ).
cnf(c_0_3534_0,axiom,
( hAPP(nat,int,semiring_1_of_nat(int),X1) = hAPP(nat,int,semiring_1_of_nat(int),X2)
| X1 != X2 ),
inference(literals_permutation,[status(thm)],[c_0_3534]) ).
cnf(c_0_3534_1,axiom,
( X1 != X2
| hAPP(nat,int,semiring_1_of_nat(int),X1) = hAPP(nat,int,semiring_1_of_nat(int),X2) ),
inference(literals_permutation,[status(thm)],[c_0_3534]) ).
cnf(c_0_3538_0,axiom,
( hAPP(int,int,bit0,X1) = hAPP(int,int,bit0,X2)
| X1 != X2 ),
inference(literals_permutation,[status(thm)],[c_0_3538]) ).
cnf(c_0_3538_1,axiom,
( X1 != X2
| hAPP(int,int,bit0,X1) = hAPP(int,int,bit0,X2) ),
inference(literals_permutation,[status(thm)],[c_0_3538]) ).
cnf(c_0_3539_0,axiom,
( hAPP(int,int,bit1,X1) = hAPP(int,int,bit1,X2)
| X1 != X2 ),
inference(literals_permutation,[status(thm)],[c_0_3539]) ).
cnf(c_0_3539_1,axiom,
( X1 != X2
| hAPP(int,int,bit1,X1) = hAPP(int,int,bit1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_3539]) ).
cnf(c_0_3541_0,axiom,
( ti(X1,X2) = zero_zero(X1)
| ~ zero_neq_one(X1)
| ~ no_zero_divisors(X1)
| ~ mult_zero(X1)
| ~ power(X1)
| hAPP(nat,X1,power_power(X1,X2),X3) != zero_zero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3541]) ).
cnf(c_0_3541_1,axiom,
( ~ zero_neq_one(X1)
| ti(X1,X2) = zero_zero(X1)
| ~ no_zero_divisors(X1)
| ~ mult_zero(X1)
| ~ power(X1)
| hAPP(nat,X1,power_power(X1,X2),X3) != zero_zero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3541]) ).
cnf(c_0_3541_2,axiom,
( ~ no_zero_divisors(X1)
| ~ zero_neq_one(X1)
| ti(X1,X2) = zero_zero(X1)
| ~ mult_zero(X1)
| ~ power(X1)
| hAPP(nat,X1,power_power(X1,X2),X3) != zero_zero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3541]) ).
cnf(c_0_3541_3,axiom,
( ~ mult_zero(X1)
| ~ no_zero_divisors(X1)
| ~ zero_neq_one(X1)
| ti(X1,X2) = zero_zero(X1)
| ~ power(X1)
| hAPP(nat,X1,power_power(X1,X2),X3) != zero_zero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3541]) ).
cnf(c_0_3541_4,axiom,
( ~ power(X1)
| ~ mult_zero(X1)
| ~ no_zero_divisors(X1)
| ~ zero_neq_one(X1)
| ti(X1,X2) = zero_zero(X1)
| hAPP(nat,X1,power_power(X1,X2),X3) != zero_zero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3541]) ).
cnf(c_0_3541_5,axiom,
( hAPP(nat,X1,power_power(X1,X2),X3) != zero_zero(X1)
| ~ power(X1)
| ~ mult_zero(X1)
| ~ no_zero_divisors(X1)
| ~ zero_neq_one(X1)
| ti(X1,X2) = zero_zero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3541]) ).
cnf(c_0_3542_0,axiom,
( ti(X1,X2) = zero_zero(X1)
| ~ semiri456707255roduct(X1)
| hAPP(X1,X1,plus_plus(X1,X3),X2) != ti(X1,X3) ),
inference(literals_permutation,[status(thm)],[c_0_3542]) ).
cnf(c_0_3542_1,axiom,
( ~ semiri456707255roduct(X1)
| ti(X1,X2) = zero_zero(X1)
| hAPP(X1,X1,plus_plus(X1,X3),X2) != ti(X1,X3) ),
inference(literals_permutation,[status(thm)],[c_0_3542]) ).
cnf(c_0_3542_2,axiom,
( hAPP(X1,X1,plus_plus(X1,X3),X2) != ti(X1,X3)
| ~ semiri456707255roduct(X1)
| ti(X1,X2) = zero_zero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3542]) ).
cnf(c_0_3543_0,axiom,
( ~ zero_neq_one(X1)
| ~ no_zero_divisors(X1)
| ~ mult_zero(X1)
| ~ power(X1)
| hAPP(nat,X1,power_power(X1,X2),X3) != zero_zero(X1)
| X3 != zero_zero(nat) ),
inference(literals_permutation,[status(thm)],[c_0_3543]) ).
cnf(c_0_3543_1,axiom,
( ~ no_zero_divisors(X1)
| ~ zero_neq_one(X1)
| ~ mult_zero(X1)
| ~ power(X1)
| hAPP(nat,X1,power_power(X1,X2),X3) != zero_zero(X1)
| X3 != zero_zero(nat) ),
inference(literals_permutation,[status(thm)],[c_0_3543]) ).
cnf(c_0_3543_2,axiom,
( ~ mult_zero(X1)
| ~ no_zero_divisors(X1)
| ~ zero_neq_one(X1)
| ~ power(X1)
| hAPP(nat,X1,power_power(X1,X2),X3) != zero_zero(X1)
| X3 != zero_zero(nat) ),
inference(literals_permutation,[status(thm)],[c_0_3543]) ).
cnf(c_0_3543_3,axiom,
( ~ power(X1)
| ~ mult_zero(X1)
| ~ no_zero_divisors(X1)
| ~ zero_neq_one(X1)
| hAPP(nat,X1,power_power(X1,X2),X3) != zero_zero(X1)
| X3 != zero_zero(nat) ),
inference(literals_permutation,[status(thm)],[c_0_3543]) ).
cnf(c_0_3543_4,axiom,
( hAPP(nat,X1,power_power(X1,X2),X3) != zero_zero(X1)
| ~ power(X1)
| ~ mult_zero(X1)
| ~ no_zero_divisors(X1)
| ~ zero_neq_one(X1)
| X3 != zero_zero(nat) ),
inference(literals_permutation,[status(thm)],[c_0_3543]) ).
cnf(c_0_3543_5,axiom,
( X3 != zero_zero(nat)
| hAPP(nat,X1,power_power(X1,X2),X3) != zero_zero(X1)
| ~ power(X1)
| ~ mult_zero(X1)
| ~ no_zero_divisors(X1)
| ~ zero_neq_one(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3543]) ).
cnf(c_0_3544_0,axiom,
( ti(X1,X2) = zero_zero(X1)
| ~ linord219039673up_add(X1)
| hAPP(X1,X1,plus_plus(X1,X2),X2) != zero_zero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3544]) ).
cnf(c_0_3544_1,axiom,
( ~ linord219039673up_add(X1)
| ti(X1,X2) = zero_zero(X1)
| hAPP(X1,X1,plus_plus(X1,X2),X2) != zero_zero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3544]) ).
cnf(c_0_3544_2,axiom,
( hAPP(X1,X1,plus_plus(X1,X2),X2) != zero_zero(X1)
| ~ linord219039673up_add(X1)
| ti(X1,X2) = zero_zero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3544]) ).
cnf(c_0_3545_0,axiom,
( ti(X1,X2) = zero_zero(X1)
| ~ linord219039673up_add(X1)
| hAPP(X1,X1,plus_plus(X1,X2),X2) != zero_zero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3545]) ).
cnf(c_0_3545_1,axiom,
( ~ linord219039673up_add(X1)
| ti(X1,X2) = zero_zero(X1)
| hAPP(X1,X1,plus_plus(X1,X2),X2) != zero_zero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3545]) ).
cnf(c_0_3545_2,axiom,
( hAPP(X1,X1,plus_plus(X1,X2),X2) != zero_zero(X1)
| ~ linord219039673up_add(X1)
| ti(X1,X2) = zero_zero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3545]) ).
cnf(c_0_3546_0,axiom,
( ti(X1,X2) = zero_zero(X1)
| hAPP(nat,X1,power_power(X1,X2),X3) != zero_zero(X1)
| ~ ring_11004092258visors(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3546]) ).
cnf(c_0_3546_1,axiom,
( hAPP(nat,X1,power_power(X1,X2),X3) != zero_zero(X1)
| ti(X1,X2) = zero_zero(X1)
| ~ ring_11004092258visors(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3546]) ).
cnf(c_0_3546_2,axiom,
( ~ ring_11004092258visors(X1)
| hAPP(nat,X1,power_power(X1,X2),X3) != zero_zero(X1)
| ti(X1,X2) = zero_zero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3546]) ).
cnf(c_0_3547_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_3547]) ).
cnf(c_0_3547_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_3547]) ).
cnf(c_0_3547_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_3547]) ).
cnf(c_0_3548_0,axiom,
( hAPP(nat,nat,power_power(nat,X1),X2) != zero_zero(nat)
| X2 != zero_zero(nat) ),
inference(literals_permutation,[status(thm)],[c_0_3548]) ).
cnf(c_0_3548_1,axiom,
( X2 != zero_zero(nat)
| hAPP(nat,nat,power_power(nat,X1),X2) != zero_zero(nat) ),
inference(literals_permutation,[status(thm)],[c_0_3548]) ).
cnf(c_0_3549_0,axiom,
( X1 = zero_zero(nat)
| hAPP(nat,nat,power_power(nat,X1),X2) != zero_zero(nat) ),
inference(literals_permutation,[status(thm)],[c_0_3549]) ).
cnf(c_0_3549_1,axiom,
( hAPP(nat,nat,power_power(nat,X1),X2) != zero_zero(nat)
| X1 = zero_zero(nat) ),
inference(literals_permutation,[status(thm)],[c_0_3549]) ).
cnf(c_0_3550_0,axiom,
( X1 = zero_zero(nat)
| hAPP(nat,nat,plus_plus(nat,X1),X2) != zero_zero(nat) ),
inference(literals_permutation,[status(thm)],[c_0_3550]) ).
cnf(c_0_3550_1,axiom,
( hAPP(nat,nat,plus_plus(nat,X1),X2) != zero_zero(nat)
| X1 = zero_zero(nat) ),
inference(literals_permutation,[status(thm)],[c_0_3550]) ).
cnf(c_0_3551_0,axiom,
( X2 = zero_zero(nat)
| hAPP(nat,nat,plus_plus(nat,X1),X2) != zero_zero(nat) ),
inference(literals_permutation,[status(thm)],[c_0_3551]) ).
cnf(c_0_3551_1,axiom,
( hAPP(nat,nat,plus_plus(nat,X1),X2) != zero_zero(nat)
| X2 = zero_zero(nat) ),
inference(literals_permutation,[status(thm)],[c_0_3551]) ).
cnf(c_0_3552_0,axiom,
( X1 = zero_zero(nat)
| hAPP(nat,nat,plus_plus(nat,X2),X1) != X2 ),
inference(literals_permutation,[status(thm)],[c_0_3552]) ).
cnf(c_0_3552_1,axiom,
( hAPP(nat,nat,plus_plus(nat,X2),X1) != X2
| X1 = zero_zero(nat) ),
inference(literals_permutation,[status(thm)],[c_0_3552]) ).
cnf(c_0_3553_0,axiom,
( X1 = zero_zero(nat)
| hAPP(nat,int,semiring_1_of_nat(int),X1) != zero_zero(int) ),
inference(literals_permutation,[status(thm)],[c_0_3553]) ).
cnf(c_0_3553_1,axiom,
( hAPP(nat,int,semiring_1_of_nat(int),X1) != zero_zero(int)
| X1 = zero_zero(nat) ),
inference(literals_permutation,[status(thm)],[c_0_3553]) ).
cnf(c_0_3554_0,axiom,
( pls = X1
| hAPP(int,int,bit0,X1) != pls ),
inference(literals_permutation,[status(thm)],[c_0_3554]) ).
cnf(c_0_3554_1,axiom,
( hAPP(int,int,bit0,X1) != pls
| pls = X1 ),
inference(literals_permutation,[status(thm)],[c_0_3554]) ).
cnf(c_0_3555_0,axiom,
( X1 = pls
| hAPP(int,int,bit0,X1) != pls ),
inference(literals_permutation,[status(thm)],[c_0_3555]) ).
cnf(c_0_3555_1,axiom,
( hAPP(int,int,bit0,X1) != pls
| X1 = pls ),
inference(literals_permutation,[status(thm)],[c_0_3555]) ).
cnf(c_0_3558_0,axiom,
( hAPP(nat,X1,power_power(X1,X2),number_number_of(nat,X3)) = zero_zero(X1)
| number_number_of(nat,X3) = zero_zero(nat)
| ~ zero_neq_one(X1)
| ~ no_zero_divisors(X1)
| ~ mult_zero(X1)
| ~ power(X1)
| ti(X1,X2) != zero_zero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3558]) ).
cnf(c_0_3558_1,axiom,
( number_number_of(nat,X3) = zero_zero(nat)
| hAPP(nat,X1,power_power(X1,X2),number_number_of(nat,X3)) = zero_zero(X1)
| ~ zero_neq_one(X1)
| ~ no_zero_divisors(X1)
| ~ mult_zero(X1)
| ~ power(X1)
| ti(X1,X2) != zero_zero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3558]) ).
cnf(c_0_3558_2,axiom,
( ~ zero_neq_one(X1)
| number_number_of(nat,X3) = zero_zero(nat)
| hAPP(nat,X1,power_power(X1,X2),number_number_of(nat,X3)) = zero_zero(X1)
| ~ no_zero_divisors(X1)
| ~ mult_zero(X1)
| ~ power(X1)
| ti(X1,X2) != zero_zero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3558]) ).
cnf(c_0_3558_3,axiom,
( ~ no_zero_divisors(X1)
| ~ zero_neq_one(X1)
| number_number_of(nat,X3) = zero_zero(nat)
| hAPP(nat,X1,power_power(X1,X2),number_number_of(nat,X3)) = zero_zero(X1)
| ~ mult_zero(X1)
| ~ power(X1)
| ti(X1,X2) != zero_zero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3558]) ).
cnf(c_0_3558_4,axiom,
( ~ mult_zero(X1)
| ~ no_zero_divisors(X1)
| ~ zero_neq_one(X1)
| number_number_of(nat,X3) = zero_zero(nat)
| hAPP(nat,X1,power_power(X1,X2),number_number_of(nat,X3)) = zero_zero(X1)
| ~ power(X1)
| ti(X1,X2) != zero_zero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3558]) ).
cnf(c_0_3558_5,axiom,
( ~ power(X1)
| ~ mult_zero(X1)
| ~ no_zero_divisors(X1)
| ~ zero_neq_one(X1)
| number_number_of(nat,X3) = zero_zero(nat)
| hAPP(nat,X1,power_power(X1,X2),number_number_of(nat,X3)) = zero_zero(X1)
| ti(X1,X2) != zero_zero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3558]) ).
cnf(c_0_3558_6,axiom,
( ti(X1,X2) != zero_zero(X1)
| ~ power(X1)
| ~ mult_zero(X1)
| ~ no_zero_divisors(X1)
| ~ zero_neq_one(X1)
| number_number_of(nat,X3) = zero_zero(nat)
| hAPP(nat,X1,power_power(X1,X2),number_number_of(nat,X3)) = zero_zero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3558]) ).
cnf(c_0_3559_0,axiom,
( hAPP(nat,X1,power_power(X1,zero_zero(X1)),number_number_of(nat,X2)) = one_one(X1)
| ~ semiring_0(X1)
| ~ power(X1)
| number_number_of(nat,X2) != zero_zero(nat) ),
inference(literals_permutation,[status(thm)],[c_0_3559]) ).
cnf(c_0_3559_1,axiom,
( ~ semiring_0(X1)
| hAPP(nat,X1,power_power(X1,zero_zero(X1)),number_number_of(nat,X2)) = one_one(X1)
| ~ power(X1)
| number_number_of(nat,X2) != zero_zero(nat) ),
inference(literals_permutation,[status(thm)],[c_0_3559]) ).
cnf(c_0_3559_2,axiom,
( ~ power(X1)
| ~ semiring_0(X1)
| hAPP(nat,X1,power_power(X1,zero_zero(X1)),number_number_of(nat,X2)) = one_one(X1)
| number_number_of(nat,X2) != zero_zero(nat) ),
inference(literals_permutation,[status(thm)],[c_0_3559]) ).
cnf(c_0_3559_3,axiom,
( number_number_of(nat,X2) != zero_zero(nat)
| ~ power(X1)
| ~ semiring_0(X1)
| hAPP(nat,X1,power_power(X1,zero_zero(X1)),number_number_of(nat,X2)) = one_one(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3559]) ).
cnf(c_0_3560_0,axiom,
( hAPP(nat,X1,power_power(X1,zero_zero(X1)),number_number_of(nat,X2)) = zero_zero(X1)
| number_number_of(nat,X2) = zero_zero(nat)
| ~ semiring_0(X1)
| ~ power(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3560]) ).
cnf(c_0_3560_1,axiom,
( number_number_of(nat,X2) = zero_zero(nat)
| hAPP(nat,X1,power_power(X1,zero_zero(X1)),number_number_of(nat,X2)) = zero_zero(X1)
| ~ semiring_0(X1)
| ~ power(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3560]) ).
cnf(c_0_3560_2,axiom,
( ~ semiring_0(X1)
| number_number_of(nat,X2) = zero_zero(nat)
| hAPP(nat,X1,power_power(X1,zero_zero(X1)),number_number_of(nat,X2)) = zero_zero(X1)
| ~ power(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3560]) ).
cnf(c_0_3560_3,axiom,
( ~ power(X1)
| ~ semiring_0(X1)
| number_number_of(nat,X2) = zero_zero(nat)
| hAPP(nat,X1,power_power(X1,zero_zero(X1)),number_number_of(nat,X2)) = zero_zero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3560]) ).
cnf(c_0_3561_0,axiom,
( hAPP(X1,X1,plus_plus(X1,number_number_of(X1,pls)),X2) = ti(X1,X2)
| ~ number_ring(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3561]) ).
cnf(c_0_3561_1,axiom,
( ~ number_ring(X1)
| hAPP(X1,X1,plus_plus(X1,number_number_of(X1,pls)),X2) = ti(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_3561]) ).
cnf(c_0_3562_0,axiom,
( hAPP(nat,X1,power_power(X1,X2),X3) = zero_zero(X1)
| X3 = zero_zero(nat)
| ~ zero_neq_one(X1)
| ~ no_zero_divisors(X1)
| ~ mult_zero(X1)
| ~ power(X1)
| ti(X1,X2) != zero_zero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3562]) ).
cnf(c_0_3562_1,axiom,
( X3 = zero_zero(nat)
| hAPP(nat,X1,power_power(X1,X2),X3) = zero_zero(X1)
| ~ zero_neq_one(X1)
| ~ no_zero_divisors(X1)
| ~ mult_zero(X1)
| ~ power(X1)
| ti(X1,X2) != zero_zero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3562]) ).
cnf(c_0_3562_2,axiom,
( ~ zero_neq_one(X1)
| X3 = zero_zero(nat)
| hAPP(nat,X1,power_power(X1,X2),X3) = zero_zero(X1)
| ~ no_zero_divisors(X1)
| ~ mult_zero(X1)
| ~ power(X1)
| ti(X1,X2) != zero_zero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3562]) ).
cnf(c_0_3562_3,axiom,
( ~ no_zero_divisors(X1)
| ~ zero_neq_one(X1)
| X3 = zero_zero(nat)
| hAPP(nat,X1,power_power(X1,X2),X3) = zero_zero(X1)
| ~ mult_zero(X1)
| ~ power(X1)
| ti(X1,X2) != zero_zero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3562]) ).
cnf(c_0_3562_4,axiom,
( ~ mult_zero(X1)
| ~ no_zero_divisors(X1)
| ~ zero_neq_one(X1)
| X3 = zero_zero(nat)
| hAPP(nat,X1,power_power(X1,X2),X3) = zero_zero(X1)
| ~ power(X1)
| ti(X1,X2) != zero_zero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3562]) ).
cnf(c_0_3562_5,axiom,
( ~ power(X1)
| ~ mult_zero(X1)
| ~ no_zero_divisors(X1)
| ~ zero_neq_one(X1)
| X3 = zero_zero(nat)
| hAPP(nat,X1,power_power(X1,X2),X3) = zero_zero(X1)
| ti(X1,X2) != zero_zero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3562]) ).
cnf(c_0_3562_6,axiom,
( ti(X1,X2) != zero_zero(X1)
| ~ power(X1)
| ~ mult_zero(X1)
| ~ no_zero_divisors(X1)
| ~ zero_neq_one(X1)
| X3 = zero_zero(nat)
| hAPP(nat,X1,power_power(X1,X2),X3) = zero_zero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3562]) ).
cnf(c_0_3563_0,axiom,
( hAPP(X1,X1,plus_plus(X1,X2),X3) = ti(X1,X2)
| ~ semiri456707255roduct(X1)
| ti(X1,X3) != zero_zero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3563]) ).
cnf(c_0_3563_1,axiom,
( ~ semiri456707255roduct(X1)
| hAPP(X1,X1,plus_plus(X1,X2),X3) = ti(X1,X2)
| ti(X1,X3) != zero_zero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3563]) ).
cnf(c_0_3563_2,axiom,
( ti(X1,X3) != zero_zero(X1)
| ~ semiri456707255roduct(X1)
| hAPP(X1,X1,plus_plus(X1,X2),X3) = ti(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_3563]) ).
cnf(c_0_3564_0,axiom,
( hAPP(X1,X1,plus_plus(X1,X2),number_number_of(X1,pls)) = ti(X1,X2)
| ~ number_ring(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3564]) ).
cnf(c_0_3564_1,axiom,
( ~ number_ring(X1)
| hAPP(X1,X1,plus_plus(X1,X2),number_number_of(X1,pls)) = ti(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_3564]) ).
cnf(c_0_3565_0,axiom,
( hAPP(X1,X1,plus_plus(X1,X2),X2) = zero_zero(X1)
| ~ linord219039673up_add(X1)
| ti(X1,X2) != zero_zero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3565]) ).
cnf(c_0_3565_1,axiom,
( ~ linord219039673up_add(X1)
| hAPP(X1,X1,plus_plus(X1,X2),X2) = zero_zero(X1)
| ti(X1,X2) != zero_zero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3565]) ).
cnf(c_0_3565_2,axiom,
( ti(X1,X2) != zero_zero(X1)
| ~ linord219039673up_add(X1)
| hAPP(X1,X1,plus_plus(X1,X2),X2) = zero_zero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3565]) ).
cnf(c_0_3566_0,axiom,
( hAPP(X1,X1,plus_plus(X1,X2),X2) = zero_zero(X1)
| ~ linord219039673up_add(X1)
| ti(X1,X2) != zero_zero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3566]) ).
cnf(c_0_3566_1,axiom,
( ~ linord219039673up_add(X1)
| hAPP(X1,X1,plus_plus(X1,X2),X2) = zero_zero(X1)
| ti(X1,X2) != zero_zero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3566]) ).
cnf(c_0_3566_2,axiom,
( ti(X1,X2) != zero_zero(X1)
| ~ linord219039673up_add(X1)
| hAPP(X1,X1,plus_plus(X1,X2),X2) = zero_zero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3566]) ).
cnf(c_0_3567_0,axiom,
( hAPP(nat,X1,power_power(X1,zero_zero(X1)),X2) = one_one(X1)
| ~ semiring_0(X1)
| ~ power(X1)
| X2 != zero_zero(nat) ),
inference(literals_permutation,[status(thm)],[c_0_3567]) ).
cnf(c_0_3567_1,axiom,
( ~ semiring_0(X1)
| hAPP(nat,X1,power_power(X1,zero_zero(X1)),X2) = one_one(X1)
| ~ power(X1)
| X2 != zero_zero(nat) ),
inference(literals_permutation,[status(thm)],[c_0_3567]) ).
cnf(c_0_3567_2,axiom,
( ~ power(X1)
| ~ semiring_0(X1)
| hAPP(nat,X1,power_power(X1,zero_zero(X1)),X2) = one_one(X1)
| X2 != zero_zero(nat) ),
inference(literals_permutation,[status(thm)],[c_0_3567]) ).
cnf(c_0_3567_3,axiom,
( X2 != zero_zero(nat)
| ~ power(X1)
| ~ semiring_0(X1)
| hAPP(nat,X1,power_power(X1,zero_zero(X1)),X2) = one_one(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3567]) ).
cnf(c_0_3568_0,axiom,
( hAPP(X1,X1,plus_plus(X1,zero_zero(X1)),X2) = ti(X1,X2)
| ~ monoid_add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3568]) ).
cnf(c_0_3568_1,axiom,
( ~ monoid_add(X1)
| hAPP(X1,X1,plus_plus(X1,zero_zero(X1)),X2) = ti(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_3568]) ).
cnf(c_0_3569_0,axiom,
( hAPP(X1,X1,plus_plus(X1,zero_zero(X1)),X2) = ti(X1,X2)
| ~ comm_semiring_1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3569]) ).
cnf(c_0_3569_1,axiom,
( ~ comm_semiring_1(X1)
| hAPP(X1,X1,plus_plus(X1,zero_zero(X1)),X2) = ti(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_3569]) ).
cnf(c_0_3570_0,axiom,
( hAPP(X1,X1,plus_plus(X1,zero_zero(X1)),X2) = ti(X1,X2)
| ~ comm_monoid_add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3570]) ).
cnf(c_0_3570_1,axiom,
( ~ comm_monoid_add(X1)
| hAPP(X1,X1,plus_plus(X1,zero_zero(X1)),X2) = ti(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_3570]) ).
cnf(c_0_3571_0,axiom,
( hAPP(nat,X1,power_power(X1,zero_zero(X1)),X2) = zero_zero(X1)
| X2 = zero_zero(nat)
| ~ semiring_0(X1)
| ~ power(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3571]) ).
cnf(c_0_3571_1,axiom,
( X2 = zero_zero(nat)
| hAPP(nat,X1,power_power(X1,zero_zero(X1)),X2) = zero_zero(X1)
| ~ semiring_0(X1)
| ~ power(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3571]) ).
cnf(c_0_3571_2,axiom,
( ~ semiring_0(X1)
| X2 = zero_zero(nat)
| hAPP(nat,X1,power_power(X1,zero_zero(X1)),X2) = zero_zero(X1)
| ~ power(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3571]) ).
cnf(c_0_3571_3,axiom,
( ~ power(X1)
| ~ semiring_0(X1)
| X2 = zero_zero(nat)
| hAPP(nat,X1,power_power(X1,zero_zero(X1)),X2) = zero_zero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3571]) ).
cnf(c_0_3572_0,axiom,
( hAPP(X1,X1,plus_plus(X1,X2),zero_zero(X1)) = ti(X1,X2)
| ~ monoid_add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3572]) ).
cnf(c_0_3572_1,axiom,
( ~ monoid_add(X1)
| hAPP(X1,X1,plus_plus(X1,X2),zero_zero(X1)) = ti(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_3572]) ).
cnf(c_0_3573_0,axiom,
( hAPP(X1,X1,plus_plus(X1,X2),zero_zero(X1)) = ti(X1,X2)
| ~ comm_semiring_1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3573]) ).
cnf(c_0_3573_1,axiom,
( ~ comm_semiring_1(X1)
| hAPP(X1,X1,plus_plus(X1,X2),zero_zero(X1)) = ti(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_3573]) ).
cnf(c_0_3574_0,axiom,
( hAPP(X1,X1,plus_plus(X1,X2),zero_zero(X1)) = ti(X1,X2)
| ~ comm_monoid_add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3574]) ).
cnf(c_0_3574_1,axiom,
( ~ comm_monoid_add(X1)
| hAPP(X1,X1,plus_plus(X1,X2),zero_zero(X1)) = ti(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_3574]) ).
cnf(c_0_3575_0,axiom,
( hAPP(nat,X1,power_power(X1,X2),one_one(nat)) = ti(X1,X2)
| ~ comm_semiring_1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3575]) ).
cnf(c_0_3575_1,axiom,
( ~ comm_semiring_1(X1)
| hAPP(nat,X1,power_power(X1,X2),one_one(nat)) = ti(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_3575]) ).
cnf(c_0_3576_0,axiom,
( hAPP(nat,X1,power_power(X1,X2),one_one(nat)) = ti(X1,X2)
| ~ monoid_mult(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3576]) ).
cnf(c_0_3576_1,axiom,
( ~ monoid_mult(X1)
| hAPP(nat,X1,power_power(X1,X2),one_one(nat)) = ti(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_3576]) ).
cnf(c_0_3577_0,axiom,
( hAPP(nat,X1,power_power(X1,one_one(X1)),X2) = one_one(X1)
| ~ monoid_mult(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3577]) ).
cnf(c_0_3577_1,axiom,
( ~ monoid_mult(X1)
| hAPP(nat,X1,power_power(X1,one_one(X1)),X2) = one_one(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3577]) ).
cnf(c_0_3578_0,axiom,
( hAPP(nat,X1,power_power(X1,X2),zero_zero(nat)) = one_one(X1)
| ~ comm_semiring_1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3578]) ).
cnf(c_0_3578_1,axiom,
( ~ comm_semiring_1(X1)
| hAPP(nat,X1,power_power(X1,X2),zero_zero(nat)) = one_one(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3578]) ).
cnf(c_0_3579_0,axiom,
( hAPP(nat,X1,power_power(X1,X2),zero_zero(nat)) = one_one(X1)
| ~ power(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3579]) ).
cnf(c_0_3579_1,axiom,
( ~ power(X1)
| hAPP(nat,X1,power_power(X1,X2),zero_zero(nat)) = one_one(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3579]) ).
cnf(c_0_3580_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_3580]) ).
cnf(c_0_3580_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_3580]) ).
cnf(c_0_3580_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_3580]) ).
cnf(c_0_3581_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_3581]) ).
cnf(c_0_3581_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_3581]) ).
cnf(c_0_3581_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_3581]) ).
cnf(c_0_3582_0,axiom,
( hAPP(nat,nat,power_power(nat,X1),X2) = one_one(nat)
| X1 != one_one(nat) ),
inference(literals_permutation,[status(thm)],[c_0_3582]) ).
cnf(c_0_3582_1,axiom,
( X1 != one_one(nat)
| hAPP(nat,nat,power_power(nat,X1),X2) = one_one(nat) ),
inference(literals_permutation,[status(thm)],[c_0_3582]) ).
cnf(c_0_3583_0,axiom,
( hAPP(nat,nat,power_power(nat,X1),X2) = one_one(nat)
| X2 != zero_zero(nat) ),
inference(literals_permutation,[status(thm)],[c_0_3583]) ).
cnf(c_0_3583_1,axiom,
( X2 != zero_zero(nat)
| hAPP(nat,nat,power_power(nat,X1),X2) = one_one(nat) ),
inference(literals_permutation,[status(thm)],[c_0_3583]) ).
cnf(c_0_3589_0,axiom,
( hAPP(nat,X1,semiring_1_of_nat(X1),zero_zero(nat)) = zero_zero(X1)
| ~ semiring_1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3589]) ).
cnf(c_0_3589_1,axiom,
( ~ semiring_1(X1)
| hAPP(nat,X1,semiring_1_of_nat(X1),zero_zero(nat)) = zero_zero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3589]) ).
cnf(c_0_3590_0,axiom,
( hAPP(nat,X1,semiring_1_of_nat(X1),one_one(nat)) = one_one(X1)
| ~ semiring_1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3590]) ).
cnf(c_0_3590_1,axiom,
( ~ semiring_1(X1)
| hAPP(nat,X1,semiring_1_of_nat(X1),one_one(nat)) = one_one(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3590]) ).
cnf(c_0_3592_0,axiom,
( hAPP(nat,int,semiring_1_of_nat(int),X1) = zero_zero(int)
| X1 != zero_zero(nat) ),
inference(literals_permutation,[status(thm)],[c_0_3592]) ).
cnf(c_0_3592_1,axiom,
( X1 != zero_zero(nat)
| hAPP(nat,int,semiring_1_of_nat(int),X1) = zero_zero(int) ),
inference(literals_permutation,[status(thm)],[c_0_3592]) ).
cnf(c_0_3597_0,axiom,
( hAPP(int,int,bit0,X1) = pls
| pls != X1 ),
inference(literals_permutation,[status(thm)],[c_0_3597]) ).
cnf(c_0_3597_1,axiom,
( pls != X1
| hAPP(int,int,bit0,X1) = pls ),
inference(literals_permutation,[status(thm)],[c_0_3597]) ).
cnf(c_0_3598_0,axiom,
( hAPP(int,int,bit0,X1) = pls
| X1 != pls ),
inference(literals_permutation,[status(thm)],[c_0_3598]) ).
cnf(c_0_3598_1,axiom,
( X1 != pls
| hAPP(int,int,bit0,X1) = pls ),
inference(literals_permutation,[status(thm)],[c_0_3598]) ).
cnf(c_0_3601_0,axiom,
( ti(fun(X1,fun(X1,X1)),times_times(X1)) = times_times(X1)
| ~ linordered_semiring(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3601]) ).
cnf(c_0_3601_1,axiom,
( ~ linordered_semiring(X1)
| ti(fun(X1,fun(X1,X1)),times_times(X1)) = times_times(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3601]) ).
cnf(c_0_3602_0,axiom,
( ti(fun(X1,fun(X1,bool)),ord_less_eq(X1)) = ord_less_eq(X1)
| ~ ord(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3602]) ).
cnf(c_0_3602_1,axiom,
( ~ ord(X1)
| ti(fun(X1,fun(X1,bool)),ord_less_eq(X1)) = ord_less_eq(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3602]) ).
cnf(c_0_3603_0,axiom,
( ti(fun(X1,fun(X1,bool)),ord_less(X1)) = ord_less(X1)
| ~ ord(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3603]) ).
cnf(c_0_3603_1,axiom,
( ~ ord(X1)
| ti(fun(X1,fun(X1,bool)),ord_less(X1)) = ord_less(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3603]) ).
cnf(c_0_3604_0,axiom,
( ti(fun(X1,X1),plus_plus(X1,X2)) = plus_plus(X1,X2)
| ~ cancel_semigroup_add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3604]) ).
cnf(c_0_3604_1,axiom,
( ~ cancel_semigroup_add(X1)
| ti(fun(X1,X1),plus_plus(X1,X2)) = plus_plus(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_3604]) ).
cnf(c_0_3605_0,axiom,
( ti(fun(X1,X1),plus_plus(X1,X2)) = plus_plus(X1,X2)
| ~ ab_semigroup_add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3605]) ).
cnf(c_0_3605_1,axiom,
( ~ ab_semigroup_add(X1)
| ti(fun(X1,X1),plus_plus(X1,X2)) = plus_plus(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_3605]) ).
cnf(c_0_3606_0,axiom,
( ti(fun(X1,X1),plus_plus(X1,X2)) = plus_plus(X1,X2)
| ~ monoid_add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3606]) ).
cnf(c_0_3606_1,axiom,
( ~ monoid_add(X1)
| ti(fun(X1,X1),plus_plus(X1,X2)) = plus_plus(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_3606]) ).
cnf(c_0_3607_0,axiom,
( ti(fun(nat,X1),power_power(X1,X2)) = power_power(X1,X2)
| ~ power(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3607]) ).
cnf(c_0_3607_1,axiom,
( ~ power(X1)
| ti(fun(nat,X1),power_power(X1,X2)) = power_power(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_3607]) ).
cnf(c_0_3608_0,axiom,
( ti(X1,X2) = number_number_of(X1,X3)
| ~ number(X1)
| number_number_of(X1,X3) != ti(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_3608]) ).
cnf(c_0_3608_1,axiom,
( ~ number(X1)
| ti(X1,X2) = number_number_of(X1,X3)
| number_number_of(X1,X3) != ti(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_3608]) ).
cnf(c_0_3608_2,axiom,
( number_number_of(X1,X3) != ti(X1,X2)
| ~ number(X1)
| ti(X1,X2) = number_number_of(X1,X3) ),
inference(literals_permutation,[status(thm)],[c_0_3608]) ).
cnf(c_0_3609_0,axiom,
( number_number_of(X1,X2) = ti(X1,X3)
| ~ number(X1)
| ti(X1,X3) != number_number_of(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_3609]) ).
cnf(c_0_3609_1,axiom,
( ~ number(X1)
| number_number_of(X1,X2) = ti(X1,X3)
| ti(X1,X3) != number_number_of(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_3609]) ).
cnf(c_0_3609_2,axiom,
( ti(X1,X3) != number_number_of(X1,X2)
| ~ number(X1)
| number_number_of(X1,X2) = ti(X1,X3) ),
inference(literals_permutation,[status(thm)],[c_0_3609]) ).
cnf(c_0_3610_0,axiom,
( power_power(X1,ti(X1,X2)) = power_power(X1,X2)
| ~ power(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3610]) ).
cnf(c_0_3610_1,axiom,
( ~ power(X1)
| power_power(X1,ti(X1,X2)) = power_power(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_3610]) ).
cnf(c_0_3611_0,axiom,
( ti(X1,number_number_of(X1,X2)) = number_number_of(X1,X2)
| ~ number(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3611]) ).
cnf(c_0_3611_1,axiom,
( ~ number(X1)
| ti(X1,number_number_of(X1,X2)) = number_number_of(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_3611]) ).
cnf(c_0_3612_0,axiom,
( plus_plus(X1,ti(X1,X2)) = plus_plus(X1,X2)
| ~ cancel_semigroup_add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3612]) ).
cnf(c_0_3612_1,axiom,
( ~ cancel_semigroup_add(X1)
| plus_plus(X1,ti(X1,X2)) = plus_plus(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_3612]) ).
cnf(c_0_3613_0,axiom,
( plus_plus(X1,ti(X1,X2)) = plus_plus(X1,X2)
| ~ ab_semigroup_add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3613]) ).
cnf(c_0_3613_1,axiom,
( ~ ab_semigroup_add(X1)
| plus_plus(X1,ti(X1,X2)) = plus_plus(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_3613]) ).
cnf(c_0_3614_0,axiom,
( plus_plus(X1,ti(X1,X2)) = plus_plus(X1,X2)
| ~ monoid_add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3614]) ).
cnf(c_0_3614_1,axiom,
( ~ monoid_add(X1)
| plus_plus(X1,ti(X1,X2)) = plus_plus(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_3614]) ).
cnf(c_0_3615_0,axiom,
( X2 = X3
| ~ ring_char_0(X1)
| ~ number_ring(X1)
| number_number_of(X1,X2) != number_number_of(X1,X3) ),
inference(literals_permutation,[status(thm)],[c_0_3615]) ).
cnf(c_0_3615_1,axiom,
( ~ ring_char_0(X1)
| X2 = X3
| ~ number_ring(X1)
| number_number_of(X1,X2) != number_number_of(X1,X3) ),
inference(literals_permutation,[status(thm)],[c_0_3615]) ).
cnf(c_0_3615_2,axiom,
( ~ number_ring(X1)
| ~ ring_char_0(X1)
| X2 = X3
| number_number_of(X1,X2) != number_number_of(X1,X3) ),
inference(literals_permutation,[status(thm)],[c_0_3615]) ).
cnf(c_0_3615_3,axiom,
( number_number_of(X1,X2) != number_number_of(X1,X3)
| ~ number_ring(X1)
| ~ ring_char_0(X1)
| X2 = X3 ),
inference(literals_permutation,[status(thm)],[c_0_3615]) ).
cnf(c_0_3616_0,axiom,
( number_number_of(X1,ti(int,X2)) = number_number_of(X1,X2)
| ~ number(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3616]) ).
cnf(c_0_3616_1,axiom,
( ~ number(X1)
| number_number_of(X1,ti(int,X2)) = number_number_of(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_3616]) ).
cnf(c_0_3617_0,axiom,
( ti(fun(nat,X1),semiring_1_of_nat(X1)) = semiring_1_of_nat(X1)
| ~ semiring_1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3617]) ).
cnf(c_0_3617_1,axiom,
( ~ semiring_1(X1)
| ti(fun(nat,X1),semiring_1_of_nat(X1)) = semiring_1_of_nat(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3617]) ).
cnf(c_0_3618_0,axiom,
( ti(X1,X2) = one_one(X1)
| ~ one(X1)
| ti(X1,X2) != one_one(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3618]) ).
cnf(c_0_3618_1,axiom,
( ~ one(X1)
| ti(X1,X2) = one_one(X1)
| ti(X1,X2) != one_one(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3618]) ).
cnf(c_0_3618_2,axiom,
( ti(X1,X2) != one_one(X1)
| ~ one(X1)
| ti(X1,X2) = one_one(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3618]) ).
cnf(c_0_3619_0,axiom,
( ti(X1,X2) = one_one(X1)
| ~ one(X1)
| ti(X1,X2) != one_one(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3619]) ).
cnf(c_0_3619_1,axiom,
( ~ one(X1)
| ti(X1,X2) = one_one(X1)
| ti(X1,X2) != one_one(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3619]) ).
cnf(c_0_3619_2,axiom,
( ti(X1,X2) != one_one(X1)
| ~ one(X1)
| ti(X1,X2) = one_one(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3619]) ).
cnf(c_0_3620_0,axiom,
( ti(X1,X2) = zero_zero(X1)
| ~ zero(X1)
| ti(X1,X2) != zero_zero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3620]) ).
cnf(c_0_3620_1,axiom,
( ~ zero(X1)
| ti(X1,X2) = zero_zero(X1)
| ti(X1,X2) != zero_zero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3620]) ).
cnf(c_0_3620_2,axiom,
( ti(X1,X2) != zero_zero(X1)
| ~ zero(X1)
| ti(X1,X2) = zero_zero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3620]) ).
cnf(c_0_3621_0,axiom,
( ti(X1,X2) = zero_zero(X1)
| ~ zero(X1)
| ti(X1,X2) != zero_zero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3621]) ).
cnf(c_0_3621_1,axiom,
( ~ zero(X1)
| ti(X1,X2) = zero_zero(X1)
| ti(X1,X2) != zero_zero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3621]) ).
cnf(c_0_3621_2,axiom,
( ti(X1,X2) != zero_zero(X1)
| ~ zero(X1)
| ti(X1,X2) = zero_zero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3621]) ).
cnf(c_0_3623_0,axiom,
( hBOOL(X1)
| ~ hBOOL(ti(bool,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_3623]) ).
cnf(c_0_3623_1,axiom,
( ~ hBOOL(ti(bool,X1))
| hBOOL(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3623]) ).
cnf(c_0_3624_0,axiom,
( number_number_of(X1,X2) = number_number_of(X1,X3)
| ~ ring_char_0(X1)
| ~ number_ring(X1)
| X2 != X3 ),
inference(literals_permutation,[status(thm)],[c_0_3624]) ).
cnf(c_0_3624_1,axiom,
( ~ ring_char_0(X1)
| number_number_of(X1,X2) = number_number_of(X1,X3)
| ~ number_ring(X1)
| X2 != X3 ),
inference(literals_permutation,[status(thm)],[c_0_3624]) ).
cnf(c_0_3624_2,axiom,
( ~ number_ring(X1)
| ~ ring_char_0(X1)
| number_number_of(X1,X2) = number_number_of(X1,X3)
| X2 != X3 ),
inference(literals_permutation,[status(thm)],[c_0_3624]) ).
cnf(c_0_3624_3,axiom,
( X2 != X3
| ~ number_ring(X1)
| ~ ring_char_0(X1)
| number_number_of(X1,X2) = number_number_of(X1,X3) ),
inference(literals_permutation,[status(thm)],[c_0_3624]) ).
cnf(c_0_3625_0,axiom,
( ord(fun(X1,X2))
| ~ ord(X2) ),
inference(literals_permutation,[status(thm)],[c_0_3625]) ).
cnf(c_0_3625_1,axiom,
( ~ ord(X2)
| ord(fun(X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3625]) ).
cnf(c_0_3626_0,axiom,
( order(fun(X1,X2))
| ~ order(X2) ),
inference(literals_permutation,[status(thm)],[c_0_3626]) ).
cnf(c_0_3626_1,axiom,
( ~ order(X2)
| order(fun(X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3626]) ).
cnf(c_0_3627_0,axiom,
( preorder(fun(X1,X2))
| ~ preorder(X2) ),
inference(literals_permutation,[status(thm)],[c_0_3627]) ).
cnf(c_0_3627_1,axiom,
( ~ preorder(X2)
| preorder(fun(X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3627]) ).
cnf(c_0_3628_0,axiom,
( hBOOL(ti(bool,X1))
| ~ hBOOL(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3628]) ).
cnf(c_0_3628_1,axiom,
( ~ hBOOL(X1)
| hBOOL(ti(bool,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_3628]) ).
cnf(c_0_3631_0,axiom,
( ti(X1,zero_zero(X1)) = zero_zero(X1)
| ~ zero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3631]) ).
cnf(c_0_3631_1,axiom,
( ~ zero(X1)
| ti(X1,zero_zero(X1)) = zero_zero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3631]) ).
cnf(c_0_3632_0,axiom,
( ti(X1,one_one(X1)) = one_one(X1)
| ~ one(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3632]) ).
cnf(c_0_3632_1,axiom,
( ~ one(X1)
| ti(X1,one_one(X1)) = one_one(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3632]) ).
cnf(c_0_3633_0,axiom,
( ti(bool,X1) = fFalse
| ti(bool,X1) = fTrue ),
inference(literals_permutation,[status(thm)],[c_0_3633]) ).
cnf(c_0_3633_1,axiom,
( ti(bool,X1) = fTrue
| ti(bool,X1) = fFalse ),
inference(literals_permutation,[status(thm)],[c_0_3633]) ).
cnf(c_0_3635_0,axiom,
( number_number_of(X1,pls) = zero_zero(X1)
| ~ number_ring(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3635]) ).
cnf(c_0_3635_1,axiom,
( ~ number_ring(X1)
| number_number_of(X1,pls) = zero_zero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3635]) ).
cnf(c_0_3636_0,axiom,
( number_number_of(X1,pls) = zero_zero(X1)
| ~ number_ring(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3636]) ).
cnf(c_0_3636_1,axiom,
( ~ number_ring(X1)
| number_number_of(X1,pls) = zero_zero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3636]) ).
cnf(c_0_3637_0,axiom,
( number_number_of(X1,pls) = zero_zero(X1)
| ~ number_semiring(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3637]) ).
cnf(c_0_3637_1,axiom,
( ~ number_semiring(X1)
| number_number_of(X1,pls) = zero_zero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3637]) ).
cnf(c_0_3638_0,axiom,
( zero_zero(X1) != one_one(X1)
| ~ zero_neq_one(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3638]) ).
cnf(c_0_3638_1,axiom,
( ~ zero_neq_one(X1)
| zero_zero(X1) != one_one(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3638]) ).
cnf(c_0_3639_0,axiom,
( zero_zero(X1) != one_one(X1)
| ~ zero_neq_one(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3639]) ).
cnf(c_0_3639_1,axiom,
( ~ zero_neq_one(X1)
| zero_zero(X1) != one_one(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3639]) ).
cnf(c_0_3135_0,axiom,
~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,plus_plus(nat,X1),X2)),X2)),
inference(literals_permutation,[status(thm)],[c_0_3135]) ).
cnf(c_0_3136_0,axiom,
~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,plus_plus(nat,X1),X2)),X1)),
inference(literals_permutation,[status(thm)],[c_0_3136]) ).
cnf(c_0_3158_0,axiom,
~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(nat,int,semiring_1_of_nat(int),X1)),zero_zero(int))),
inference(literals_permutation,[status(thm)],[c_0_3158]) ).
cnf(c_0_3409_0,axiom,
~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),zero_zero(nat))),
inference(literals_permutation,[status(thm)],[c_0_3409]) ).
cnf(c_0_3410_0,axiom,
~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),zero_zero(nat))),
inference(literals_permutation,[status(thm)],[c_0_3410]) ).
cnf(c_0_3411_0,axiom,
~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),zero_zero(nat))),
inference(literals_permutation,[status(thm)],[c_0_3411]) ).
cnf(c_0_3420_0,axiom,
~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X1)),
inference(literals_permutation,[status(thm)],[c_0_3420]) ).
cnf(c_0_3421_0,axiom,
~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X1)),
inference(literals_permutation,[status(thm)],[c_0_3421]) ).
cnf(c_0_3422_0,axiom,
~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),zero_zero(int))),
inference(literals_permutation,[status(thm)],[c_0_3422]) ).
cnf(c_0_3423_0,axiom,
~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),pls)),
inference(literals_permutation,[status(thm)],[c_0_3423]) ).
cnf(c_0_3430_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_3430]) ).
cnf(c_0_3504_0,axiom,
hAPP(int,int,bit0,X1) != hAPP(int,int,bit1,X2),
inference(literals_permutation,[status(thm)],[c_0_3504]) ).
cnf(c_0_3505_0,axiom,
hAPP(int,int,bit1,X1) != hAPP(int,int,bit0,X2),
inference(literals_permutation,[status(thm)],[c_0_3505]) ).
cnf(c_0_3556_0,axiom,
hAPP(int,int,bit1,X1) != pls,
inference(literals_permutation,[status(thm)],[c_0_3556]) ).
cnf(c_0_3557_0,axiom,
hAPP(int,int,bit1,X1) != pls,
inference(literals_permutation,[status(thm)],[c_0_3557]) ).
cnf(c_0_3649_0,axiom,
zero_zero(real) != one_one(real),
inference(literals_permutation,[status(thm)],[c_0_3649]) ).
cnf(c_0_3650_0,axiom,
zero_zero(int) != one_one(int),
inference(literals_permutation,[status(thm)],[c_0_3650]) ).
cnf(c_0_2864_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,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),number_number_of(int,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),X1)),X2))),hAPP(nat,int,power_power(int,X2),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) = hAPP(nat,int,power_power(int,hAPP(int,int,plus_plus(int,X1),X2)),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),
inference(literals_permutation,[status(thm)],[c_0_2864]) ).
cnf(c_0_2876_0,axiom,
hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),hAPP(real,real,sqrt,hAPP(real,real,plus_plus(real,hAPP(nat,real,power_power(real,X1),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,real,power_power(real,X2),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))))),
inference(literals_permutation,[status(thm)],[c_0_2876]) ).
cnf(c_0_2900_0,axiom,
hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),one_one(real)),hAPP(nat,real,power_power(real,number_number_of(real,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),X1))),
inference(literals_permutation,[status(thm)],[c_0_2900]) ).
cnf(c_0_2902_0,axiom,
hAPP(nat,int,power_power(int,hAPP(nat,int,power_power(int,X1),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) = hAPP(nat,int,power_power(int,X1),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),
inference(literals_permutation,[status(thm)],[c_0_2902]) ).
cnf(c_0_2938_0,axiom,
hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X1),hAPP(nat,int,power_power(int,X1),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),
inference(literals_permutation,[status(thm)],[c_0_2938]) ).
cnf(c_0_2976_0,axiom,
hAPP(int,int,plus_plus(int,hAPP(int,int,bit0,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),X1),X2))),X2) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,bit1,X1)),X2),
inference(literals_permutation,[status(thm)],[c_0_2976]) ).
cnf(c_0_3033_0,axiom,
hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),number_number_of(int,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),
inference(literals_permutation,[status(thm)],[c_0_3033]) ).
cnf(c_0_3034_0,axiom,
hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),number_number_of(int,hAPP(int,int,bit1,hAPP(int,int,bit1,pls))))),
inference(literals_permutation,[status(thm)],[c_0_3034]) ).
cnf(c_0_3035_0,axiom,
hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),
inference(literals_permutation,[status(thm)],[c_0_3035]) ).
cnf(c_0_3060_0,axiom,
hAPP(int,int,plus_plus(int,hAPP(nat,int,semiring_1_of_nat(int),X1)),hAPP(int,int,plus_plus(int,hAPP(nat,int,semiring_1_of_nat(int),X2)),X3)) = hAPP(int,int,plus_plus(int,hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,plus_plus(nat,X1),X2))),X3),
inference(literals_permutation,[status(thm)],[c_0_3060]) ).
cnf(c_0_3228_0,axiom,
hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(int,int,plus_plus(int,one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),n)))),
inference(literals_permutation,[status(thm)],[c_0_3228]) ).
cnf(c_0_3229_0,axiom,
hAPP(nat,int,semiring_1_of_nat(int),number_number_of(nat,hAPP(int,int,bit1,hAPP(int,int,bit1,pls)))) = number_number_of(int,hAPP(int,int,bit1,hAPP(int,int,bit1,pls))),
inference(literals_permutation,[status(thm)],[c_0_3229]) ).
cnf(c_0_3230_0,axiom,
hAPP(nat,int,semiring_1_of_nat(int),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) = number_number_of(int,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))),
inference(literals_permutation,[status(thm)],[c_0_3230]) ).
cnf(c_0_3231_0,axiom,
hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),m1),hAPP(int,int,plus_plus(int,one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),n)))),
inference(literals_permutation,[status(thm)],[c_0_3231]) ).
cnf(c_0_3319_0,axiom,
hAPP(int,int,plus_plus(int,hAPP(int,int,bit1,X1)),hAPP(int,int,bit1,X2)) = hAPP(int,int,bit0,hAPP(int,int,plus_plus(int,X1),hAPP(int,int,succ,X2))),
inference(literals_permutation,[status(thm)],[c_0_3319]) ).
cnf(c_0_3377_0,axiom,
hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),hAPP(nat,nat,plus_plus(nat,X1),X2))),
inference(literals_permutation,[status(thm)],[c_0_3377]) ).
cnf(c_0_3378_0,axiom,
hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),hAPP(nat,nat,plus_plus(nat,X2),X1))),
inference(literals_permutation,[status(thm)],[c_0_3378]) ).
cnf(c_0_3382_0,axiom,
hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(nat,int,semiring_1_of_nat(int),X1))),
inference(literals_permutation,[status(thm)],[c_0_3382]) ).
cnf(c_0_3383_0,axiom,
hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(nat,int,semiring_1_of_nat(int),X1))),
inference(literals_permutation,[status(thm)],[c_0_3383]) ).
cnf(c_0_3391_0,axiom,
hAPP(int,int,plus_plus(int,hAPP(nat,int,semiring_1_of_nat(int),X1)),hAPP(nat,int,semiring_1_of_nat(int),X2)) = hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,plus_plus(nat,X1),X2)),
inference(literals_permutation,[status(thm)],[c_0_3391]) ).
cnf(c_0_3392_0,axiom,
hAPP(int,int,plus_plus(int,hAPP(nat,int,semiring_1_of_nat(int),X1)),hAPP(nat,int,semiring_1_of_nat(int),X2)) = hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,plus_plus(nat,X1),X2)),
inference(literals_permutation,[status(thm)],[c_0_3392]) ).
cnf(c_0_3402_0,axiom,
hAPP(int,int,plus_plus(int,hAPP(int,int,bit0,X1)),hAPP(int,int,bit1,X2)) = hAPP(int,int,bit1,hAPP(int,int,plus_plus(int,X1),X2)),
inference(literals_permutation,[status(thm)],[c_0_3402]) ).
cnf(c_0_3403_0,axiom,
hAPP(int,int,plus_plus(int,hAPP(int,int,bit1,X1)),hAPP(int,int,bit0,X2)) = hAPP(int,int,bit1,hAPP(int,int,plus_plus(int,X1),X2)),
inference(literals_permutation,[status(thm)],[c_0_3403]) ).
cnf(c_0_3404_0,axiom,
hAPP(int,int,plus_plus(int,hAPP(int,int,bit0,X1)),hAPP(int,int,bit0,X2)) = hAPP(int,int,bit0,hAPP(int,int,plus_plus(int,X1),X2)),
inference(literals_permutation,[status(thm)],[c_0_3404]) ).
cnf(c_0_3431_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_3431]) ).
cnf(c_0_3432_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_3432]) ).
cnf(c_0_3433_0,axiom,
hAPP(X1,X1,hAPP(X1,fun(X1,X1),hAPP(bool,fun(X1,fun(X1,X1)),if(X1),fFalse),X2),X3) = ti(X1,X3),
inference(literals_permutation,[status(thm)],[c_0_3433]) ).
cnf(c_0_3434_0,axiom,
hAPP(X1,X1,hAPP(X1,fun(X1,X1),hAPP(bool,fun(X1,fun(X1,X1)),if(X1),fTrue),X2),X3) = ti(X1,X2),
inference(literals_permutation,[status(thm)],[c_0_3434]) ).
cnf(c_0_3438_0,axiom,
hAPP(nat,int,power_power(int,hAPP(nat,int,semiring_1_of_nat(int),X1)),X2) = hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,power_power(nat,X1),X2)),
inference(literals_permutation,[status(thm)],[c_0_3438]) ).
cnf(c_0_3439_0,axiom,
hAPP(nat,int,power_power(int,hAPP(nat,int,semiring_1_of_nat(int),X1)),X2) = hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,power_power(nat,X1),X2)),
inference(literals_permutation,[status(thm)],[c_0_3439]) ).
cnf(c_0_3440_0,axiom,
hAPP(nat,int,power_power(int,hAPP(nat,int,semiring_1_of_nat(int),X1)),X2) = hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,power_power(nat,X1),X2)),
inference(literals_permutation,[status(thm)],[c_0_3440]) ).
cnf(c_0_3447_0,axiom,
number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))) = hAPP(nat,nat,plus_plus(nat,one_one(nat)),one_one(nat)),
inference(literals_permutation,[status(thm)],[c_0_3447]) ).
cnf(c_0_3454_0,axiom,
hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),number_number_of(int,pls))),
inference(literals_permutation,[status(thm)],[c_0_3454]) ).
cnf(c_0_3457_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_3457]) ).
cnf(c_0_3458_0,axiom,
hAPP(int,int,plus_plus(int,hAPP(int,int,plus_plus(int,one_one(int)),X1)),X1) = hAPP(int,int,bit1,X1),
inference(literals_permutation,[status(thm)],[c_0_3458]) ).
cnf(c_0_3459_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_3459]) ).
cnf(c_0_3462_0,axiom,
hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),one_one(int))),
inference(literals_permutation,[status(thm)],[c_0_3462]) ).
cnf(c_0_3463_0,axiom,
hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),zero_zero(int))),
inference(literals_permutation,[status(thm)],[c_0_3463]) ).
cnf(c_0_3464_0,axiom,
hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),one_one(int))),
inference(literals_permutation,[status(thm)],[c_0_3464]) ).
cnf(c_0_3467_0,axiom,
hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),zero_zero(nat)),X1)),
inference(literals_permutation,[status(thm)],[c_0_3467]) ).
cnf(c_0_3468_0,axiom,
hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),zero_zero(nat)),X1)),
inference(literals_permutation,[status(thm)],[c_0_3468]) ).
cnf(c_0_3470_0,axiom,
hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),one_one(int)),t)),
inference(literals_permutation,[status(thm)],[c_0_3470]) ).
cnf(c_0_3471_0,axiom,
hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),tn)),
inference(literals_permutation,[status(thm)],[c_0_3471]) ).
cnf(c_0_3472_0,axiom,
hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),n)),
inference(literals_permutation,[status(thm)],[c_0_3472]) ).
cnf(c_0_3473_0,axiom,
hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),t)),
inference(literals_permutation,[status(thm)],[c_0_3473]) ).
cnf(c_0_3478_0,axiom,
hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X1),X1)),
inference(literals_permutation,[status(thm)],[c_0_3478]) ).
cnf(c_0_3479_0,axiom,
hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X1)),
inference(literals_permutation,[status(thm)],[c_0_3479]) ).
cnf(c_0_3480_0,axiom,
hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X1),X1)),
inference(literals_permutation,[status(thm)],[c_0_3480]) ).
cnf(c_0_3481_0,axiom,
hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),pls)),
inference(literals_permutation,[status(thm)],[c_0_3481]) ).
cnf(c_0_3482_0,axiom,
hAPP(int,int,bit0,hAPP(int,int,succ,X1)) = hAPP(int,int,succ,hAPP(int,int,bit1,X1)),
inference(literals_permutation,[status(thm)],[c_0_3482]) ).
cnf(c_0_3483_0,axiom,
ti(fun(X1,fun(X1,X1)),hAPP(bool,fun(X1,fun(X1,X1)),X2,X3)) = hAPP(bool,fun(X1,fun(X1,X1)),X2,X3),
inference(literals_permutation,[status(thm)],[c_0_3483]) ).
cnf(c_0_3484_0,axiom,
hAPP(bool,fun(X1,fun(X1,X1)),ti(fun(bool,fun(X1,fun(X1,X1))),X2),X3) = hAPP(bool,fun(X1,fun(X1,X1)),X2,X3),
inference(literals_permutation,[status(thm)],[c_0_3484]) ).
cnf(c_0_3485_0,axiom,
hAPP(int,int,succ,hAPP(int,int,bit0,X1)) = hAPP(int,int,bit1,X1),
inference(literals_permutation,[status(thm)],[c_0_3485]) ).
cnf(c_0_3493_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_3493]) ).
cnf(c_0_3494_0,axiom,
ti(fun(X1,X1),hAPP(X1,fun(X1,X1),X2,X3)) = hAPP(X1,fun(X1,X1),X2,X3),
inference(literals_permutation,[status(thm)],[c_0_3494]) ).
cnf(c_0_3508_0,axiom,
ti(X1,hAPP(X1,X1,X2,X3)) = hAPP(X1,X1,X2,X3),
inference(literals_permutation,[status(thm)],[c_0_3508]) ).
cnf(c_0_3509_0,axiom,
hAPP(X1,fun(X1,X1),ti(fun(X1,fun(X1,X1)),X2),X3) = hAPP(X1,fun(X1,X1),X2,X3),
inference(literals_permutation,[status(thm)],[c_0_3509]) ).
cnf(c_0_3510_0,axiom,
hAPP(bool,fun(X1,fun(X1,X1)),X2,ti(bool,X3)) = hAPP(bool,fun(X1,fun(X1,X1)),X2,X3),
inference(literals_permutation,[status(thm)],[c_0_3510]) ).
cnf(c_0_3514_0,axiom,
hAPP(X1,X1,ti(fun(X1,X1),X2),X3) = hAPP(X1,X1,X2,X3),
inference(literals_permutation,[status(thm)],[c_0_3514]) ).
cnf(c_0_3515_0,axiom,
hAPP(X1,fun(X1,X1),X2,ti(X1,X3)) = hAPP(X1,fun(X1,X1),X2,X3),
inference(literals_permutation,[status(thm)],[c_0_3515]) ).
cnf(c_0_3520_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_3520]) ).
cnf(c_0_3521_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_3521]) ).
cnf(c_0_3525_0,axiom,
hAPP(X1,X1,X2,ti(X1,X3)) = hAPP(X1,X1,X2,X3),
inference(literals_permutation,[status(thm)],[c_0_3525]) ).
cnf(c_0_3528_0,axiom,
hAPP(int,int,plus_plus(int,X1),one_one(int)) = hAPP(int,int,succ,X1),
inference(literals_permutation,[status(thm)],[c_0_3528]) ).
cnf(c_0_3529_0,axiom,
hAPP(int,int,plus_plus(int,X1),X1) = hAPP(int,int,bit0,X1),
inference(literals_permutation,[status(thm)],[c_0_3529]) ).
cnf(c_0_3535_0,axiom,
number_number_of(nat,hAPP(int,int,bit1,pls)) = one_one(nat),
inference(literals_permutation,[status(thm)],[c_0_3535]) ).
cnf(c_0_3536_0,axiom,
number_number_of(nat,hAPP(int,int,bit1,pls)) = one_one(nat),
inference(literals_permutation,[status(thm)],[c_0_3536]) ).
cnf(c_0_3537_0,axiom,
number_number_of(int,hAPP(int,int,bit1,pls)) = one_one(int),
inference(literals_permutation,[status(thm)],[c_0_3537]) ).
cnf(c_0_3540_0,axiom,
hAPP(int,int,bit1,pls) = hAPP(int,int,succ,pls),
inference(literals_permutation,[status(thm)],[c_0_3540]) ).
cnf(c_0_3584_0,axiom,
hAPP(nat,nat,plus_plus(nat,zero_zero(nat)),X1) = X1,
inference(literals_permutation,[status(thm)],[c_0_3584]) ).
cnf(c_0_3585_0,axiom,
hAPP(int,int,plus_plus(int,zero_zero(int)),X1) = X1,
inference(literals_permutation,[status(thm)],[c_0_3585]) ).
cnf(c_0_3586_0,axiom,
hAPP(nat,nat,plus_plus(nat,X1),zero_zero(nat)) = X1,
inference(literals_permutation,[status(thm)],[c_0_3586]) ).
cnf(c_0_3587_0,axiom,
hAPP(int,int,plus_plus(int,X1),zero_zero(int)) = X1,
inference(literals_permutation,[status(thm)],[c_0_3587]) ).
cnf(c_0_3588_0,axiom,
hAPP(int,int,plus_plus(int,X1),pls) = X1,
inference(literals_permutation,[status(thm)],[c_0_3588]) ).
cnf(c_0_3591_0,axiom,
hAPP(int,int,plus_plus(int,pls),X1) = X1,
inference(literals_permutation,[status(thm)],[c_0_3591]) ).
cnf(c_0_3593_0,axiom,
hAPP(nat,int,semiring_1_of_nat(int),zero_zero(nat)) = zero_zero(int),
inference(literals_permutation,[status(thm)],[c_0_3593]) ).
cnf(c_0_3594_0,axiom,
hAPP(nat,int,semiring_1_of_nat(int),one_one(nat)) = one_one(int),
inference(literals_permutation,[status(thm)],[c_0_3594]) ).
cnf(c_0_3595_0,axiom,
hAPP(nat,int,semiring_1_of_nat(int),zero_zero(nat)) = zero_zero(int),
inference(literals_permutation,[status(thm)],[c_0_3595]) ).
cnf(c_0_3596_0,axiom,
hAPP(nat,int,semiring_1_of_nat(int),one_one(nat)) = one_one(int),
inference(literals_permutation,[status(thm)],[c_0_3596]) ).
cnf(c_0_3599_0,axiom,
hAPP(int,int,bit0,pls) = pls,
inference(literals_permutation,[status(thm)],[c_0_3599]) ).
cnf(c_0_3600_0,axiom,
ti(fun(bool,fun(X1,fun(X1,X1))),if(X1)) = if(X1),
inference(literals_permutation,[status(thm)],[c_0_3600]) ).
cnf(c_0_3622_0,axiom,
ti(X1,ti(X1,X2)) = ti(X1,X2),
inference(literals_permutation,[status(thm)],[c_0_3622]) ).
cnf(c_0_3629_0,axiom,
ti(fun(real,real),sqrt) = sqrt,
inference(literals_permutation,[status(thm)],[c_0_3629]) ).
cnf(c_0_3630_0,axiom,
ti(fun(int,int),succ) = succ,
inference(literals_permutation,[status(thm)],[c_0_3630]) ).
cnf(c_0_3634_0,axiom,
ti(X1,undefined(X1)) = undefined(X1),
inference(literals_permutation,[status(thm)],[c_0_3634]) ).
cnf(c_0_3640_0,axiom,
number_number_of(int,X1) = X1,
inference(literals_permutation,[status(thm)],[c_0_3640]) ).
cnf(c_0_3641_0,axiom,
number_number_of(nat,pls) = zero_zero(nat),
inference(literals_permutation,[status(thm)],[c_0_3641]) ).
cnf(c_0_3642_0,axiom,
number_number_of(nat,pls) = zero_zero(nat),
inference(literals_permutation,[status(thm)],[c_0_3642]) ).
cnf(c_0_3643_0,axiom,
number_number_of(int,pls) = zero_zero(int),
inference(literals_permutation,[status(thm)],[c_0_3643]) ).
cnf(c_0_3644_0,axiom,
ti(nat,tn) = tn,
inference(literals_permutation,[status(thm)],[c_0_3644]) ).
cnf(c_0_3645_0,axiom,
ti(int,t) = t,
inference(literals_permutation,[status(thm)],[c_0_3645]) ).
cnf(c_0_3646_0,axiom,
ti(int,m1) = m1,
inference(literals_permutation,[status(thm)],[c_0_3646]) ).
cnf(c_0_3647_0,axiom,
ti(bool,fTrue) = fTrue,
inference(literals_permutation,[status(thm)],[c_0_3647]) ).
cnf(c_0_3648_0,axiom,
ti(bool,fFalse) = fFalse,
inference(literals_permutation,[status(thm)],[c_0_3648]) ).
cnf(c_0_3651_0,axiom,
one(real),
inference(literals_permutation,[status(thm)],[c_0_3651]) ).
cnf(c_0_3652_0,axiom,
number(real),
inference(literals_permutation,[status(thm)],[c_0_3652]) ).
cnf(c_0_3653_0,axiom,
zero(real),
inference(literals_permutation,[status(thm)],[c_0_3653]) ).
cnf(c_0_3654_0,axiom,
power(real),
inference(literals_permutation,[status(thm)],[c_0_3654]) ).
cnf(c_0_3655_0,axiom,
ord(real),
inference(literals_permutation,[status(thm)],[c_0_3655]) ).
cnf(c_0_3656_0,axiom,
number_ring(real),
inference(literals_permutation,[status(thm)],[c_0_3656]) ).
cnf(c_0_3657_0,axiom,
ring_char_0(real),
inference(literals_permutation,[status(thm)],[c_0_3657]) ).
cnf(c_0_3658_0,axiom,
order(real),
inference(literals_permutation,[status(thm)],[c_0_3658]) ).
cnf(c_0_3659_0,axiom,
mult_zero(real),
inference(literals_permutation,[status(thm)],[c_0_3659]) ).
cnf(c_0_3660_0,axiom,
semiring_0(real),
inference(literals_permutation,[status(thm)],[c_0_3660]) ).
cnf(c_0_3661_0,axiom,
semiring_1(real),
inference(literals_permutation,[status(thm)],[c_0_3661]) ).
cnf(c_0_3662_0,axiom,
monoid_add(real),
inference(literals_permutation,[status(thm)],[c_0_3662]) ).
cnf(c_0_3663_0,axiom,
monoid_mult(real),
inference(literals_permutation,[status(thm)],[c_0_3663]) ).
cnf(c_0_3664_0,axiom,
linorder(real),
inference(literals_permutation,[status(thm)],[c_0_3664]) ).
cnf(c_0_3665_0,axiom,
preorder(real),
inference(literals_permutation,[status(thm)],[c_0_3665]) ).
cnf(c_0_3666_0,axiom,
zero_neq_one(real),
inference(literals_permutation,[status(thm)],[c_0_3666]) ).
cnf(c_0_3667_0,axiom,
number_semiring(real),
inference(literals_permutation,[status(thm)],[c_0_3667]) ).
cnf(c_0_3668_0,axiom,
semiring_char_0(real),
inference(literals_permutation,[status(thm)],[c_0_3668]) ).
cnf(c_0_3669_0,axiom,
comm_semiring_1(real),
inference(literals_permutation,[status(thm)],[c_0_3669]) ).
cnf(c_0_3670_0,axiom,
linordered_idom(real),
inference(literals_permutation,[status(thm)],[c_0_3670]) ).
cnf(c_0_3671_0,axiom,
linordered_ring(real),
inference(literals_permutation,[status(thm)],[c_0_3671]) ).
cnf(c_0_3672_0,axiom,
comm_monoid_add(real),
inference(literals_permutation,[status(thm)],[c_0_3672]) ).
cnf(c_0_3673_0,axiom,
no_zero_divisors(real),
inference(literals_permutation,[status(thm)],[c_0_3673]) ).
cnf(c_0_3674_0,axiom,
ab_semigroup_add(real),
inference(literals_permutation,[status(thm)],[c_0_3674]) ).
cnf(c_0_3675_0,axiom,
dense_linorder(real),
inference(literals_permutation,[status(thm)],[c_0_3675]) ).
cnf(c_0_3676_0,axiom,
linordered_semidom(real),
inference(literals_permutation,[status(thm)],[c_0_3676]) ).
cnf(c_0_3677_0,axiom,
linordered_semiring(real),
inference(literals_permutation,[status(thm)],[c_0_3677]) ).
cnf(c_0_3678_0,axiom,
cancel_semigroup_add(real),
inference(literals_permutation,[status(thm)],[c_0_3678]) ).
cnf(c_0_3679_0,axiom,
linord581940658strict(real),
inference(literals_permutation,[status(thm)],[c_0_3679]) ).
cnf(c_0_3680_0,axiom,
ring_11004092258visors(real),
inference(literals_permutation,[status(thm)],[c_0_3680]) ).
cnf(c_0_3681_0,axiom,
cancel146912293up_add(real),
inference(literals_permutation,[status(thm)],[c_0_3681]) ).
cnf(c_0_3682_0,axiom,
linord219039673up_add(real),
inference(literals_permutation,[status(thm)],[c_0_3682]) ).
cnf(c_0_3683_0,axiom,
ordere216010020id_add(real),
inference(literals_permutation,[status(thm)],[c_0_3683]) ).
cnf(c_0_3684_0,axiom,
ordere779506340up_add(real),
inference(literals_permutation,[status(thm)],[c_0_3684]) ).
cnf(c_0_3685_0,axiom,
linord20386208strict(real),
inference(literals_permutation,[status(thm)],[c_0_3685]) ).
cnf(c_0_3686_0,axiom,
linord893533164strict(real),
inference(literals_permutation,[status(thm)],[c_0_3686]) ).
cnf(c_0_3687_0,axiom,
ordere236663937imp_le(real),
inference(literals_permutation,[status(thm)],[c_0_3687]) ).
cnf(c_0_3688_0,axiom,
ordere223160158up_add(real),
inference(literals_permutation,[status(thm)],[c_0_3688]) ).
cnf(c_0_3689_0,axiom,
semiri456707255roduct(real),
inference(literals_permutation,[status(thm)],[c_0_3689]) ).
cnf(c_0_3690_0,axiom,
ord(bool),
inference(literals_permutation,[status(thm)],[c_0_3690]) ).
cnf(c_0_3691_0,axiom,
order(bool),
inference(literals_permutation,[status(thm)],[c_0_3691]) ).
cnf(c_0_3692_0,axiom,
preorder(bool),
inference(literals_permutation,[status(thm)],[c_0_3692]) ).
cnf(c_0_3693_0,axiom,
one(nat),
inference(literals_permutation,[status(thm)],[c_0_3693]) ).
cnf(c_0_3694_0,axiom,
number(nat),
inference(literals_permutation,[status(thm)],[c_0_3694]) ).
cnf(c_0_3695_0,axiom,
zero(nat),
inference(literals_permutation,[status(thm)],[c_0_3695]) ).
cnf(c_0_3696_0,axiom,
power(nat),
inference(literals_permutation,[status(thm)],[c_0_3696]) ).
cnf(c_0_3697_0,axiom,
ord(nat),
inference(literals_permutation,[status(thm)],[c_0_3697]) ).
cnf(c_0_3698_0,axiom,
order(nat),
inference(literals_permutation,[status(thm)],[c_0_3698]) ).
cnf(c_0_3699_0,axiom,
mult_zero(nat),
inference(literals_permutation,[status(thm)],[c_0_3699]) ).
cnf(c_0_3700_0,axiom,
semiring_0(nat),
inference(literals_permutation,[status(thm)],[c_0_3700]) ).
cnf(c_0_3701_0,axiom,
semiring_1(nat),
inference(literals_permutation,[status(thm)],[c_0_3701]) ).
cnf(c_0_3702_0,axiom,
monoid_add(nat),
inference(literals_permutation,[status(thm)],[c_0_3702]) ).
cnf(c_0_3703_0,axiom,
monoid_mult(nat),
inference(literals_permutation,[status(thm)],[c_0_3703]) ).
cnf(c_0_3704_0,axiom,
linorder(nat),
inference(literals_permutation,[status(thm)],[c_0_3704]) ).
cnf(c_0_3705_0,axiom,
preorder(nat),
inference(literals_permutation,[status(thm)],[c_0_3705]) ).
cnf(c_0_3706_0,axiom,
zero_neq_one(nat),
inference(literals_permutation,[status(thm)],[c_0_3706]) ).
cnf(c_0_3707_0,axiom,
number_semiring(nat),
inference(literals_permutation,[status(thm)],[c_0_3707]) ).
cnf(c_0_3708_0,axiom,
semiring_char_0(nat),
inference(literals_permutation,[status(thm)],[c_0_3708]) ).
cnf(c_0_3709_0,axiom,
comm_semiring_1(nat),
inference(literals_permutation,[status(thm)],[c_0_3709]) ).
cnf(c_0_3710_0,axiom,
comm_monoid_add(nat),
inference(literals_permutation,[status(thm)],[c_0_3710]) ).
cnf(c_0_3711_0,axiom,
no_zero_divisors(nat),
inference(literals_permutation,[status(thm)],[c_0_3711]) ).
cnf(c_0_3712_0,axiom,
ab_semigroup_add(nat),
inference(literals_permutation,[status(thm)],[c_0_3712]) ).
cnf(c_0_3713_0,axiom,
linordered_semidom(nat),
inference(literals_permutation,[status(thm)],[c_0_3713]) ).
cnf(c_0_3714_0,axiom,
linordered_semiring(nat),
inference(literals_permutation,[status(thm)],[c_0_3714]) ).
cnf(c_0_3715_0,axiom,
cancel_semigroup_add(nat),
inference(literals_permutation,[status(thm)],[c_0_3715]) ).
cnf(c_0_3716_0,axiom,
cancel146912293up_add(nat),
inference(literals_permutation,[status(thm)],[c_0_3716]) ).
cnf(c_0_3717_0,axiom,
ordere216010020id_add(nat),
inference(literals_permutation,[status(thm)],[c_0_3717]) ).
cnf(c_0_3718_0,axiom,
ordere779506340up_add(nat),
inference(literals_permutation,[status(thm)],[c_0_3718]) ).
cnf(c_0_3719_0,axiom,
linord20386208strict(nat),
inference(literals_permutation,[status(thm)],[c_0_3719]) ).
cnf(c_0_3720_0,axiom,
linord893533164strict(nat),
inference(literals_permutation,[status(thm)],[c_0_3720]) ).
cnf(c_0_3721_0,axiom,
ordere236663937imp_le(nat),
inference(literals_permutation,[status(thm)],[c_0_3721]) ).
cnf(c_0_3722_0,axiom,
ordere223160158up_add(nat),
inference(literals_permutation,[status(thm)],[c_0_3722]) ).
cnf(c_0_3723_0,axiom,
semiri456707255roduct(nat),
inference(literals_permutation,[status(thm)],[c_0_3723]) ).
cnf(c_0_3724_0,axiom,
one(int),
inference(literals_permutation,[status(thm)],[c_0_3724]) ).
cnf(c_0_3725_0,axiom,
number(int),
inference(literals_permutation,[status(thm)],[c_0_3725]) ).
cnf(c_0_3726_0,axiom,
zero(int),
inference(literals_permutation,[status(thm)],[c_0_3726]) ).
cnf(c_0_3727_0,axiom,
power(int),
inference(literals_permutation,[status(thm)],[c_0_3727]) ).
cnf(c_0_3728_0,axiom,
ord(int),
inference(literals_permutation,[status(thm)],[c_0_3728]) ).
cnf(c_0_3729_0,axiom,
number_ring(int),
inference(literals_permutation,[status(thm)],[c_0_3729]) ).
cnf(c_0_3730_0,axiom,
ring_char_0(int),
inference(literals_permutation,[status(thm)],[c_0_3730]) ).
cnf(c_0_3731_0,axiom,
order(int),
inference(literals_permutation,[status(thm)],[c_0_3731]) ).
cnf(c_0_3732_0,axiom,
mult_zero(int),
inference(literals_permutation,[status(thm)],[c_0_3732]) ).
cnf(c_0_3733_0,axiom,
semiring_0(int),
inference(literals_permutation,[status(thm)],[c_0_3733]) ).
cnf(c_0_3734_0,axiom,
semiring_1(int),
inference(literals_permutation,[status(thm)],[c_0_3734]) ).
cnf(c_0_3735_0,axiom,
monoid_add(int),
inference(literals_permutation,[status(thm)],[c_0_3735]) ).
cnf(c_0_3736_0,axiom,
monoid_mult(int),
inference(literals_permutation,[status(thm)],[c_0_3736]) ).
cnf(c_0_3737_0,axiom,
linorder(int),
inference(literals_permutation,[status(thm)],[c_0_3737]) ).
cnf(c_0_3738_0,axiom,
preorder(int),
inference(literals_permutation,[status(thm)],[c_0_3738]) ).
cnf(c_0_3739_0,axiom,
zero_neq_one(int),
inference(literals_permutation,[status(thm)],[c_0_3739]) ).
cnf(c_0_3740_0,axiom,
number_semiring(int),
inference(literals_permutation,[status(thm)],[c_0_3740]) ).
cnf(c_0_3741_0,axiom,
semiring_char_0(int),
inference(literals_permutation,[status(thm)],[c_0_3741]) ).
cnf(c_0_3742_0,axiom,
comm_semiring_1(int),
inference(literals_permutation,[status(thm)],[c_0_3742]) ).
cnf(c_0_3743_0,axiom,
linordered_idom(int),
inference(literals_permutation,[status(thm)],[c_0_3743]) ).
cnf(c_0_3744_0,axiom,
linordered_ring(int),
inference(literals_permutation,[status(thm)],[c_0_3744]) ).
cnf(c_0_3745_0,axiom,
comm_monoid_add(int),
inference(literals_permutation,[status(thm)],[c_0_3745]) ).
cnf(c_0_3746_0,axiom,
no_zero_divisors(int),
inference(literals_permutation,[status(thm)],[c_0_3746]) ).
cnf(c_0_3747_0,axiom,
ab_semigroup_add(int),
inference(literals_permutation,[status(thm)],[c_0_3747]) ).
cnf(c_0_3748_0,axiom,
linordered_semidom(int),
inference(literals_permutation,[status(thm)],[c_0_3748]) ).
cnf(c_0_3749_0,axiom,
linordered_semiring(int),
inference(literals_permutation,[status(thm)],[c_0_3749]) ).
cnf(c_0_3750_0,axiom,
cancel_semigroup_add(int),
inference(literals_permutation,[status(thm)],[c_0_3750]) ).
cnf(c_0_3751_0,axiom,
linord581940658strict(int),
inference(literals_permutation,[status(thm)],[c_0_3751]) ).
cnf(c_0_3752_0,axiom,
ring_11004092258visors(int),
inference(literals_permutation,[status(thm)],[c_0_3752]) ).
cnf(c_0_3753_0,axiom,
cancel146912293up_add(int),
inference(literals_permutation,[status(thm)],[c_0_3753]) ).
cnf(c_0_3754_0,axiom,
linord219039673up_add(int),
inference(literals_permutation,[status(thm)],[c_0_3754]) ).
cnf(c_0_3755_0,axiom,
ordere216010020id_add(int),
inference(literals_permutation,[status(thm)],[c_0_3755]) ).
cnf(c_0_3756_0,axiom,
ordere779506340up_add(int),
inference(literals_permutation,[status(thm)],[c_0_3756]) ).
cnf(c_0_3757_0,axiom,
linord20386208strict(int),
inference(literals_permutation,[status(thm)],[c_0_3757]) ).
cnf(c_0_3758_0,axiom,
linord893533164strict(int),
inference(literals_permutation,[status(thm)],[c_0_3758]) ).
cnf(c_0_3759_0,axiom,
ordere236663937imp_le(int),
inference(literals_permutation,[status(thm)],[c_0_3759]) ).
cnf(c_0_3760_0,axiom,
ordere223160158up_add(int),
inference(literals_permutation,[status(thm)],[c_0_3760]) ).
cnf(c_0_3761_0,axiom,
semiri456707255roduct(int),
inference(literals_permutation,[status(thm)],[c_0_3761]) ).
cnf(c_0_3762_0,axiom,
zero_zero(int) = pls,
inference(literals_permutation,[status(thm)],[c_0_3762]) ).
% 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,semiring_1_of_nat(int),n))),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) != zero_zero(int),
file('<stdin>',conj_0) ).
fof(c_0_1_002,hypothesis,
ti(fun(int,int),bit1) = bit1,
file('<stdin>',tsy_c_Int_OBit1_res) ).
fof(c_0_2_003,hypothesis,
ti(fun(int,int),bit0) = bit0,
file('<stdin>',tsy_c_Int_OBit0_res) ).
fof(c_0_3_004,hypothesis,
ti(nat,n) = n,
file('<stdin>',tsy_v_n_____res) ).
fof(c_0_4_005,hypothesis,
ti(int,pls) = pls,
file('<stdin>',tsy_c_Int_OPls_res) ).
fof(c_0_5_006,negated_conjecture,
hAPP(nat,int,power_power(int,hAPP(int,int,plus_plus(int,one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),n))),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) = zero_zero(int),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[c_0_0])]) ).
fof(c_0_6_007,hypothesis,
ti(fun(int,int),bit1) = bit1,
c_0_1 ).
fof(c_0_7_008,hypothesis,
ti(fun(int,int),bit0) = bit0,
c_0_2 ).
fof(c_0_8_009,hypothesis,
ti(nat,n) = n,
c_0_3 ).
fof(c_0_9_010,hypothesis,
ti(int,pls) = pls,
c_0_4 ).
fof(c_0_10_011,negated_conjecture,
hAPP(nat,int,power_power(int,hAPP(int,int,plus_plus(int,one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),n))),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) = zero_zero(int),
c_0_5 ).
fof(c_0_11_012,hypothesis,
ti(fun(int,int),bit1) = bit1,
c_0_6 ).
fof(c_0_12_013,hypothesis,
ti(fun(int,int),bit0) = bit0,
c_0_7 ).
fof(c_0_13_014,hypothesis,
ti(nat,n) = n,
c_0_8 ).
fof(c_0_14_015,hypothesis,
ti(int,pls) = pls,
c_0_9 ).
cnf(c_0_15_016,negated_conjecture,
hAPP(nat,int,power_power(int,hAPP(int,int,plus_plus(int,one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),n))),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) = zero_zero(int),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_16_017,hypothesis,
ti(fun(int,int),bit1) = bit1,
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_17_018,hypothesis,
ti(fun(int,int),bit0) = bit0,
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_18_019,hypothesis,
ti(nat,n) = n,
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_19_020,hypothesis,
ti(int,pls) = pls,
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_20_021,negated_conjecture,
hAPP(nat,int,power_power(int,hAPP(int,int,plus_plus(int,one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),n))),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) = zero_zero(int),
c_0_15,
[final] ).
cnf(c_0_21_022,hypothesis,
ti(fun(int,int),bit1) = bit1,
c_0_16,
[final] ).
cnf(c_0_22_023,hypothesis,
ti(fun(int,int),bit0) = bit0,
c_0_17,
[final] ).
cnf(c_0_23_024,hypothesis,
ti(nat,n) = n,
c_0_18,
[final] ).
cnf(c_0_24_025,hypothesis,
ti(int,pls) = pls,
c_0_19,
[final] ).
% End CNF derivation
%-------------------------------------------------------------
% Proof by iprover
cnf(c_2244,negated_conjecture,
hAPP(nat,int,power_power(int,hAPP(int,int,plus_plus(int,one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),n))),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) = zero_zero(int),
file('/export/starexec/sandbox/tmp/iprover_modulo_9ff437.p',c_0_20) ).
cnf(c_2767,negated_conjecture,
hAPP(nat,int,power_power(int,hAPP(int,int,plus_plus(int,one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),n))),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) = zero_zero(int),
inference(copy,[status(esa)],[c_2244]) ).
cnf(c_2771,negated_conjecture,
hAPP(nat,int,power_power(int,hAPP(int,int,plus_plus(int,one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),n))),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) = zero_zero(int),
inference(copy,[status(esa)],[c_2767]) ).
cnf(c_2780,negated_conjecture,
hAPP(nat,int,power_power(int,hAPP(int,int,plus_plus(int,one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),n))),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) = zero_zero(int),
inference(copy,[status(esa)],[c_2771]) ).
cnf(c_2781,negated_conjecture,
hAPP(nat,int,power_power(int,hAPP(int,int,plus_plus(int,one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),n))),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) = zero_zero(int),
inference(copy,[status(esa)],[c_2780]) ).
cnf(c_9458,negated_conjecture,
hAPP(nat,int,power_power(int,hAPP(int,int,plus_plus(int,one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),n))),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) = zero_zero(int),
inference(copy,[status(esa)],[c_2781]) ).
cnf(c_9459,plain,
hAPP(nat,int,power_power(int,hAPP(int,int,plus_plus(int,one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),n))),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) = pls,
inference(rewriting,[status(thm)],[c_9458]) ).
cnf(c_974,plain,
( ~ ord(X0)
| ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X1),X2))
| hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X1),X3))
| X2 != X3 ),
file('/export/starexec/sandbox/tmp/iprover_modulo_9ff437.p',c_0_3275_1) ).
cnf(c_6918,plain,
( ~ ord(X0)
| ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X1),X2))
| hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X1),X3))
| X2 != X3 ),
inference(copy,[status(esa)],[c_974]) ).
cnf(c_9496,plain,
( ~ ord(X0)
| hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X1),pls))
| ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X1),hAPP(nat,int,power_power(int,hAPP(int,int,plus_plus(int,one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),n))),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))) ),
inference(resolution,[status(thm)],[c_9459,c_6918]) ).
cnf(c_9501,plain,
( ~ ord(X0)
| hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X1),pls))
| ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X1),hAPP(nat,int,power_power(int,hAPP(int,int,plus_plus(int,one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),n))),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))) ),
inference(rewriting,[status(thm)],[c_9496]) ).
cnf(c_1510,plain,
( ~ order(X0)
| ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),X1),X2))
| ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X3),X1))
| hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X3),X2)) ),
file('/export/starexec/sandbox/tmp/iprover_modulo_9ff437.p',c_0_3096_0) ).
cnf(c_7990,plain,
( ~ order(X0)
| ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),X1),X2))
| ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X3),X1))
| hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X3),X2)) ),
inference(copy,[status(esa)],[c_1510]) ).
cnf(c_9998,plain,
( ~ order(X0)
| ~ ord(X0)
| ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),X1),hAPP(nat,int,power_power(int,hAPP(int,int,plus_plus(int,one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),n))),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))
| hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X2),pls))
| ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X2),X1)) ),
inference(resolution,[status(thm)],[c_9501,c_7990]) ).
cnf(c_10001,plain,
( ~ order(X0)
| ~ ord(X0)
| ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),X1),hAPP(nat,int,power_power(int,hAPP(int,int,plus_plus(int,one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),n))),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))
| hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X2),pls))
| ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X2),X1)) ),
inference(rewriting,[status(thm)],[c_9998]) ).
cnf(c_195,plain,
hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(int,int,plus_plus(int,one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),n)))),
file('/export/starexec/sandbox/tmp/iprover_modulo_9ff437.p',c_0_3228_0) ).
cnf(c_5364,plain,
hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(int,int,plus_plus(int,one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),n)))),
inference(copy,[status(esa)],[c_195]) ).
cnf(c_5365,plain,
hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),hAPP(int,int,plus_plus(int,one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),n)))),
inference(rewriting,[status(thm)],[c_5364]) ).
cnf(c_13819,plain,
( ~ order(int)
| ~ ord(int)
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,plus_plus(int,one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),n))),hAPP(nat,int,power_power(int,hAPP(int,int,plus_plus(int,one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),n))),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),pls)) ),
inference(resolution,[status(thm)],[c_10001,c_5365]) ).
cnf(c_13820,plain,
( ~ order(int)
| ~ ord(int)
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,plus_plus(int,one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),n))),hAPP(nat,int,power_power(int,hAPP(int,int,plus_plus(int,one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),n))),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),pls)) ),
inference(rewriting,[status(thm)],[c_13819]) ).
cnf(c_213,plain,
~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),pls)),
file('/export/starexec/sandbox/tmp/iprover_modulo_9ff437.p',c_0_3423_0) ).
cnf(c_5396,plain,
~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),pls)),
inference(copy,[status(esa)],[c_213]) ).
cnf(c_201,plain,
hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X0),hAPP(nat,int,power_power(int,X0),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),
file('/export/starexec/sandbox/tmp/iprover_modulo_9ff437.p',c_0_2938_0) ).
cnf(c_5374,plain,
hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X0),hAPP(nat,int,power_power(int,X0),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),
inference(copy,[status(esa)],[c_201]) ).
cnf(c_34,plain,
ord(int),
file('/export/starexec/sandbox/tmp/iprover_modulo_9ff437.p',c_0_3728_0) ).
cnf(c_5102,plain,
ord(int),
inference(copy,[status(esa)],[c_34]) ).
cnf(c_31,plain,
order(int),
file('/export/starexec/sandbox/tmp/iprover_modulo_9ff437.p',c_0_3731_0) ).
cnf(c_5096,plain,
order(int),
inference(copy,[status(esa)],[c_31]) ).
cnf(c_29791,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_13820,c_5396,c_5374,c_5102,c_5096]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : NUM925+6 : TPTP v8.1.0. Released v5.3.0.
% 0.07/0.13 % Command : iprover_modulo %s %d
% 0.12/0.34 % Computer : n012.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Thu Jul 7 09:27:45 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.35 % Running in mono-core mode
% 0.37/0.60 % Orienting using strategy Equiv(ClausalAll)
% 0.37/0.60 % FOF problem with conjecture
% 0.37/0.60 % 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_701151.s --tptp_safe_out true --time_out_real 150 /export/starexec/sandbox/tmp/iprover_modulo_9ff437.p | tee /export/starexec/sandbox/tmp/iprover_modulo_out_f67b32 | grep -v "SZS"
% 0.37/0.63
% 0.37/0.63 %---------------- iProver v2.5 (CASC-J8 2016) ----------------%
% 0.37/0.63
% 0.37/0.63 %
% 0.37/0.63 % ------ iProver source info
% 0.37/0.63
% 0.37/0.63 % git: sha1: 57accf6c58032223c7708532cf852a99fa48c1b3
% 0.37/0.63 % git: non_committed_changes: true
% 0.37/0.63 % git: last_make_outside_of_git: true
% 0.37/0.63
% 0.37/0.63 %
% 0.37/0.63 % ------ Input Options
% 0.37/0.63
% 0.37/0.63 % --out_options all
% 0.37/0.63 % --tptp_safe_out true
% 0.37/0.63 % --problem_path ""
% 0.37/0.63 % --include_path ""
% 0.37/0.63 % --clausifier .//eprover
% 0.37/0.63 % --clausifier_options --tstp-format
% 0.37/0.63 % --stdin false
% 0.37/0.63 % --dbg_backtrace false
% 0.37/0.63 % --dbg_dump_prop_clauses false
% 0.37/0.63 % --dbg_dump_prop_clauses_file -
% 0.37/0.63 % --dbg_out_stat false
% 0.37/0.63
% 0.37/0.63 % ------ General Options
% 0.37/0.63
% 0.37/0.63 % --fof false
% 0.37/0.63 % --time_out_real 150.
% 0.37/0.63 % --time_out_prep_mult 0.2
% 0.37/0.63 % --time_out_virtual -1.
% 0.37/0.63 % --schedule none
% 0.37/0.63 % --ground_splitting input
% 0.37/0.63 % --splitting_nvd 16
% 0.37/0.63 % --non_eq_to_eq false
% 0.37/0.63 % --prep_gs_sim true
% 0.37/0.63 % --prep_unflatten false
% 0.37/0.63 % --prep_res_sim true
% 0.37/0.63 % --prep_upred true
% 0.37/0.63 % --res_sim_input true
% 0.37/0.63 % --clause_weak_htbl true
% 0.37/0.63 % --gc_record_bc_elim false
% 0.37/0.63 % --symbol_type_check false
% 0.37/0.63 % --clausify_out false
% 0.37/0.63 % --large_theory_mode false
% 0.37/0.63 % --prep_sem_filter none
% 0.37/0.63 % --prep_sem_filter_out false
% 0.37/0.63 % --preprocessed_out false
% 0.37/0.63 % --sub_typing false
% 0.37/0.63 % --brand_transform false
% 0.37/0.63 % --pure_diseq_elim true
% 0.37/0.63 % --min_unsat_core false
% 0.37/0.63 % --pred_elim true
% 0.37/0.63 % --add_important_lit false
% 0.37/0.63 % --soft_assumptions false
% 0.37/0.63 % --reset_solvers false
% 0.37/0.63 % --bc_imp_inh []
% 0.37/0.63 % --conj_cone_tolerance 1.5
% 0.37/0.63 % --prolific_symb_bound 500
% 0.37/0.63 % --lt_threshold 2000
% 0.37/0.63
% 0.37/0.63 % ------ SAT Options
% 0.37/0.63
% 0.37/0.63 % --sat_mode false
% 0.37/0.63 % --sat_fm_restart_options ""
% 0.37/0.63 % --sat_gr_def false
% 0.37/0.63 % --sat_epr_types true
% 0.37/0.63 % --sat_non_cyclic_types false
% 0.37/0.63 % --sat_finite_models false
% 0.37/0.63 % --sat_fm_lemmas false
% 0.37/0.63 % --sat_fm_prep false
% 0.37/0.63 % --sat_fm_uc_incr true
% 0.37/0.63 % --sat_out_model small
% 0.37/0.63 % --sat_out_clauses false
% 0.37/0.63
% 0.37/0.63 % ------ QBF Options
% 0.37/0.63
% 0.37/0.63 % --qbf_mode false
% 0.37/0.63 % --qbf_elim_univ true
% 0.37/0.63 % --qbf_sk_in true
% 0.37/0.63 % --qbf_pred_elim true
% 0.37/0.63 % --qbf_split 32
% 0.37/0.63
% 0.37/0.63 % ------ BMC1 Options
% 0.37/0.63
% 0.37/0.63 % --bmc1_incremental false
% 0.37/0.63 % --bmc1_axioms reachable_all
% 0.37/0.63 % --bmc1_min_bound 0
% 0.37/0.63 % --bmc1_max_bound -1
% 0.37/0.63 % --bmc1_max_bound_default -1
% 0.37/0.63 % --bmc1_symbol_reachability true
% 0.37/0.63 % --bmc1_property_lemmas false
% 0.37/0.63 % --bmc1_k_induction false
% 0.37/0.63 % --bmc1_non_equiv_states false
% 0.37/0.63 % --bmc1_deadlock false
% 0.37/0.63 % --bmc1_ucm false
% 0.37/0.63 % --bmc1_add_unsat_core none
% 0.37/0.63 % --bmc1_unsat_core_children false
% 0.37/0.63 % --bmc1_unsat_core_extrapolate_axioms false
% 0.37/0.63 % --bmc1_out_stat full
% 0.37/0.63 % --bmc1_ground_init false
% 0.37/0.63 % --bmc1_pre_inst_next_state false
% 0.37/0.63 % --bmc1_pre_inst_state false
% 0.37/0.63 % --bmc1_pre_inst_reach_state false
% 0.37/0.63 % --bmc1_out_unsat_core false
% 0.37/0.63 % --bmc1_aig_witness_out false
% 0.37/0.63 % --bmc1_verbose false
% 0.37/0.63 % --bmc1_dump_clauses_tptp false
% 0.45/0.70 % --bmc1_dump_unsat_core_tptp false
% 0.45/0.70 % --bmc1_dump_file -
% 0.45/0.70 % --bmc1_ucm_expand_uc_limit 128
% 0.45/0.70 % --bmc1_ucm_n_expand_iterations 6
% 0.45/0.70 % --bmc1_ucm_extend_mode 1
% 0.45/0.70 % --bmc1_ucm_init_mode 2
% 0.45/0.70 % --bmc1_ucm_cone_mode none
% 0.45/0.70 % --bmc1_ucm_reduced_relation_type 0
% 0.45/0.70 % --bmc1_ucm_relax_model 4
% 0.45/0.70 % --bmc1_ucm_full_tr_after_sat true
% 0.45/0.70 % --bmc1_ucm_expand_neg_assumptions false
% 0.45/0.70 % --bmc1_ucm_layered_model none
% 0.45/0.70 % --bmc1_ucm_max_lemma_size 10
% 0.45/0.70
% 0.45/0.70 % ------ AIG Options
% 0.45/0.70
% 0.45/0.70 % --aig_mode false
% 0.45/0.70
% 0.45/0.70 % ------ Instantiation Options
% 0.45/0.70
% 0.45/0.70 % --instantiation_flag true
% 0.45/0.70 % --inst_lit_sel [+prop;+sign;+ground;-num_var;-num_symb]
% 0.45/0.70 % --inst_solver_per_active 750
% 0.45/0.70 % --inst_solver_calls_frac 0.5
% 0.45/0.70 % --inst_passive_queue_type priority_queues
% 0.45/0.70 % --inst_passive_queues [[-conj_dist;+conj_symb;-num_var];[+age;-num_symb]]
% 0.45/0.70 % --inst_passive_queues_freq [25;2]
% 0.45/0.70 % --inst_dismatching true
% 0.45/0.70 % --inst_eager_unprocessed_to_passive true
% 0.45/0.70 % --inst_prop_sim_given true
% 0.45/0.70 % --inst_prop_sim_new false
% 0.45/0.70 % --inst_orphan_elimination true
% 0.45/0.70 % --inst_learning_loop_flag true
% 0.45/0.70 % --inst_learning_start 3000
% 0.45/0.70 % --inst_learning_factor 2
% 0.45/0.70 % --inst_start_prop_sim_after_learn 3
% 0.45/0.70 % --inst_sel_renew solver
% 0.45/0.70 % --inst_lit_activity_flag true
% 0.45/0.70 % --inst_out_proof true
% 0.45/0.70
% 0.45/0.70 % ------ Resolution Options
% 0.45/0.70
% 0.45/0.70 % --resolution_flag true
% 0.45/0.70 % --res_lit_sel kbo_max
% 0.45/0.70 % --res_to_prop_solver none
% 0.45/0.70 % --res_prop_simpl_new false
% 0.45/0.70 % --res_prop_simpl_given false
% 0.45/0.70 % --res_passive_queue_type priority_queues
% 0.45/0.70 % --res_passive_queues [[-conj_dist;+conj_symb;-num_symb];[+age;-num_symb]]
% 0.45/0.70 % --res_passive_queues_freq [15;5]
% 0.45/0.70 % --res_forward_subs full
% 0.45/0.70 % --res_backward_subs full
% 0.45/0.70 % --res_forward_subs_resolution true
% 0.45/0.70 % --res_backward_subs_resolution true
% 0.45/0.70 % --res_orphan_elimination false
% 0.45/0.70 % --res_time_limit 1000.
% 0.45/0.70 % --res_out_proof true
% 0.45/0.70 % --proof_out_file /export/starexec/sandbox/tmp/iprover_proof_701151.s
% 0.45/0.70 % --modulo true
% 0.45/0.70
% 0.45/0.70 % ------ Combination Options
% 0.45/0.70
% 0.45/0.70 % --comb_res_mult 1000
% 0.45/0.70 % --comb_inst_mult 300
% 0.45/0.70 % ------
% 0.45/0.70
% 0.45/0.70 % ------ Parsing...%
% 0.45/0.70
% 0.45/0.70
% 0.45/0.70 % ------ Statistics
% 0.45/0.70
% 0.45/0.70 % ------ General
% 0.45/0.70
% 0.45/0.70 % num_of_input_clauses: 836
% 0.45/0.70 % num_of_input_neg_conjectures: 0
% 0.45/0.70 % num_of_splits: 0
% 0.45/0.70 % num_of_split_atoms: 0
% 0.45/0.70 % num_of_sem_filtered_clauses: 0
% 0.45/0.70 % num_of_subtypes: 0
% 0.45/0.70 % monotx_restored_types: 0
% 0.45/0.70 % sat_num_of_epr_types: 0
% 0.45/0.70 % sat_num_of_non_cyclic_types: 0
% 0.45/0.70 % sat_guarded_non_collapsed_types: 0
% 0.45/0.70 % is_epr: 0
% 0.45/0.70 % is_horn: 0
% 0.45/0.70 % has_eq: 0
% 0.45/0.70 % num_pure_diseq_elim: 0
% 0.45/0.70 % simp_replaced_by: 0
% 0.45/0.70 % res_preprocessed: 0
% 0.45/0.70 % prep_upred: 0
% 0.45/0.70 % prep_unflattend: 0
% 0.45/0.70 % pred_elim_cands: 0
% 0.45/0.70 % pred_elim: 0
% 0.45/0.70 % pred_elim_cl: 0
% 0.45/0.70 % pred_elim_cycles: 0
% 0.45/0.70 % forced_gc_time: 0
% 0.45/0.70 % gc_basic_clause_elim: 0
% 0.45/0.70 % parsing_time: 0.
% 0.45/0.70 % sem_filter_time: 0.
% 0.45/0.70 % pred_elim_time: 0.
% 0.45/0.70 % out_proof_time: 0.
% 0.45/0.70 % monotx_time: 0.
% 0.45/0.70 % subtype_inf_time: 0.
% 0.45/0.70 % unif_index_cands_time: 0.
% 0.45/0.70 % uFatal error: exception Failure("Parse error in: /export/starexec/sandbox/tmp/iprover_modulo_9ff437.p line: 839 near token: '!='")
% 0.45/0.70 nif_index_add_time: 0.
% 0.45/0.70 % total_time: 0.09
% 0.45/0.70 % num_of_symbols: 124
% 0.45/0.70 % num_of_terms: 2274
% 0.45/0.70
% 0.45/0.70 % ------ Propositional Solver
% 0.45/0.70
% 0.45/0.70 % prop_solver_calls: 0
% 0.45/0.70 % prop_fast_solver_calls: 0
% 0.45/0.70 % prop_num_of_clauses: 0
% 0.45/0.70 % prop_preprocess_simplified: 0
% 0.45/0.70 % prop_fo_subsumed: 0
% 0.45/0.70 % prop_solver_time: 0.
% 0.45/0.70 % prop_fast_solver_time: 0.
% 0.45/0.70 % prop_unsat_core_time: 0.
% 0.45/0.70
% 0.45/0.70 % ------ QBF
% 0.45/0.70
% 0.45/0.70 % qbf_q_res: 0
% 0.45/0.70 % qbf_num_tautologies: 0
% 0.45/0.70 % qbf_prep_cycles: 0
% 0.45/0.70
% 0.45/0.70 % ------ BMC1
% 0.45/0.70
% 0.45/0.70 % bmc1_current_bound: -1
% 0.45/0.70 % bmc1_last_solved_bound: -1
% 0.45/0.70 % bmc1_unsat_core_size: -1
% 0.45/0.70 % bmc1_unsat_core_parents_size: -1
% 0.45/0.70 % bmc1_merge_next_fun: 0
% 0.45/0.70 % bmc1_unsat_core_clauses_time: 0.
% 0.45/0.70
% 0.45/0.70 % ------ Instantiation
% 0.45/0.70
% 0.45/0.70 % inst_num_of_clauses: undef
% 0.45/0.70 % inst_num_in_passive: undef
% 0.45/0.70 % inst_num_in_active: 0
% 0.45/0.70 % inst_num_in_unprocessed: 0
% 0.45/0.70 % inst_num_of_loops: 0
% 0.45/0.70 % inst_num_of_learning_restarts: 0
% 0.45/0.70 % inst_num_moves_active_passive: 0
% 0.45/0.70 % inst_lit_activity: 0
% 0.45/0.70 % inst_lit_activity_moves: 0
% 0.45/0.70 % inst_num_tautologies: 0
% 0.45/0.70 % inst_num_prop_implied: 0
% 0.45/0.70 % inst_num_existing_simplified: 0
% 0.45/0.70 % inst_num_eq_res_simplified: 0
% 0.45/0.70 % inst_num_child_elim: 0
% 0.45/0.70 % inst_num_of_dismatching_blockings: 0
% 0.45/0.70 % inst_num_of_non_proper_insts: 0
% 0.45/0.70 % inst_num_of_duplicates: 0
% 0.45/0.70 % inst_inst_num_from_inst_to_res: 0
% 0.45/0.70 % inst_dismatching_checking_time: 0.
% 0.45/0.70
% 0.45/0.70 % ------ Resolution
% 0.45/0.70
% 0.45/0.70 % res_num_of_clauses: undef
% 0.45/0.70 % res_num_in_passive: undef
% 0.45/0.70 % res_num_in_active: 0
% 0.45/0.70 % res_num_of_loops: 0
% 0.45/0.70 % res_forward_subset_subsumed: 0
% 0.45/0.70 % res_backward_subset_subsumed: 0
% 0.45/0.70 % res_forward_subsumed: 0
% 0.45/0.70 % res_backward_subsumed: 0
% 0.45/0.70 % res_forward_subsumption_resolution: 0
% 0.45/0.70 % res_backward_subsumption_resolution: 0
% 0.45/0.70 % res_clause_to_clause_subsumption: 0
% 0.45/0.70 % res_orphan_elimination: 0
% 0.45/0.70 % res_tautology_del: 0
% 0.45/0.70 % res_num_eq_res_simplified: 0
% 0.45/0.70 % res_num_sel_changes: 0
% 0.45/0.70 % res_moves_from_active_to_pass: 0
% 0.45/0.70
% 0.45/0.70 % Status Unknown
% 0.56/0.93 % Orienting using strategy ClausalAll
% 0.56/0.93 % FOF problem with conjecture
% 0.56/0.93 % 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_701151.s --tptp_safe_out true --time_out_real 150 /export/starexec/sandbox/tmp/iprover_modulo_9ff437.p | tee /export/starexec/sandbox/tmp/iprover_modulo_out_502dc4 | grep -v "SZS"
% 0.79/0.95
% 0.79/0.95 %---------------- iProver v2.5 (CASC-J8 2016) ----------------%
% 0.79/0.95
% 0.79/0.95 %
% 0.79/0.95 % ------ iProver source info
% 0.79/0.95
% 0.79/0.95 % git: sha1: 57accf6c58032223c7708532cf852a99fa48c1b3
% 0.79/0.95 % git: non_committed_changes: true
% 0.79/0.95 % git: last_make_outside_of_git: true
% 0.79/0.95
% 0.79/0.95 %
% 0.79/0.95 % ------ Input Options
% 0.79/0.95
% 0.79/0.95 % --out_options all
% 0.79/0.95 % --tptp_safe_out true
% 0.79/0.95 % --problem_path ""
% 0.79/0.95 % --include_path ""
% 0.79/0.95 % --clausifier .//eprover
% 0.79/0.95 % --clausifier_options --tstp-format
% 0.79/0.95 % --stdin false
% 0.79/0.95 % --dbg_backtrace false
% 0.79/0.95 % --dbg_dump_prop_clauses false
% 0.79/0.95 % --dbg_dump_prop_clauses_file -
% 0.79/0.95 % --dbg_out_stat false
% 0.79/0.95
% 0.79/0.95 % ------ General Options
% 0.79/0.95
% 0.79/0.95 % --fof false
% 0.79/0.95 % --time_out_real 150.
% 0.79/0.95 % --time_out_prep_mult 0.2
% 0.79/0.95 % --time_out_virtual -1.
% 0.79/0.95 % --schedule none
% 0.79/0.95 % --ground_splitting input
% 0.79/0.95 % --splitting_nvd 16
% 0.79/0.95 % --non_eq_to_eq false
% 0.79/0.95 % --prep_gs_sim true
% 0.79/0.95 % --prep_unflatten false
% 0.79/0.95 % --prep_res_sim true
% 0.79/0.95 % --prep_upred true
% 0.79/0.95 % --res_sim_input true
% 0.79/0.95 % --clause_weak_htbl true
% 0.79/0.95 % --gc_record_bc_elim false
% 0.79/0.95 % --symbol_type_check false
% 0.79/0.95 % --clausify_out false
% 0.79/0.95 % --large_theory_mode false
% 0.79/0.95 % --prep_sem_filter none
% 0.79/0.95 % --prep_sem_filter_out false
% 0.79/0.95 % --preprocessed_out false
% 0.79/0.95 % --sub_typing false
% 0.79/0.95 % --brand_transform false
% 0.79/0.95 % --pure_diseq_elim true
% 0.79/0.95 % --min_unsat_core false
% 0.79/0.95 % --pred_elim true
% 0.79/0.95 % --add_important_lit false
% 0.79/0.95 % --soft_assumptions false
% 0.79/0.95 % --reset_solvers false
% 0.79/0.95 % --bc_imp_inh []
% 0.79/0.95 % --conj_cone_tolerance 1.5
% 0.79/0.95 % --prolific_symb_bound 500
% 0.79/0.95 % --lt_threshold 2000
% 0.79/0.95
% 0.79/0.95 % ------ SAT Options
% 0.79/0.95
% 0.79/0.95 % --sat_mode false
% 0.79/0.95 % --sat_fm_restart_options ""
% 0.79/0.95 % --sat_gr_def false
% 0.79/0.95 % --sat_epr_types true
% 0.79/0.95 % --sat_non_cyclic_types false
% 0.79/0.95 % --sat_finite_models false
% 0.79/0.95 % --sat_fm_lemmas false
% 0.79/0.95 % --sat_fm_prep false
% 0.79/0.95 % --sat_fm_uc_incr true
% 0.79/0.95 % --sat_out_model small
% 0.79/0.95 % --sat_out_clauses false
% 0.79/0.95
% 0.79/0.95 % ------ QBF Options
% 0.79/0.95
% 0.79/0.95 % --qbf_mode false
% 0.79/0.95 % --qbf_elim_univ true
% 0.79/0.95 % --qbf_sk_in true
% 0.79/0.95 % --qbf_pred_elim true
% 0.79/0.95 % --qbf_split 32
% 0.79/0.95
% 0.79/0.95 % ------ BMC1 Options
% 0.79/0.95
% 0.79/0.95 % --bmc1_incremental false
% 0.79/0.95 % --bmc1_axioms reachable_all
% 0.79/0.95 % --bmc1_min_bound 0
% 0.79/0.95 % --bmc1_max_bound -1
% 0.79/0.95 % --bmc1_max_bound_default -1
% 0.79/0.95 % --bmc1_symbol_reachability true
% 0.79/0.95 % --bmc1_property_lemmas false
% 0.79/0.95 % --bmc1_k_induction false
% 0.79/0.95 % --bmc1_non_equiv_states false
% 0.79/0.95 % --bmc1_deadlock false
% 0.79/0.95 % --bmc1_ucm false
% 0.79/0.95 % --bmc1_add_unsat_core none
% 0.79/0.95 % --bmc1_unsat_core_children false
% 0.79/0.95 % --bmc1_unsat_core_extrapolate_axioms false
% 0.79/0.95 % --bmc1_out_stat full
% 0.79/0.95 % --bmc1_ground_init false
% 0.79/0.95 % --bmc1_pre_inst_next_state false
% 0.79/0.95 % --bmc1_pre_inst_state false
% 0.79/0.95 % --bmc1_pre_inst_reach_state false
% 0.79/0.95 % --bmc1_out_unsat_core false
% 0.79/0.95 % --bmc1_aig_witness_out false
% 0.79/0.95 % --bmc1_verbose false
% 0.79/0.95 % --bmc1_dump_clauses_tptp false
% 6.41/6.62 % --bmc1_dump_unsat_core_tptp false
% 6.41/6.62 % --bmc1_dump_file -
% 6.41/6.62 % --bmc1_ucm_expand_uc_limit 128
% 6.41/6.62 % --bmc1_ucm_n_expand_iterations 6
% 6.41/6.62 % --bmc1_ucm_extend_mode 1
% 6.41/6.62 % --bmc1_ucm_init_mode 2
% 6.41/6.62 % --bmc1_ucm_cone_mode none
% 6.41/6.62 % --bmc1_ucm_reduced_relation_type 0
% 6.41/6.62 % --bmc1_ucm_relax_model 4
% 6.41/6.62 % --bmc1_ucm_full_tr_after_sat true
% 6.41/6.62 % --bmc1_ucm_expand_neg_assumptions false
% 6.41/6.62 % --bmc1_ucm_layered_model none
% 6.41/6.62 % --bmc1_ucm_max_lemma_size 10
% 6.41/6.62
% 6.41/6.62 % ------ AIG Options
% 6.41/6.62
% 6.41/6.62 % --aig_mode false
% 6.41/6.62
% 6.41/6.62 % ------ Instantiation Options
% 6.41/6.62
% 6.41/6.62 % --instantiation_flag true
% 6.41/6.62 % --inst_lit_sel [+prop;+sign;+ground;-num_var;-num_symb]
% 6.41/6.62 % --inst_solver_per_active 750
% 6.41/6.62 % --inst_solver_calls_frac 0.5
% 6.41/6.62 % --inst_passive_queue_type priority_queues
% 6.41/6.62 % --inst_passive_queues [[-conj_dist;+conj_symb;-num_var];[+age;-num_symb]]
% 6.41/6.62 % --inst_passive_queues_freq [25;2]
% 6.41/6.62 % --inst_dismatching true
% 6.41/6.62 % --inst_eager_unprocessed_to_passive true
% 6.41/6.62 % --inst_prop_sim_given true
% 6.41/6.62 % --inst_prop_sim_new false
% 6.41/6.62 % --inst_orphan_elimination true
% 6.41/6.62 % --inst_learning_loop_flag true
% 6.41/6.62 % --inst_learning_start 3000
% 6.41/6.62 % --inst_learning_factor 2
% 6.41/6.62 % --inst_start_prop_sim_after_learn 3
% 6.41/6.62 % --inst_sel_renew solver
% 6.41/6.62 % --inst_lit_activity_flag true
% 6.41/6.62 % --inst_out_proof true
% 6.41/6.62
% 6.41/6.62 % ------ Resolution Options
% 6.41/6.62
% 6.41/6.62 % --resolution_flag true
% 6.41/6.62 % --res_lit_sel kbo_max
% 6.41/6.62 % --res_to_prop_solver none
% 6.41/6.62 % --res_prop_simpl_new false
% 6.41/6.62 % --res_prop_simpl_given false
% 6.41/6.62 % --res_passive_queue_type priority_queues
% 6.41/6.62 % --res_passive_queues [[-conj_dist;+conj_symb;-num_symb];[+age;-num_symb]]
% 6.41/6.62 % --res_passive_queues_freq [15;5]
% 6.41/6.62 % --res_forward_subs full
% 6.41/6.62 % --res_backward_subs full
% 6.41/6.62 % --res_forward_subs_resolution true
% 6.41/6.62 % --res_backward_subs_resolution true
% 6.41/6.62 % --res_orphan_elimination false
% 6.41/6.62 % --res_time_limit 1000.
% 6.41/6.62 % --res_out_proof true
% 6.41/6.62 % --proof_out_file /export/starexec/sandbox/tmp/iprover_proof_701151.s
% 6.41/6.62 % --modulo true
% 6.41/6.62
% 6.41/6.62 % ------ Combination Options
% 6.41/6.62
% 6.41/6.62 % --comb_res_mult 1000
% 6.41/6.62 % --comb_inst_mult 300
% 6.41/6.62 % ------
% 6.41/6.62
% 6.41/6.62 % ------ Parsing...% successful
% 6.41/6.62
% 6.41/6.62 % ------ 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 %
% 6.41/6.62
% 6.41/6.62 % ------ Proving...
% 6.41/6.62 % ------ Problem Properties
% 6.41/6.62
% 6.41/6.62 %
% 6.41/6.62 % EPR false
% 6.41/6.62 % Horn false
% 6.41/6.62 % Has equality true
% 6.41/6.62
% 6.41/6.62 % % ------ Input Options Time Limit: Unbounded
% 6.41/6.62
% 6.41/6.62
% 6.41/6.62 Compiling...
% 6.41/6.62 Loading plugin: done.
% 6.41/6.62 Compiling...
% 6.41/6.62 Loading plugin: done.
% 6.41/6.62 Compiling...
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% 6.41/6.62 Compiling...
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% 6.41/6.62 Compiling...
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% 6.41/6.62 Compiling...
% 6.41/6.62 Loading plugin: done.
% 6.41/6.62 Compiling...
% 6.41/6.62 Loading plugin: done.
% 6.41/6.62 Compiling...
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% 6.41/6.62 Compiling...
% 6.41/6.62 Loading plugin: done.
% 6.41/6.62 Compiling...
% 6.41/6.62 Loading plugin: done.
% 6.41/6.62 Compiling...
% 6.41/6.62 Loading plugin: done.
% 6.41/6.62 % % ------ Current options:
% 6.41/6.62
% 6.41/6.62 % ------ Input Options
% 6.41/6.62
% 6.41/6.62 % --out_options all
% 6.41/6.62 % --tptp_safe_out true
% 6.41/6.62 % --problem_path ""
% 6.41/6.62 % --include_path ""
% 6.41/6.62 % --clausifier .//eprover
% 6.41/6.62 % --clausifier_options --tstp-format
% 6.41/6.62 % --stdin false
% 6.41/6.62 % --dbg_backtrace false
% 6.41/6.62 % --dbg_dump_prop_clauses false
% 6.41/6.62 % --dbg_dump_prop_clauses_file -
% 6.41/6.62 % --dbg_out_stat false
% 6.41/6.62
% 6.41/6.62 % ------ General Options
% 6.41/6.62
% 6.41/6.62 % --fof false
% 6.41/6.62 % --time_out_real 150.
% 6.41/6.62 % --time_out_prep_mult 0.2
% 6.41/6.62 % --time_out_virtual -1.
% 6.41/6.62 % --schedule none
% 6.41/6.62 % --ground_splitting input
% 6.41/6.62 % --splitting_nvd 16
% 6.41/6.62 % --non_eq_to_eq false
% 6.41/6.62 % --prep_gs_sim true
% 6.41/6.62 % --prep_unflatten false
% 6.41/6.62 % --prep_res_sim true
% 6.41/6.62 % --prep_upred true
% 6.41/6.62 % --res_sim_input true
% 6.41/6.62 % --clause_weak_htbl true
% 6.41/6.62 % --gc_record_bc_elim false
% 6.41/6.62 % --symbol_type_check false
% 6.41/6.62 % --clausify_out false
% 6.41/6.62 % --large_theory_mode false
% 6.41/6.62 % --prep_sem_filter none
% 6.41/6.62 % --prep_sem_filter_out false
% 6.41/6.62 % --preprocessed_out false
% 6.41/6.62 % --sub_typing false
% 6.41/6.62 % --brand_transform false
% 6.41/6.62 % --pure_diseq_elim true
% 6.41/6.62 % --min_unsat_core false
% 6.41/6.62 % --pred_elim true
% 6.41/6.62 % --add_important_lit false
% 6.41/6.62 % --soft_assumptions false
% 6.41/6.62 % --reset_solvers false
% 6.41/6.62 % --bc_imp_inh []
% 6.41/6.62 % --conj_cone_tolerance 1.5
% 6.41/6.62 % --prolific_symb_bound 500
% 6.41/6.62 % --lt_threshold 2000
% 6.41/6.62
% 6.41/6.62 % ------ SAT Options
% 6.41/6.62
% 6.41/6.62 % --sat_mode false
% 6.41/6.62 % --sat_fm_restart_options ""
% 6.41/6.62 % --sat_gr_def false
% 6.41/6.62 % --sat_epr_types true
% 6.41/6.62 % --sat_non_cyclic_types false
% 6.41/6.62 % --sat_finite_models false
% 6.41/6.62 % --sat_fm_lemmas false
% 6.41/6.62 % --sat_fm_prep false
% 6.41/6.62 % --sat_fm_uc_incr true
% 6.41/6.62 % --sat_out_model small
% 6.41/6.62 % --sat_out_clauses false
% 6.41/6.62
% 6.41/6.62 % ------ QBF Options
% 6.41/6.62
% 6.41/6.62 % --qbf_mode false
% 6.41/6.62 % --qbf_elim_univ true
% 6.41/6.62 % --qbf_sk_in true
% 6.41/6.62 % --qbf_pred_elim true
% 6.41/6.62 % --qbf_split 32
% 6.41/6.62
% 6.41/6.62 % ------ BMC1 Options
% 6.41/6.62
% 6.41/6.62 % --bmc1_incremental false
% 6.41/6.62 % --bmc1_axioms reachable_all
% 6.41/6.62 % --bmc1_min_bound 0
% 6.41/6.62 % --bmc1_max_bound -1
% 6.41/6.62 % --bmc1_max_bound_default -1
% 6.41/6.62 % --bmc1_symbol_reachability true
% 6.41/6.62 % --bmc1_property_lemmas false
% 6.41/6.62 % --bmc1_k_induction false
% 6.41/6.62 % --bmc1_non_equiv_states false
% 6.41/6.62 % --bmc1_deadlock false
% 6.41/6.62 % --bmc1_ucm false
% 6.41/6.62 % --bmc1_add_unsat_core none
% 6.41/6.62 % --bmc1_unsat_core_children false
% 6.41/6.62 % --bmc1_unsat_core_extrapolate_axioms false
% 6.41/6.62 % --bmc1_out_stat full
% 6.41/6.62 % --bmc1_ground_init false
% 6.41/6.62 % --bmc1_pre_inst_next_state false
% 6.41/6.62 % --bmc1_pre_inst_state false
% 6.41/6.62 % --bmc1_pre_inst_reach_state false
% 6.41/6.62 % --bmc1_out_unsat_core false
% 6.41/6.62 % --bmc1_aig_witness_out false
% 6.41/6.62 % --bmc1_verbose false
% 6.41/6.62 % --bmc1_dump_clauses_tptp false
% 6.41/6.62 % --bmc1_dump_unsat_core_tptp false
% 6.41/6.62 % --bmc1_dump_file -
% 6.41/6.62 % --bmc1_ucm_expand_uc_limit 128
% 6.41/6.62 % --bmc1_ucm_n_expand_iterations 6
% 6.41/6.62 % --bmc1_ucm_extend_mode 1
% 6.41/6.62 % --bmc1_ucm_init_mode 2
% 6.41/6.62 % --bmc1_ucm_cone_mode none
% 6.41/6.62 % --bmc1_ucm_reduced_relation_type 0
% 6.41/6.62 % --bmc1_ucm_relax_model 4
% 6.41/6.62 % --bmc1_ucm_full_tr_after_sat true
% 6.41/6.62 % --bmc1_ucm_expand_neg_assumptions false
% 6.41/6.62 % --bmc1_ucm_layered_model none
% 6.41/6.62 % --bmc1_ucm_max_lemma_size 10
% 6.41/6.62
% 6.41/6.62 % ------ AIG Options
% 6.41/6.62
% 6.41/6.62 % --aig_mode false
% 6.41/6.62
% 6.41/6.62 % ------ Instantiation Options
% 6.41/6.62
% 6.41/6.62 % --instantiation_flag true
% 6.41/6.62 % --inst_lit_sel [+prop;+sign;+ground;-num_var;-num_symb]
% 6.41/6.62 % --inst_solver_per_active 750
% 7.61/7.84 % --inst_solver_calls_frac 0.5
% 7.61/7.84 % --inst_passive_queue_type priority_queues
% 7.61/7.84 % --inst_passive_queues [[-conj_dist;+conj_symb;-num_var];[+age;-num_symb]]
% 7.61/7.84 % --inst_passive_queues_freq [25;2]
% 7.61/7.84 % --inst_dismatching true
% 7.61/7.84 % --inst_eager_unprocessed_to_passive true
% 7.61/7.84 % --inst_prop_sim_given true
% 7.61/7.84 % --inst_prop_sim_new false
% 7.61/7.84 % --inst_orphan_elimination true
% 7.61/7.84 % --inst_learning_loop_flag true
% 7.61/7.84 % --inst_learning_start 3000
% 7.61/7.84 % --inst_learning_factor 2
% 7.61/7.84 % --inst_start_prop_sim_after_learn 3
% 7.61/7.84 % --inst_sel_renew solver
% 7.61/7.84 % --inst_lit_activity_flag true
% 7.61/7.84 % --inst_out_proof true
% 7.61/7.84
% 7.61/7.84 % ------ Resolution Options
% 7.61/7.84
% 7.61/7.84 % --resolution_flag true
% 7.61/7.84 % --res_lit_sel kbo_max
% 7.61/7.84 % --res_to_prop_solver none
% 7.61/7.84 % --res_prop_simpl_new false
% 7.61/7.84 % --res_prop_simpl_given false
% 7.61/7.84 % --res_passive_queue_type priority_queues
% 7.61/7.84 % --res_passive_queues [[-conj_dist;+conj_symb;-num_symb];[+age;-num_symb]]
% 7.61/7.84 % --res_passive_queues_freq [15;5]
% 7.61/7.84 % --res_forward_subs full
% 7.61/7.84 % --res_backward_subs full
% 7.61/7.84 % --res_forward_subs_resolution true
% 7.61/7.84 % --res_backward_subs_resolution true
% 7.61/7.84 % --res_orphan_elimination false
% 7.61/7.84 % --res_time_limit 1000.
% 7.61/7.84 % --res_out_proof true
% 7.61/7.84 % --proof_out_file /export/starexec/sandbox/tmp/iprover_proof_701151.s
% 7.61/7.84 % --modulo true
% 7.61/7.84
% 7.61/7.84 % ------ Combination Options
% 7.61/7.84
% 7.61/7.84 % --comb_res_mult 1000
% 7.61/7.84 % --comb_inst_mult 300
% 7.61/7.84 % ------
% 7.61/7.84
% 7.61/7.84
% 7.61/7.84
% 7.61/7.84 % ------ Proving...
% 7.61/7.84 %
% 7.61/7.84
% 7.61/7.84
% 7.61/7.84 % Resolution empty clause
% 7.61/7.84
% 7.61/7.84 % ------ Statistics
% 7.61/7.84
% 7.61/7.84 % ------ General
% 7.61/7.84
% 7.61/7.84 % num_of_input_clauses: 2249
% 7.61/7.84 % num_of_input_neg_conjectures: 1
% 7.61/7.84 % num_of_splits: 0
% 7.61/7.84 % num_of_split_atoms: 0
% 7.61/7.84 % num_of_sem_filtered_clauses: 0
% 7.61/7.84 % num_of_subtypes: 0
% 7.61/7.84 % monotx_restored_types: 0
% 7.61/7.84 % sat_num_of_epr_types: 0
% 7.61/7.84 % sat_num_of_non_cyclic_types: 0
% 7.61/7.84 % sat_guarded_non_collapsed_types: 0
% 7.61/7.84 % is_epr: 0
% 7.61/7.84 % is_horn: 0
% 7.61/7.84 % has_eq: 1
% 7.61/7.84 % num_pure_diseq_elim: 0
% 7.61/7.84 % simp_replaced_by: 0
% 7.61/7.84 % res_preprocessed: 6
% 7.61/7.84 % prep_upred: 0
% 7.61/7.84 % prep_unflattend: 0
% 7.61/7.84 % pred_elim_cands: 0
% 7.61/7.84 % pred_elim: 0
% 7.61/7.84 % pred_elim_cl: 0
% 7.61/7.84 % pred_elim_cycles: 0
% 7.61/7.84 % forced_gc_time: 0
% 7.61/7.84 % gc_basic_clause_elim: 0
% 7.61/7.84 % parsing_time: 0.173
% 7.61/7.84 % sem_filter_time: 0.
% 7.61/7.84 % pred_elim_time: 0.
% 7.61/7.84 % out_proof_time: 0.001
% 7.61/7.84 % monotx_time: 0.
% 7.61/7.84 % subtype_inf_time: 0.
% 7.61/7.84 % unif_index_cands_time: 0.002
% 7.61/7.84 % unif_index_add_time: 0.004
% 7.61/7.84 % total_time: 6.908
% 7.61/7.84 % num_of_symbols: 140
% 7.61/7.84 % num_of_terms: 37338
% 7.61/7.84
% 7.61/7.84 % ------ Propositional Solver
% 7.61/7.84
% 7.61/7.84 % prop_solver_calls: 1
% 7.61/7.84 % prop_fast_solver_calls: 11
% 7.61/7.84 % prop_num_of_clauses: 1499
% 7.61/7.84 % prop_preprocess_simplified: 7211
% 7.61/7.84 % prop_fo_subsumed: 0
% 7.61/7.84 % prop_solver_time: 0.
% 7.61/7.84 % prop_fast_solver_time: 0.
% 7.61/7.84 % prop_unsat_core_time: 0.
% 7.61/7.84
% 7.61/7.84 % ------ QBF
% 7.61/7.84
% 7.61/7.84 % qbf_q_res: 0
% 7.61/7.84 % qbf_num_tautologies: 0
% 7.61/7.84 % qbf_prep_cycles: 0
% 7.61/7.84
% 7.61/7.84 % ------ BMC1
% 7.61/7.84
% 7.61/7.84 % bmc1_current_bound: -1
% 7.61/7.84 % bmc1_last_solved_bound: -1
% 7.61/7.84 % bmc1_unsat_core_size: -1
% 7.61/7.84 % bmc1_unsat_core_parents_size: -1
% 7.61/7.84 % bmc1_merge_next_fun: 0
% 7.61/7.84 % bmc1_unsat_core_clauses_time: 0.
% 7.61/7.84
% 7.61/7.84 % ------ Instantiation
% 7.61/7.84
% 7.61/7.84 % inst_num_of_clauses: 2000
% 7.61/7.84 % inst_num_in_passive: 0
% 7.61/7.84 % inst_num_in_active: 0
% 7.61/7.84 % inst_num_in_unprocessed: 2249
% 7.61/7.84 % inst_num_of_loops: 0
% 7.61/7.84 % inst_num_of_learning_restarts: 0
% 7.61/7.84 % inst_num_moves_active_passive: 0
% 7.61/7.84 % inst_lit_activity: 0
% 7.61/7.84 % inst_lit_activity_moves: 0
% 7.61/7.84 % inst_num_tautologies: 0
% 7.61/7.84 % inst_num_prop_implied: 0
% 7.61/7.84 % inst_num_existing_simplified: 0
% 7.61/7.84 % inst_num_eq_res_simplified: 0
% 7.61/7.84 % inst_num_child_elim: 0
% 7.61/7.84 % inst_num_of_dismatching_blockings: 0
% 7.61/7.84 % inst_num_of_non_proper_insts: 0
% 7.61/7.84 % inst_num_of_duplicates: 0
% 7.61/7.84 % inst_inst_num_from_inst_to_res: 0
% 7.61/7.84 % inst_dismatching_checking_time: 0.
% 7.61/7.84
% 7.61/7.84 % ------ Resolution
% 7.61/7.84
% 7.61/7.84 % res_num_of_clauses: 10380
% 7.61/7.84 % res_num_in_passive: 7736
% 7.61/7.84 % res_num_in_active: 1182
% 7.61/7.84 % res_num_of_loops: 434
% 7.61/7.84 % res_forward_subset_subsumed: 2310
% 7.61/7.84 % res_backward_subset_subsumed: 26
% 7.61/7.84 % res_forward_subsumed: 36
% 7.61/7.84 % res_backward_subsumed: 1
% 7.61/7.84 % res_forward_subsumption_resolution: 99
% 7.61/7.84 % res_backward_subsumption_resolution: 1
% 7.61/7.84 % res_clause_to_clause_subsumption: 640
% 7.61/7.84 % res_orphan_elimination: 0
% 7.61/7.84 % res_tautology_del: 166
% 7.61/7.84 % res_num_eq_res_simplified: 0
% 7.61/7.84 % res_num_sel_changes: 0
% 7.61/7.84 % res_moves_from_active_to_pass: 0
% 7.61/7.84
% 7.61/7.84 % Status Unsatisfiable
% 7.61/7.84 % SZS status Theorem
% 7.61/7.84 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------