%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SWW246+1 : TPTP v9.2.1. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n029.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 : 300s
% DateTime : Tue May 5 05:30:48 PM UTC 2026
% Result : Theorem 145.80s 112.06s
% Output : CNFRefutation 219.80s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named 2963)
% Comments :
%------------------------------------------------------------------------------
fof(fact_dvd_Ostrict__monoD,axiom,
! [X28,X27,X2,X5] :
( class_Orderings_Oorder(X5)
=> ( c_Orderings_Oorder_Ostrict__mono(tc_Nat_Onat,X5,hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool,c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),X2)
=> ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X27),X28))
& ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X28),X27)) )
=> c_Orderings_Oord__class_Oless(X5,hAPP(X2,X27),hAPP(X2,X28)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd_Ostrict__monoD) ).
fof(fact_order__2,axiom,
! [X8,X7,X9] :
( class_Rings_Oidom(X9)
=> ( X7 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X9))
=> ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X9)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(X9)),hAPP(hAPP(c_Polynomial_OpCons(X9),hAPP(c_Groups_Ouminus__class_Ouminus(X9),X8)),hAPP(hAPP(c_Polynomial_OpCons(X9),c_Groups_Oone__class_Oone(X9)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X9))))),hAPP(c_Nat_OSuc,c_Polynomial_Oorder(X9,X8,X7)))),X7)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__2) ).
fof(fact_order,axiom,
! [X8,X7,X9] :
( class_Rings_Oidom(X9)
=> ( X7 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X9))
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X9)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(X9)),hAPP(hAPP(c_Polynomial_OpCons(X9),hAPP(c_Groups_Ouminus__class_Ouminus(X9),X8)),hAPP(hAPP(c_Polynomial_OpCons(X9),c_Groups_Oone__class_Oone(X9)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X9))))),c_Polynomial_Oorder(X9,X8,X7))),X7))
& ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X9)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(X9)),hAPP(hAPP(c_Polynomial_OpCons(X9),hAPP(c_Groups_Ouminus__class_Ouminus(X9),X8)),hAPP(hAPP(c_Polynomial_OpCons(X9),c_Groups_Oone__class_Oone(X9)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X9))))),hAPP(c_Nat_OSuc,c_Polynomial_Oorder(X9,X8,X7)))),X7)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order) ).
fof(conj_0,conjecture,
? [X66,X103] :
( X103 != c_Groups_Ozero__class_Ozero(t_a)
& X66 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& ? [X77] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(t_a,X77)),X66)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(t_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)))
& ! [X104] : hAPP(c_Polynomial_Opoly(t_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),X104) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(t_a),hAPP(c_Polynomial_Opoly(t_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),c_Groups_Ozero__class_Ozero(t_a))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),hAPP(hAPP(c_Power_Opower__class_Opower(t_a),X104),X66)),hAPP(c_Polynomial_Opoly(t_a,hAPP(hAPP(c_Polynomial_OpCons(t_a),X103),X77)),X104))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
fof(fact_not__sum__squares__lt__zero,axiom,
! [X33,X6,X9] :
( class_Rings_Olinordered__ring(X9)
=> ~ c_Orderings_Oord__class_Oless(X9,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X9),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X9),X6),X6)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X9),X33),X33)),c_Groups_Ozero__class_Ozero(X9)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__sum__squares__lt__zero) ).
fof(fact_Least__Suc,axiom,
! [X14,X68] :
( hBOOL(hAPP(X68,X14))
=> ( ~ hBOOL(hAPP(X68,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
=> c_Orderings_Oord__class_OLeast(tc_Nat_Onat,X68) = hAPP(c_Nat_OSuc,c_Orderings_Oord__class_OLeast(tc_Nat_Onat,hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_Nat_Onat),X68),c_Nat_OSuc))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Least__Suc) ).
fof(fact_divide__less__eq,axiom,
! [X11,X31,X25,X5] :
( class_Fields_Olinordered__field__inverse__zero(X5)
=> ( c_Orderings_Oord__class_Oless(X5,hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X5),X25),X31),X11)
<=> ( ( c_Orderings_Oord__class_Oless(X5,c_Groups_Ozero__class_Ozero(X5),X31)
=> c_Orderings_Oord__class_Oless(X5,X25,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X11),X31)) )
& ( ~ c_Orderings_Oord__class_Oless(X5,c_Groups_Ozero__class_Ozero(X5),X31)
=> ( ( c_Orderings_Oord__class_Oless(X5,X31,c_Groups_Ozero__class_Ozero(X5))
=> c_Orderings_Oord__class_Oless(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X11),X31),X25) )
& ( ~ c_Orderings_Oord__class_Oless(X5,X31,c_Groups_Ozero__class_Ozero(X5))
=> c_Orderings_Oord__class_Oless(X5,c_Groups_Ozero__class_Ozero(X5),X11) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide__less__eq) ).
fof(fact_less__divide__eq,axiom,
! [X31,X25,X11,X5] :
( class_Fields_Olinordered__field__inverse__zero(X5)
=> ( c_Orderings_Oord__class_Oless(X5,X11,hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X5),X25),X31))
<=> ( ( c_Orderings_Oord__class_Oless(X5,c_Groups_Ozero__class_Ozero(X5),X31)
=> c_Orderings_Oord__class_Oless(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X11),X31),X25) )
& ( ~ c_Orderings_Oord__class_Oless(X5,c_Groups_Ozero__class_Ozero(X5),X31)
=> ( ( c_Orderings_Oord__class_Oless(X5,X31,c_Groups_Ozero__class_Ozero(X5))
=> c_Orderings_Oord__class_Oless(X5,X25,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X11),X31)) )
& ( ~ c_Orderings_Oord__class_Oless(X5,X31,c_Groups_Ozero__class_Ozero(X5))
=> c_Orderings_Oord__class_Oless(X5,X11,c_Groups_Ozero__class_Ozero(X5)) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__divide__eq) ).
fof(fact_nat__diff__split__asm,axiom,
! [X25,X11,X68] :
( hBOOL(hAPP(X68,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X11),X25)))
<=> ~ ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X11,X25)
& ~ hBOOL(hAPP(X68,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) )
| ? [X93] :
( X11 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X25),X93)
& ~ hBOOL(hAPP(X68,X93)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__diff__split__asm) ).
fof(fact_dvd_Oless__trans,axiom,
! [X32,X33,X6] :
( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X6),X33))
& ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X33),X6)) )
=> ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X33),X32))
& ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X32),X33)) )
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X6),X32))
& ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X32),X6)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd_Oless__trans) ).
fof(fact_dvd_Ole__less__trans,axiom,
! [X32,X33,X6] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X6),X33))
=> ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X33),X32))
& ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X32),X33)) )
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X6),X32))
& ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X32),X6)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd_Ole__less__trans) ).
fof(fact_dvd_Oless__le__trans,axiom,
! [X32,X33,X6] :
( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X6),X33))
& ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X33),X6)) )
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X33),X32))
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X6),X32))
& ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X32),X6)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd_Oless__le__trans) ).
fof(fact_zdvd__not__zless,axiom,
! [X10,X12] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X12)
=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X12,X10)
=> ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X10),X12)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zdvd__not__zless) ).
fof(fact_nat__dvd__not__less,axiom,
! [X10,X12] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X12)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X12,X10)
=> ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X10),X12)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__dvd__not__less) ).
fof(fact_dvd_Ole__less,axiom,
! [X28,X27] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X27),X28))
<=> ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X27),X28))
& ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X28),X27)) )
| X27 = X28 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd_Ole__less) ).
fof(fact_dvd_Oless__le,axiom,
! [X28,X27] :
( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X27),X28))
& ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X28),X27)) )
<=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X27),X28))
& X27 != X28 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd_Oless__le) ).
fof(fact_dvd_Oneq__le__trans,axiom,
! [X21,X8] :
( X8 != X21
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X8),X21))
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X8),X21))
& ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X21),X8)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd_Oneq__le__trans) ).
fof(fact_dvd_Ole__imp__less__or__eq,axiom,
! [X33,X6] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X6),X33))
=> ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X6),X33))
& ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X33),X6)) )
| X6 = X33 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd_Ole__imp__less__or__eq) ).
fof(fact_dvd_Ole__neq__trans,axiom,
! [X21,X8] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X8),X21))
=> ( X8 != X21
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X8),X21))
& ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X21),X8)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd_Ole__neq__trans) ).
fof(fact_not__square__less__zero,axiom,
! [X8,X9] :
( class_Rings_Olinordered__ring(X9)
=> ~ c_Orderings_Oord__class_Oless(X9,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X9),X8),X8),c_Groups_Ozero__class_Ozero(X9)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__square__less__zero) ).
fof(fact_mod__geq,axiom,
! [X10,X12] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X12,X10)
=> c_Divides_Odiv__class_Omod(tc_Nat_Onat,X12,X10) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X12),X10),X10) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__geq) ).
fof(fact_mod__if,axiom,
! [X10,X12] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X12,X10)
=> c_Divides_Odiv__class_Omod(tc_Nat_Onat,X12,X10) = X12 )
& ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X12,X10)
=> c_Divides_Odiv__class_Omod(tc_Nat_Onat,X12,X10) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X12),X10),X10) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__if) ).
fof(fact_not__int__zless__negative,axiom,
! [X12,X10] : ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,X10),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,X12))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__int__zless__negative) ).
fof(fact_not__add__less1,axiom,
! [X40,X42] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X42),X40),X42),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__add__less1) ).
fof(fact_not__add__less2,axiom,
! [X42,X40] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X40),X42),X42),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__add__less2) ).
fof(fact_not__less__eq,axiom,
! [X14,X35] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X35,X14)
<=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X14,hAPP(c_Nat_OSuc,X35)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__less__eq) ).
fof(fact_add__diff__inverse,axiom,
! [X10,X12] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X12,X10)
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X10),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X12),X10)) = X12 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__diff__inverse) ).
fof(fact_not__less__Least,axiom,
! [X68,X39,X5] :
( class_Orderings_Owellorder(X5)
=> ( c_Orderings_Oord__class_Oless(X5,X39,c_Orderings_Oord__class_OLeast(X5,X68))
=> ~ hBOOL(hAPP(X68,X39)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__less__Least) ).
fof(fact_xt1_I9_J,axiom,
! [X8,X21,X9] :
( class_Orderings_Oorder(X9)
=> ( c_Orderings_Oord__class_Oless(X9,X21,X8)
=> ~ c_Orderings_Oord__class_Oless(X9,X8,X21) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_xt1_I9_J) ).
fof(fact_not__less__iff__gr__or__eq,axiom,
! [X28,X27,X5] :
( class_Orderings_Olinorder(X5)
=> ( ~ c_Orderings_Oord__class_Oless(X5,X27,X28)
<=> ( c_Orderings_Oord__class_Oless(X5,X28,X27)
| X27 = X28 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__less__iff__gr__or__eq) ).
fof(fact_order__less__asym,axiom,
! [X33,X6,X9] :
( class_Orderings_Opreorder(X9)
=> ( c_Orderings_Oord__class_Oless(X9,X6,X33)
=> ~ c_Orderings_Oord__class_Oless(X9,X33,X6) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__less__asym) ).
fof(fact_order__less__asym_H,axiom,
! [X21,X8,X9] :
( class_Orderings_Opreorder(X9)
=> ( c_Orderings_Oord__class_Oless(X9,X8,X21)
=> ~ c_Orderings_Oord__class_Oless(X9,X21,X8) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__less__asym_H) ).
fof(fact_order__less__imp__not__less,axiom,
! [X33,X6,X9] :
( class_Orderings_Opreorder(X9)
=> ( c_Orderings_Oord__class_Oless(X9,X6,X33)
=> ~ c_Orderings_Oord__class_Oless(X9,X33,X6) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__less__imp__not__less) ).
fof(fact_order__less__not__sym,axiom,
! [X33,X6,X9] :
( class_Orderings_Opreorder(X9)
=> ( c_Orderings_Oord__class_Oless(X9,X6,X33)
=> ~ c_Orderings_Oord__class_Oless(X9,X33,X6) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__less__not__sym) ).
fof(fact_not__less__less__Suc__eq,axiom,
! [X35,X14] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X14,X35)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X14,hAPP(c_Nat_OSuc,X35))
<=> X14 = X35 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__less__less__Suc__eq) ).
fof(fact_less__antisym,axiom,
! [X12,X10] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X10,X12)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X10,hAPP(c_Nat_OSuc,X12))
=> X12 = X10 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__antisym) ).
fof(fact_less__SucE,axiom,
! [X10,X12] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X12,hAPP(c_Nat_OSuc,X10))
=> ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X12,X10)
=> X12 = X10 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__SucE) ).
fof(fact_sgn__poly__def,axiom,
! [X6,X9] :
( class_Rings_Olinordered__idom(X9)
=> ( ( X6 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X9))
=> c_Groups_Osgn__class_Osgn(tc_Polynomial_Opoly(X9),X6) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X9)) )
& ( X6 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X9))
=> ( ( c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(X9),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X9)),X6)
=> c_Groups_Osgn__class_Osgn(tc_Polynomial_Opoly(X9),X6) = c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(X9)) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(X9),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X9)),X6)
=> c_Groups_Osgn__class_Osgn(tc_Polynomial_Opoly(X9),X6) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X9)),c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(X9))) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sgn__poly__def) ).
fof(fact__C0_C,axiom,
( class_Rings_Oidom(t_a)
=> ~ c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(t_a,t_a,c_Polynomial_Opoly(t_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact__C0_C) ).
fof(fact_of__nat__less__0__iff,axiom,
! [X12,X9] :
( class_Rings_Olinordered__semidom(X9)
=> ~ c_Orderings_Oord__class_Oless(X9,c_Nat_Osemiring__1__class_Oof__nat(X9,X12),c_Groups_Ozero__class_Ozero(X9)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_of__nat__less__0__iff) ).
fof(fact_int__less__0__conv,axiom,
! [X36] : ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,X36),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_int__less__0__conv) ).
fof(help_c__fconj__2,axiom,
! [X101,X68] :
( ~ hBOOL(hAPP(hAPP(c_fconj,X68),X101))
| hBOOL(X68) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__fconj__2) ).
fof(help_c__fconj__3,axiom,
! [X101,X68] :
( ~ hBOOL(hAPP(hAPP(c_fconj,X68),X101))
| hBOOL(X101) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__fconj__3) ).
fof(fact_linorder__cases,axiom,
! [X33,X6,X9] :
( class_Orderings_Olinorder(X9)
=> ( ~ c_Orderings_Oord__class_Oless(X9,X6,X33)
=> ( X6 != X33
=> c_Orderings_Oord__class_Oless(X9,X33,X6) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_linorder__cases) ).
fof(fact_linorder__neqE,axiom,
! [X33,X6,X9] :
( class_Orderings_Olinorder(X9)
=> ( X6 != X33
=> ( ~ c_Orderings_Oord__class_Oless(X9,X6,X33)
=> c_Orderings_Oord__class_Oless(X9,X33,X6) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_linorder__neqE) ).
fof(fact_linorder__antisym__conv3,axiom,
! [X27,X28,X5] :
( class_Orderings_Olinorder(X5)
=> ( ~ c_Orderings_Oord__class_Oless(X5,X28,X27)
=> ( ~ c_Orderings_Oord__class_Oless(X5,X27,X28)
<=> X27 = X28 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_linorder__antisym__conv3) ).
fof(fact_linorder__neqE__linordered__idom,axiom,
! [X33,X6,X9] :
( class_Rings_Olinordered__idom(X9)
=> ( X6 != X33
=> ( ~ c_Orderings_Oord__class_Oless(X9,X6,X33)
=> c_Orderings_Oord__class_Oless(X9,X33,X6) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_linorder__neqE__linordered__idom) ).
fof(fact_assms,axiom,
( class_Rings_Oidom(t_a)
=> ~ c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(t_a,t_a,c_Polynomial_Opoly(t_a,v_p)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_assms) ).
fof(fact_not__one__less__zero,axiom,
! [X9] :
( class_Rings_Olinordered__semidom(X9)
=> ~ c_Orderings_Oord__class_Oless(X9,c_Groups_Oone__class_Oone(X9),c_Groups_Ozero__class_Ozero(X9)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__one__less__zero) ).
fof(fact_linorder__neqE__nat,axiom,
! [X33,X6] :
( X6 != X33
=> ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X6,X33)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X33,X6) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_linorder__neqE__nat) ).
fof(fact_order__less__irrefl,axiom,
! [X6,X9] :
( class_Orderings_Opreorder(X9)
=> ~ c_Orderings_Oord__class_Oless(X9,X6,X6) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__less__irrefl) ).
fof(help_c__fconj__1,axiom,
! [X101,X68] :
( ~ hBOOL(X68)
| ~ hBOOL(X101)
| hBOOL(hAPP(hAPP(c_fconj,X68),X101)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__fconj__1) ).
fof(fact_not__less0,axiom,
! [X10] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X10,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__less0) ).
fof(fact_less__nat__zero__code,axiom,
! [X10] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X10,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__nat__zero__code) ).
fof(fact_less__zeroE,axiom,
! [X10] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X10,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__zeroE) ).
fof(fact_less__irrefl__nat,axiom,
! [X10] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X10,X10),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__irrefl__nat) ).
fof(fact_less__not__refl,axiom,
! [X10] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X10,X10),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__not__refl) ).
fof(help_c__fequal__1,axiom,
! [X28,X27] :
( ~ hBOOL(hAPP(c_fequal(X27),X28))
| X27 = X28 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__fequal__1) ).
fof(fact_not__pos__poly__0,axiom,
! [X9] :
( class_Rings_Olinordered__idom(X9)
=> ~ c_Polynomial_Opos__poly(X9,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X9))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__pos__poly__0) ).
fof(help_c__fNot__1,axiom,
! [X68] :
( ~ hBOOL(hAPP(c_fNot,X68))
| ~ hBOOL(X68) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__fNot__1) ).
fof(help_c__fNot__2,axiom,
! [X68] :
( ~ ~ hBOOL(X68)
| hBOOL(hAPP(c_fNot,X68)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__fNot__2) ).
fof(fact_order__def,axiom,
! [X4,X11,X5] :
( class_Rings_Oidom(X5)
=> c_Polynomial_Oorder(X5,X11,X4) = c_Orderings_Oord__class_OLeast(tc_Nat_Onat,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot),hAPP(c_COMBC(tc_Nat_Onat,tc_Polynomial_Opoly(X5),tc_HOL_Obool,hAPP(hAPP(c_COMBB(tc_Polynomial_Opoly(X5),tc_fun(tc_Polynomial_Opoly(X5),tc_HOL_Obool),tc_Nat_Onat),c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X5))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Polynomial_Opoly(X5),tc_Nat_Onat),hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(X5)),hAPP(hAPP(c_Polynomial_OpCons(X5),hAPP(c_Groups_Ouminus__class_Ouminus(X5),X11)),hAPP(hAPP(c_Polynomial_OpCons(X5),c_Groups_Oone__class_Oone(X5)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X5)))))),c_Nat_OSuc))),X4))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__def) ).
fof(fact_pcompose__def,axiom,
! [X24,X4,X5] :
( class_Rings_Ocomm__semiring__0(X5)
=> c_Polynomial_Opcompose(X5,X4,X24) = c_Polynomial_Opoly__rec(tc_Polynomial_Opoly(X5),X5,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X5)),hAPP(hAPP(c_COMBB(tc_fun(tc_Polynomial_Opoly(X5),tc_Polynomial_Opoly(X5)),tc_fun(tc_Polynomial_Opoly(X5),tc_fun(tc_Polynomial_Opoly(X5),tc_Polynomial_Opoly(X5))),X5),c_COMBK(tc_fun(tc_Polynomial_Opoly(X5),tc_Polynomial_Opoly(X5)),tc_Polynomial_Opoly(X5))),hAPP(c_COMBC(X5,tc_fun(tc_Polynomial_Opoly(X5),tc_Polynomial_Opoly(X5)),tc_fun(tc_Polynomial_Opoly(X5),tc_Polynomial_Opoly(X5)),hAPP(hAPP(c_COMBB(tc_fun(tc_Polynomial_Opoly(X5),tc_Polynomial_Opoly(X5)),tc_fun(tc_fun(tc_Polynomial_Opoly(X5),tc_Polynomial_Opoly(X5)),tc_fun(tc_Polynomial_Opoly(X5),tc_Polynomial_Opoly(X5))),X5),c_COMBB(tc_Polynomial_Opoly(X5),tc_Polynomial_Opoly(X5),tc_Polynomial_Opoly(X5))),hAPP(hAPP(c_COMBB(tc_Polynomial_Opoly(X5),tc_fun(tc_Polynomial_Opoly(X5),tc_Polynomial_Opoly(X5)),X5),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X5))),hAPP(c_COMBC(X5,tc_Polynomial_Opoly(X5),tc_Polynomial_Opoly(X5),c_Polynomial_OpCons(X5)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X5)))))),hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X5)),X24))),X4) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pcompose__def) ).
fof(fact_times__poly__def,axiom,
! [X24,X4,X5] :
( class_Rings_Ocomm__semiring__0(X5)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X5)),X4),X24) = c_Polynomial_Opoly__rec(tc_Polynomial_Opoly(X5),X5,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X5)),hAPP(hAPP(c_COMBB(tc_fun(tc_Polynomial_Opoly(X5),tc_Polynomial_Opoly(X5)),tc_fun(tc_Polynomial_Opoly(X5),tc_fun(tc_Polynomial_Opoly(X5),tc_Polynomial_Opoly(X5))),X5),c_COMBK(tc_fun(tc_Polynomial_Opoly(X5),tc_Polynomial_Opoly(X5)),tc_Polynomial_Opoly(X5))),hAPP(c_COMBC(X5,tc_fun(tc_Polynomial_Opoly(X5),tc_Polynomial_Opoly(X5)),tc_fun(tc_Polynomial_Opoly(X5),tc_Polynomial_Opoly(X5)),hAPP(hAPP(c_COMBB(tc_fun(tc_Polynomial_Opoly(X5),tc_Polynomial_Opoly(X5)),tc_fun(tc_fun(tc_Polynomial_Opoly(X5),tc_Polynomial_Opoly(X5)),tc_fun(tc_Polynomial_Opoly(X5),tc_Polynomial_Opoly(X5))),X5),c_COMBB(tc_Polynomial_Opoly(X5),tc_Polynomial_Opoly(X5),tc_Polynomial_Opoly(X5))),hAPP(hAPP(c_COMBB(tc_Polynomial_Opoly(X5),tc_fun(tc_Polynomial_Opoly(X5),tc_Polynomial_Opoly(X5)),X5),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X5))),hAPP(c_COMBC(X5,tc_Polynomial_Opoly(X5),tc_Polynomial_Opoly(X5),c_Polynomial_Osmult(X5)),X24)))),hAPP(c_Polynomial_OpCons(X5),c_Groups_Ozero__class_Ozero(X5)))),X4) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_times__poly__def) ).
fof(fact_dvd_Ostrict__mono__mono,axiom,
! [X2,X5] :
( class_Orderings_Oorder(X5)
=> ( c_Orderings_Oorder_Ostrict__mono(tc_Nat_Onat,X5,hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool,c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),X2)
=> c_Orderings_Oorder_Omono(tc_Nat_Onat,X5,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd_Ostrict__mono__mono) ).
fof(fact_offset__poly__def,axiom,
! [X50,X4,X5] :
( class_Rings_Ocomm__semiring__0(X5)
=> c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X5,X4,X50) = c_Polynomial_Opoly__rec(tc_Polynomial_Opoly(X5),X5,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X5)),hAPP(hAPP(c_COMBB(tc_fun(tc_Polynomial_Opoly(X5),tc_Polynomial_Opoly(X5)),tc_fun(tc_Polynomial_Opoly(X5),tc_fun(tc_Polynomial_Opoly(X5),tc_Polynomial_Opoly(X5))),X5),c_COMBK(tc_fun(tc_Polynomial_Opoly(X5),tc_Polynomial_Opoly(X5)),tc_Polynomial_Opoly(X5))),hAPP(hAPP(c_COMBB(tc_fun(tc_Polynomial_Opoly(X5),tc_Polynomial_Opoly(X5)),tc_fun(tc_Polynomial_Opoly(X5),tc_Polynomial_Opoly(X5)),X5),hAPP(c_COMBS(tc_Polynomial_Opoly(X5),tc_Polynomial_Opoly(X5),tc_Polynomial_Opoly(X5)),hAPP(hAPP(c_COMBB(tc_Polynomial_Opoly(X5),tc_fun(tc_Polynomial_Opoly(X5),tc_Polynomial_Opoly(X5)),tc_Polynomial_Opoly(X5)),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X5))),hAPP(c_Polynomial_Osmult(X5),X50)))),c_Polynomial_OpCons(X5))),X4) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_offset__poly__def) ).
fof(fact_mod__pCons,axiom,
! [X6,X8,X33,X9] :
( class_Fields_Ofield(X9)
=> ( X33 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X9))
=> c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(X9),hAPP(hAPP(c_Polynomial_OpCons(X9),X8),X6),X33) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X9)),hAPP(hAPP(c_Polynomial_OpCons(X9),X8),c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(X9),X6,X33))),hAPP(hAPP(c_Polynomial_Osmult(X9),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X9),hAPP(c_Polynomial_Ocoeff(X9,hAPP(hAPP(c_Polynomial_OpCons(X9),X8),c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(X9),X6,X33))),c_Polynomial_Odegree(X9,X33))),hAPP(c_Polynomial_Ocoeff(X9,X33),c_Polynomial_Odegree(X9,X33)))),X33)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__pCons) ).
fof(fact_monom__def,axiom,
! [X35,X11,X5] :
( class_Groups_Ozero(X5)
=> c_Polynomial_Omonom(X5,X11,X35) = c_Polynomial_OAbs__poly(X5,hAPP(c_COMBC(tc_Nat_Onat,X5,X5,hAPP(c_COMBC(tc_Nat_Onat,X5,tc_fun(X5,X5),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X5,tc_fun(X5,X5)),tc_Nat_Onat),c_If(X5)),c_fequal(X35))),X11)),c_Groups_Ozero__class_Ozero(X5))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_monom__def) ).
fof(fact_order__1,axiom,
! [X7,X8,X9] :
( class_Rings_Oidom(X9)
=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X9)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(X9)),hAPP(hAPP(c_Polynomial_OpCons(X9),hAPP(c_Groups_Ouminus__class_Ouminus(X9),X8)),hAPP(hAPP(c_Polynomial_OpCons(X9),c_Groups_Oone__class_Oone(X9)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X9))))),c_Polynomial_Oorder(X9,X8,X7))),X7)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__1) ).
fof(fact_DERIV__divide,axiom,
! [X71,X1,X65,X27,X2,X5] :
( class_RealVector_Oreal__normed__field(X5)
=> ( c_Deriv_Oderiv(X5,X2,X27,X65)
=> ( c_Deriv_Oderiv(X5,X1,X27,X71)
=> ( hAPP(X1,X27) != c_Groups_Ozero__class_Ozero(X5)
=> c_Deriv_Oderiv(X5,hAPP(hAPP(c_COMBS(X5,X5,X5),hAPP(hAPP(c_COMBB(X5,tc_fun(X5,X5),X5),c_Rings_Oinverse__class_Odivide(X5)),X2)),X1),X27,hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X5),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X65),hAPP(X1,X27))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),hAPP(X2,X27)),X71))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),hAPP(X1,X27)),hAPP(X1,X27)))) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_DERIV__divide) ).
fof(fact_DERIV__quotient,axiom,
! [X55,X1,X30,X27,X2,X5] :
( class_RealVector_Oreal__normed__field(X5)
=> ( c_Deriv_Oderiv(X5,X2,X27,X30)
=> ( c_Deriv_Oderiv(X5,X1,X27,X55)
=> ( hAPP(X1,X27) != c_Groups_Ozero__class_Ozero(X5)
=> c_Deriv_Oderiv(X5,hAPP(hAPP(c_COMBS(X5,X5,X5),hAPP(hAPP(c_COMBB(X5,tc_fun(X5,X5),X5),c_Rings_Oinverse__class_Odivide(X5)),X2)),X1),X27,hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X5),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X30),hAPP(X1,X27))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X55),hAPP(X2,X27)))),hAPP(hAPP(c_Power_Opower__class_Opower(X5),hAPP(X1,X27)),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_DERIV__quotient) ).
fof(fact_mult_Oprod__diff__prod,axiom,
! [X21,X8,X33,X6,X9] :
( class_RealVector_Oreal__normed__algebra(X9)
=> hAPP(hAPP(c_Groups_Ominus__class_Ominus(X9),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X9),X6),X33)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X9),X8),X21)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X9),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X9),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X9),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X9),X6),X8)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X9),X33),X21))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X9),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X9),X6),X8)),X21))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X9),X8),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X9),X33),X21))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult_Oprod__diff__prod) ).
fof(fact_poly__rec_Osimps,axiom,
! [X4,X11,X2,X26,X5,X15] :
( class_Groups_Ozero(X15)
=> c_Polynomial_Opoly__rec(X5,X15,X26,X2,hAPP(hAPP(c_Polynomial_OpCons(X15),X11),X4)) = hAPP(hAPP(hAPP(X2,X11),X4),hAPP(hAPP(hAPP(c_If(X5),hAPP(c_fequal(X4),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X15)))),X26),c_Polynomial_Opoly__rec(X5,X15,X26,X2,X4))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_poly__rec_Osimps) ).
fof(fact_DERIV__power,axiom,
! [X14,X65,X27,X2,X5] :
( class_RealVector_Oreal__normed__field(X5)
=> ( c_Deriv_Oderiv(X5,X2,X27,X65)
=> c_Deriv_Oderiv(X5,hAPP(c_COMBC(X5,tc_Nat_Onat,X5,hAPP(hAPP(c_COMBB(X5,tc_fun(tc_Nat_Onat,X5),X5),c_Power_Opower__class_Opower(X5)),X2)),X14),X27,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),c_Nat_Osemiring__1__class_Oof__nat(X5,X14)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X65),hAPP(hAPP(c_Power_Opower__class_Opower(X5),hAPP(X2,X27)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X14),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_DERIV__power) ).
fof(fact_DERIV__power__Suc,axiom,
! [X14,X65,X27,X2,X5] :
( class_RealVector_Oreal__normed__field(X5)
=> ( c_Deriv_Oderiv(X5,X2,X27,X65)
=> c_Deriv_Oderiv(X5,hAPP(c_COMBC(X5,tc_Nat_Onat,X5,hAPP(hAPP(c_COMBB(X5,tc_fun(tc_Nat_Onat,X5),X5),c_Power_Opower__class_Opower(X5)),X2)),hAPP(c_Nat_OSuc,X14)),X27,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),c_Groups_Oone__class_Oone(X5)),c_Nat_Osemiring__1__class_Oof__nat(X5,X14))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X65),hAPP(hAPP(c_Power_Opower__class_Opower(X5),hAPP(X2,X27)),X14)))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_DERIV__power__Suc) ).
fof(fact_pdivmod__rel__pCons,axiom,
! [X8,X21,X34,X13,X33,X6,X9] :
( class_Fields_Ofield(X9)
=> ( c_Polynomial_Opdivmod__rel(X9,X6,X33,X13,X34)
=> ( X33 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X9))
=> ( X21 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X9),hAPP(c_Polynomial_Ocoeff(X9,hAPP(hAPP(c_Polynomial_OpCons(X9),X8),X34)),c_Polynomial_Odegree(X9,X33))),hAPP(c_Polynomial_Ocoeff(X9,X33),c_Polynomial_Odegree(X9,X33)))
=> c_Polynomial_Opdivmod__rel(X9,hAPP(hAPP(c_Polynomial_OpCons(X9),X8),X6),X33,hAPP(hAPP(c_Polynomial_OpCons(X9),X21),X13),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X9)),hAPP(hAPP(c_Polynomial_OpCons(X9),X8),X34)),hAPP(hAPP(c_Polynomial_Osmult(X9),X21),X33))) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pdivmod__rel__pCons) ).
fof(fact_DERIV__inverse__lemma,axiom,
! [X48,X21,X8,X9] :
( class_RealVector_Oreal__normed__field(X9)
=> ( X8 != c_Groups_Ozero__class_Ozero(X9)
=> ( X21 != c_Groups_Ozero__class_Ozero(X9)
=> hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X9),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X9),hAPP(c_Rings_Oinverse__class_Oinverse(X9),X8)),hAPP(c_Rings_Oinverse__class_Oinverse(X9),X21))),X48) = hAPP(c_Groups_Ouminus__class_Ouminus(X9),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X9),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X9),hAPP(c_Rings_Oinverse__class_Oinverse(X9),X8)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X9),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X9),X8),X21)),X48))),hAPP(c_Rings_Oinverse__class_Oinverse(X9),X21))) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_DERIV__inverse__lemma) ).
fof(fact_DERIV__mult__lemma,axiom,
! [X48,X22,X23,X21,X8,X9] :
( class_RealVector_Oreal__field(X9)
=> hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X9),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X9),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X9),X8),X21)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X9),X23),X22))),X48) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X9),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X9),X8),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X9),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X9),X21),X22)),X48))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X9),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X9),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X9),X8),X23)),X48)),X22)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_DERIV__mult__lemma) ).
fof(fact_synthetic__div__correct_H,axiom,
! [X7,X23,X9] :
( class_Rings_Ocomm__ring__1(X9)
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X9)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X9)),hAPP(hAPP(c_Polynomial_OpCons(X9),hAPP(c_Groups_Ouminus__class_Ouminus(X9),X23)),hAPP(hAPP(c_Polynomial_OpCons(X9),c_Groups_Oone__class_Oone(X9)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X9))))),c_Polynomial_Osynthetic__div(X9,X7,X23))),hAPP(hAPP(c_Polynomial_OpCons(X9),hAPP(c_Polynomial_Opoly(X9,X7),X23)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X9)))) = X7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_synthetic__div__correct_H) ).
fof(fact_pdivmod__rel__mult,axiom,
! [X85,X86,X32,X34,X13,X33,X6,X9] :
( class_Fields_Ofield(X9)
=> ( c_Polynomial_Opdivmod__rel(X9,X6,X33,X13,X34)
=> ( c_Polynomial_Opdivmod__rel(X9,X13,X32,X86,X85)
=> c_Polynomial_Opdivmod__rel(X9,X6,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X9)),X33),X32),X86,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X9)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X9)),X33),X85)),X34)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pdivmod__rel__mult) ).
fof(fact_DERIV__add__minus,axiom,
! [X71,X1,X65,X27,X2,X5] :
( class_RealVector_Oreal__normed__field(X5)
=> ( c_Deriv_Oderiv(X5,X2,X27,X65)
=> ( c_Deriv_Oderiv(X5,X1,X27,X71)
=> c_Deriv_Oderiv(X5,hAPP(hAPP(c_COMBS(X5,X5,X5),hAPP(hAPP(c_COMBB(X5,tc_fun(X5,X5),X5),c_Groups_Oplus__class_Oplus(X5)),X2)),hAPP(hAPP(c_COMBB(X5,X5,X5),c_Groups_Ouminus__class_Ouminus(X5)),X1)),X27,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X65),hAPP(c_Groups_Ouminus__class_Ouminus(X5),X71))) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_DERIV__add__minus) ).
fof(fact_DERIV__mult_H,axiom,
! [X71,X1,X65,X27,X2,X5] :
( class_RealVector_Oreal__normed__field(X5)
=> ( c_Deriv_Oderiv(X5,X2,X27,X65)
=> ( c_Deriv_Oderiv(X5,X1,X27,X71)
=> c_Deriv_Oderiv(X5,hAPP(hAPP(c_COMBS(X5,X5,X5),hAPP(hAPP(c_COMBB(X5,tc_fun(X5,X5),X5),c_Groups_Otimes__class_Otimes(X5)),X2)),X1),X27,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),hAPP(X2,X27)),X71)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X65),hAPP(X1,X27)))) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_DERIV__mult_H) ).
fof(fact_DERIV__mult,axiom,
! [X69,X1,X70,X27,X2,X5] :
( class_RealVector_Oreal__normed__field(X5)
=> ( c_Deriv_Oderiv(X5,X2,X27,X70)
=> ( c_Deriv_Oderiv(X5,X1,X27,X69)
=> c_Deriv_Oderiv(X5,hAPP(hAPP(c_COMBS(X5,X5,X5),hAPP(hAPP(c_COMBB(X5,tc_fun(X5,X5),X5),c_Groups_Otimes__class_Otimes(X5)),X2)),X1),X27,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X70),hAPP(X1,X27))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X69),hAPP(X2,X27)))) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_DERIV__mult) ).
fof(fact_DERIV__inverse_H,axiom,
! [X65,X27,X2,X5] :
( class_RealVector_Oreal__normed__field(X5)
=> ( c_Deriv_Oderiv(X5,X2,X27,X65)
=> ( hAPP(X2,X27) != c_Groups_Ozero__class_Ozero(X5)
=> c_Deriv_Oderiv(X5,hAPP(hAPP(c_COMBB(X5,X5,X5),c_Rings_Oinverse__class_Oinverse(X5)),X2),X27,hAPP(c_Groups_Ouminus__class_Ouminus(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),hAPP(c_Rings_Oinverse__class_Oinverse(X5),hAPP(X2,X27))),X65)),hAPP(c_Rings_Oinverse__class_Oinverse(X5),hAPP(X2,X27))))) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_DERIV__inverse_H) ).
fof(fact_div__mod__equality,axiom,
! [X23,X21,X8,X9] :
( class_Divides_Osemiring__div(X9)
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(X9),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X9),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X9),c_Divides_Odiv__class_Odiv(X9,X8,X21)),X21)),c_Divides_Odiv__class_Omod(X9,X8,X21))),X23) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X9),X8),X23) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_div__mod__equality) ).
fof(fact_inf__period_I3_J,axiom,
! [X64,X65,X30,X5] :
( ( class_Rings_Ocomm__ring(X5)
& class_Rings_Odvd(X5) )
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X5),X30),X65))
=> ! [X3,X66] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X5),X30),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X3),X64)))
<=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X5),X30),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X5),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X66),X65))),X64))) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf__period_I3_J) ).
fof(fact_inf__period_I4_J,axiom,
! [X64,X65,X30,X5] :
( ( class_Rings_Ocomm__ring(X5)
& class_Rings_Odvd(X5) )
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X5),X30),X65))
=> ! [X3,X66] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X5),X30),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X3),X64)))
<=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X5),X30),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X5),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X66),X65))),X64))) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf__period_I4_J) ).
fof(fact_zdiv__zmod__equality2,axiom,
! [X36,X21,X8] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X8,X21)),X21)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X8,X21))),X36) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X8),X36),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zdiv__zmod__equality2) ).
fof(fact_DERIV__cdivide,axiom,
! [X31,X65,X27,X2,X5] :
( class_RealVector_Oreal__normed__field(X5)
=> ( c_Deriv_Oderiv(X5,X2,X27,X65)
=> c_Deriv_Oderiv(X5,hAPP(c_COMBC(X5,X5,X5,hAPP(hAPP(c_COMBB(X5,tc_fun(X5,X5),X5),c_Rings_Oinverse__class_Odivide(X5)),X2)),X31),X27,hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X5),X65),X31)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_DERIV__cdivide) ).
fof(fact_DERIV__diff,axiom,
! [X71,X1,X65,X27,X2,X5] :
( class_RealVector_Oreal__normed__field(X5)
=> ( c_Deriv_Oderiv(X5,X2,X27,X65)
=> ( c_Deriv_Oderiv(X5,X1,X27,X71)
=> c_Deriv_Oderiv(X5,hAPP(hAPP(c_COMBS(X5,X5,X5),hAPP(hAPP(c_COMBB(X5,tc_fun(X5,X5),X5),c_Groups_Ominus__class_Ominus(X5)),X2)),X1),X27,hAPP(hAPP(c_Groups_Ominus__class_Ominus(X5),X65),X71)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_DERIV__diff) ).
fof(fact_DERIV__add,axiom,
! [X71,X1,X65,X27,X2,X5] :
( class_RealVector_Oreal__normed__field(X5)
=> ( c_Deriv_Oderiv(X5,X2,X27,X65)
=> ( c_Deriv_Oderiv(X5,X1,X27,X71)
=> c_Deriv_Oderiv(X5,hAPP(hAPP(c_COMBS(X5,X5,X5),hAPP(hAPP(c_COMBB(X5,tc_fun(X5,X5),X5),c_Groups_Oplus__class_Oplus(X5)),X2)),X1),X27,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X65),X71)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_DERIV__add) ).
fof(fact_less__add__iff1,axiom,
! [X30,X25,X31,X55,X11,X5] :
( class_Rings_Oordered__ring(X5)
=> ( c_Orderings_Oord__class_Oless(X5,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X11),X55)),X31),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X25),X55)),X30))
<=> c_Orderings_Oord__class_Oless(X5,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X5),X11),X25)),X55)),X31),X30) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__add__iff1) ).
fof(fact_less__add__iff2,axiom,
! [X30,X25,X31,X55,X11,X5] :
( class_Rings_Oordered__ring(X5)
=> ( c_Orderings_Oord__class_Oless(X5,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X11),X55)),X31),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X25),X55)),X30))
<=> c_Orderings_Oord__class_Oless(X5,X31,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X5),X25),X11)),X55)),X30)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__add__iff2) ).
fof(fact_DERIV__inverse__fun,axiom,
! [X30,X27,X2,X5] :
( class_RealVector_Oreal__normed__field(X5)
=> ( c_Deriv_Oderiv(X5,X2,X27,X30)
=> ( hAPP(X2,X27) != c_Groups_Ozero__class_Ozero(X5)
=> c_Deriv_Oderiv(X5,hAPP(hAPP(c_COMBB(X5,X5,X5),c_Rings_Oinverse__class_Oinverse(X5)),X2),X27,hAPP(c_Groups_Ouminus__class_Ouminus(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X30),hAPP(c_Rings_Oinverse__class_Oinverse(X5),hAPP(hAPP(c_Power_Opower__class_Opower(X5),hAPP(X2,X27)),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))))) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_DERIV__inverse__fun) ).
fof(fact_zdvd__period,axiom,
! [X31,X64,X27,X30,X11] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X11),X30))
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X11),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X27),X64)))
<=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X11),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X27),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X31),X30))),X64))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zdvd__period) ).
fof(fact_poly__gcd__unique,axiom,
! [X33,X6,X22,X9] :
( class_Fields_Ofield(X9)
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X9)),X22),X6))
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X9)),X22),X33))
=> ( ! [X66] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X9)),X66),X6))
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X9)),X66),X33))
=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X9)),X66),X22)) ) )
=> ( ( ( ( X6 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X9))
& X33 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X9)) )
=> hAPP(c_Polynomial_Ocoeff(X9,X22),c_Polynomial_Odegree(X9,X22)) = c_Groups_Ozero__class_Ozero(X9) )
& ( ~ ( X6 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X9))
& X33 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X9)) )
=> hAPP(c_Polynomial_Ocoeff(X9,X22),c_Polynomial_Odegree(X9,X22)) = c_Groups_Oone__class_Oone(X9) ) )
=> c_Polynomial_Opoly__gcd(X9,X6,X33) = X22 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_poly__gcd__unique) ).
fof(fact_poly__rec__pCons,axiom,
! [X4,X11,X5,X26,X2,X15] :
( class_Groups_Ozero(X15)
=> ( hAPP(hAPP(hAPP(X2,c_Groups_Ozero__class_Ozero(X15)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X15))),X26) = X26
=> c_Polynomial_Opoly__rec(X5,X15,X26,X2,hAPP(hAPP(c_Polynomial_OpCons(X15),X11),X4)) = hAPP(hAPP(hAPP(X2,X11),X4),c_Polynomial_Opoly__rec(X5,X15,X26,X2,X4)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_poly__rec__pCons) ).
fof(fact_poly__eq__0__iff__dvd,axiom,
! [X31,X4,X5] :
( class_Rings_Oidom(X5)
=> ( hAPP(c_Polynomial_Opoly(X5,X4),X31) = c_Groups_Ozero__class_Ozero(X5)
<=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X5)),hAPP(hAPP(c_Polynomial_OpCons(X5),hAPP(c_Groups_Ouminus__class_Ouminus(X5),X31)),hAPP(hAPP(c_Polynomial_OpCons(X5),c_Groups_Oone__class_Oone(X5)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X5))))),X4)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_poly__eq__0__iff__dvd) ).
fof(fact_pdivmod__rel__unique,axiom,
! [X79,X80,X81,X82,X33,X6,X9] :
( class_Fields_Ofield(X9)
=> ( c_Polynomial_Opdivmod__rel(X9,X6,X33,X82,X81)
=> ( c_Polynomial_Opdivmod__rel(X9,X6,X33,X80,X79)
=> ( X82 = X80
& X81 = X79 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pdivmod__rel__unique) ).
fof(fact_pdivmod__rel__unique__div,axiom,
! [X79,X80,X81,X82,X33,X6,X9] :
( class_Fields_Ofield(X9)
=> ( c_Polynomial_Opdivmod__rel(X9,X6,X33,X82,X81)
=> ( c_Polynomial_Opdivmod__rel(X9,X6,X33,X80,X79)
=> X82 = X80 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pdivmod__rel__unique__div) ).
fof(fact_pdivmod__rel__unique__mod,axiom,
! [X79,X80,X81,X82,X33,X6,X9] :
( class_Fields_Ofield(X9)
=> ( c_Polynomial_Opdivmod__rel(X9,X6,X33,X82,X81)
=> ( c_Polynomial_Opdivmod__rel(X9,X6,X33,X80,X79)
=> X81 = X79 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pdivmod__rel__unique__mod) ).
fof(fact_coeff__linear__power,axiom,
! [X10,X8,X9] :
( class_Rings_Ocomm__semiring__1(X9)
=> hAPP(c_Polynomial_Ocoeff(X9,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(X9)),hAPP(hAPP(c_Polynomial_OpCons(X9),X8),hAPP(hAPP(c_Polynomial_OpCons(X9),c_Groups_Oone__class_Oone(X9)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X9))))),X10)),X10) = c_Groups_Oone__class_Oone(X9) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_coeff__linear__power) ).
fof(fact_minus__poly__def,axiom,
! [X24,X4,X5] :
( class_Groups_Oab__group__add(X5)
=> hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X5)),X4),X24) = c_Polynomial_OAbs__poly(X5,hAPP(hAPP(c_COMBS(tc_Nat_Onat,X5,X5),hAPP(hAPP(c_COMBB(X5,tc_fun(X5,X5),tc_Nat_Onat),c_Groups_Ominus__class_Ominus(X5)),c_Polynomial_Ocoeff(X5,X4))),c_Polynomial_Ocoeff(X5,X24))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__poly__def) ).
fof(fact_plus__poly__def,axiom,
! [X24,X4,X5] :
( class_Groups_Ocomm__monoid__add(X5)
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X5)),X4),X24) = c_Polynomial_OAbs__poly(X5,hAPP(hAPP(c_COMBS(tc_Nat_Onat,X5,X5),hAPP(hAPP(c_COMBB(X5,tc_fun(X5,X5),tc_Nat_Onat),c_Groups_Oplus__class_Oplus(X5)),c_Polynomial_Ocoeff(X5,X4))),c_Polynomial_Ocoeff(X5,X24))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_plus__poly__def) ).
fof(fact_pdivmod__rel__smult__right,axiom,
! [X34,X13,X33,X6,X8,X9] :
( class_Fields_Ofield(X9)
=> ( X8 != c_Groups_Ozero__class_Ozero(X9)
=> ( c_Polynomial_Opdivmod__rel(X9,X6,X33,X13,X34)
=> c_Polynomial_Opdivmod__rel(X9,X6,hAPP(hAPP(c_Polynomial_Osmult(X9),X8),X33),hAPP(hAPP(c_Polynomial_Osmult(X9),hAPP(c_Rings_Oinverse__class_Oinverse(X9),X8)),X13),X34) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pdivmod__rel__smult__right) ).
fof(fact_pdivmod__rel__smult__left,axiom,
! [X8,X34,X13,X33,X6,X9] :
( class_Fields_Ofield(X9)
=> ( c_Polynomial_Opdivmod__rel(X9,X6,X33,X13,X34)
=> c_Polynomial_Opdivmod__rel(X9,hAPP(hAPP(c_Polynomial_Osmult(X9),X8),X6),X33,hAPP(hAPP(c_Polynomial_Osmult(X9),X8),X13),hAPP(hAPP(c_Polynomial_Osmult(X9),X8),X34)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pdivmod__rel__smult__left) ).
fof(fact_div__mod__equality2,axiom,
! [X23,X8,X21,X9] :
( class_Divides_Osemiring__div(X9)
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(X9),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X9),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X9),X21),c_Divides_Odiv__class_Odiv(X9,X8,X21))),c_Divides_Odiv__class_Omod(X9,X8,X21))),X23) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X9),X8),X23) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_div__mod__equality2) ).
fof(fact_zdiv__zadd1__eq,axiom,
! [X23,X21,X8] : c_Divides_Odiv__class_Odiv(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X8),X21),X23) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X8,X23)),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X21,X23))),c_Divides_Odiv__class_Odiv(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,X8,X23)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X21,X23)),X23)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zdiv__zadd1__eq) ).
fof(fact_zdiv__zmod__equality,axiom,
! [X36,X8,X21] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X21),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X8,X21))),c_Divides_Odiv__class_Omod(tc_Int_Oint,X8,X21))),X36) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X8),X36),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zdiv__zmod__equality) ).
fof(fact_dvd__iff__poly__eq__0,axiom,
! [X4,X31,X5] :
( class_Rings_Oidom(X5)
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X5)),hAPP(hAPP(c_Polynomial_OpCons(X5),X31),hAPP(hAPP(c_Polynomial_OpCons(X5),c_Groups_Oone__class_Oone(X5)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X5))))),X4))
<=> hAPP(c_Polynomial_Opoly(X5,X4),hAPP(c_Groups_Ouminus__class_Ouminus(X5),X31)) = c_Groups_Ozero__class_Ozero(X5) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__iff__poly__eq__0) ).
fof(fact_pdivmod__rel__def,axiom,
! [X78,X24,X28,X27,X5] :
( class_Fields_Ofield(X5)
=> ( c_Polynomial_Opdivmod__rel(X5,X27,X28,X24,X78)
<=> ( X27 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X5)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X5)),X24),X28)),X78)
& ( X28 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X5))
=> X24 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X5)) )
& ( X28 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X5))
=> ( X78 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X5))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(X5,X78),c_Polynomial_Odegree(X5,X28)) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pdivmod__rel__def) ).
fof(fact_Deriv_Oinverse__diff__inverse,axiom,
! [X21,X8,X9] :
( class_Rings_Odivision__ring(X9)
=> ( X8 != c_Groups_Ozero__class_Ozero(X9)
=> ( X21 != c_Groups_Ozero__class_Ozero(X9)
=> hAPP(hAPP(c_Groups_Ominus__class_Ominus(X9),hAPP(c_Rings_Oinverse__class_Oinverse(X9),X8)),hAPP(c_Rings_Oinverse__class_Oinverse(X9),X21)) = hAPP(c_Groups_Ouminus__class_Ouminus(X9),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X9),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X9),hAPP(c_Rings_Oinverse__class_Oinverse(X9),X8)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X9),X8),X21))),hAPP(c_Rings_Oinverse__class_Oinverse(X9),X21))) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Deriv_Oinverse__diff__inverse) ).
fof(fact_eq__add__iff1,axiom,
! [X30,X25,X31,X55,X11,X5] :
( class_Rings_Oring(X5)
=> ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X11),X55)),X31) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X25),X55)),X30)
<=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X5),X11),X25)),X55)),X31) = X30 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_eq__add__iff1) ).
fof(fact_eq__add__iff2,axiom,
! [X30,X25,X31,X55,X11,X5] :
( class_Rings_Oring(X5)
=> ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X11),X55)),X31) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X25),X55)),X30)
<=> X31 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X5),X25),X11)),X55)),X30) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_eq__add__iff2) ).
fof(fact_diff__frac__eq,axiom,
! [X51,X6,X32,X33,X9] :
( class_Fields_Ofield(X9)
=> ( X33 != c_Groups_Ozero__class_Ozero(X9)
=> ( X32 != c_Groups_Ozero__class_Ozero(X9)
=> hAPP(hAPP(c_Groups_Ominus__class_Ominus(X9),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X9),X6),X33)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X9),X51),X32)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X9),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X9),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X9),X6),X32)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X9),X51),X33))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X9),X33),X32)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__frac__eq) ).
fof(fact_add__frac__eq,axiom,
! [X51,X6,X32,X33,X9] :
( class_Fields_Ofield(X9)
=> ( X33 != c_Groups_Ozero__class_Ozero(X9)
=> ( X32 != c_Groups_Ozero__class_Ozero(X9)
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(X9),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X9),X6),X33)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X9),X51),X32)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X9),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X9),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X9),X6),X32)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X9),X51),X33))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X9),X33),X32)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__frac__eq) ).
fof(fact_mod__poly__eq,axiom,
! [X34,X13,X33,X6,X9] :
( class_Fields_Ofield(X9)
=> ( c_Polynomial_Opdivmod__rel(X9,X6,X33,X13,X34)
=> c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(X9),X6,X33) = X34 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__poly__eq) ).
fof(fact_pdivmod__rel__0__iff,axiom,
! [X78,X24,X28,X5] :
( class_Fields_Ofield(X5)
=> ( c_Polynomial_Opdivmod__rel(X5,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X5)),X28,X24,X78)
<=> ( X24 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X5))
& X78 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X5)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pdivmod__rel__0__iff) ).
fof(fact_pdivmod__rel__by__0__iff,axiom,
! [X78,X24,X27,X5] :
( class_Fields_Ofield(X5)
=> ( c_Polynomial_Opdivmod__rel(X5,X27,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X5)),X24,X78)
<=> ( X24 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X5))
& X78 = X27 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pdivmod__rel__by__0__iff) ).
fof(fact_split__pos__lemma,axiom,
! [X14,X68,X39] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X39)
=> ( hBOOL(hAPP(hAPP(X68,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X14,X39)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X14,X39)))
<=> ! [X94,X90] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X90)
& c_Orderings_Oord__class_Oless(tc_Int_Oint,X90,X39)
& X14 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X39),X94)),X90) )
=> hBOOL(hAPP(hAPP(X68,X94),X90)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_split__pos__lemma) ).
fof(fact_degree__linear__power,axiom,
! [X10,X8,X9] :
( class_Rings_Ocomm__semiring__1(X9)
=> c_Polynomial_Odegree(X9,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(X9)),hAPP(hAPP(c_Polynomial_OpCons(X9),X8),hAPP(hAPP(c_Polynomial_OpCons(X9),c_Groups_Oone__class_Oone(X9)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X9))))),X10)) = X10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_degree__linear__power) ).
fof(fact_combine__common__factor,axiom,
! [X23,X21,X47,X8,X9] :
( class_Rings_Osemiring(X9)
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(X9),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X9),X8),X47)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X9),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X9),X21),X47)),X23)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X9),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X9),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X9),X8),X21)),X47)),X23) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_combine__common__factor) ).
fof(fact_zmod__zmult2__eq,axiom,
! [X21,X8,X23] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X23)
=> c_Divides_Odiv__class_Omod(tc_Int_Oint,X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X21),X23)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X21),c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X8,X21),X23))),c_Divides_Odiv__class_Omod(tc_Int_Oint,X8,X21)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zmod__zmult2__eq) ).
fof(fact_mod__mult2__eq,axiom,
! [X23,X21,X8] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X21),X23)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X21),c_Divides_Odiv__class_Omod(tc_Nat_Onat,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X8,X21),X23))),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X8,X21)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__mult2__eq) ).
fof(fact_DERIV__chain2,axiom,
! [X69,X70,X27,X1,X2,X5] :
( class_RealVector_Oreal__normed__field(X5)
=> ( c_Deriv_Oderiv(X5,X2,hAPP(X1,X27),X70)
=> ( c_Deriv_Oderiv(X5,X1,X27,X69)
=> c_Deriv_Oderiv(X5,hAPP(hAPP(c_COMBB(X5,X5,X5),X2),X1),X27,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X70),X69)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_DERIV__chain2) ).
fof(fact_DERIV__chain_H,axiom,
! [X71,X1,X65,X27,X2,X5] :
( class_RealVector_Oreal__normed__field(X5)
=> ( c_Deriv_Oderiv(X5,X2,X27,X65)
=> ( c_Deriv_Oderiv(X5,X1,hAPP(X2,X27),X71)
=> c_Deriv_Oderiv(X5,hAPP(hAPP(c_COMBB(X5,X5,X5),X1),X2),X27,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X71),X65)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_DERIV__chain_H) ).
fof(fact_poly__replicate__append,axiom,
! [X6,X7,X10,X9] :
( class_Rings_Ocomm__ring__1(X9)
=> hAPP(c_Polynomial_Opoly(X9,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X9)),c_Polynomial_Omonom(X9,c_Groups_Oone__class_Oone(X9),X10)),X7)),X6) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X9),hAPP(hAPP(c_Power_Opower__class_Opower(X9),X6),X10)),hAPP(c_Polynomial_Opoly(X9,X7),X6)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_poly__replicate__append) ).
fof(fact_div__dvd__div,axiom,
! [X31,X25,X11,X5] :
( class_Divides_Osemiring__div(X5)
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X5),X11),X25))
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X5),X11),X31))
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X5),c_Divides_Odiv__class_Odiv(X5,X25,X11)),c_Divides_Odiv__class_Odiv(X5,X31,X11)))
<=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X5),X25),X31)) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_div__dvd__div) ).
fof(fact_left__add__mult__distrib,axiom,
! [X36,X40,X41,X42] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X42),X41)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X40),X41)),X36)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X42),X40)),X41)),X36),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_left__add__mult__distrib) ).
fof(fact_mod__lemma,axiom,
! [X13,X21,X34,X23] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X23)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X34,X21)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X21),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X13,X23))),X34),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X21),X23)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__lemma) ).
fof(fact_unity__coeff__ex,axiom,
! [X67,X68,X5] :
( ( class_Rings_Odvd(X5)
& class_Rings_Osemiring__0(X5) )
=> ( ? [X3] : hBOOL(hAPP(X68,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X67),X3)))
<=> ? [X3] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X5),X67),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X3),c_Groups_Ozero__class_Ozero(X5))))
& hBOOL(hAPP(X68,X3)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_unity__coeff__ex) ).
fof(fact_mult__diff__mult,axiom,
! [X21,X8,X33,X6,X9] :
( class_Rings_Oring(X9)
=> hAPP(hAPP(c_Groups_Ominus__class_Ominus(X9),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X9),X6),X33)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X9),X8),X21)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X9),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X9),X6),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X9),X33),X21))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X9),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X9),X6),X8)),X21)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__diff__mult) ).
fof(fact_zdiv__zmult1__eq,axiom,
! [X23,X21,X8] : c_Divides_Odiv__class_Odiv(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X8),X21),X23) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X8),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X21,X23))),c_Divides_Odiv__class_Odiv(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X8),c_Divides_Odiv__class_Omod(tc_Int_Oint,X21,X23)),X23)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zdiv__zmult1__eq) ).
fof(fact_div__mult1__eq,axiom,
! [X23,X21,X8] : c_Divides_Odiv__class_Odiv(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X8),X21),X23) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X8),c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X21,X23))),c_Divides_Odiv__class_Odiv(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X8),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X21,X23)),X23)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_div__mult1__eq) ).
fof(fact_poly__rec__0,axiom,
! [X5,X26,X2,X15] :
( class_Groups_Ozero(X15)
=> ( hAPP(hAPP(hAPP(X2,c_Groups_Ozero__class_Ozero(X15)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X15))),X26) = X26
=> c_Polynomial_Opoly__rec(X5,X15,X26,X2,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X15))) = X26 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_poly__rec__0) ).
fof(fact_inverse__add,axiom,
! [X21,X8,X9] :
( class_Fields_Ofield(X9)
=> ( X8 != c_Groups_Ozero__class_Ozero(X9)
=> ( X21 != c_Groups_Ozero__class_Ozero(X9)
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(X9),hAPP(c_Rings_Oinverse__class_Oinverse(X9),X8)),hAPP(c_Rings_Oinverse__class_Oinverse(X9),X21)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X9),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X9),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X9),X8),X21)),hAPP(c_Rings_Oinverse__class_Oinverse(X9),X8))),hAPP(c_Rings_Oinverse__class_Oinverse(X9),X21)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inverse__add) ).
fof(fact_pdivmod__rel,axiom,
! [X33,X6,X9] :
( class_Fields_Ofield(X9)
=> c_Polynomial_Opdivmod__rel(X9,X6,X33,c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(X9),X6,X33),c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(X9),X6,X33)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pdivmod__rel) ).
fof(fact_DERIV__cmult,axiom,
! [X31,X65,X27,X2,X5] :
( class_RealVector_Oreal__normed__field(X5)
=> ( c_Deriv_Oderiv(X5,X2,X27,X65)
=> c_Deriv_Oderiv(X5,hAPP(hAPP(c_COMBB(X5,X5,X5),hAPP(c_Groups_Otimes__class_Otimes(X5),X31)),X2),X27,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X31),X65)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_DERIV__cmult) ).
fof(fact_semiring__1__class_Oof__nat__code,axiom,
! [X14,X5] :
( class_Rings_Osemiring__1(X5)
=> c_Nat_Osemiring__1__class_Oof__nat(X5,X14) = c_Nat_Osemiring__1__class_Oof__nat__aux(X5,hAPP(c_COMBC(X5,X5,X5,c_Groups_Oplus__class_Oplus(X5)),c_Groups_Oone__class_Oone(X5)),X14,c_Groups_Ozero__class_Ozero(X5)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_semiring__1__class_Oof__nat__code) ).
fof(fact_pdivmod__rel__0,axiom,
! [X33,X9] :
( class_Fields_Ofield(X9)
=> c_Polynomial_Opdivmod__rel(X9,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X9)),X33,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X9)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X9))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pdivmod__rel__0) ).
fof(fact_dvd__mult__cancel__left,axiom,
! [X25,X11,X31,X5] :
( class_Rings_Oidom(X5)
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X31),X11)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X31),X25)))
<=> ( X31 = c_Groups_Ozero__class_Ozero(X5)
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X5),X11),X25)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__mult__cancel__left) ).
fof(fact_dvd__mult__cancel__right,axiom,
! [X25,X31,X11,X5] :
( class_Rings_Oidom(X5)
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X11),X31)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X25),X31)))
<=> ( X31 = c_Groups_Ozero__class_Ozero(X5)
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X5),X11),X25)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__mult__cancel__right) ).
fof(fact_pdivmod__rel__by__0,axiom,
! [X6,X9] :
( class_Fields_Ofield(X9)
=> c_Polynomial_Opdivmod__rel(X9,X6,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X9)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X9)),X6) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pdivmod__rel__by__0) ).
fof(fact_sum__squares__gt__zero__iff,axiom,
! [X28,X27,X5] :
( class_Rings_Olinordered__ring__strict(X5)
=> ( c_Orderings_Oord__class_Oless(X5,c_Groups_Ozero__class_Ozero(X5),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X27),X27)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X28),X28)))
<=> ( X27 != c_Groups_Ozero__class_Ozero(X5)
| X28 != c_Groups_Ozero__class_Ozero(X5) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sum__squares__gt__zero__iff) ).
fof(fact_diff__divide__eq__iff,axiom,
! [X33,X6,X32,X9] :
( class_Fields_Ofield(X9)
=> ( X32 != c_Groups_Ozero__class_Ozero(X9)
=> hAPP(hAPP(c_Groups_Ominus__class_Ominus(X9),X6),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X9),X33),X32)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X9),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X9),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X9),X32),X6)),X33)),X32) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__divide__eq__iff) ).
fof(fact_add__divide__eq__iff,axiom,
! [X33,X6,X32,X9] :
( class_Fields_Ofield(X9)
=> ( X32 != c_Groups_Ozero__class_Ozero(X9)
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(X9),X6),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X9),X33),X32)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X9),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X9),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X9),X32),X6)),X33)),X32) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__divide__eq__iff) ).
fof(fact_mod__div__equality,axiom,
! [X21,X8,X9] :
( class_Divides_Osemiring__div(X9)
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(X9),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X9),c_Divides_Odiv__class_Odiv(X9,X8,X21)),X21)),c_Divides_Odiv__class_Omod(X9,X8,X21)) = X8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__div__equality) ).
fof(fact_DERIV__minus,axiom,
! [X65,X27,X2,X5] :
( class_RealVector_Oreal__normed__field(X5)
=> ( c_Deriv_Oderiv(X5,X2,X27,X65)
=> c_Deriv_Oderiv(X5,hAPP(hAPP(c_COMBB(X5,X5,X5),c_Groups_Ouminus__class_Ouminus(X5)),X2),X27,hAPP(c_Groups_Ouminus__class_Ouminus(X5),X65)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_DERIV__minus) ).
fof(fact_realpow__two__diff,axiom,
! [X33,X6,X9] :
( class_Rings_Ocomm__ring__1(X9)
=> hAPP(hAPP(c_Groups_Ominus__class_Ominus(X9),hAPP(hAPP(c_Power_Opower__class_Opower(X9),X6),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))),hAPP(hAPP(c_Power_Opower__class_Opower(X9),X33),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X9),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X9),X6),X33)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X9),X6),X33)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_realpow__two__diff) ).
fof(fact_division__ring__inverse__diff,axiom,
! [X21,X8,X9] :
( class_Rings_Odivision__ring(X9)
=> ( X8 != c_Groups_Ozero__class_Ozero(X9)
=> ( X21 != c_Groups_Ozero__class_Ozero(X9)
=> hAPP(hAPP(c_Groups_Ominus__class_Ominus(X9),hAPP(c_Rings_Oinverse__class_Oinverse(X9),X8)),hAPP(c_Rings_Oinverse__class_Oinverse(X9),X21)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X9),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X9),hAPP(c_Rings_Oinverse__class_Oinverse(X9),X8)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X9),X21),X8))),hAPP(c_Rings_Oinverse__class_Oinverse(X9),X21)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_division__ring__inverse__diff) ).
fof(fact_division__ring__inverse__add,axiom,
! [X21,X8,X9] :
( class_Rings_Odivision__ring(X9)
=> ( X8 != c_Groups_Ozero__class_Ozero(X9)
=> ( X21 != c_Groups_Ozero__class_Ozero(X9)
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(X9),hAPP(c_Rings_Oinverse__class_Oinverse(X9),X8)),hAPP(c_Rings_Oinverse__class_Oinverse(X9),X21)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X9),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X9),hAPP(c_Rings_Oinverse__class_Oinverse(X9),X8)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X9),X8),X21))),hAPP(c_Rings_Oinverse__class_Oinverse(X9),X21)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_division__ring__inverse__add) ).
fof(fact_offset__poly__pCons,axiom,
! [X48,X7,X8,X9] :
( class_Rings_Ocomm__semiring__0(X9)
=> c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X9,hAPP(hAPP(c_Polynomial_OpCons(X9),X8),X7),X48) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X9)),hAPP(hAPP(c_Polynomial_Osmult(X9),X48),c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X9,X7,X48))),hAPP(hAPP(c_Polynomial_OpCons(X9),X8),c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X9,X7,X48))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_offset__poly__pCons) ).
fof(fact_dvd__mult__cancel,axiom,
! [X10,X12,X36] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X36),X12)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X36),X10)))
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X36)
=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X12),X10)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__mult__cancel) ).
fof(fact_nat__mult__dvd__cancel1,axiom,
! [X14,X35,X39] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X39)
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X39),X35)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X39),X14)))
<=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X35),X14)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__mult__dvd__cancel1) ).
fof(fact_crossproduct__noteq,axiom,
! [X30,X31,X25,X11,X5] :
( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X5)
=> ( ( X11 != X25
& X31 != X30 )
<=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X11),X31)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X25),X30)) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X11),X30)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X25),X31)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_crossproduct__noteq) ).
fof(fact_crossproduct__eq,axiom,
! [X26,X27,X28,X29,X5] :
( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X5)
=> ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X29),X28)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X27),X26)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X29),X26)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X27),X28))
<=> ( X29 = X27
| X28 = X26 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_crossproduct__eq) ).
fof(fact_DERIV__inverse,axiom,
! [X27,X5] :
( class_RealVector_Oreal__normed__field(X5)
=> ( X27 != c_Groups_Ozero__class_Ozero(X5)
=> c_Deriv_Oderiv(X5,c_Rings_Oinverse__class_Oinverse(X5),X27,hAPP(c_Groups_Ouminus__class_Ouminus(X5),hAPP(hAPP(c_Power_Opower__class_Opower(X5),hAPP(c_Rings_Oinverse__class_Oinverse(X5),X27)),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_DERIV__inverse) ).
fof(fact_zdvd__mult__cancel,axiom,
! [X10,X12,X36] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X36),X12)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X36),X10)))
=> ( X36 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X12),X10)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zdvd__mult__cancel) ).
fof(fact_zdvd__mono,axiom,
! [X64,X35,X39] :
( X39 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X35),X64))
<=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X39),X35)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X39),X64))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zdvd__mono) ).
fof(fact_nat__mult__dvd__cancel__disj,axiom,
! [X14,X35,X39] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X39),X35)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X39),X14)))
<=> ( X39 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X35),X14)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__mult__dvd__cancel__disj) ).
fof(fact_pow__divides__eq__int,axiom,
! [X25,X11,X14] :
( X14 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X11),X14)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X25),X14)))
<=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X11),X25)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pow__divides__eq__int) ).
fof(fact_pow__divides__pow__int,axiom,
! [X21,X10,X8] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X8),X10)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X21),X10)))
=> ( X10 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X8),X21)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pow__divides__pow__int) ).
fof(fact_pow__divides__eq__nat,axiom,
! [X25,X11,X14] :
( X14 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X11),X14)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X25),X14)))
<=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X11),X25)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pow__divides__eq__nat) ).
fof(fact_pow__divides__pow__nat,axiom,
! [X21,X10,X8] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X8),X10)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X21),X10)))
=> ( X10 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X8),X21)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pow__divides__pow__nat) ).
fof(fact_zdvd__reduce,axiom,
! [X35,X14,X39] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X39),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X14),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X39),X35))))
<=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X39),X14)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zdvd__reduce) ).
fof(help_c__COMBC__1,axiom,
! [X100,X101,X68,X5,X102,X15] : hAPP(hAPP(c_COMBC(X15,X102,X5,X68),X101),X100) = hAPP(hAPP(X68,X100),X101),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__COMBC__1) ).
fof(fact_mult__dvd__mono,axiom,
! [X22,X23,X21,X8,X9] :
( class_Rings_Ocomm__semiring__1(X9)
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X9),X8),X21))
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X9),X23),X22))
=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X9),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X9),X8),X23)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X9),X21),X22))) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__dvd__mono) ).
fof(fact_smult__dvd__iff,axiom,
! [X24,X4,X11,X5] :
( class_Fields_Ofield(X5)
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X5)),hAPP(hAPP(c_Polynomial_Osmult(X5),X11),X4)),X24))
<=> ( ( X11 = c_Groups_Ozero__class_Ozero(X5)
=> X24 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X5)) )
& ( X11 != c_Groups_Ozero__class_Ozero(X5)
=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X5)),X4),X24)) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_smult__dvd__iff) ).
fof(fact_mod__mult__self4,axiom,
! [X12,X10,X36] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X36),X10)),X12)),X10) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,X12),X10),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__mult__self4) ).
fof(fact_smult__dvd__cancel,axiom,
! [X13,X7,X8,X9] :
( class_Rings_Ocomm__semiring__1(X9)
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X9)),hAPP(hAPP(c_Polynomial_Osmult(X9),X8),X7)),X13))
=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X9)),X7),X13)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_smult__dvd__cancel) ).
fof(fact_split__mod,axiom,
! [X39,X14,X68] :
( hBOOL(hAPP(X68,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X14,X39)))
<=> ( ( X39 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> hBOOL(hAPP(X68,X14)) )
& ( X39 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> ! [X94,X90] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X90,X39)
=> ( X14 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X39),X94)),X90)
=> hBOOL(hAPP(X68,X90)) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_split__mod) ).
fof(fact_coeff__mult__degree__sum,axiom,
! [X13,X7,X9] :
( class_Rings_Ocomm__semiring__0(X9)
=> hAPP(c_Polynomial_Ocoeff(X9,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X9)),X7),X13)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Polynomial_Odegree(X9,X7)),c_Polynomial_Odegree(X9,X13))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X9),hAPP(c_Polynomial_Ocoeff(X9,X7),c_Polynomial_Odegree(X9,X7))),hAPP(c_Polynomial_Ocoeff(X9,X13),c_Polynomial_Odegree(X9,X13))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_coeff__mult__degree__sum) ).
fof(fact_mult__pCons__left,axiom,
! [X13,X7,X8,X9] :
( class_Rings_Ocomm__semiring__0(X9)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X9)),hAPP(hAPP(c_Polynomial_OpCons(X9),X8),X7)),X13) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X9)),hAPP(hAPP(c_Polynomial_Osmult(X9),X8),X13)),hAPP(hAPP(c_Polynomial_OpCons(X9),c_Groups_Ozero__class_Ozero(X9)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X9)),X7),X13))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__pCons__left) ).
fof(fact_div__mult__div__if__dvd,axiom,
! [X51,X32,X6,X33,X9] :
( class_Divides_Osemiring__div(X9)
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X9),X33),X6))
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X9),X32),X51))
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X9),c_Divides_Odiv__class_Odiv(X9,X6,X33)),c_Divides_Odiv__class_Odiv(X9,X51,X32)) = c_Divides_Odiv__class_Odiv(X9,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X9),X6),X51),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X9),X33),X32)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_div__mult__div__if__dvd) ).
fof(fact_mod__diff__eq,axiom,
! [X23,X21,X8,X9] :
( class_Divides_Oring__div(X9)
=> c_Divides_Odiv__class_Omod(X9,hAPP(hAPP(c_Groups_Ominus__class_Ominus(X9),X8),X21),X23) = c_Divides_Odiv__class_Omod(X9,hAPP(hAPP(c_Groups_Ominus__class_Ominus(X9),c_Divides_Odiv__class_Omod(X9,X8,X23)),c_Divides_Odiv__class_Omod(X9,X21,X23)),X23) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__diff__eq) ).
fof(fact_mod__mult__eq,axiom,
! [X23,X21,X8,X9] :
( class_Divides_Osemiring__div(X9)
=> c_Divides_Odiv__class_Omod(X9,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X9),X8),X21),X23) = c_Divides_Odiv__class_Omod(X9,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X9),c_Divides_Odiv__class_Omod(X9,X8,X23)),c_Divides_Odiv__class_Omod(X9,X21,X23)),X23) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__mult__eq) ).
fof(fact_mod__add__eq,axiom,
! [X23,X21,X8,X9] :
( class_Divides_Osemiring__div(X9)
=> c_Divides_Odiv__class_Omod(X9,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X9),X8),X21),X23) = c_Divides_Odiv__class_Omod(X9,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X9),c_Divides_Odiv__class_Omod(X9,X8,X23)),c_Divides_Odiv__class_Omod(X9,X21,X23)),X23) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__add__eq) ).
fof(fact_gt__half__sum,axiom,
! [X21,X8,X9] :
( class_Fields_Olinordered__field(X9)
=> ( c_Orderings_Oord__class_Oless(X9,X8,X21)
=> c_Orderings_Oord__class_Oless(X9,hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X9),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X9),X8),X21)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X9),c_Groups_Oone__class_Oone(X9)),c_Groups_Oone__class_Oone(X9))),X21) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_gt__half__sum) ).
fof(fact_less__half__sum,axiom,
! [X21,X8,X9] :
( class_Fields_Olinordered__field(X9)
=> ( c_Orderings_Oord__class_Oless(X9,X8,X21)
=> c_Orderings_Oord__class_Oless(X9,X8,hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X9),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X9),X8),X21)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X9),c_Groups_Oone__class_Oone(X9)),c_Groups_Oone__class_Oone(X9)))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__half__sum) ).
fof(fact_divide__diff__eq__iff,axiom,
! [X33,X6,X32,X9] :
( class_Fields_Ofield(X9)
=> ( X32 != c_Groups_Ozero__class_Ozero(X9)
=> hAPP(hAPP(c_Groups_Ominus__class_Ominus(X9),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X9),X6),X32)),X33) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X9),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X9),X6),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X9),X32),X33))),X32) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide__diff__eq__iff) ).
fof(fact_divide__add__eq__iff,axiom,
! [X33,X6,X32,X9] :
( class_Fields_Ofield(X9)
=> ( X32 != c_Groups_Ozero__class_Ozero(X9)
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(X9),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X9),X6),X32)),X33) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X9),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X9),X6),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X9),X32),X33))),X32) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide__add__eq__iff) ).
fof(fact_add__frac__num,axiom,
! [X32,X6,X33,X9] :
( class_Fields_Ofield__inverse__zero(X9)
=> ( X33 != c_Groups_Ozero__class_Ozero(X9)
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(X9),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X9),X6),X33)),X32) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X9),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X9),X6),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X9),X32),X33))),X33) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__frac__num) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J,axiom,
! [X17,X18,X19,X20,X9] :
( class_Rings_Ocomm__semiring__1(X9)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X9),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X9),X20),X19)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X9),X18),X17)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X9),X18),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X9),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X9),X20),X19)),X17)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J) ).
fof(fact_odd__less__0,axiom,
! [X26] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X26)),X26),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
<=> c_Orderings_Oord__class_Oless(tc_Int_Oint,X26,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_odd__less__0) ).
fof(fact_dvd__mult__left,axiom,
! [X23,X21,X8,X9] :
( class_Rings_Ocomm__semiring__1(X9)
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X9),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X9),X8),X21)),X23))
=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X9),X8),X23)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__mult__left) ).
fof(fact_dvd__mult__right,axiom,
! [X23,X21,X8,X9] :
( class_Rings_Ocomm__semiring__1(X9)
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X9),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X9),X8),X21)),X23))
=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X9),X21),X23)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__mult__right) ).
fof(fact_mult__poly__add__left,axiom,
! [X34,X13,X7,X9] :
( class_Rings_Ocomm__semiring__0(X9)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X9)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X9)),X7),X13)),X34) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X9)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X9)),X7),X34)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X9)),X13),X34)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__poly__add__left) ).
fof(fact_power__minus,axiom,
! [X10,X8,X9] :
( class_Rings_Oring__1(X9)
=> hAPP(hAPP(c_Power_Opower__class_Opower(X9),hAPP(c_Groups_Ouminus__class_Ouminus(X9),X8)),X10) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X9),hAPP(hAPP(c_Power_Opower__class_Opower(X9),hAPP(c_Groups_Ouminus__class_Ouminus(X9),c_Groups_Oone__class_Oone(X9))),X10)),hAPP(hAPP(c_Power_Opower__class_Opower(X9),X8),X10)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__minus) ).
fof(fact_mult__pCons__right,axiom,
! [X13,X8,X7,X9] :
( class_Rings_Ocomm__semiring__0(X9)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X9)),X7),hAPP(hAPP(c_Polynomial_OpCons(X9),X8),X13)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X9)),hAPP(hAPP(c_Polynomial_Osmult(X9),X8),X7)),hAPP(hAPP(c_Polynomial_OpCons(X9),c_Groups_Ozero__class_Ozero(X9)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X9)),X7),X13))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__pCons__right) ).
fof(fact_dvd__power__same,axiom,
! [X10,X33,X6,X9] :
( class_Rings_Ocomm__semiring__1(X9)
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X9),X6),X33))
=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X9),hAPP(hAPP(c_Power_Opower__class_Opower(X9),X6),X10)),hAPP(hAPP(c_Power_Opower__class_Opower(X9),X33),X10))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__power__same) ).
fof(fact_pcompose__pCons,axiom,
! [X13,X7,X8,X9] :
( class_Rings_Ocomm__semiring__0(X9)
=> c_Polynomial_Opcompose(X9,hAPP(hAPP(c_Polynomial_OpCons(X9),X8),X7),X13) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X9)),hAPP(hAPP(c_Polynomial_OpCons(X9),X8),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X9)))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X9)),X13),c_Polynomial_Opcompose(X9,X7,X13))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pcompose__pCons) ).
fof(fact_div__add,axiom,
! [X33,X6,X32,X9] :
( class_Divides_Osemiring__div(X9)
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X9),X32),X6))
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X9),X32),X33))
=> c_Divides_Odiv__class_Odiv(X9,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X9),X6),X33),X32) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X9),c_Divides_Odiv__class_Odiv(X9,X6,X32)),c_Divides_Odiv__class_Odiv(X9,X33,X32)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_div__add) ).
fof(fact_dvd__poly__gcd__iff,axiom,
! [X28,X27,X39,X5] :
( class_Fields_Ofield(X5)
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X5)),X39),c_Polynomial_Opoly__gcd(X5,X27,X28)))
<=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X5)),X39),X27))
& hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X5)),X39),X28)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__poly__gcd__iff) ).
fof(fact_poly__gcd__greatest,axiom,
! [X33,X6,X36,X9] :
( class_Fields_Ofield(X9)
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X9)),X36),X6))
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X9)),X36),X33))
=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X9)),X36),c_Polynomial_Opoly__gcd(X9,X6,X33))) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_poly__gcd__greatest) ).
fof(fact_add__num__frac,axiom,
! [X6,X32,X33,X9] :
( class_Fields_Ofield__inverse__zero(X9)
=> ( X33 != c_Groups_Ozero__class_Ozero(X9)
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(X9),X32),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X9),X6),X33)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X9),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X9),X6),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X9),X32),X33))),X33) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__num__frac) ).
fof(fact_smult__dvd,axiom,
! [X8,X13,X7,X9] :
( class_Fields_Ofield(X9)
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X9)),X7),X13))
=> ( X8 != c_Groups_Ozero__class_Ozero(X9)
=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X9)),hAPP(hAPP(c_Polynomial_Osmult(X9),X8),X7)),X13)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_smult__dvd) ).
fof(fact_power_Opower_Opower__Suc,axiom,
! [X14,X11,X37,X38,X5] : hAPP(hAPP(c_Power_Opower_Opower(X5,X38,X37),X11),hAPP(c_Nat_OSuc,X14)) = hAPP(hAPP(X37,X11),hAPP(hAPP(c_Power_Opower_Opower(X5,X38,X37),X11),X14)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power_Opower_Opower__Suc) ).
fof(fact_dvd__mult__cancel2,axiom,
! [X14,X35] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X35)
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X14),X35)),X35))
<=> X14 = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__mult__cancel2) ).
fof(fact_dvd__mult__cancel1,axiom,
! [X14,X35] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X35)
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X35),X14)),X35))
<=> X14 = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__mult__cancel1) ).
fof(fact_semiring__div__class_Omod__div__equality_H,axiom,
! [X21,X8,X9] :
( class_Divides_Osemiring__div(X9)
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(X9),c_Divides_Odiv__class_Omod(X9,X8,X21)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X9),c_Divides_Odiv__class_Odiv(X9,X8,X21)),X21)) = X8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_semiring__div__class_Omod__div__equality_H) ).
fof(fact_mod__div__equality2,axiom,
! [X8,X21,X9] :
( class_Divides_Osemiring__div(X9)
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(X9),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X9),X21),c_Divides_Odiv__class_Odiv(X9,X8,X21))),c_Divides_Odiv__class_Omod(X9,X8,X21)) = X8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__div__equality2) ).
fof(fact_diff__pCons,axiom,
! [X13,X21,X7,X8,X9] :
( class_Groups_Oab__group__add(X9)
=> hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X9)),hAPP(hAPP(c_Polynomial_OpCons(X9),X8),X7)),hAPP(hAPP(c_Polynomial_OpCons(X9),X21),X13)) = hAPP(hAPP(c_Polynomial_OpCons(X9),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X9),X8),X21)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X9)),X7),X13)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__pCons) ).
fof(fact_add__pCons,axiom,
! [X13,X21,X7,X8,X9] :
( class_Groups_Ocomm__monoid__add(X9)
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X9)),hAPP(hAPP(c_Polynomial_OpCons(X9),X8),X7)),hAPP(hAPP(c_Polynomial_OpCons(X9),X21),X13)) = hAPP(hAPP(c_Polynomial_OpCons(X9),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X9),X8),X21)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X9)),X7),X13)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__pCons) ).
fof(fact_realpow__minus__mult,axiom,
! [X6,X10,X9] :
( class_Groups_Omonoid__mult(X9)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X10)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X9),hAPP(hAPP(c_Power_Opower__class_Opower(X9),X6),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X10),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),X6) = hAPP(hAPP(c_Power_Opower__class_Opower(X9),X6),X10) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_realpow__minus__mult) ).
fof(fact_DERIV__unique,axiom,
! [X71,X65,X27,X2,X5] :
( class_RealVector_Oreal__normed__field(X5)
=> ( c_Deriv_Oderiv(X5,X2,X27,X65)
=> ( c_Deriv_Oderiv(X5,X2,X27,X71)
=> X65 = X71 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_DERIV__unique) ).
fof(fact_dvd__mod__iff,axiom,
! [X35,X14,X39,X5] :
( class_Divides_Osemiring__div(X5)
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X5),X39),X14))
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X5),X39),c_Divides_Odiv__class_Omod(X5,X35,X14)))
<=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X5),X39),X35)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__mod__iff) ).
fof(fact_dvd__mod__imp__dvd,axiom,
! [X10,X12,X36,X9] :
( class_Divides_Osemiring__div(X9)
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X9),X36),c_Divides_Odiv__class_Omod(X9,X12,X10)))
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X9),X36),X10))
=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X9),X36),X12)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__mod__imp__dvd) ).
fof(fact_smult__def,axiom,
! [X4,X11,X5] :
( class_Rings_Ocomm__semiring__0(X5)
=> hAPP(hAPP(c_Polynomial_Osmult(X5),X11),X4) = c_Polynomial_OAbs__poly(X5,hAPP(hAPP(c_COMBB(X5,X5,tc_Nat_Onat),hAPP(c_Groups_Otimes__class_Otimes(X5),X11)),c_Polynomial_Ocoeff(X5,X4))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_smult__def) ).
fof(fact_zmod__simps_I4_J,axiom,
! [X21,X23,X8,X9] :
( class_Divides_Osemiring__div(X9)
=> c_Divides_Odiv__class_Omod(X9,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X9),c_Divides_Odiv__class_Omod(X9,X8,X23)),X21),X23) = c_Divides_Odiv__class_Omod(X9,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X9),X8),X21),X23) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zmod__simps_I4_J) ).
fof(fact_zmod__simps_I1_J,axiom,
! [X21,X23,X8,X9] :
( class_Divides_Osemiring__div(X9)
=> c_Divides_Odiv__class_Omod(X9,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X9),c_Divides_Odiv__class_Omod(X9,X8,X23)),X21),X23) = c_Divides_Odiv__class_Omod(X9,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X9),X8),X21),X23) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zmod__simps_I1_J) ).
fof(fact_mod__diff__left__eq,axiom,
! [X23,X21,X8,X9] :
( class_Divides_Oring__div(X9)
=> c_Divides_Odiv__class_Omod(X9,hAPP(hAPP(c_Groups_Ominus__class_Ominus(X9),X8),X21),X23) = c_Divides_Odiv__class_Omod(X9,hAPP(hAPP(c_Groups_Ominus__class_Ominus(X9),c_Divides_Odiv__class_Omod(X9,X8,X23)),X21),X23) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__diff__left__eq) ).
fof(fact_mod__mult__left__eq,axiom,
! [X23,X21,X8,X9] :
( class_Divides_Osemiring__div(X9)
=> c_Divides_Odiv__class_Omod(X9,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X9),X8),X21),X23) = c_Divides_Odiv__class_Omod(X9,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X9),c_Divides_Odiv__class_Omod(X9,X8,X23)),X21),X23) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__mult__left__eq) ).
fof(fact_mod__add__left__eq,axiom,
! [X23,X21,X8,X9] :
( class_Divides_Osemiring__div(X9)
=> c_Divides_Odiv__class_Omod(X9,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X9),X8),X21),X23) = c_Divides_Odiv__class_Omod(X9,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X9),c_Divides_Odiv__class_Omod(X9,X8,X23)),X21),X23) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__add__left__eq) ).
fof(fact_zmod__zdiv__equality,axiom,
! [X21,X8] : X8 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X21),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X8,X21))),c_Divides_Odiv__class_Omod(tc_Int_Oint,X8,X21)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zmod__zdiv__equality) ).
fof(fact_dvd__smult__iff,axiom,
! [X24,X4,X11,X5] :
( class_Fields_Ofield(X5)
=> ( X11 != c_Groups_Ozero__class_Ozero(X5)
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X5)),X4),hAPP(hAPP(c_Polynomial_Osmult(X5),X11),X24)))
<=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X5)),X4),X24)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__smult__iff) ).
fof(fact_dvd__smult__cancel,axiom,
! [X13,X8,X7,X9] :
( class_Fields_Ofield(X9)
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X9)),X7),hAPP(hAPP(c_Polynomial_Osmult(X9),X8),X13)))
=> ( X8 != c_Groups_Ozero__class_Ozero(X9)
=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X9)),X7),X13)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__smult__cancel) ).
fof(fact_poly__gcd_Osimps_I1_J,axiom,
! [X6,X9] :
( class_Fields_Ofield(X9)
=> c_Polynomial_Opoly__gcd(X9,X6,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X9))) = hAPP(hAPP(c_Polynomial_Osmult(X9),hAPP(c_Rings_Oinverse__class_Oinverse(X9),hAPP(c_Polynomial_Ocoeff(X9,X6),c_Polynomial_Odegree(X9,X6)))),X6) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_poly__gcd_Osimps_I1_J) ).
fof(fact_poly__gcd__code,axiom,
! [X6,X33,X9] :
( class_Fields_Ofield(X9)
=> ( ( X33 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X9))
=> c_Polynomial_Opoly__gcd(X9,X6,X33) = hAPP(hAPP(c_Polynomial_Osmult(X9),hAPP(c_Rings_Oinverse__class_Oinverse(X9),hAPP(c_Polynomial_Ocoeff(X9,X6),c_Polynomial_Odegree(X9,X6)))),X6) )
& ( X33 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X9))
=> c_Polynomial_Opoly__gcd(X9,X6,X33) = c_Polynomial_Opoly__gcd(X9,X33,c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(X9),X6,X33)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_poly__gcd__code) ).
fof(fact_zadd__int__left,axiom,
! [X32,X10,X12] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,X12)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,X10)),X32)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X12),X10))),X32),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zadd__int__left) ).
fof(fact_times__divide__times__eq,axiom,
! [X51,X32,X33,X6,X9] :
( class_Fields_Ofield__inverse__zero(X9)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X9),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X9),X6),X33)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X9),X32),X51)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X9),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X9),X6),X32)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X9),X33),X51)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_times__divide__times__eq) ).
fof(fact_Deriv_Oadd__diff__add,axiom,
! [X22,X21,X23,X8,X9] :
( class_Groups_Oab__group__add(X9)
=> hAPP(hAPP(c_Groups_Ominus__class_Ominus(X9),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X9),X8),X23)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X9),X21),X22)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X9),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X9),X8),X21)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X9),X23),X22)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Deriv_Oadd__diff__add) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J,axiom,
! [X17,X18,X19,X20,X9] :
( class_Rings_Ocomm__semiring__1(X9)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X9),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X9),X20),X19)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X9),X18),X17)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X9),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X9),X20),X18)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X9),X19),X17)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J,axiom,
! [X22,X23,X21,X8,X9] :
( class_Rings_Ocomm__semiring__1(X9)
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(X9),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X9),X8),X21)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X9),X23),X22)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X9),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X9),X8),X23)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X9),X21),X22)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I14_J,axiom,
! [X17,X18,X19,X20,X9] :
( class_Rings_Ocomm__semiring__1(X9)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X9),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X9),X20),X19)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X9),X18),X17)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X9),X20),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X9),X19),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X9),X18),X17))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I14_J) ).
fof(fact_zdvd__zmod__imp__zdvd,axiom,
! [X10,X12,X36] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X36),c_Divides_Odiv__class_Omod(tc_Int_Oint,X12,X10)))
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X36),X10))
=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X36),X12)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zdvd__zmod__imp__zdvd) ).
fof(fact_synthetic__div__correct,axiom,
! [X23,X7,X9] :
( class_Rings_Ocomm__semiring__0(X9)
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X9)),X7),hAPP(hAPP(c_Polynomial_Osmult(X9),X23),c_Polynomial_Osynthetic__div(X9,X7,X23))) = hAPP(hAPP(c_Polynomial_OpCons(X9),hAPP(c_Polynomial_Opoly(X9,X7),X23)),c_Polynomial_Osynthetic__div(X9,X7,X23)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_synthetic__div__correct) ).
fof(fact_Suc__mult__less__cancel1,axiom,
! [X14,X35,X39] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,X39)),X35),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,X39)),X14))
<=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X35,X14) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__mult__less__cancel1) ).
fof(fact_poly__dvd__antisym,axiom,
! [X13,X7,X9] :
( class_Rings_Oidom(X9)
=> ( hAPP(c_Polynomial_Ocoeff(X9,X7),c_Polynomial_Odegree(X9,X7)) = hAPP(c_Polynomial_Ocoeff(X9,X13),c_Polynomial_Odegree(X9,X13))
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X9)),X7),X13))
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X9)),X13),X7))
=> X7 = X13 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_poly__dvd__antisym) ).
fof(fact_diffs__minus,axiom,
! [X14,X31,X5] :
( class_Rings_Oring__1(X5)
=> c_Transcendental_Odiffs(X5,hAPP(hAPP(c_COMBB(X5,X5,tc_Nat_Onat),c_Groups_Ouminus__class_Ouminus(X5)),X31),X14) = hAPP(c_Groups_Ouminus__class_Ouminus(X5),c_Transcendental_Odiffs(X5,X31,X14)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diffs__minus) ).
fof(fact_divide__strict__left__mono,axiom,
! [X23,X8,X21,X9] :
( class_Fields_Olinordered__field(X9)
=> ( c_Orderings_Oord__class_Oless(X9,X21,X8)
=> ( c_Orderings_Oord__class_Oless(X9,c_Groups_Ozero__class_Ozero(X9),X23)
=> ( c_Orderings_Oord__class_Oless(X9,c_Groups_Ozero__class_Ozero(X9),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X9),X8),X21))
=> c_Orderings_Oord__class_Oless(X9,hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X9),X23),X8),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X9),X23),X21)) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide__strict__left__mono) ).
fof(fact_divide__strict__left__mono__neg,axiom,
! [X23,X21,X8,X9] :
( class_Fields_Olinordered__field(X9)
=> ( c_Orderings_Oord__class_Oless(X9,X8,X21)
=> ( c_Orderings_Oord__class_Oless(X9,X23,c_Groups_Ozero__class_Ozero(X9))
=> ( c_Orderings_Oord__class_Oless(X9,c_Groups_Ozero__class_Ozero(X9),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X9),X8),X21))
=> c_Orderings_Oord__class_Oless(X9,hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X9),X23),X8),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X9),X23),X21)) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide__strict__left__mono__neg) ).
fof(fact_zdiff__zmod__left,axiom,
! [X33,X12,X6] : c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,X6,X12)),X33),X12) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X6),X33),X12),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zdiff__zmod__left) ).
fof(fact_zpower__zmod,axiom,
! [X33,X12,X6] : c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,X6,X12)),X33),X12) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X6),X33),X12),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zpower__zmod) ).
fof(fact_div__power,axiom,
! [X10,X6,X33,X9] :
( class_Divides_Osemiring__div(X9)
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X9),X33),X6))
=> hAPP(hAPP(c_Power_Opower__class_Opower(X9),c_Divides_Odiv__class_Odiv(X9,X6,X33)),X10) = c_Divides_Odiv__class_Odiv(X9,hAPP(hAPP(c_Power_Opower__class_Opower(X9),X6),X10),hAPP(hAPP(c_Power_Opower__class_Opower(X9),X33),X10)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_div__power) ).
fof(fact_zdvd__zdiffD,axiom,
! [X10,X12,X36] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X36),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X12),X10)))
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X36),X10))
=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X36),X12)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zdvd__zdiffD) ).
fof(fact_zdiv__zminus1__eq__if,axiom,
! [X8,X21] :
( X21 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
=> ( ( c_Divides_Odiv__class_Omod(tc_Int_Oint,X8,X21) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
=> c_Divides_Odiv__class_Odiv(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X8),X21) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X8,X21)) )
& ( c_Divides_Odiv__class_Omod(tc_Int_Oint,X8,X21) != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
=> c_Divides_Odiv__class_Odiv(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X8),X21) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X8,X21))),c_Groups_Oone__class_Oone(tc_Int_Oint)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zdiv__zminus1__eq__if) ).
fof(fact_zdiv__zminus2__eq__if,axiom,
! [X8,X21] :
( X21 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
=> ( ( c_Divides_Odiv__class_Omod(tc_Int_Oint,X8,X21) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
=> c_Divides_Odiv__class_Odiv(tc_Int_Oint,X8,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X21)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X8,X21)) )
& ( c_Divides_Odiv__class_Omod(tc_Int_Oint,X8,X21) != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
=> c_Divides_Odiv__class_Odiv(tc_Int_Oint,X8,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X21)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X8,X21))),c_Groups_Oone__class_Oone(tc_Int_Oint)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zdiv__zminus2__eq__if) ).
fof(fact_real__squared__diff__one__factored,axiom,
! [X6,X9] :
( class_Rings_Oring__1(X9)
=> hAPP(hAPP(c_Groups_Ominus__class_Ominus(X9),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X9),X6),X6)),c_Groups_Oone__class_Oone(X9)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X9),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X9),X6),c_Groups_Oone__class_Oone(X9))),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X9),X6),c_Groups_Oone__class_Oone(X9))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__squared__diff__one__factored) ).
fof(fact_mod__diff__cong,axiom,
! [X43,X21,X45,X23,X8,X9] :
( class_Divides_Oring__div(X9)
=> ( c_Divides_Odiv__class_Omod(X9,X8,X23) = c_Divides_Odiv__class_Omod(X9,X45,X23)
=> ( c_Divides_Odiv__class_Omod(X9,X21,X23) = c_Divides_Odiv__class_Omod(X9,X43,X23)
=> c_Divides_Odiv__class_Omod(X9,hAPP(hAPP(c_Groups_Ominus__class_Ominus(X9),X8),X21),X23) = c_Divides_Odiv__class_Omod(X9,hAPP(hAPP(c_Groups_Ominus__class_Ominus(X9),X45),X43),X23) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__diff__cong) ).
fof(fact_mod__mult__cong,axiom,
! [X43,X21,X45,X23,X8,X9] :
( class_Divides_Osemiring__div(X9)
=> ( c_Divides_Odiv__class_Omod(X9,X8,X23) = c_Divides_Odiv__class_Omod(X9,X45,X23)
=> ( c_Divides_Odiv__class_Omod(X9,X21,X23) = c_Divides_Odiv__class_Omod(X9,X43,X23)
=> c_Divides_Odiv__class_Omod(X9,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X9),X8),X21),X23) = c_Divides_Odiv__class_Omod(X9,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X9),X45),X43),X23) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__mult__cong) ).
fof(fact_mod__add__cong,axiom,
! [X43,X21,X45,X23,X8,X9] :
( class_Divides_Osemiring__div(X9)
=> ( c_Divides_Odiv__class_Omod(X9,X8,X23) = c_Divides_Odiv__class_Omod(X9,X45,X23)
=> ( c_Divides_Odiv__class_Omod(X9,X21,X23) = c_Divides_Odiv__class_Omod(X9,X43,X23)
=> c_Divides_Odiv__class_Omod(X9,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X9),X8),X21),X23) = c_Divides_Odiv__class_Omod(X9,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X9),X45),X43),X23) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__add__cong) ).
fof(fact_dvd__mod,axiom,
! [X10,X12,X36,X9] :
( class_Divides_Osemiring__div(X9)
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X9),X36),X12))
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X9),X36),X10))
=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X9),X36),c_Divides_Odiv__class_Omod(X9,X12,X10))) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__mod) ).
fof(fact_power__Suc__less,axiom,
! [X10,X8,X9] :
( class_Rings_Olinordered__semidom(X9)
=> ( c_Orderings_Oord__class_Oless(X9,c_Groups_Ozero__class_Ozero(X9),X8)
=> ( c_Orderings_Oord__class_Oless(X9,X8,c_Groups_Oone__class_Oone(X9))
=> c_Orderings_Oord__class_Oless(X9,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X9),X8),hAPP(hAPP(c_Power_Opower__class_Opower(X9),X8),X10)),hAPP(hAPP(c_Power_Opower__class_Opower(X9),X8),X10)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__Suc__less) ).
fof(fact_Suc__diff__diff,axiom,
! [X36,X10,X12] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,X12)),X10)),hAPP(c_Nat_OSuc,X36)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X12),X10)),X36),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__diff__diff) ).
fof(fact_dvd__diff,axiom,
! [X32,X33,X6,X9] :
( class_Rings_Ocomm__ring__1(X9)
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X9),X6),X33))
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X9),X6),X32))
=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X9),X6),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X9),X33),X32))) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__diff) ).
fof(fact_dvd__add,axiom,
! [X23,X21,X8,X9] :
( class_Rings_Ocomm__semiring__1(X9)
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X9),X8),X21))
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X9),X8),X23))
=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X9),X8),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X9),X21),X23))) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__add) ).
fof(fact_nat__diff__split,axiom,
! [X25,X11,X68] :
( hBOOL(hAPP(X68,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X11),X25)))
<=> ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X11,X25)
=> hBOOL(hAPP(X68,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) )
& ! [X93] :
( X11 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X25),X93)
=> hBOOL(hAPP(X68,X93)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__diff__split) ).
fof(fact_mult__monom,axiom,
! [X10,X21,X12,X8,X9] :
( class_Rings_Ocomm__semiring__0(X9)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X9)),c_Polynomial_Omonom(X9,X8,X12)),c_Polynomial_Omonom(X9,X21,X10)) = c_Polynomial_Omonom(X9,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X9),X8),X21),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X12),X10)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__monom) ).
fof(fact_smult__diff__left,axiom,
! [X7,X21,X8,X9] :
( class_Rings_Ocomm__ring(X9)
=> hAPP(hAPP(c_Polynomial_Osmult(X9),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X9),X8),X21)),X7) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X9)),hAPP(hAPP(c_Polynomial_Osmult(X9),X8),X7)),hAPP(hAPP(c_Polynomial_Osmult(X9),X21),X7)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_smult__diff__left) ).
fof(fact_smult__add__left,axiom,
! [X7,X21,X8,X9] :
( class_Rings_Ocomm__semiring__0(X9)
=> hAPP(hAPP(c_Polynomial_Osmult(X9),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X9),X8),X21)),X7) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X9)),hAPP(hAPP(c_Polynomial_Osmult(X9),X8),X7)),hAPP(hAPP(c_Polynomial_Osmult(X9),X21),X7)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_smult__add__left) ).
fof(fact_degree__diff__less,axiom,
! [X13,X10,X7,X9] :
( class_Groups_Oab__group__add(X9)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(X9,X7),X10)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(X9,X13),X10)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(X9,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X9)),X7),X13)),X10) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_degree__diff__less) ).
fof(fact_degree__add__less,axiom,
! [X13,X10,X7,X9] :
( class_Groups_Ocomm__monoid__add(X9)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(X9,X7),X10)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(X9,X13),X10)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(X9,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X9)),X7),X13)),X10) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_degree__add__less) ).
fof(fact_offset__poly__eq__0__lemma,axiom,
! [X8,X7,X23,X9] :
( class_Rings_Ocomm__semiring__0(X9)
=> ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X9)),hAPP(hAPP(c_Polynomial_Osmult(X9),X23),X7)),hAPP(hAPP(c_Polynomial_OpCons(X9),X8),X7)) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X9))
=> X7 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X9)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_offset__poly__eq__0__lemma) ).
fof(fact_coeff__diff,axiom,
! [X10,X13,X7,X9] :
( class_Groups_Oab__group__add(X9)
=> hAPP(c_Polynomial_Ocoeff(X9,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X9)),X7),X13)),X10) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(X9),hAPP(c_Polynomial_Ocoeff(X9,X7),X10)),hAPP(c_Polynomial_Ocoeff(X9,X13),X10)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_coeff__diff) ).
fof(fact_coeff__add,axiom,
! [X10,X13,X7,X9] :
( class_Groups_Ocomm__monoid__add(X9)
=> hAPP(c_Polynomial_Ocoeff(X9,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X9)),X7),X13)),X10) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X9),hAPP(c_Polynomial_Ocoeff(X9,X7),X10)),hAPP(c_Polynomial_Ocoeff(X9,X13),X10)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_coeff__add) ).
fof(fact_poly__diff,axiom,
! [X6,X13,X7,X9] :
( class_Rings_Ocomm__ring(X9)
=> hAPP(c_Polynomial_Opoly(X9,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X9)),X7),X13)),X6) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(X9),hAPP(c_Polynomial_Opoly(X9,X7),X6)),hAPP(c_Polynomial_Opoly(X9,X13),X6)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_poly__diff) ).
fof(fact_poly__mult,axiom,
! [X6,X13,X7,X9] :
( class_Rings_Ocomm__semiring__0(X9)
=> hAPP(c_Polynomial_Opoly(X9,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X9)),X7),X13)),X6) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X9),hAPP(c_Polynomial_Opoly(X9,X7),X6)),hAPP(c_Polynomial_Opoly(X9,X13),X6)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_poly__mult) ).
fof(fact_poly__add,axiom,
! [X6,X13,X7,X9] :
( class_Rings_Ocomm__semiring__0(X9)
=> hAPP(c_Polynomial_Opoly(X9,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X9)),X7),X13)),X6) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X9),hAPP(c_Polynomial_Opoly(X9,X7),X6)),hAPP(c_Polynomial_Opoly(X9,X13),X6)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_poly__add) ).
fof(fact_dvd__div__div__eq__mult,axiom,
! [X30,X25,X31,X11,X5] :
( class_Divides_Osemiring__div(X5)
=> ( X11 != c_Groups_Ozero__class_Ozero(X5)
=> ( X31 != c_Groups_Ozero__class_Ozero(X5)
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X5),X11),X25))
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X5),X31),X30))
=> ( c_Divides_Odiv__class_Odiv(X5,X25,X11) = c_Divides_Odiv__class_Odiv(X5,X30,X31)
<=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X25),X31) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X11),X30) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__div__div__eq__mult) ).
fof(fact_nonzero__power__divide,axiom,
! [X10,X8,X21,X9] :
( class_Fields_Ofield(X9)
=> ( X21 != c_Groups_Ozero__class_Ozero(X9)
=> hAPP(hAPP(c_Power_Opower__class_Opower(X9),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X9),X8),X21)),X10) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X9),hAPP(hAPP(c_Power_Opower__class_Opower(X9),X8),X10)),hAPP(hAPP(c_Power_Opower__class_Opower(X9),X21),X10)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nonzero__power__divide) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J,axiom,
! [X21,X12,X8,X9] :
( class_Rings_Ocomm__semiring__1(X9)
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(X9),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X9),X8),X12)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X9),X21),X12)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X9),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X9),X8),X21)),X12) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J) ).
fof(fact_divide_Odiff,axiom,
! [X46,X33,X6,X9] :
( class_RealVector_Oreal__normed__field(X9)
=> hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X9),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X9),X6),X33)),X46) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(X9),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X9),X6),X46)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X9),X33),X46)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide_Odiff) ).
fof(fact_diff__divide__distrib,axiom,
! [X23,X21,X8,X9] :
( class_Rings_Odivision__ring(X9)
=> hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X9),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X9),X8),X21)),X23) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(X9),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X9),X8),X23)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X9),X21),X23)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__divide__distrib) ).
fof(fact_divide_Oadd,axiom,
! [X46,X33,X6,X9] :
( class_RealVector_Oreal__normed__field(X9)
=> hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X9),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X9),X6),X33)),X46) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X9),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X9),X6),X46)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X9),X33),X46)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide_Oadd) ).
fof(fact_add__divide__distrib,axiom,
! [X23,X21,X8,X9] :
( class_Rings_Odivision__ring(X9)
=> hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X9),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X9),X8),X21)),X23) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X9),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X9),X8),X23)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X9),X21),X23)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__divide__distrib) ).
fof(fact_power__divide,axiom,
! [X10,X21,X8,X9] :
( class_Fields_Ofield__inverse__zero(X9)
=> hAPP(hAPP(c_Power_Opower__class_Opower(X9),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X9),X8),X21)),X10) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X9),hAPP(hAPP(c_Power_Opower__class_Opower(X9),X8),X10)),hAPP(hAPP(c_Power_Opower__class_Opower(X9),X21),X10)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__divide) ).
fof(fact_power__mult__distrib,axiom,
! [X10,X21,X8,X9] :
( class_Groups_Ocomm__monoid__mult(X9)
=> hAPP(hAPP(c_Power_Opower__class_Opower(X9),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X9),X8),X21)),X10) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X9),hAPP(hAPP(c_Power_Opower__class_Opower(X9),X8),X10)),hAPP(hAPP(c_Power_Opower__class_Opower(X9),X21),X10)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__mult__distrib) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I30_J,axiom,
! [X13,X33,X6,X9] :
( class_Rings_Ocomm__semiring__1(X9)
=> hAPP(hAPP(c_Power_Opower__class_Opower(X9),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X9),X6),X33)),X13) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X9),hAPP(hAPP(c_Power_Opower__class_Opower(X9),X6),X13)),hAPP(hAPP(c_Power_Opower__class_Opower(X9),X33),X13)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I30_J) ).
fof(fact_mult_Odiff__left,axiom,
! [X21,X45,X8,X9] :
( class_RealVector_Oreal__normed__algebra(X9)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X9),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X9),X8),X45)),X21) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(X9),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X9),X8),X21)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X9),X45),X21)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult_Odiff__left) ).
fof(fact_mult__left_Odiff,axiom,
! [X46,X33,X6,X9] :
( class_RealVector_Oreal__normed__algebra(X9)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X9),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X9),X6),X33)),X46) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(X9),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X9),X6),X46)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X9),X33),X46)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__left_Odiff) ).
fof(fact_comm__semiring__class_Odistrib,axiom,
! [X23,X21,X8,X9] :
( class_Rings_Ocomm__semiring(X9)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X9),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X9),X8),X21)),X23) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X9),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X9),X8),X23)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X9),X21),X23)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__class_Odistrib) ).
fof(fact_mult__left_Oadd,axiom,
! [X46,X33,X6,X9] :
( class_RealVector_Oreal__normed__algebra(X9)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X9),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X9),X6),X33)),X46) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X9),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X9),X6),X46)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X9),X33),X46)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__left_Oadd) ).
fof(fact_mult_Oadd__left,axiom,
! [X21,X45,X8,X9] :
( class_RealVector_Oreal__normed__algebra(X9)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X9),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X9),X8),X45)),X21) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X9),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X9),X8),X21)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X9),X45),X21)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult_Oadd__left) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J,axiom,
! [X23,X21,X8,X9] :
( class_Rings_Ocomm__semiring__1(X9)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X9),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X9),X8),X21)),X23) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X9),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X9),X8),X23)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X9),X21),X23)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J) ).
fof(fact_uminus__poly__def,axiom,
! [X4,X5] :
( class_Groups_Oab__group__add(X5)
=> hAPP(c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X5)),X4) = c_Polynomial_OAbs__poly(X5,hAPP(hAPP(c_COMBB(X5,X5,tc_Nat_Onat),c_Groups_Ouminus__class_Ouminus(X5)),c_Polynomial_Ocoeff(X5,X4))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_uminus__poly__def) ).
fof(fact_dvd__smult,axiom,
! [X8,X13,X7,X9] :
( class_Rings_Ocomm__semiring__1(X9)
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X9)),X7),X13))
=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X9)),X7),hAPP(hAPP(c_Polynomial_Osmult(X9),X8),X13))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__smult) ).
fof(fact_zmod__zdiv__equality_H,axiom,
! [X10,X12] : c_Divides_Odiv__class_Omod(tc_Int_Oint,X12,X10) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X12),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X12,X10)),X10)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zmod__zdiv__equality_H) ).
fof(fact_zdvd__zmod,axiom,
! [X10,X12,X75] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X75),X12))
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X75),X10))
=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X75),c_Divides_Odiv__class_Omod(tc_Int_Oint,X12,X10))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zdvd__zmod) ).
fof(fact_dvd__div__mult,axiom,
! [X23,X21,X8,X9] :
( class_Divides_Osemiring__div(X9)
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X9),X8),X21))
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X9),c_Divides_Odiv__class_Odiv(X9,X21,X8)),X23) = c_Divides_Odiv__class_Odiv(X9,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X9),X21),X23),X8) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__div__mult) ).
fof(fact_smult__diff__right,axiom,
! [X13,X7,X8,X9] :
( class_Rings_Ocomm__ring(X9)
=> hAPP(hAPP(c_Polynomial_Osmult(X9),X8),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X9)),X7),X13)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X9)),hAPP(hAPP(c_Polynomial_Osmult(X9),X8),X7)),hAPP(hAPP(c_Polynomial_Osmult(X9),X8),X13)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_smult__diff__right) ).
fof(fact_smult__add__right,axiom,
! [X13,X7,X8,X9] :
( class_Rings_Ocomm__semiring__0(X9)
=> hAPP(hAPP(c_Polynomial_Osmult(X9),X8),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X9)),X7),X13)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X9)),hAPP(hAPP(c_Polynomial_Osmult(X9),X8),X7)),hAPP(hAPP(c_Polynomial_Osmult(X9),X8),X13)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_smult__add__right) ).
fof(fact_poly__gcd__dvd1,axiom,
! [X33,X6,X9] :
( class_Fields_Ofield(X9)
=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X9)),c_Polynomial_Opoly__gcd(X9,X6,X33)),X6)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_poly__gcd__dvd1) ).
fof(fact_poly__gcd__dvd2,axiom,
! [X33,X6,X9] :
( class_Fields_Ofield(X9)
=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X9)),c_Polynomial_Opoly__gcd(X9,X6,X33)),X33)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_poly__gcd__dvd2) ).
fof(fact_zmult__zless__mono2__lemma,axiom,
! [X36,X40,X42] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X42,X40)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X36)
=> c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,X36)),X42),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,X36)),X40)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zmult__zless__mono2__lemma) ).
fof(help_c__COMBS__1,axiom,
! [X100,X101,X68,X5,X102,X15] : hAPP(hAPP(hAPP(c_COMBS(X15,X102,X5),X68),X101),X100) = hAPP(hAPP(X68,X100),hAPP(X101,X100)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__COMBS__1) ).
fof(fact_sum__squares__eq__zero__iff,axiom,
! [X28,X27,X5] :
( class_Rings_Olinordered__ring__strict(X5)
=> ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X27),X27)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X28),X28)) = c_Groups_Ozero__class_Ozero(X5)
<=> ( X27 = c_Groups_Ozero__class_Ozero(X5)
& X28 = c_Groups_Ozero__class_Ozero(X5) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sum__squares__eq__zero__iff) ).
fof(fact_dvd__diff__nat,axiom,
! [X10,X12,X36] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X36),X12))
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X36),X10))
=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X36),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X12),X10))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__diff__nat) ).
fof(fact_mult__eq__if,axiom,
! [X10,X12] :
( ( X12 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X12),X10) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( X12 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X12),X10) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X10),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X12),c_Groups_Oone__class_Oone(tc_Nat_Onat))),X10)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__eq__if) ).
fof(fact_power__less__power__Suc,axiom,
! [X10,X8,X9] :
( class_Rings_Olinordered__semidom(X9)
=> ( c_Orderings_Oord__class_Oless(X9,c_Groups_Oone__class_Oone(X9),X8)
=> c_Orderings_Oord__class_Oless(X9,hAPP(hAPP(c_Power_Opower__class_Opower(X9),X8),X10),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X9),X8),hAPP(hAPP(c_Power_Opower__class_Opower(X9),X8),X10))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__less__power__Suc) ).
fof(fact_mult__less__cancel__left__pos,axiom,
! [X25,X11,X31,X5] :
( class_Rings_Olinordered__ring__strict(X5)
=> ( c_Orderings_Oord__class_Oless(X5,c_Groups_Ozero__class_Ozero(X5),X31)
=> ( c_Orderings_Oord__class_Oless(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X31),X11),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X31),X25))
<=> c_Orderings_Oord__class_Oless(X5,X11,X25) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__less__cancel__left__pos) ).
fof(fact_mult__less__cancel__left__neg,axiom,
! [X25,X11,X31,X5] :
( class_Rings_Olinordered__ring__strict(X5)
=> ( c_Orderings_Oord__class_Oless(X5,X31,c_Groups_Ozero__class_Ozero(X5))
=> ( c_Orderings_Oord__class_Oless(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X31),X11),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X31),X25))
<=> c_Orderings_Oord__class_Oless(X5,X25,X11) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__less__cancel__left__neg) ).
fof(fact_power__strict__increasing__iff,axiom,
! [X28,X27,X25,X5] :
( class_Rings_Olinordered__semidom(X5)
=> ( c_Orderings_Oord__class_Oless(X5,c_Groups_Oone__class_Oone(X5),X25)
=> ( c_Orderings_Oord__class_Oless(X5,hAPP(hAPP(c_Power_Opower__class_Opower(X5),X25),X27),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X25),X28))
<=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X27,X28) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__strict__increasing__iff) ).
fof(fact_power__less__imp__less__exp,axiom,
! [X10,X12,X8,X9] :
( class_Rings_Olinordered__semidom(X9)
=> ( c_Orderings_Oord__class_Oless(X9,c_Groups_Oone__class_Oone(X9),X8)
=> ( c_Orderings_Oord__class_Oless(X9,hAPP(hAPP(c_Power_Opower__class_Opower(X9),X8),X12),hAPP(hAPP(c_Power_Opower__class_Opower(X9),X8),X10))
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X12,X10) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__less__imp__less__exp) ).
fof(fact_poly__pCons,axiom,
! [X6,X7,X8,X9] :
( class_Rings_Ocomm__semiring__0(X9)
=> hAPP(c_Polynomial_Opoly(X9,hAPP(hAPP(c_Polynomial_OpCons(X9),X8),X7)),X6) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X9),X8),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X9),X6),hAPP(c_Polynomial_Opoly(X9,X7),X6))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_poly__pCons) ).
fof(fact_diff__monom,axiom,
! [X21,X10,X8,X9] :
( class_Groups_Oab__group__add(X9)
=> hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X9)),c_Polynomial_Omonom(X9,X8,X10)),c_Polynomial_Omonom(X9,X21,X10)) = c_Polynomial_Omonom(X9,hAPP(hAPP(c_Groups_Ominus__class_Ominus(X9),X8),X21),X10) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__monom) ).
fof(fact_add__monom,axiom,
! [X21,X10,X8,X9] :
( class_Groups_Ocomm__monoid__add(X9)
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X9)),c_Polynomial_Omonom(X9,X8,X10)),c_Polynomial_Omonom(X9,X21,X10)) = c_Polynomial_Omonom(X9,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X9),X8),X21),X10) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__monom) ).
fof(help_c__COMBB__1,axiom,
! [X100,X101,X68,X102,X5,X15] : hAPP(hAPP(hAPP(c_COMBB(X15,X5,X102),X68),X101),X100) = hAPP(X68,hAPP(X101,X100)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__COMBB__1) ).
fof(fact_poly__power,axiom,
! [X6,X10,X7,X9] :
( class_Rings_Ocomm__semiring__1(X9)
=> hAPP(c_Polynomial_Opoly(X9,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(X9)),X7),X10)),X6) = hAPP(hAPP(c_Power_Opower__class_Opower(X9),hAPP(c_Polynomial_Opoly(X9,X7),X6)),X10) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_poly__power) ).
fof(fact_mod__mult__self3,axiom,
! [X12,X10,X36] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X36),X10)),X12),X10) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,X12,X10),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__mult__self3) ).
fof(fact_of__nat__aux_Osimps_I2_J,axiom,
! [X83,X14,X84,X5] :
( class_Rings_Osemiring__1(X5)
=> c_Nat_Osemiring__1__class_Oof__nat__aux(X5,X84,hAPP(c_Nat_OSuc,X14),X83) = c_Nat_Osemiring__1__class_Oof__nat__aux(X5,X84,X14,hAPP(X84,X83)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_of__nat__aux_Osimps_I2_J) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I2_J,axiom,
! [X12,X8,X9] :
( class_Rings_Ocomm__semiring__1(X9)
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(X9),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X9),X8),X12)),X12) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X9),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X9),X8),c_Groups_Oone__class_Oone(X9))),X12) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I2_J) ).
fof(fact_zdiff__zmult__distrib,axiom,
! [X51,X52,X53] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X53),X52)),X51) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X53),X51)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X52),X51)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zdiff__zmult__distrib) ).
fof(fact_zadd__zmult__distrib,axiom,
! [X51,X52,X53] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X53),X52)),X51) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X53),X51)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X52),X51)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zadd__zmult__distrib) ).
fof(fact_diff__mult__distrib,axiom,
! [X36,X10,X12] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X12),X10)),X36) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X12),X36)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X10),X36)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__mult__distrib) ).
fof(fact_add__mult__distrib,axiom,
! [X36,X10,X12] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X12),X10)),X36) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X12),X36)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X10),X36)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__mult__distrib) ).
fof(fact_power__strict__decreasing,axiom,
! [X8,X87,X10,X9] :
( class_Rings_Olinordered__semidom(X9)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X10,X87)
=> ( c_Orderings_Oord__class_Oless(X9,c_Groups_Ozero__class_Ozero(X9),X8)
=> ( c_Orderings_Oord__class_Oless(X9,X8,c_Groups_Oone__class_Oone(X9))
=> c_Orderings_Oord__class_Oless(X9,hAPP(hAPP(c_Power_Opower__class_Opower(X9),X8),X87),hAPP(hAPP(c_Power_Opower__class_Opower(X9),X8),X10)) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__strict__decreasing) ).
fof(fact_poly__gcd__monic,axiom,
! [X33,X6,X9] :
( class_Fields_Ofield(X9)
=> ( ( ( X6 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X9))
& X33 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X9)) )
=> hAPP(c_Polynomial_Ocoeff(X9,c_Polynomial_Opoly__gcd(X9,X6,X33)),c_Polynomial_Odegree(X9,c_Polynomial_Opoly__gcd(X9,X6,X33))) = c_Groups_Ozero__class_Ozero(X9) )
& ( ~ ( X6 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X9))
& X33 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X9)) )
=> hAPP(c_Polynomial_Ocoeff(X9,c_Polynomial_Opoly__gcd(X9,X6,X33)),c_Polynomial_Odegree(X9,c_Polynomial_Opoly__gcd(X9,X6,X33))) = c_Groups_Oone__class_Oone(X9) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_poly__gcd__monic) ).
fof(fact_zmod__eq__dvd__iff,axiom,
! [X28,X14,X27] :
( c_Divides_Odiv__class_Omod(tc_Int_Oint,X27,X14) = c_Divides_Odiv__class_Omod(tc_Int_Oint,X28,X14)
<=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X14),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X27),X28))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zmod__eq__dvd__iff) ).
fof(fact_add__eq__if,axiom,
! [X10,X12] :
( ( X12 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X12),X10) = X10 )
& ( X12 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X12),X10) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X12),c_Groups_Oone__class_Oone(tc_Nat_Onat))),X10)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__eq__if) ).
fof(fact_mult__less__cancel__left__disj,axiom,
! [X25,X11,X31,X5] :
( class_Rings_Olinordered__ring__strict(X5)
=> ( c_Orderings_Oord__class_Oless(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X31),X11),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X31),X25))
<=> ( ( c_Orderings_Oord__class_Oless(X5,c_Groups_Ozero__class_Ozero(X5),X31)
& c_Orderings_Oord__class_Oless(X5,X11,X25) )
| ( c_Orderings_Oord__class_Oless(X5,X31,c_Groups_Ozero__class_Ozero(X5))
& c_Orderings_Oord__class_Oless(X5,X25,X11) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__less__cancel__left__disj) ).
fof(fact_mult__less__cancel__right__disj,axiom,
! [X25,X31,X11,X5] :
( class_Rings_Olinordered__ring__strict(X5)
=> ( c_Orderings_Oord__class_Oless(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X11),X31),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X25),X31))
<=> ( ( c_Orderings_Oord__class_Oless(X5,c_Groups_Ozero__class_Ozero(X5),X31)
& c_Orderings_Oord__class_Oless(X5,X11,X25) )
| ( c_Orderings_Oord__class_Oless(X5,X31,c_Groups_Ozero__class_Ozero(X5))
& c_Orderings_Oord__class_Oless(X5,X25,X11) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__less__cancel__right__disj) ).
fof(fact_zmod__simps_I2_J,axiom,
! [X23,X21,X8,X9] :
( class_Divides_Osemiring__div(X9)
=> c_Divides_Odiv__class_Omod(X9,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X9),X8),c_Divides_Odiv__class_Omod(X9,X21,X23)),X23) = c_Divides_Odiv__class_Omod(X9,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X9),X8),X21),X23) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zmod__simps_I2_J) ).
fof(fact_mod__diff__right__eq,axiom,
! [X23,X21,X8,X9] :
( class_Divides_Oring__div(X9)
=> c_Divides_Odiv__class_Omod(X9,hAPP(hAPP(c_Groups_Ominus__class_Ominus(X9),X8),X21),X23) = c_Divides_Odiv__class_Omod(X9,hAPP(hAPP(c_Groups_Ominus__class_Ominus(X9),X8),c_Divides_Odiv__class_Omod(X9,X21,X23)),X23) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__diff__right__eq) ).
fof(fact_mod__mult__right__eq,axiom,
! [X23,X21,X8,X9] :
( class_Divides_Osemiring__div(X9)
=> c_Divides_Odiv__class_Omod(X9,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X9),X8),X21),X23) = c_Divides_Odiv__class_Omod(X9,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X9),X8),c_Divides_Odiv__class_Omod(X9,X21,X23)),X23) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__mult__right__eq) ).
fof(fact_mod__add__right__eq,axiom,
! [X23,X21,X8,X9] :
( class_Divides_Osemiring__div(X9)
=> c_Divides_Odiv__class_Omod(X9,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X9),X8),X21),X23) = c_Divides_Odiv__class_Omod(X9,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X9),X8),c_Divides_Odiv__class_Omod(X9,X21,X23)),X23) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__add__right__eq) ).
fof(fact_div__mult__self2,axiom,
! [X23,X8,X21,X9] :
( class_Divides_Osemiring__div(X9)
=> ( X21 != c_Groups_Ozero__class_Ozero(X9)
=> c_Divides_Odiv__class_Odiv(X9,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X9),X8),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X9),X21),X23)),X21) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X9),X23),c_Divides_Odiv__class_Odiv(X9,X8,X21)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_div__mult__self2) ).
fof(fact_div__mult__self1,axiom,
! [X23,X8,X21,X9] :
( class_Divides_Osemiring__div(X9)
=> ( X21 != c_Groups_Ozero__class_Ozero(X9)
=> c_Divides_Odiv__class_Odiv(X9,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X9),X8),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X9),X23),X21)),X21) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X9),X23),c_Divides_Odiv__class_Odiv(X9,X8,X21)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_div__mult__self1) ).
fof(fact_mod__mult__mult2,axiom,
! [X21,X23,X8,X9] :
( class_Divides_Osemiring__div(X9)
=> c_Divides_Odiv__class_Omod(X9,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X9),X8),X23),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X9),X21),X23)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X9),c_Divides_Odiv__class_Omod(X9,X8,X21)),X23) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__mult__mult2) ).
fof(fact_dvd__reduce,axiom,
! [X14,X39] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X39),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X14),X39)))
<=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X39),X14)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__reduce) ).
fof(fact_minus__dvd__iff,axiom,
! [X28,X27,X5] :
( class_Rings_Ocomm__ring__1(X5)
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X5),hAPP(c_Groups_Ouminus__class_Ouminus(X5),X27)),X28))
<=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X5),X27),X28)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__dvd__iff) ).
fof(fact_smult__pCons,axiom,
! [X7,X21,X8,X9] :
( class_Rings_Ocomm__semiring__0(X9)
=> hAPP(hAPP(c_Polynomial_Osmult(X9),X8),hAPP(hAPP(c_Polynomial_OpCons(X9),X21),X7)) = hAPP(hAPP(c_Polynomial_OpCons(X9),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X9),X8),X21)),hAPP(hAPP(c_Polynomial_Osmult(X9),X8),X7)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_smult__pCons) ).
fof(fact_mult_Odiff__right,axiom,
! [X43,X21,X8,X9] :
( class_RealVector_Oreal__normed__algebra(X9)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X9),X8),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X9),X21),X43)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(X9),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X9),X8),X21)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X9),X8),X43)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult_Odiff__right) ).
fof(fact_mult__right_Odiff,axiom,
! [X33,X6,X44,X9] :
( class_RealVector_Oreal__normed__algebra(X9)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X9),X44),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X9),X6),X33)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(X9),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X9),X44),X6)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X9),X44),X33)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__right_Odiff) ).
fof(fact_mult__right_Oadd,axiom,
! [X33,X6,X44,X9] :
( class_RealVector_Oreal__normed__algebra(X9)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X9),X44),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X9),X6),X33)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X9),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X9),X44),X6)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X9),X44),X33)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__right_Oadd) ).
fof(fact_mult_Oadd__right,axiom,
! [X43,X21,X8,X9] :
( class_RealVector_Oreal__normed__algebra(X9)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X9),X8),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X9),X21),X43)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X9),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X9),X8),X21)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X9),X8),X43)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult_Oadd__right) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I34_J,axiom,
! [X32,X33,X6,X9] :
( class_Rings_Ocomm__semiring__1(X9)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X9),X6),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X9),X33),X32)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X9),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X9),X6),X33)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X9),X6),X32)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I34_J) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J,axiom,
! [X18,X19,X20,X9] :
( class_Rings_Ocomm__semiring__1(X9)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X9),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X9),X20),X19)),X18) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X9),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X9),X20),X18)),X19) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J,axiom,
! [X23,X21,X8,X9] :
( class_Rings_Ocomm__semiring__1(X9)
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(X9),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X9),X8),X21)),X23) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X9),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X9),X8),X23)),X21) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J) ).
fof(fact_int__power__div__base,axiom,
! [X36,X12] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X12)
=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X36)
=> c_Divides_Odiv__class_Odiv(tc_Int_Oint,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X36),X12),X36) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X36),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X12),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_int__power__div__base) ).
fof(fact_nat__power__less__imp__less,axiom,
! [X10,X12,X42] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X42)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X42),X12),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X42),X10))
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X12,X10) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__power__less__imp__less) ).
fof(fact_nat__mult__less__cancel1,axiom,
! [X14,X35,X39] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X39)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X39),X35),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X39),X14))
<=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X35,X14) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__mult__less__cancel1) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I26_J,axiom,
! [X13,X7,X6,X9] :
( class_Rings_Ocomm__semiring__1(X9)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X9),hAPP(hAPP(c_Power_Opower__class_Opower(X9),X6),X7)),hAPP(hAPP(c_Power_Opower__class_Opower(X9),X6),X13)) = hAPP(hAPP(c_Power_Opower__class_Opower(X9),X6),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X7),X13)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I26_J) ).
fof(fact_power__add,axiom,
! [X10,X12,X8,X9] :
( class_Groups_Omonoid__mult(X9)
=> hAPP(hAPP(c_Power_Opower__class_Opower(X9),X8),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X12),X10)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X9),hAPP(hAPP(c_Power_Opower__class_Opower(X9),X8),X12)),hAPP(hAPP(c_Power_Opower__class_Opower(X9),X8),X10)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__add) ).
fof(fact_pos__divide__less__eq,axiom,
! [X11,X25,X31,X5] :
( class_Fields_Olinordered__field(X5)
=> ( c_Orderings_Oord__class_Oless(X5,c_Groups_Ozero__class_Ozero(X5),X31)
=> ( c_Orderings_Oord__class_Oless(X5,hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X5),X25),X31),X11)
<=> c_Orderings_Oord__class_Oless(X5,X25,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X11),X31)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pos__divide__less__eq) ).
fof(fact_mult__imp__div__pos__less,axiom,
! [X32,X6,X33,X9] :
( class_Fields_Olinordered__field(X9)
=> ( c_Orderings_Oord__class_Oless(X9,c_Groups_Ozero__class_Ozero(X9),X33)
=> ( c_Orderings_Oord__class_Oless(X9,X6,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X9),X32),X33))
=> c_Orderings_Oord__class_Oless(X9,hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X9),X6),X33),X32) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__imp__div__pos__less) ).
fof(fact_pos__less__divide__eq,axiom,
! [X25,X11,X31,X5] :
( class_Fields_Olinordered__field(X5)
=> ( c_Orderings_Oord__class_Oless(X5,c_Groups_Ozero__class_Ozero(X5),X31)
=> ( c_Orderings_Oord__class_Oless(X5,X11,hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X5),X25),X31))
<=> c_Orderings_Oord__class_Oless(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X11),X31),X25) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pos__less__divide__eq) ).
fof(fact_neg__divide__less__eq,axiom,
! [X11,X25,X31,X5] :
( class_Fields_Olinordered__field(X5)
=> ( c_Orderings_Oord__class_Oless(X5,X31,c_Groups_Ozero__class_Ozero(X5))
=> ( c_Orderings_Oord__class_Oless(X5,hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X5),X25),X31),X11)
<=> c_Orderings_Oord__class_Oless(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X11),X31),X25) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_neg__divide__less__eq) ).
fof(fact_mult__imp__less__div__pos,axiom,
! [X6,X32,X33,X9] :
( class_Fields_Olinordered__field(X9)
=> ( c_Orderings_Oord__class_Oless(X9,c_Groups_Ozero__class_Ozero(X9),X33)
=> ( c_Orderings_Oord__class_Oless(X9,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X9),X32),X33),X6)
=> c_Orderings_Oord__class_Oless(X9,X32,hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X9),X6),X33)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__imp__less__div__pos) ).
fof(fact_neg__less__divide__eq,axiom,
! [X25,X11,X31,X5] :
( class_Fields_Olinordered__field(X5)
=> ( c_Orderings_Oord__class_Oless(X5,X31,c_Groups_Ozero__class_Ozero(X5))
=> ( c_Orderings_Oord__class_Oless(X5,X11,hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X5),X25),X31))
<=> c_Orderings_Oord__class_Oless(X5,X25,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X11),X31)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_neg__less__divide__eq) ).
fof(fact_add__scale__eq__noteq,axiom,
! [X22,X23,X21,X8,X34,X9] :
( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X9)
=> ( X34 != c_Groups_Ozero__class_Ozero(X9)
=> ( ( X8 = X21
& X23 != X22 )
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(X9),X8),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X9),X34),X23)) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(X9),X21),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X9),X34),X22)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__scale__eq__noteq) ).
fof(fact_zdiff__zmod__right,axiom,
! [X12,X33,X6] : c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X6),c_Divides_Odiv__class_Omod(tc_Int_Oint,X33,X12)),X12) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X6),X33),X12),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zdiff__zmod__right) ).
fof(fact_zmod__simps_I3_J,axiom,
! [X23,X21,X8] : c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X8),c_Divides_Odiv__class_Omod(tc_Int_Oint,X21,X23)),X23) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X8),X21),X23),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zmod__simps_I3_J) ).
fof(fact_zmod__zmult1__eq,axiom,
! [X23,X21,X8] : c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X8),X21),X23) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X8),c_Divides_Odiv__class_Omod(tc_Int_Oint,X21,X23)),X23),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zmod__zmult1__eq) ).
fof(fact_mult__smult__left,axiom,
! [X13,X7,X8,X9] :
( class_Rings_Ocomm__semiring__0(X9)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X9)),hAPP(hAPP(c_Polynomial_Osmult(X9),X8),X7)),X13) = hAPP(hAPP(c_Polynomial_Osmult(X9),X8),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X9)),X7),X13)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__smult__left) ).
fof(fact_div__mult__swap,axiom,
! [X8,X21,X23,X9] :
( class_Divides_Osemiring__div(X9)
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X9),X23),X21))
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X9),X8),c_Divides_Odiv__class_Odiv(X9,X21,X23)) = c_Divides_Odiv__class_Odiv(X9,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X9),X8),X21),X23) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_div__mult__swap) ).
fof(fact_mod__mult__distrib,axiom,
! [X36,X10,X12] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X12,X10)),X36) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X12),X36),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X10),X36)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__mult__distrib) ).
fof(fact_dvd__mult2,axiom,
! [X23,X21,X8,X9] :
( class_Rings_Ocomm__semiring__1(X9)
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X9),X8),X21))
=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X9),X8),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X9),X21),X23))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__mult2) ).
fof(fact_dvd__mult,axiom,
! [X21,X23,X8,X9] :
( class_Rings_Ocomm__semiring__1(X9)
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X9),X8),X23))
=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X9),X8),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X9),X21),X23))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__mult) ).
fof(fact_power__one__over,axiom,
! [X10,X8,X9] :
( class_Fields_Ofield__inverse__zero(X9)
=> hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X9),c_Groups_Oone__class_Oone(X9)),hAPP(hAPP(c_Power_Opower__class_Opower(X9),X8),X10)) = hAPP(hAPP(c_Power_Opower__class_Opower(X9),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X9),c_Groups_Oone__class_Oone(X9)),X8)),X10) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__one__over) ).
fof(fact_synthetic__div__pCons,axiom,
! [X23,X7,X8,X9] :
( class_Rings_Ocomm__semiring__0(X9)
=> c_Polynomial_Osynthetic__div(X9,hAPP(hAPP(c_Polynomial_OpCons(X9),X8),X7),X23) = hAPP(hAPP(c_Polynomial_OpCons(X9),hAPP(c_Polynomial_Opoly(X9,X7),X23)),c_Polynomial_Osynthetic__div(X9,X7,X23)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_synthetic__div__pCons) ).
fof(fact_expand__poly__eq,axiom,
! [X24,X4,X5] :
( class_Groups_Ozero(X5)
=> ( X4 = X24
<=> ! [X49] : hAPP(c_Polynomial_Ocoeff(X5,X4),X49) = hAPP(c_Polynomial_Ocoeff(X5,X24),X49) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_expand__poly__eq) ).
fof(fact_power__gt1__lemma,axiom,
! [X10,X8,X9] :
( class_Rings_Olinordered__semidom(X9)
=> ( c_Orderings_Oord__class_Oless(X9,c_Groups_Oone__class_Oone(X9),X8)
=> c_Orderings_Oord__class_Oless(X9,c_Groups_Oone__class_Oone(X9),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X9),X8),hAPP(hAPP(c_Power_Opower__class_Opower(X9),X8),X10))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__gt1__lemma) ).
fof(fact_add__less__cancel__right,axiom,
! [X25,X31,X11,X5] :
( class_Groups_Oordered__ab__semigroup__add__imp__le(X5)
=> ( c_Orderings_Oord__class_Oless(X5,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X11),X31),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X25),X31))
<=> c_Orderings_Oord__class_Oless(X5,X11,X25) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__less__cancel__right) ).
fof(fact_add__less__imp__less__right,axiom,
! [X21,X23,X8,X9] :
( class_Groups_Oordered__ab__semigroup__add__imp__le(X9)
=> ( c_Orderings_Oord__class_Oless(X9,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X9),X8),X23),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X9),X21),X23))
=> c_Orderings_Oord__class_Oless(X9,X8,X21) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__less__imp__less__right) ).
fof(fact_add__less__cancel__left,axiom,
! [X25,X11,X31,X5] :
( class_Groups_Oordered__ab__semigroup__add__imp__le(X5)
=> ( c_Orderings_Oord__class_Oless(X5,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X31),X11),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X31),X25))
<=> c_Orderings_Oord__class_Oless(X5,X11,X25) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__less__cancel__left) ).
fof(fact_add__less__imp__less__left,axiom,
! [X21,X8,X23,X9] :
( class_Groups_Oordered__ab__semigroup__add__imp__le(X9)
=> ( c_Orderings_Oord__class_Oless(X9,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X9),X23),X8),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X9),X23),X21))
=> c_Orderings_Oord__class_Oless(X9,X8,X21) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__less__imp__less__left) ).
fof(fact_minus__apply,axiom,
! [X27,X58,X59,X15,X5] :
( class_Groups_Ominus(X5)
=> hAPP(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X15,X5)),X59),X58),X27) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(X5),hAPP(X59,X27)),hAPP(X58,X27)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__apply) ).
fof(fact_fun__diff__def,axiom,
! [X27,X58,X59,X15,X5] :
( class_Groups_Ominus(X5)
=> hAPP(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X15,X5)),X59),X58),X27) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(X5),hAPP(X59,X27)),hAPP(X58,X27)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fun__diff__def) ).
fof(fact_Nat__Transfer_Otransfer__int__nat__relations_I4_J,axiom,
! [X28,X27] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,X27)),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,X28)))
<=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X27),X28)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__int__nat__relations_I4_J) ).
fof(fact_zdvd__int,axiom,
! [X28,X27] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X27),X28))
<=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,X27)),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,X28))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zdvd__int) ).
fof(fact_zpower__zadd__distrib,axiom,
! [X32,X33,X6] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X6),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X33),X32)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X6),X33)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X6),X32)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zpower__zadd__distrib) ).
fof(fact_zdiff__zmult__distrib2,axiom,
! [X52,X53,X51] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X51),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X53),X52)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X51),X53)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X51),X52)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zdiff__zmult__distrib2) ).
fof(fact_zadd__zmult__distrib2,axiom,
! [X52,X53,X51] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X51),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X53),X52)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X51),X53)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X51),X52)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zadd__zmult__distrib2) ).
fof(fact_diff__mult__distrib2,axiom,
! [X10,X12,X36] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X36),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X12),X10)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X36),X12)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X36),X10)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__mult__distrib2) ).
fof(fact_add__mult__distrib2,axiom,
! [X10,X12,X36] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X36),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X12),X10)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X36),X12)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X36),X10)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__mult__distrib2) ).
fof(fact_diff__commute,axiom,
! [X36,X40,X42] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X42),X40)),X36) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X42),X36)),X40),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__commute) ).
fof(fact_dvd__trans,axiom,
! [X23,X21,X8,X9] :
( class_Rings_Ocomm__semiring__1(X9)
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X9),X8),X21))
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X9),X21),X23))
=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X9),X8),X23)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__trans) ).
fof(fact_realpow__two__disj,axiom,
! [X28,X27,X5] :
( class_Rings_Oidom(X5)
=> ( hAPP(hAPP(c_Power_Opower__class_Opower(X5),X27),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = hAPP(hAPP(c_Power_Opower__class_Opower(X5),X28),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))
<=> ( X27 = X28
| X27 = hAPP(c_Groups_Ouminus__class_Ouminus(X5),X28) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_realpow__two__disj) ).
fof(fact_divide__strict__right__mono,axiom,
! [X23,X21,X8,X9] :
( class_Fields_Olinordered__field(X9)
=> ( c_Orderings_Oord__class_Oless(X9,X8,X21)
=> ( c_Orderings_Oord__class_Oless(X9,c_Groups_Ozero__class_Ozero(X9),X23)
=> c_Orderings_Oord__class_Oless(X9,hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X9),X8),X23),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X9),X21),X23)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide__strict__right__mono) ).
fof(fact_mult__strict__right__mono,axiom,
! [X23,X21,X8,X9] :
( class_Rings_Olinordered__semiring__strict(X9)
=> ( c_Orderings_Oord__class_Oless(X9,X8,X21)
=> ( c_Orderings_Oord__class_Oless(X9,c_Groups_Ozero__class_Ozero(X9),X23)
=> c_Orderings_Oord__class_Oless(X9,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X9),X8),X23),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X9),X21),X23)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__strict__right__mono) ).
fof(fact_mult__strict__left__mono,axiom,
! [X23,X21,X8,X9] :
( class_Rings_Olinordered__semiring__strict(X9)
=> ( c_Orderings_Oord__class_Oless(X9,X8,X21)
=> ( c_Orderings_Oord__class_Oless(X9,c_Groups_Ozero__class_Ozero(X9),X23)
=> c_Orderings_Oord__class_Oless(X9,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X9),X23),X8),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X9),X23),X21)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__strict__left__mono) ).
fof(fact_comm__mult__strict__left__mono,axiom,
! [X23,X21,X8,X9] :
( class_Rings_Olinordered__comm__semiring__strict(X9)
=> ( c_Orderings_Oord__class_Oless(X9,X8,X21)
=> ( c_Orderings_Oord__class_Oless(X9,c_Groups_Ozero__class_Ozero(X9),X23)
=> c_Orderings_Oord__class_Oless(X9,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X9),X23),X8),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X9),X23),X21)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__mult__strict__left__mono) ).
fof(fact_divide__strict__right__mono__neg,axiom,
! [X23,X8,X21,X9] :
( class_Fields_Olinordered__field(X9)
=> ( c_Orderings_Oord__class_Oless(X9,X21,X8)
=> ( c_Orderings_Oord__class_Oless(X9,X23,c_Groups_Ozero__class_Ozero(X9))
=> c_Orderings_Oord__class_Oless(X9,hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X9),X8),X23),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X9),X21),X23)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide__strict__right__mono__neg) ).
fof(fact_mult__strict__right__mono__neg,axiom,
! [X23,X8,X21,X9] :
( class_Rings_Olinordered__ring__strict(X9)
=> ( c_Orderings_Oord__class_Oless(X9,X21,X8)
=> ( c_Orderings_Oord__class_Oless(X9,X23,c_Groups_Ozero__class_Ozero(X9))
=> c_Orderings_Oord__class_Oless(X9,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X9),X8),X23),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X9),X21),X23)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__strict__right__mono__neg) ).
fof(fact_mult__strict__left__mono__neg,axiom,
! [X23,X8,X21,X9] :
( class_Rings_Olinordered__ring__strict(X9)
=> ( c_Orderings_Oord__class_Oless(X9,X21,X8)
=> ( c_Orderings_Oord__class_Oless(X9,X23,c_Groups_Ozero__class_Ozero(X9))
=> c_Orderings_Oord__class_Oless(X9,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X9),X23),X8),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X9),X23),X21)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__strict__left__mono__neg) ).
fof(fact_power__strict__increasing,axiom,
! [X8,X87,X10,X9] :
( class_Rings_Olinordered__semidom(X9)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X10,X87)
=> ( c_Orderings_Oord__class_Oless(X9,c_Groups_Oone__class_Oone(X9),X8)
=> c_Orderings_Oord__class_Oless(X9,hAPP(hAPP(c_Power_Opower__class_Opower(X9),X8),X10),hAPP(hAPP(c_Power_Opower__class_Opower(X9),X8),X87)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__strict__increasing) ).
fof(fact_uminus__dvd__conv_I1_J,axiom,
! [X64,X30] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X30),X64))
<=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X30)),X64)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_uminus__dvd__conv_I1_J) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I3_J,axiom,
! [X8,X12,X9] :
( class_Rings_Ocomm__semiring__1(X9)
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(X9),X12),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X9),X8),X12)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X9),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X9),X8),c_Groups_Oone__class_Oone(X9))),X12) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I3_J) ).
fof(fact_dvd__div__mult__self,axiom,
! [X21,X8,X9] :
( class_Divides_Osemiring__div(X9)
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X9),X8),X21))
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X9),c_Divides_Odiv__class_Odiv(X9,X21,X8)),X8) = X21 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__div__mult__self) ).
fof(fact_div__add__self1,axiom,
! [X8,X21,X9] :
( class_Divides_Osemiring__div(X9)
=> ( X21 != c_Groups_Ozero__class_Ozero(X9)
=> c_Divides_Odiv__class_Odiv(X9,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X9),X21),X8),X21) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X9),c_Divides_Odiv__class_Odiv(X9,X8,X21)),c_Groups_Oone__class_Oone(X9)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_div__add__self1) ).
fof(fact_div__add__self2,axiom,
! [X8,X21,X9] :
( class_Divides_Osemiring__div(X9)
=> ( X21 != c_Groups_Ozero__class_Ozero(X9)
=> c_Divides_Odiv__class_Odiv(X9,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X9),X8),X21),X21) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X9),c_Divides_Odiv__class_Odiv(X9,X8,X21)),c_Groups_Oone__class_Oone(X9)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_div__add__self2) ).
fof(fact_add__strict__mono,axiom,
! [X22,X23,X21,X8,X9] :
( class_Groups_Oordered__cancel__ab__semigroup__add(X9)
=> ( c_Orderings_Oord__class_Oless(X9,X8,X21)
=> ( c_Orderings_Oord__class_Oless(X9,X23,X22)
=> c_Orderings_Oord__class_Oless(X9,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X9),X8),X23),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X9),X21),X22)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__strict__mono) ).
fof(fact_degree__mod__less,axiom,
! [X6,X33,X9] :
( class_Fields_Ofield(X9)
=> ( X33 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X9))
=> ( c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(X9),X6,X33) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X9))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(X9,c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(X9),X6,X33)),c_Polynomial_Odegree(X9,X33)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_degree__mod__less) ).
fof(fact_one__less__mult,axiom,
! [X12,X10] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X10)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X12)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X12),X10)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_one__less__mult) ).
fof(fact_synthetic__div__unique,axiom,
! [X34,X13,X23,X7,X9] :
( class_Rings_Ocomm__semiring__0(X9)
=> ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X9)),X7),hAPP(hAPP(c_Polynomial_Osmult(X9),X23),X13)) = hAPP(hAPP(c_Polynomial_OpCons(X9),X34),X13)
=> ( X34 = hAPP(c_Polynomial_Opoly(X9,X7),X23)
& X13 = c_Polynomial_Osynthetic__div(X9,X7,X23) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_synthetic__div__unique) ).
fof(fact_mod__mult__mult1,axiom,
! [X21,X8,X23,X9] :
( class_Divides_Osemiring__div(X9)
=> c_Divides_Odiv__class_Omod(X9,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X9),X23),X8),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X9),X23),X21)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X9),X23),c_Divides_Odiv__class_Omod(X9,X8,X21)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__mult__mult1) ).
fof(fact_mult__divide__mult__cancel__left,axiom,
! [X21,X8,X23,X9] :
( class_Fields_Ofield__inverse__zero(X9)
=> ( X23 != c_Groups_Ozero__class_Ozero(X9)
=> hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X9),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X9),X23),X8)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X9),X23),X21)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X9),X8),X21) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__divide__mult__cancel__left) ).
fof(fact_mult__divide__mult__cancel__right,axiom,
! [X21,X8,X23,X9] :
( class_Fields_Ofield__inverse__zero(X9)
=> ( X23 != c_Groups_Ozero__class_Ozero(X9)
=> hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X9),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X9),X8),X23)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X9),X21),X23)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X9),X8),X21) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__divide__mult__cancel__right) ).
fof(fact_mult__less__cancel1,axiom,
! [X14,X35,X39] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X39),X35),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X39),X14))
<=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X39)
& c_Orderings_Oord__class_Oless(tc_Nat_Onat,X35,X14) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__less__cancel1) ).
fof(fact_mult__less__cancel2,axiom,
! [X14,X39,X35] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X35),X39),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X14),X39))
<=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X39)
& c_Orderings_Oord__class_Oless(tc_Nat_Onat,X35,X14) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__less__cancel2) ).
fof(fact_mod__mult__self2,axiom,
! [X23,X21,X8,X9] :
( class_Divides_Osemiring__div(X9)
=> c_Divides_Odiv__class_Omod(X9,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X9),X8),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X9),X21),X23)),X21) = c_Divides_Odiv__class_Omod(X9,X8,X21) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__mult__self2) ).
fof(fact_mod__mult__self1,axiom,
! [X21,X23,X8,X9] :
( class_Divides_Osemiring__div(X9)
=> c_Divides_Odiv__class_Omod(X9,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X9),X8),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X9),X23),X21)),X21) = c_Divides_Odiv__class_Omod(X9,X8,X21) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__mult__self1) ).
fof(fact_zero__less__mult__pos2,axiom,
! [X8,X21,X9] :
( class_Rings_Olinordered__semiring__strict(X9)
=> ( c_Orderings_Oord__class_Oless(X9,c_Groups_Ozero__class_Ozero(X9),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X9),X21),X8))
=> ( c_Orderings_Oord__class_Oless(X9,c_Groups_Ozero__class_Ozero(X9),X8)
=> c_Orderings_Oord__class_Oless(X9,c_Groups_Ozero__class_Ozero(X9),X21) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__less__mult__pos2) ).
fof(fact_zero__less__mult__pos,axiom,
! [X21,X8,X9] :
( class_Rings_Olinordered__semiring__strict(X9)
=> ( c_Orderings_Oord__class_Oless(X9,c_Groups_Ozero__class_Ozero(X9),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X9),X8),X21))
=> ( c_Orderings_Oord__class_Oless(X9,c_Groups_Ozero__class_Ozero(X9),X8)
=> c_Orderings_Oord__class_Oless(X9,c_Groups_Ozero__class_Ozero(X9),X21) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__less__mult__pos) ).
fof(fact_nat__add__left__cancel__less,axiom,
! [X14,X35,X39] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X39),X35),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X39),X14))
<=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X35,X14) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__add__left__cancel__less) ).
fof(fact_power__commutes,axiom,
! [X10,X8,X9] :
( class_Groups_Omonoid__mult(X9)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X9),hAPP(hAPP(c_Power_Opower__class_Opower(X9),X8),X10)),X8) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X9),X8),hAPP(hAPP(c_Power_Opower__class_Opower(X9),X8),X10)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__commutes) ).
fof(fact_ab__semigroup__mult__class_Omult__ac_I1_J,axiom,
! [X23,X21,X8,X9] :
( class_Groups_Oab__semigroup__mult(X9)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X9),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X9),X8),X21)),X23) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X9),X8),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X9),X21),X23)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ab__semigroup__mult__class_Omult__ac_I1_J) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J,axiom,
! [X18,X19,X20,X9] :
( class_Rings_Ocomm__semiring__1(X9)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X9),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X9),X20),X19)),X18) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X9),X20),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X9),X19),X18)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J) ).
fof(fact_ab__semigroup__add__class_Oadd__ac_I1_J,axiom,
! [X23,X21,X8,X9] :
( class_Groups_Oab__semigroup__add(X9)
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(X9),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X9),X8),X21)),X23) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X9),X8),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X9),X21),X23)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ab__semigroup__add__class_Oadd__ac_I1_J) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J,axiom,
! [X23,X21,X8,X9] :
( class_Rings_Ocomm__semiring__1(X9)
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(X9),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X9),X8),X21)),X23) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X9),X8),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X9),X21),X23)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J) ).
fof(fact_smult__smult,axiom,
! [X7,X21,X8,X9] :
( class_Rings_Ocomm__semiring__0(X9)
=> hAPP(hAPP(c_Polynomial_Osmult(X9),X8),hAPP(hAPP(c_Polynomial_Osmult(X9),X21),X7)) = hAPP(hAPP(c_Polynomial_Osmult(X9),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X9),X8),X21)),X7) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_smult__smult) ).
fof(fact_times__divide__eq__right,axiom,
! [X23,X21,X8,X9] :
( class_Rings_Odivision__ring(X9)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X9),X8),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X9),X21),X23)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X9),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X9),X8),X21)),X23) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_times__divide__eq__right) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J,axiom,
! [X17,X18,X20,X9] :
( class_Rings_Ocomm__semiring__1(X9)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X9),X20),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X9),X18),X17)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X9),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X9),X20),X18)),X17) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J,axiom,
! [X22,X23,X8,X9] :
( class_Rings_Ocomm__semiring__1(X9)
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(X9),X8),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X9),X23),X22)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X9),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X9),X8),X23)),X22) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J) ).
fof(fact_poly__monom,axiom,
! [X6,X10,X8,X9] :
( class_Rings_Ocomm__semiring__1(X9)
=> hAPP(c_Polynomial_Opoly(X9,c_Polynomial_Omonom(X9,X8,X10)),X6) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X9),X8),hAPP(hAPP(c_Power_Opower__class_Opower(X9),X6),X10)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_poly__monom) ).
fof(fact_realpow__num__eq__if,axiom,
! [X12,X10,X9] :
( class_Power_Opower(X9)
=> ( ( X10 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> hAPP(hAPP(c_Power_Opower__class_Opower(X9),X12),X10) = c_Groups_Oone__class_Oone(X9) )
& ( X10 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> hAPP(hAPP(c_Power_Opower__class_Opower(X9),X12),X10) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X9),X12),hAPP(hAPP(c_Power_Opower__class_Opower(X9),X12),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X10),c_Groups_Oone__class_Oone(tc_Nat_Onat)))) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_realpow__num__eq__if) ).
fof(fact_power__Suc__less__one,axiom,
! [X10,X8,X9] :
( class_Rings_Olinordered__semidom(X9)
=> ( c_Orderings_Oord__class_Oless(X9,c_Groups_Ozero__class_Ozero(X9),X8)
=> ( c_Orderings_Oord__class_Oless(X9,X8,c_Groups_Oone__class_Oone(X9))
=> c_Orderings_Oord__class_Oless(X9,hAPP(hAPP(c_Power_Opower__class_Opower(X9),X8),hAPP(c_Nat_OSuc,X10)),c_Groups_Oone__class_Oone(X9)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__Suc__less__one) ).
fof(fact_dvd__power,axiom,
! [X6,X10,X9] :
( class_Rings_Ocomm__semiring__1(X9)
=> ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X10)
| X6 = c_Groups_Oone__class_Oone(X9) )
=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X9),X6),hAPP(hAPP(c_Power_Opower__class_Opower(X9),X6),X10))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__power) ).
fof(fact_power__mult,axiom,
! [X10,X12,X8,X9] :
( class_Groups_Omonoid__mult(X9)
=> hAPP(hAPP(c_Power_Opower__class_Opower(X9),X8),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X12),X10)) = hAPP(hAPP(c_Power_Opower__class_Opower(X9),hAPP(hAPP(c_Power_Opower__class_Opower(X9),X8),X12)),X10) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__mult) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I31_J,axiom,
! [X13,X7,X6,X9] :
( class_Rings_Ocomm__semiring__1(X9)
=> hAPP(hAPP(c_Power_Opower__class_Opower(X9),hAPP(hAPP(c_Power_Opower__class_Opower(X9),X6),X7)),X13) = hAPP(hAPP(c_Power_Opower__class_Opower(X9),X6),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X7),X13)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I31_J) ).
fof(fact_mod__minus__eq,axiom,
! [X21,X8,X9] :
( class_Divides_Oring__div(X9)
=> c_Divides_Odiv__class_Omod(X9,hAPP(c_Groups_Ouminus__class_Ouminus(X9),X8),X21) = c_Divides_Odiv__class_Omod(X9,hAPP(c_Groups_Ouminus__class_Ouminus(X9),c_Divides_Odiv__class_Omod(X9,X8,X21)),X21) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__minus__eq) ).
fof(fact_zmult__zless__mono2,axiom,
! [X36,X40,X42] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X42,X40)
=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X36)
=> c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X36),X42),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X36),X40)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zmult__zless__mono2) ).
fof(fact_mult__less__mono1,axiom,
! [X36,X40,X42] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X42,X40)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X36)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X42),X36),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X40),X36)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__less__mono1) ).
fof(fact_mult__less__mono2,axiom,
! [X36,X40,X42] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X42,X40)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X36)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X36),X42),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X36),X40)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__less__mono2) ).
fof(fact_poly__offset__poly,axiom,
! [X6,X48,X7,X9] :
( class_Rings_Ocomm__semiring__0(X9)
=> hAPP(c_Polynomial_Opoly(X9,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X9,X7,X48)),X6) = hAPP(c_Polynomial_Opoly(X9,X7),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X9),X48),X6)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_poly__offset__poly) ).
fof(fact_n__less__n__mult__m,axiom,
! [X12,X10] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X10)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X12)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X10,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X10),X12)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_n__less__n__mult__m) ).
fof(fact_n__less__m__mult__n,axiom,
! [X12,X10] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X10)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X12)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X10,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X12),X10)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_n__less__m__mult__n) ).
fof(fact_dvd__minus__iff,axiom,
! [X28,X27,X5] :
( class_Rings_Ocomm__ring__1(X5)
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X5),X27),hAPP(c_Groups_Ouminus__class_Ouminus(X5),X28)))
<=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X5),X27),X28)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__minus__iff) ).
fof(fact_diff__less__mono2,axiom,
! [X76,X10,X12] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X12,X10)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X12,X76)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X76),X10),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X76),X12)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__less__mono2) ).
fof(fact_add__less__mono,axiom,
! [X76,X36,X40,X42] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X42,X40)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X36,X76)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X42),X36),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X40),X76)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__less__mono) ).
fof(fact_odd__nonzero,axiom,
! [X32] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X32)),X32) != c_Groups_Ozero__class_Ozero(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_odd__nonzero) ).
fof(fact_neg__imp__zdiv__neg__iff,axiom,
! [X11,X25] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X25,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X11,X25),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
<=> c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X11) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_neg__imp__zdiv__neg__iff) ).
fof(fact_pos__imp__zdiv__neg__iff,axiom,
! [X11,X25] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X25)
=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X11,X25),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
<=> c_Orderings_Oord__class_Oless(tc_Int_Oint,X11,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pos__imp__zdiv__neg__iff) ).
fof(fact_dvd__neg__div,axiom,
! [X6,X33,X9] :
( class_Divides_Oring__div(X9)
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X9),X33),X6))
=> c_Divides_Odiv__class_Odiv(X9,hAPP(c_Groups_Ouminus__class_Ouminus(X9),X6),X33) = hAPP(c_Groups_Ouminus__class_Ouminus(X9),c_Divides_Odiv__class_Odiv(X9,X6,X33)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__neg__div) ).
fof(fact_dvd__div__neg,axiom,
! [X6,X33,X9] :
( class_Divides_Oring__div(X9)
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X9),X33),X6))
=> c_Divides_Odiv__class_Odiv(X9,X6,hAPP(c_Groups_Ouminus__class_Ouminus(X9),X33)) = hAPP(c_Groups_Ouminus__class_Ouminus(X9),c_Divides_Odiv__class_Odiv(X9,X6,X33)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__div__neg) ).
fof(fact_zmod__zminus2__eq__if,axiom,
! [X21,X8] :
( ( c_Divides_Odiv__class_Omod(tc_Int_Oint,X8,X21) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
=> c_Divides_Odiv__class_Omod(tc_Int_Oint,X8,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X21)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
& ( c_Divides_Odiv__class_Omod(tc_Int_Oint,X8,X21) != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
=> c_Divides_Odiv__class_Omod(tc_Int_Oint,X8,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X21)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,X8,X21)),X21) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zmod__zminus2__eq__if) ).
fof(fact_dvd_Oorder__trans,axiom,
! [X32,X33,X6] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X6),X33))
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X33),X32))
=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X6),X32)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd_Oorder__trans) ).
fof(fact_mod__mod__cancel,axiom,
! [X8,X21,X23,X9] :
( class_Divides_Osemiring__div(X9)
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X9),X23),X21))
=> c_Divides_Odiv__class_Omod(X9,c_Divides_Odiv__class_Omod(X9,X8,X21),X23) = c_Divides_Odiv__class_Omod(X9,X8,X23) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__mod__cancel) ).
fof(fact_mult__smult__right,axiom,
! [X13,X8,X7,X9] :
( class_Rings_Ocomm__semiring__0(X9)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X9)),X7),hAPP(hAPP(c_Polynomial_Osmult(X9),X8),X13)) = hAPP(hAPP(c_Polynomial_Osmult(X9),X8),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X9)),X7),X13)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__smult__right) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J,axiom,
! [X12,X9] :
( class_Rings_Ocomm__semiring__1(X9)
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(X9),X12),X12) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X9),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X9),c_Groups_Oone__class_Oone(X9)),c_Groups_Oone__class_Oone(X9))),X12) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J) ).
fof(fact_zdiv__zmult2__eq,axiom,
! [X21,X8,X23] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X23)
=> c_Divides_Odiv__class_Odiv(tc_Int_Oint,X8,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X21),X23)) = c_Divides_Odiv__class_Odiv(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X8,X21),X23) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zdiv__zmult2__eq) ).
fof(fact_divide__less__0__iff,axiom,
! [X25,X11,X5] :
( class_Fields_Olinordered__field__inverse__zero(X5)
=> ( c_Orderings_Oord__class_Oless(X5,hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X5),X11),X25),c_Groups_Ozero__class_Ozero(X5))
<=> ( ( c_Orderings_Oord__class_Oless(X5,c_Groups_Ozero__class_Ozero(X5),X11)
& c_Orderings_Oord__class_Oless(X5,X25,c_Groups_Ozero__class_Ozero(X5)) )
| ( c_Orderings_Oord__class_Oless(X5,X11,c_Groups_Ozero__class_Ozero(X5))
& c_Orderings_Oord__class_Oless(X5,c_Groups_Ozero__class_Ozero(X5),X25) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide__less__0__iff) ).
fof(fact_zero__less__divide__iff,axiom,
! [X25,X11,X5] :
( class_Fields_Olinordered__field__inverse__zero(X5)
=> ( c_Orderings_Oord__class_Oless(X5,c_Groups_Ozero__class_Ozero(X5),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X5),X11),X25))
<=> ( ( c_Orderings_Oord__class_Oless(X5,c_Groups_Ozero__class_Ozero(X5),X11)
& c_Orderings_Oord__class_Oless(X5,c_Groups_Ozero__class_Ozero(X5),X25) )
| ( c_Orderings_Oord__class_Oless(X5,X11,c_Groups_Ozero__class_Ozero(X5))
& c_Orderings_Oord__class_Oless(X5,X25,c_Groups_Ozero__class_Ozero(X5)) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__less__divide__iff) ).
fof(fact_mod__mult__distrib2,axiom,
! [X10,X12,X36] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X36),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X12,X10)) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X36),X12),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X36),X10)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__mult__distrib2) ).
fof(fact_coeff__smult,axiom,
! [X10,X7,X8,X9] :
( class_Rings_Ocomm__semiring__0(X9)
=> hAPP(c_Polynomial_Ocoeff(X9,hAPP(hAPP(c_Polynomial_Osmult(X9),X8),X7)),X10) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X9),X8),hAPP(c_Polynomial_Ocoeff(X9,X7),X10)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_coeff__smult) ).
fof(fact_poly__smult,axiom,
! [X6,X7,X8,X9] :
( class_Rings_Ocomm__semiring__0(X9)
=> hAPP(c_Polynomial_Opoly(X9,hAPP(hAPP(c_Polynomial_Osmult(X9),X8),X7)),X6) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X9),X8),hAPP(c_Polynomial_Opoly(X9,X7),X6)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_poly__smult) ).
fof(fact_poly__pcompose,axiom,
! [X6,X13,X7,X9] :
( class_Rings_Ocomm__semiring__0(X9)
=> hAPP(c_Polynomial_Opoly(X9,c_Polynomial_Opcompose(X9,X7,X13)),X6) = hAPP(c_Polynomial_Opoly(X9,X7),hAPP(c_Polynomial_Opoly(X9,X13),X6)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_poly__pcompose) ).
fof(fact_power__eq__if,axiom,
! [X7,X12] :
( ( X12 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X7),X12) = c_Groups_Oone__class_Oone(tc_Nat_Onat) )
& ( X12 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X7),X12) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X7),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X7),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X12),c_Groups_Oone__class_Oone(tc_Nat_Onat)))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__eq__if) ).
fof(fact_zminus__zmod,axiom,
! [X12,X6] : c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,X6,X12)),X12) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X6),X12),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zminus__zmod) ).
fof(fact_less__diff__conv,axiom,
! [X39,X92,X83] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X83,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X92),X39))
<=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X83),X39),X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__diff__conv) ).
fof(fact_inverse__less__imp__less,axiom,
! [X21,X8,X9] :
( class_Fields_Olinordered__field(X9)
=> ( c_Orderings_Oord__class_Oless(X9,hAPP(c_Rings_Oinverse__class_Oinverse(X9),X8),hAPP(c_Rings_Oinverse__class_Oinverse(X9),X21))
=> ( c_Orderings_Oord__class_Oless(X9,c_Groups_Ozero__class_Ozero(X9),X8)
=> c_Orderings_Oord__class_Oless(X9,X21,X8) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inverse__less__imp__less) ).
fof(fact_inverse__less__imp__less__neg,axiom,
! [X21,X8,X9] :
( class_Fields_Olinordered__field(X9)
=> ( c_Orderings_Oord__class_Oless(X9,hAPP(c_Rings_Oinverse__class_Oinverse(X9),X8),hAPP(c_Rings_Oinverse__class_Oinverse(X9),X21))
=> ( c_Orderings_Oord__class_Oless(X9,X21,c_Groups_Ozero__class_Ozero(X9))
=> c_Orderings_Oord__class_Oless(X9,X21,X8) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inverse__less__imp__less__neg) ).
fof(fact_mod__minus__cong,axiom,
! [X45,X21,X8,X9] :
( class_Divides_Oring__div(X9)
=> ( c_Divides_Odiv__class_Omod(X9,X8,X21) = c_Divides_Odiv__class_Omod(X9,X45,X21)
=> c_Divides_Odiv__class_Omod(X9,hAPP(c_Groups_Ouminus__class_Ouminus(X9),X8),X21) = c_Divides_Odiv__class_Omod(X9,hAPP(c_Groups_Ouminus__class_Ouminus(X9),X45),X21) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__minus__cong) ).
fof(fact_diff__cancel,axiom,
! [X10,X12,X36] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X36),X12)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X36),X10)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X12),X10),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__cancel) ).
fof(fact_diff__cancel2,axiom,
! [X10,X36,X12] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X12),X36)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X10),X36)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X12),X10),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__cancel2) ).
fof(fact_diff__diff__left,axiom,
! [X36,X40,X42] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X42),X40)),X36) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X42),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X40),X36)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__diff__left) ).
fof(fact_zpower__zpower,axiom,
! [X32,X33,X6] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X6),X33)),X32) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X6),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X33),X32)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zpower__zpower) ).
fof(fact_zmult__assoc,axiom,
! [X54,X52,X53] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X53),X52)),X54) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X53),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X52),X54)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zmult__assoc) ).
fof(fact_nat__mult__assoc,axiom,
! [X36,X10,X12] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X12),X10)),X36) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X12),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X10),X36)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__mult__assoc) ).
fof(fact_zadd__assoc,axiom,
! [X54,X52,X53] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X53),X52)),X54) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X53),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X52),X54)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zadd__assoc) ).
fof(fact_nat__add__assoc,axiom,
! [X36,X10,X12] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X12),X10)),X36) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X12),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X10),X36)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__add__assoc) ).
fof(fact_divide__neg__pos,axiom,
! [X33,X6,X9] :
( class_Fields_Olinordered__field(X9)
=> ( c_Orderings_Oord__class_Oless(X9,X6,c_Groups_Ozero__class_Ozero(X9))
=> ( c_Orderings_Oord__class_Oless(X9,c_Groups_Ozero__class_Ozero(X9),X33)
=> c_Orderings_Oord__class_Oless(X9,hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X9),X6),X33),c_Groups_Ozero__class_Ozero(X9)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide__neg__pos) ).
fof(fact_divide__pos__neg,axiom,
! [X33,X6,X9] :
( class_Fields_Olinordered__field(X9)
=> ( c_Orderings_Oord__class_Oless(X9,c_Groups_Ozero__class_Ozero(X9),X6)
=> ( c_Orderings_Oord__class_Oless(X9,X33,c_Groups_Ozero__class_Ozero(X9))
=> c_Orderings_Oord__class_Oless(X9,hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X9),X6),X33),c_Groups_Ozero__class_Ozero(X9)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide__pos__neg) ).
fof(fact_mult__neg__pos,axiom,
! [X21,X8,X9] :
( class_Rings_Olinordered__semiring__strict(X9)
=> ( c_Orderings_Oord__class_Oless(X9,X8,c_Groups_Ozero__class_Ozero(X9))
=> ( c_Orderings_Oord__class_Oless(X9,c_Groups_Ozero__class_Ozero(X9),X21)
=> c_Orderings_Oord__class_Oless(X9,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X9),X8),X21),c_Groups_Ozero__class_Ozero(X9)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__neg__pos) ).
fof(fact_mult__pos__neg,axiom,
! [X21,X8,X9] :
( class_Rings_Olinordered__semiring__strict(X9)
=> ( c_Orderings_Oord__class_Oless(X9,c_Groups_Ozero__class_Ozero(X9),X8)
=> ( c_Orderings_Oord__class_Oless(X9,X21,c_Groups_Ozero__class_Ozero(X9))
=> c_Orderings_Oord__class_Oless(X9,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X9),X8),X21),c_Groups_Ozero__class_Ozero(X9)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__pos__neg) ).
fof(fact_mult__pos__neg2,axiom,
! [X21,X8,X9] :
( class_Rings_Olinordered__semiring__strict(X9)
=> ( c_Orderings_Oord__class_Oless(X9,c_Groups_Ozero__class_Ozero(X9),X8)
=> ( c_Orderings_Oord__class_Oless(X9,X21,c_Groups_Ozero__class_Ozero(X9))
=> c_Orderings_Oord__class_Oless(X9,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X9),X21),X8),c_Groups_Ozero__class_Ozero(X9)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__pos__neg2) ).
fof(fact_add__neg__neg,axiom,
! [X21,X8,X9] :
( class_Groups_Oordered__comm__monoid__add(X9)
=> ( c_Orderings_Oord__class_Oless(X9,X8,c_Groups_Ozero__class_Ozero(X9))
=> ( c_Orderings_Oord__class_Oless(X9,X21,c_Groups_Ozero__class_Ozero(X9))
=> c_Orderings_Oord__class_Oless(X9,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X9),X8),X21),c_Groups_Ozero__class_Ozero(X9)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__neg__neg) ).
fof(fact_less__1__mult,axiom,
! [X10,X12,X9] :
( class_Rings_Olinordered__semidom(X9)
=> ( c_Orderings_Oord__class_Oless(X9,c_Groups_Oone__class_Oone(X9),X12)
=> ( c_Orderings_Oord__class_Oless(X9,c_Groups_Oone__class_Oone(X9),X10)
=> c_Orderings_Oord__class_Oless(X9,c_Groups_Oone__class_Oone(X9),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X9),X12),X10)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__1__mult) ).
fof(fact_divide__pos__pos,axiom,
! [X33,X6,X9] :
( class_Fields_Olinordered__field(X9)
=> ( c_Orderings_Oord__class_Oless(X9,c_Groups_Ozero__class_Ozero(X9),X6)
=> ( c_Orderings_Oord__class_Oless(X9,c_Groups_Ozero__class_Ozero(X9),X33)
=> c_Orderings_Oord__class_Oless(X9,c_Groups_Ozero__class_Ozero(X9),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X9),X6),X33)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide__pos__pos) ).
fof(fact_mult__pos__pos,axiom,
! [X21,X8,X9] :
( class_Rings_Olinordered__semiring__strict(X9)
=> ( c_Orderings_Oord__class_Oless(X9,c_Groups_Ozero__class_Ozero(X9),X8)
=> ( c_Orderings_Oord__class_Oless(X9,c_Groups_Ozero__class_Ozero(X9),X21)
=> c_Orderings_Oord__class_Oless(X9,c_Groups_Ozero__class_Ozero(X9),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X9),X8),X21)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__pos__pos) ).
fof(fact_add__pos__pos,axiom,
! [X21,X8,X9] :
( class_Groups_Oordered__comm__monoid__add(X9)
=> ( c_Orderings_Oord__class_Oless(X9,c_Groups_Ozero__class_Ozero(X9),X8)
=> ( c_Orderings_Oord__class_Oless(X9,c_Groups_Ozero__class_Ozero(X9),X21)
=> c_Orderings_Oord__class_Oless(X9,c_Groups_Ozero__class_Ozero(X9),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X9),X8),X21)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__pos__pos) ).
fof(fact_divide__neg__neg,axiom,
! [X33,X6,X9] :
( class_Fields_Olinordered__field(X9)
=> ( c_Orderings_Oord__class_Oless(X9,X6,c_Groups_Ozero__class_Ozero(X9))
=> ( c_Orderings_Oord__class_Oless(X9,X33,c_Groups_Ozero__class_Ozero(X9))
=> c_Orderings_Oord__class_Oless(X9,c_Groups_Ozero__class_Ozero(X9),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X9),X6),X33)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide__neg__neg) ).
fof(fact_mult__neg__neg,axiom,
! [X21,X8,X9] :
( class_Rings_Olinordered__ring__strict(X9)
=> ( c_Orderings_Oord__class_Oless(X9,X8,c_Groups_Ozero__class_Ozero(X9))
=> ( c_Orderings_Oord__class_Oless(X9,X21,c_Groups_Ozero__class_Ozero(X9))
=> c_Orderings_Oord__class_Oless(X9,c_Groups_Ozero__class_Ozero(X9),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X9),X8),X21)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__neg__neg) ).
fof(fact_mod__Suc__eq__Suc__mod,axiom,
! [X10,X12] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,X12),X10) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X12,X10)),X10),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__Suc__eq__Suc__mod) ).
fof(fact_one__less__power,axiom,
! [X10,X8,X9] :
( class_Rings_Olinordered__semidom(X9)
=> ( c_Orderings_Oord__class_Oless(X9,c_Groups_Oone__class_Oone(X9),X8)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X10)
=> c_Orderings_Oord__class_Oless(X9,c_Groups_Oone__class_Oone(X9),hAPP(hAPP(c_Power_Opower__class_Opower(X9),X8),X10)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_one__less__power) ).
fof(fact_add__strict__right__mono,axiom,
! [X23,X21,X8,X9] :
( class_Groups_Oordered__cancel__ab__semigroup__add(X9)
=> ( c_Orderings_Oord__class_Oless(X9,X8,X21)
=> c_Orderings_Oord__class_Oless(X9,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X9),X8),X23),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X9),X21),X23)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__strict__right__mono) ).
fof(fact_add__strict__left__mono,axiom,
! [X23,X21,X8,X9] :
( class_Groups_Oordered__cancel__ab__semigroup__add(X9)
=> ( c_Orderings_Oord__class_Oless(X9,X8,X21)
=> c_Orderings_Oord__class_Oless(X9,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X9),X23),X8),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X9),X23),X21)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__strict__left__mono) ).
fof(fact_degree__add__eq__right,axiom,
! [X13,X7,X9] :
( class_Groups_Ocomm__monoid__add(X9)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(X9,X7),c_Polynomial_Odegree(X9,X13))
=> c_Polynomial_Odegree(X9,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X9)),X7),X13)) = c_Polynomial_Odegree(X9,X13) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_degree__add__eq__right) ).
fof(fact_degree__add__eq__left,axiom,
! [X7,X13,X9] :
( class_Groups_Ocomm__monoid__add(X9)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(X9,X13),c_Polynomial_Odegree(X9,X7))
=> c_Polynomial_Odegree(X9,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X9)),X7),X13)) = c_Polynomial_Odegree(X9,X7) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_degree__add__eq__left) ).
fof(fact_Suc__times__mod__eq,axiom,
! [X12,X36] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X36)
=> c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X36),X12)),X36) = c_Groups_Oone__class_Oone(tc_Nat_Onat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__times__mod__eq) ).
fof(fact_pos__add__strict,axiom,
! [X23,X21,X8,X9] :
( class_Rings_Olinordered__semidom(X9)
=> ( c_Orderings_Oord__class_Oless(X9,c_Groups_Ozero__class_Ozero(X9),X8)
=> ( c_Orderings_Oord__class_Oless(X9,X21,X23)
=> c_Orderings_Oord__class_Oless(X9,X21,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X9),X8),X23)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pos__add__strict) ).
fof(fact_uminus__dvd__conv_I2_J,axiom,
! [X64,X30] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X30),X64))
<=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X30),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X64))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_uminus__dvd__conv_I2_J) ).
fof(fact_add__gr__0,axiom,
! [X14,X35] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X35),X14))
<=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X35)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X14) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__gr__0) ).
fof(fact_mod__smult__left,axiom,
! [X33,X6,X8,X9] :
( class_Fields_Ofield(X9)
=> c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(X9),hAPP(hAPP(c_Polynomial_Osmult(X9),X8),X6),X33) = hAPP(hAPP(c_Polynomial_Osmult(X9),X8),c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(X9),X6,X33)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__smult__left) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I28_J,axiom,
! [X13,X6,X9] :
( class_Rings_Ocomm__semiring__1(X9)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X9),hAPP(hAPP(c_Power_Opower__class_Opower(X9),X6),X13)),X6) = hAPP(hAPP(c_Power_Opower__class_Opower(X9),X6),hAPP(c_Nat_OSuc,X13)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I28_J) ).
fof(fact_power__Suc2,axiom,
! [X10,X8,X9] :
( class_Groups_Omonoid__mult(X9)
=> hAPP(hAPP(c_Power_Opower__class_Opower(X9),X8),hAPP(c_Nat_OSuc,X10)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X9),hAPP(hAPP(c_Power_Opower__class_Opower(X9),X8),X10)),X8) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__Suc2) ).
fof(fact_DERIV__const,axiom,
! [X27,X39,X5] :
( class_RealVector_Oreal__normed__field(X5)
=> c_Deriv_Oderiv(X5,hAPP(c_COMBK(X5,X5),X39),X27,c_Groups_Ozero__class_Ozero(X5)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_DERIV__const) ).
fof(fact_div__neg__pos__less0,axiom,
! [X21,X8] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X8,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X21)
=> c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X8,X21),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_div__neg__pos__less0) ).
fof(fact_dvd__mult__div__cancel,axiom,
! [X21,X8,X9] :
( class_Divides_Osemiring__div(X9)
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X9),X8),X21))
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X9),X8),c_Divides_Odiv__class_Odiv(X9,X21,X8)) = X21 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__mult__div__cancel) ).
fof(fact_int__div__less__self,axiom,
! [X36,X6] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X6)
=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X36)
=> c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X6,X36),X6) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_int__div__less__self) ).
fof(fact_minus__poly__code_I2_J,axiom,
! [X7,X8,X5] :
( class_Groups_Oab__group__add(X5)
=> hAPP(c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X5)),hAPP(hAPP(c_Polynomial_OpCons(X5),X8),X7)) = hAPP(hAPP(c_Polynomial_OpCons(X5),hAPP(c_Groups_Ouminus__class_Ouminus(X5),X8)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X5)),X7)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__poly__code_I2_J) ).
fof(fact_minus__pCons,axiom,
! [X7,X8,X9] :
( class_Groups_Oab__group__add(X9)
=> hAPP(c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X9)),hAPP(hAPP(c_Polynomial_OpCons(X9),X8),X7)) = hAPP(hAPP(c_Polynomial_OpCons(X9),hAPP(c_Groups_Ouminus__class_Ouminus(X9),X8)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X9)),X7)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__pCons) ).
fof(fact_poly__gcd_Oassoc,axiom,
! [X23,X21,X8,X9] :
( class_Fields_Ofield(X9)
=> c_Polynomial_Opoly__gcd(X9,c_Polynomial_Opoly__gcd(X9,X8,X21),X23) = c_Polynomial_Opoly__gcd(X9,X8,c_Polynomial_Opoly__gcd(X9,X21,X23)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_poly__gcd_Oassoc) ).
fof(fact_poly__gcd_Oleft__commute,axiom,
! [X23,X8,X21,X9] :
( class_Fields_Ofield(X9)
=> c_Polynomial_Opoly__gcd(X9,X21,c_Polynomial_Opoly__gcd(X9,X8,X23)) = c_Polynomial_Opoly__gcd(X9,X8,c_Polynomial_Opoly__gcd(X9,X21,X23)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_poly__gcd_Oleft__commute) ).
fof(fact_diffs__def,axiom,
! [X14,X31,X5] :
( class_Rings_Oring__1(X5)
=> c_Transcendental_Odiffs(X5,X31,X14) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),c_Nat_Osemiring__1__class_Oof__nat(X5,hAPP(c_Nat_OSuc,X14))),hAPP(X31,hAPP(c_Nat_OSuc,X14))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diffs__def) ).
fof(fact_less__poly__def,axiom,
! [X28,X27,X5] :
( class_Rings_Olinordered__idom(X5)
=> ( c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(X5),X27,X28)
<=> c_Polynomial_Opos__poly(X5,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X5)),X28),X27)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__poly__def) ).
fof(fact_div__mult__mult1__if,axiom,
! [X21,X8,X23,X9] :
( class_Divides_Osemiring__div(X9)
=> ( ( X23 = c_Groups_Ozero__class_Ozero(X9)
=> c_Divides_Odiv__class_Odiv(X9,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X9),X23),X8),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X9),X23),X21)) = c_Groups_Ozero__class_Ozero(X9) )
& ( X23 != c_Groups_Ozero__class_Ozero(X9)
=> c_Divides_Odiv__class_Odiv(X9,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X9),X23),X8),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X9),X23),X21)) = c_Divides_Odiv__class_Odiv(X9,X8,X21) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_div__mult__mult1__if) ).
fof(fact_div__mult__mult1,axiom,
! [X21,X8,X23,X9] :
( class_Divides_Osemiring__div(X9)
=> ( X23 != c_Groups_Ozero__class_Ozero(X9)
=> c_Divides_Odiv__class_Odiv(X9,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X9),X23),X8),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X9),X23),X21)) = c_Divides_Odiv__class_Odiv(X9,X8,X21) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_div__mult__mult1) ).
fof(fact_div__mult__mult2,axiom,
! [X21,X8,X23,X9] :
( class_Divides_Osemiring__div(X9)
=> ( X23 != c_Groups_Ozero__class_Ozero(X9)
=> c_Divides_Odiv__class_Odiv(X9,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X9),X8),X23),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X9),X21),X23)) = c_Divides_Odiv__class_Odiv(X9,X8,X21) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_div__mult__mult2) ).
fof(fact_zero__less__double__add__iff__zero__less__single__add,axiom,
! [X11,X5] :
( class_Groups_Olinordered__ab__group__add(X5)
=> ( c_Orderings_Oord__class_Oless(X5,c_Groups_Ozero__class_Ozero(X5),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X11),X11))
<=> c_Orderings_Oord__class_Oless(X5,c_Groups_Ozero__class_Ozero(X5),X11) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__less__double__add__iff__zero__less__single__add) ).
fof(fact_even__less__0__iff,axiom,
! [X11,X5] :
( class_Rings_Olinordered__idom(X5)
=> ( c_Orderings_Oord__class_Oless(X5,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X11),X11),c_Groups_Ozero__class_Ozero(X5))
<=> c_Orderings_Oord__class_Oless(X5,X11,c_Groups_Ozero__class_Ozero(X5)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_even__less__0__iff) ).
fof(fact_double__add__less__zero__iff__single__add__less__zero,axiom,
! [X11,X5] :
( class_Groups_Olinordered__ab__group__add(X5)
=> ( c_Orderings_Oord__class_Oless(X5,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X11),X11),c_Groups_Ozero__class_Ozero(X5))
<=> c_Orderings_Oord__class_Oless(X5,X11,c_Groups_Ozero__class_Ozero(X5)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_double__add__less__zero__iff__single__add__less__zero) ).
fof(fact_nat__0__less__mult__iff,axiom,
! [X14,X35] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X35),X14))
<=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X35)
& c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X14) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__0__less__mult__iff) ).
fof(fact_smult__monom,axiom,
! [X10,X21,X8,X9] :
( class_Rings_Ocomm__semiring__0(X9)
=> hAPP(hAPP(c_Polynomial_Osmult(X9),X8),c_Polynomial_Omonom(X9,X21,X10)) = c_Polynomial_Omonom(X9,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X9),X8),X21),X10) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_smult__monom) ).
fof(fact_pos__poly__def,axiom,
! [X4,X5] :
( class_Rings_Olinordered__idom(X5)
=> ( c_Polynomial_Opos__poly(X5,X4)
<=> c_Orderings_Oord__class_Oless(X5,c_Groups_Ozero__class_Ozero(X5),hAPP(c_Polynomial_Ocoeff(X5,X4),c_Polynomial_Odegree(X5,X4))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pos__poly__def) ).
fof(fact_dvd__div__eq__mult,axiom,
! [X31,X25,X11,X5] :
( class_Divides_Osemiring__div(X5)
=> ( X11 != c_Groups_Ozero__class_Ozero(X5)
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X5),X11),X25))
=> ( c_Divides_Odiv__class_Odiv(X5,X25,X11) = X31
<=> X25 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X31),X11) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__div__eq__mult) ).
fof(fact_diff__less,axiom,
! [X12,X10] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X10)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X12)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X12),X10),X12) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__less) ).
fof(fact_less__imp__inverse__less,axiom,
! [X21,X8,X9] :
( class_Fields_Olinordered__field(X9)
=> ( c_Orderings_Oord__class_Oless(X9,X8,X21)
=> ( c_Orderings_Oord__class_Oless(X9,c_Groups_Ozero__class_Ozero(X9),X8)
=> c_Orderings_Oord__class_Oless(X9,hAPP(c_Rings_Oinverse__class_Oinverse(X9),X21),hAPP(c_Rings_Oinverse__class_Oinverse(X9),X8)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__imp__inverse__less) ).
fof(fact_less__imp__inverse__less__neg,axiom,
! [X21,X8,X9] :
( class_Fields_Olinordered__field(X9)
=> ( c_Orderings_Oord__class_Oless(X9,X8,X21)
=> ( c_Orderings_Oord__class_Oless(X9,X21,c_Groups_Ozero__class_Ozero(X9))
=> c_Orderings_Oord__class_Oless(X9,hAPP(c_Rings_Oinverse__class_Oinverse(X9),X21),hAPP(c_Rings_Oinverse__class_Oinverse(X9),X8)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__imp__inverse__less__neg) ).
fof(fact_degree__mult__eq,axiom,
! [X13,X7,X9] :
( class_Rings_Oidom(X9)
=> ( X7 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X9))
=> ( X13 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X9))
=> c_Polynomial_Odegree(X9,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X9)),X7),X13)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Polynomial_Odegree(X9,X7)),c_Polynomial_Odegree(X9,X13)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_degree__mult__eq) ).
fof(fact_less__iff__diff__less__0,axiom,
! [X25,X11,X5] :
( class_Groups_Oordered__ab__group__add(X5)
=> ( c_Orderings_Oord__class_Oless(X5,X11,X25)
<=> c_Orderings_Oord__class_Oless(X5,hAPP(hAPP(c_Groups_Ominus__class_Ominus(X5),X11),X25),c_Groups_Ozero__class_Ozero(X5)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__iff__diff__less__0) ).
fof(fact_dvd__triv__left,axiom,
! [X21,X8,X9] :
( class_Rings_Ocomm__semiring__1(X9)
=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X9),X8),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X9),X8),X21))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__triv__left) ).
fof(fact_dvd__triv__right,axiom,
! [X21,X8,X9] :
( class_Rings_Ocomm__semiring__1(X9)
=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X9),X8),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X9),X21),X8))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__triv__right) ).
fof(fact_zadd__strict__right__mono,axiom,
! [X36,X40,X42] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X42,X40)
=> c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X42),X36),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X40),X36)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zadd__strict__right__mono) ).
fof(fact_add__less__mono1,axiom,
! [X36,X40,X42] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X42,X40)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X42),X36),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X40),X36)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__less__mono1) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J,axiom,
! [X17,X18,X20,X9] :
( class_Rings_Ocomm__semiring__1(X9)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X9),X20),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X9),X18),X17)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X9),X18),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X9),X20),X17)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J,axiom,
! [X22,X23,X8,X9] :
( class_Rings_Ocomm__semiring__1(X9)
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(X9),X8),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X9),X23),X22)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X9),X23),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X9),X8),X22)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J) ).
fof(fact_add__minus__cancel,axiom,
! [X21,X8,X9] :
( class_Groups_Ogroup__add(X9)
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(X9),X8),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X9),hAPP(c_Groups_Ouminus__class_Ouminus(X9),X8)),X21)) = X21 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__minus__cancel) ).
fof(fact_coeff__pCons__Suc,axiom,
! [X10,X7,X8,X9] :
( class_Groups_Ozero(X9)
=> hAPP(c_Polynomial_Ocoeff(X9,hAPP(hAPP(c_Polynomial_OpCons(X9),X8),X7)),hAPP(c_Nat_OSuc,X10)) = hAPP(c_Polynomial_Ocoeff(X9,X7),X10) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_coeff__pCons__Suc) ).
fof(fact_diff__eq__diff__less,axiom,
! [X30,X31,X25,X11,X5] :
( class_Groups_Oordered__ab__group__add(X5)
=> ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(X5),X11),X25) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(X5),X31),X30)
=> ( c_Orderings_Oord__class_Oless(X5,X11,X25)
<=> c_Orderings_Oord__class_Oless(X5,X31,X30) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__eq__diff__less) ).
fof(fact_power__gt1,axiom,
! [X10,X8,X9] :
( class_Rings_Olinordered__semidom(X9)
=> ( c_Orderings_Oord__class_Oless(X9,c_Groups_Oone__class_Oone(X9),X8)
=> c_Orderings_Oord__class_Oless(X9,c_Groups_Oone__class_Oone(X9),hAPP(hAPP(c_Power_Opower__class_Opower(X9),X8),hAPP(c_Nat_OSuc,X10))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__gt1) ).
fof(fact_mod__Suc,axiom,
! [X10,X12] :
( ( hAPP(c_Nat_OSuc,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X12,X10)) = X10
=> c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,X12),X10) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( hAPP(c_Nat_OSuc,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X12,X10)) != X10
=> c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,X12),X10) = hAPP(c_Nat_OSuc,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X12,X10)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__Suc) ).
fof(fact_diff__Suc__eq__diff__pred,axiom,
! [X10,X12] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X12),hAPP(c_Nat_OSuc,X10)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X12),c_Groups_Oone__class_Oone(tc_Nat_Onat))),X10),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__Suc__eq__diff__pred) ).
fof(fact_nonzero__inverse__mult__distrib,axiom,
! [X21,X8,X9] :
( class_Rings_Odivision__ring(X9)
=> ( X8 != c_Groups_Ozero__class_Ozero(X9)
=> ( X21 != c_Groups_Ozero__class_Ozero(X9)
=> hAPP(c_Rings_Oinverse__class_Oinverse(X9),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X9),X8),X21)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X9),hAPP(c_Rings_Oinverse__class_Oinverse(X9),X21)),hAPP(c_Rings_Oinverse__class_Oinverse(X9),X8)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nonzero__inverse__mult__distrib) ).
fof(fact_zless__iff__Suc__zadd,axiom,
! [X26,X29] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X29,X26)
<=> ? [X49] : X26 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X29),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,hAPP(c_Nat_OSuc,X49))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zless__iff__Suc__zadd) ).
fof(fact_zmult__div__cancel,axiom,
! [X12,X10] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X10),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X12,X10)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X12),c_Divides_Odiv__class_Omod(tc_Int_Oint,X12,X10)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zmult__div__cancel) ).
fof(fact_zdvd__mult__div__cancel,axiom,
! [X12,X10] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X10),X12))
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X10),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X12,X10)) = X12 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zdvd__mult__div__cancel) ).
fof(fact_dvd_Oeq__iff,axiom,
! [X28,X27] :
( X27 = X28
<=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X27),X28))
& hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X28),X27)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd_Oeq__iff) ).
fof(fact_dvd_Oantisym__conv,axiom,
! [X27,X28] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X28),X27))
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X27),X28))
<=> X27 = X28 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd_Oantisym__conv) ).
fof(fact_dvd__antisym,axiom,
! [X10,X12] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X12),X10))
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X10),X12))
=> X12 = X10 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__antisym) ).
fof(fact_dvd_Oantisym,axiom,
! [X33,X6] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X6),X33))
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X33),X6))
=> X6 = X33 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd_Oantisym) ).
fof(fact_one__less__inverse,axiom,
! [X8,X9] :
( class_Fields_Olinordered__field(X9)
=> ( c_Orderings_Oord__class_Oless(X9,c_Groups_Ozero__class_Ozero(X9),X8)
=> ( c_Orderings_Oord__class_Oless(X9,X8,c_Groups_Oone__class_Oone(X9))
=> c_Orderings_Oord__class_Oless(X9,c_Groups_Oone__class_Oone(X9),hAPP(c_Rings_Oinverse__class_Oinverse(X9),X8)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_one__less__inverse) ).
fof(fact_one__less__inverse__iff,axiom,
! [X27,X5] :
( class_Fields_Olinordered__field__inverse__zero(X5)
=> ( c_Orderings_Oord__class_Oless(X5,c_Groups_Oone__class_Oone(X5),hAPP(c_Rings_Oinverse__class_Oinverse(X5),X27))
<=> ( c_Orderings_Oord__class_Oless(X5,c_Groups_Ozero__class_Ozero(X5),X27)
& c_Orderings_Oord__class_Oless(X5,X27,c_Groups_Oone__class_Oone(X5)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_one__less__inverse__iff) ).
fof(fact_Limits_Ominus__diff__minus,axiom,
! [X21,X8,X9] :
( class_Groups_Oab__group__add(X9)
=> hAPP(hAPP(c_Groups_Ominus__class_Ominus(X9),hAPP(c_Groups_Ouminus__class_Ouminus(X9),X8)),hAPP(c_Groups_Ouminus__class_Ouminus(X9),X21)) = hAPP(c_Groups_Ouminus__class_Ouminus(X9),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X9),X8),X21)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Limits_Ominus__diff__minus) ).
fof(fact_inverse__mult__distrib,axiom,
! [X21,X8,X9] :
( class_Fields_Ofield__inverse__zero(X9)
=> hAPP(c_Rings_Oinverse__class_Oinverse(X9),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X9),X8),X21)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X9),hAPP(c_Rings_Oinverse__class_Oinverse(X9),X8)),hAPP(c_Rings_Oinverse__class_Oinverse(X9),X21)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inverse__mult__distrib) ).
fof(fact_minus__add__distrib,axiom,
! [X21,X8,X9] :
( class_Groups_Oab__group__add(X9)
=> hAPP(c_Groups_Ouminus__class_Ouminus(X9),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X9),X8),X21)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X9),hAPP(c_Groups_Ouminus__class_Ouminus(X9),X8)),hAPP(c_Groups_Ouminus__class_Ouminus(X9),X21)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__add__distrib) ).
fof(fact_minus__add,axiom,
! [X21,X8,X9] :
( class_Groups_Ogroup__add(X9)
=> hAPP(c_Groups_Ouminus__class_Ouminus(X9),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X9),X8),X21)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X9),hAPP(c_Groups_Ouminus__class_Ouminus(X9),X21)),hAPP(c_Groups_Ouminus__class_Ouminus(X9),X8)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__add) ).
fof(fact_dvd__pos__nat,axiom,
! [X12,X10] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X10)
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X12),X10))
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X12) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__pos__nat) ).
fof(fact_DERIV__cmult__Id,axiom,
! [X27,X31,X5] :
( class_RealVector_Oreal__normed__field(X5)
=> c_Deriv_Oderiv(X5,hAPP(c_Groups_Otimes__class_Otimes(X5),X31),X27,X31) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_DERIV__cmult__Id) ).
fof(fact_Suc__mult__cancel1,axiom,
! [X14,X35,X39] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,X39)),X35) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,X39)),X14)
<=> X35 = X14 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__mult__cancel1) ).
fof(fact_zless__add1__eq,axiom,
! [X26,X29] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X29,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X26),c_Groups_Oone__class_Oone(tc_Int_Oint)))
<=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X29,X26)
| X29 = X26 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zless__add1__eq) ).
fof(fact_zmod__zminus1__eq__if,axiom,
! [X21,X8] :
( ( c_Divides_Odiv__class_Omod(tc_Int_Oint,X8,X21) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
=> c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X8),X21) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
& ( c_Divides_Odiv__class_Omod(tc_Int_Oint,X8,X21) != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
=> c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X8),X21) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X21),c_Divides_Odiv__class_Omod(tc_Int_Oint,X8,X21)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zmod__zminus1__eq__if) ).
fof(fact_zero__less__power__nat__eq,axiom,
! [X14,X27] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X27),X14))
<=> ( X14 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X27) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__less__power__nat__eq) ).
fof(fact_nat__zero__less__power__iff,axiom,
! [X14,X27] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X27),X14))
<=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X27)
| X14 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__zero__less__power__iff) ).
fof(fact_diff__Suc,axiom,
! [X14,X35] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X35),hAPP(c_Nat_OSuc,X14)) = hAPP(c_Nat_Onat_Onat__case(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_COMBI(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X35),X14)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__Suc) ).
fof(fact_frac__eq__eq,axiom,
! [X29,X27,X26,X28,X5] :
( class_Fields_Ofield(X5)
=> ( X28 != c_Groups_Ozero__class_Ozero(X5)
=> ( X26 != c_Groups_Ozero__class_Ozero(X5)
=> ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X5),X27),X28) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X5),X29),X26)
<=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X27),X26) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X29),X28) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_frac__eq__eq) ).
fof(fact_less__bin__lemma,axiom,
! [X67,X39] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X39,X67)
<=> c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X39),X67),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__bin__lemma) ).
fof(fact_zero__less__diff,axiom,
! [X35,X14] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X14),X35))
<=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X35,X14) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__less__diff) ).
fof(fact_less__add__eq__less,axiom,
! [X10,X12,X76,X36] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X36,X76)
=> ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X12),X76) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X36),X10)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X12,X10) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__add__eq__less) ).
fof(fact_poly__mod__minus__left,axiom,
! [X33,X6,X9] :
( class_Fields_Ofield(X9)
=> c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(X9),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X9)),X6),X33) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X9)),c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(X9),X6,X33)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_poly__mod__minus__left) ).
fof(fact_add__lessD1,axiom,
! [X36,X40,X42] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X42),X40),X36)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X42,X36) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__lessD1) ).
fof(fact_diff__Suc__less,axiom,
! [X42,X10] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X10)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X10),hAPP(c_Nat_OSuc,X42)),X10) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__Suc__less) ).
fof(fact_zadd__left__commute,axiom,
! [X32,X33,X6] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X6),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X33),X32)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X33),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X6),X32)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zadd__left__commute) ).
fof(fact_nat__add__left__commute,axiom,
! [X32,X33,X6] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X6),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X33),X32)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X33),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X6),X32)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__add__left__commute) ).
fof(fact_offset__poly__single,axiom,
! [X48,X8,X9] :
( class_Rings_Ocomm__semiring__0(X9)
=> c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X9,hAPP(hAPP(c_Polynomial_OpCons(X9),X8),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X9))),X48) = hAPP(hAPP(c_Polynomial_OpCons(X9),X8),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X9))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_offset__poly__single) ).
fof(fact_smult__minus__left,axiom,
! [X7,X8,X9] :
( class_Rings_Ocomm__ring(X9)
=> hAPP(hAPP(c_Polynomial_Osmult(X9),hAPP(c_Groups_Ouminus__class_Ouminus(X9),X8)),X7) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X9)),hAPP(hAPP(c_Polynomial_Osmult(X9),X8),X7)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_smult__minus__left) ).
fof(fact_coeff__minus,axiom,
! [X10,X7,X9] :
( class_Groups_Oab__group__add(X9)
=> hAPP(c_Polynomial_Ocoeff(X9,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X9)),X7)),X10) = hAPP(c_Groups_Ouminus__class_Ouminus(X9),hAPP(c_Polynomial_Ocoeff(X9,X7),X10)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_coeff__minus) ).
fof(fact_poly__minus,axiom,
! [X6,X7,X9] :
( class_Rings_Ocomm__ring(X9)
=> hAPP(c_Polynomial_Opoly(X9,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X9)),X7)),X6) = hAPP(c_Groups_Ouminus__class_Ouminus(X9),hAPP(c_Polynomial_Opoly(X9,X7),X6)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_poly__minus) ).
fof(fact_zmod__zminus2,axiom,
! [X21,X8] : c_Divides_Odiv__class_Omod(tc_Int_Oint,X8,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X21)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X8),X21)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zmod__zminus2) ).
fof(fact_power__inject__exp,axiom,
! [X14,X35,X11,X5] :
( class_Rings_Olinordered__semidom(X5)
=> ( c_Orderings_Oord__class_Oless(X5,c_Groups_Oone__class_Oone(X5),X11)
=> ( hAPP(hAPP(c_Power_Opower__class_Opower(X5),X11),X35) = hAPP(hAPP(c_Power_Opower__class_Opower(X5),X11),X14)
<=> X35 = X14 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__inject__exp) ).
fof(fact_neg__less__iff__less,axiom,
! [X11,X25,X5] :
( class_Groups_Oordered__ab__group__add(X5)
=> ( c_Orderings_Oord__class_Oless(X5,hAPP(c_Groups_Ouminus__class_Ouminus(X5),X25),hAPP(c_Groups_Ouminus__class_Ouminus(X5),X11))
<=> c_Orderings_Oord__class_Oless(X5,X11,X25) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_neg__less__iff__less) ).
fof(fact_coeff__monom,axiom,
! [X8,X10,X12,X9] :
( class_Groups_Ozero(X9)
=> ( ( X12 = X10
=> hAPP(c_Polynomial_Ocoeff(X9,c_Polynomial_Omonom(X9,X8,X12)),X10) = X8 )
& ( X12 != X10
=> hAPP(c_Polynomial_Ocoeff(X9,c_Polynomial_Omonom(X9,X8,X12)),X10) = c_Groups_Ozero__class_Ozero(X9) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_coeff__monom) ).
fof(fact_DERIV__ident,axiom,
! [X27,X5] :
( class_RealVector_Oreal__normed__field(X5)
=> c_Deriv_Oderiv(X5,c_COMBI(X5),X27,c_Groups_Oone__class_Oone(X5)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_DERIV__ident) ).
fof(fact_zero__less__power,axiom,
! [X10,X8,X9] :
( class_Rings_Olinordered__semidom(X9)
=> ( c_Orderings_Oord__class_Oless(X9,c_Groups_Ozero__class_Ozero(X9),X8)
=> c_Orderings_Oord__class_Oless(X9,c_Groups_Ozero__class_Ozero(X9),hAPP(hAPP(c_Power_Opower__class_Opower(X9),X8),X10)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__less__power) ).
fof(fact_pos__poly__pCons,axiom,
! [X4,X11,X5] :
( class_Rings_Olinordered__idom(X5)
=> ( c_Polynomial_Opos__poly(X5,hAPP(hAPP(c_Polynomial_OpCons(X5),X11),X4))
<=> ( c_Polynomial_Opos__poly(X5,X4)
| ( X4 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X5))
& c_Orderings_Oord__class_Oless(X5,c_Groups_Ozero__class_Ozero(X5),X11) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pos__poly__pCons) ).
fof(fact_add__diff__cancel,axiom,
! [X21,X8,X9] :
( class_Groups_Ogroup__add(X9)
=> hAPP(hAPP(c_Groups_Ominus__class_Ominus(X9),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X9),X8),X21)),X21) = X8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__diff__cancel) ).
fof(fact_diff__add__cancel,axiom,
! [X21,X8,X9] :
( class_Groups_Ogroup__add(X9)
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(X9),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X9),X8),X21)),X21) = X8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__add__cancel) ).
fof(fact_nonzero__power__inverse,axiom,
! [X10,X8,X9] :
( class_Rings_Odivision__ring(X9)
=> ( X8 != c_Groups_Ozero__class_Ozero(X9)
=> hAPP(c_Rings_Oinverse__class_Oinverse(X9),hAPP(hAPP(c_Power_Opower__class_Opower(X9),X8),X10)) = hAPP(hAPP(c_Power_Opower__class_Opower(X9),hAPP(c_Rings_Oinverse__class_Oinverse(X9),X8)),X10) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nonzero__power__inverse) ).
fof(fact_of__nat__aux_Osimps_I1_J,axiom,
! [X83,X84,X5] :
( class_Rings_Osemiring__1(X5)
=> c_Nat_Osemiring__1__class_Oof__nat__aux(X5,X84,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X83) = X83 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_of__nat__aux_Osimps_I1_J) ).
fof(fact_divide_Ominus,axiom,
! [X33,X6,X9] :
( class_RealVector_Oreal__normed__field(X9)
=> hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X9),hAPP(c_Groups_Ouminus__class_Ouminus(X9),X6)),X33) = hAPP(c_Groups_Ouminus__class_Ouminus(X9),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X9),X6),X33)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide_Ominus) ).
fof(fact_mult__left_Ominus,axiom,
! [X33,X6,X9] :
( class_RealVector_Oreal__normed__algebra(X9)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X9),hAPP(c_Groups_Ouminus__class_Ouminus(X9),X6)),X33) = hAPP(c_Groups_Ouminus__class_Ouminus(X9),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X9),X6),X33)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__left_Ominus) ).
fof(fact_mult_Ominus__left,axiom,
! [X21,X8,X9] :
( class_RealVector_Oreal__normed__algebra(X9)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X9),hAPP(c_Groups_Ouminus__class_Ouminus(X9),X8)),X21) = hAPP(c_Groups_Ouminus__class_Ouminus(X9),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X9),X8),X21)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult_Ominus__left) ).
fof(fact_power__inverse,axiom,
! [X10,X8,X9] :
( class_Rings_Odivision__ring__inverse__zero(X9)
=> hAPP(c_Rings_Oinverse__class_Oinverse(X9),hAPP(hAPP(c_Power_Opower__class_Opower(X9),X8),X10)) = hAPP(hAPP(c_Power_Opower__class_Opower(X9),hAPP(c_Rings_Oinverse__class_Oinverse(X9),X8)),X10) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__inverse) ).
fof(fact_minus__divide__left,axiom,
! [X21,X8,X9] :
( class_Rings_Odivision__ring(X9)
=> hAPP(c_Groups_Ouminus__class_Ouminus(X9),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X9),X8),X21)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X9),hAPP(c_Groups_Ouminus__class_Ouminus(X9),X8)),X21) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__divide__left) ).
fof(fact_minus__mult__left,axiom,
! [X21,X8,X9] :
( class_Rings_Oring(X9)
=> hAPP(c_Groups_Ouminus__class_Ouminus(X9),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X9),X8),X21)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X9),hAPP(c_Groups_Ouminus__class_Ouminus(X9),X8)),X21) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__mult__left) ).
fof(fact_power_Opower_Opower__0,axiom,
! [X11,X37,X38,X5] : hAPP(hAPP(c_Power_Opower_Opower(X5,X38,X37),X11),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X38,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power_Opower_Opower__0) ).
fof(fact_smult__minus__right,axiom,
! [X7,X8,X9] :
( class_Rings_Ocomm__ring(X9)
=> hAPP(hAPP(c_Polynomial_Osmult(X9),X8),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X9)),X7)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X9)),hAPP(hAPP(c_Polynomial_Osmult(X9),X8),X7)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_smult__minus__right) ).
fof(fact_dvd__1__iff__1,axiom,
! [X35] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X35),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))
<=> X35 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__1__iff__1) ).
fof(fact_less__add__Suc1,axiom,
! [X12,X42] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,X42,hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X42),X12))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__add__Suc1) ).
fof(fact_less__add__Suc2,axiom,
! [X12,X42] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,X42,hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X12),X42))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__add__Suc2) ).
fof(fact_monom__Suc,axiom,
! [X10,X8,X9] :
( class_Groups_Ozero(X9)
=> c_Polynomial_Omonom(X9,X8,hAPP(c_Nat_OSuc,X10)) = hAPP(hAPP(c_Polynomial_OpCons(X9),c_Groups_Ozero__class_Ozero(X9)),c_Polynomial_Omonom(X9,X8,X10)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_monom__Suc) ).
fof(fact_coeff__pCons__0,axiom,
! [X7,X8,X9] :
( class_Groups_Ozero(X9)
=> hAPP(c_Polynomial_Ocoeff(X9,hAPP(hAPP(c_Polynomial_OpCons(X9),X8),X7)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_coeff__pCons__0) ).
fof(fact_Suc__pred,axiom,
! [X10] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X10)
=> hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X10),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = X10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__pred) ).
fof(fact_zminus__zadd__distrib,axiom,
! [X51,X32] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X32),X51)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X32)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X51)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zminus__zadd__distrib) ).
fof(fact_poly__gcd_Osimps_I2_J,axiom,
! [X6,X33,X9] :
( class_Fields_Ofield(X9)
=> ( X33 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X9))
=> c_Polynomial_Opoly__gcd(X9,X6,X33) = c_Polynomial_Opoly__gcd(X9,X33,c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(X9),X6,X33)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_poly__gcd_Osimps_I2_J) ).
fof(fact_minus__less__iff,axiom,
! [X25,X11,X5] :
( class_Groups_Oordered__ab__group__add(X5)
=> ( c_Orderings_Oord__class_Oless(X5,hAPP(c_Groups_Ouminus__class_Ouminus(X5),X11),X25)
<=> c_Orderings_Oord__class_Oless(X5,hAPP(c_Groups_Ouminus__class_Ouminus(X5),X25),X11) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__less__iff) ).
fof(fact_less__minus__iff,axiom,
! [X25,X11,X5] :
( class_Groups_Oordered__ab__group__add(X5)
=> ( c_Orderings_Oord__class_Oless(X5,X11,hAPP(c_Groups_Ouminus__class_Ouminus(X5),X25))
<=> c_Orderings_Oord__class_Oless(X5,X25,hAPP(c_Groups_Ouminus__class_Ouminus(X5),X11)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__minus__iff) ).
fof(fact_pos__mod__bound,axiom,
! [X8,X21] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X21)
=> c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Divides_Odiv__class_Omod(tc_Int_Oint,X8,X21),X21) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pos__mod__bound) ).
fof(fact_mod__less__divisor,axiom,
! [X12,X10] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X10)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X12,X10),X10) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__less__divisor) ).
fof(fact_neg__mod__bound,axiom,
! [X8,X21] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X21,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
=> c_Orderings_Oord__class_Oless(tc_Int_Oint,X21,c_Divides_Odiv__class_Omod(tc_Int_Oint,X8,X21)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_neg__mod__bound) ).
fof(fact_negative__zless,axiom,
! [X12,X10] : c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,hAPP(c_Nat_OSuc,X10))),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,X12)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_negative__zless) ).
fof(fact_less__trans__Suc,axiom,
! [X36,X40,X42] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X42,X40)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X40,X36)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(c_Nat_OSuc,X42),X36) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__trans__Suc) ).
fof(fact_div__poly__less,axiom,
! [X33,X6,X9] :
( class_Fields_Ofield(X9)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(X9,X6),c_Polynomial_Odegree(X9,X33))
=> c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(X9),X6,X33) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X9)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_div__poly__less) ).
fof(fact_of__nat__mult,axiom,
! [X10,X12,X9] :
( class_Rings_Osemiring__1(X9)
=> c_Nat_Osemiring__1__class_Oof__nat(X9,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X12),X10)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X9),c_Nat_Osemiring__1__class_Oof__nat(X9,X12)),c_Nat_Osemiring__1__class_Oof__nat(X9,X10)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_of__nat__mult) ).
fof(fact_of__nat__add,axiom,
! [X10,X12,X9] :
( class_Rings_Osemiring__1(X9)
=> c_Nat_Osemiring__1__class_Oof__nat(X9,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X12),X10)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X9),c_Nat_Osemiring__1__class_Oof__nat(X9,X12)),c_Nat_Osemiring__1__class_Oof__nat(X9,X10)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_of__nat__add) ).
fof(fact_less__iff__Suc__add,axiom,
! [X14,X35] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X35,X14)
<=> ? [X66] : X14 = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X35),X66)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__iff__Suc__add) ).
fof(fact_minus__add__cancel,axiom,
! [X21,X8,X9] :
( class_Groups_Ogroup__add(X9)
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(X9),hAPP(c_Groups_Ouminus__class_Ouminus(X9),X8)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X9),X8),X21)) = X21 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__add__cancel) ).
fof(fact_minus__monom,axiom,
! [X10,X8,X9] :
( class_Groups_Oab__group__add(X9)
=> hAPP(c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X9)),c_Polynomial_Omonom(X9,X8,X10)) = c_Polynomial_Omonom(X9,hAPP(c_Groups_Ouminus__class_Ouminus(X9),X8),X10) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__monom) ).
fof(fact_zmod__zminus__zminus,axiom,
! [X21,X8] : c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X8),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X21)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,X8,X21)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zmod__zminus__zminus) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I27_J,axiom,
! [X13,X6,X9] :
( class_Rings_Ocomm__semiring__1(X9)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X9),X6),hAPP(hAPP(c_Power_Opower__class_Opower(X9),X6),X13)) = hAPP(hAPP(c_Power_Opower__class_Opower(X9),X6),hAPP(c_Nat_OSuc,X13)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I27_J) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I35_J,axiom,
! [X13,X6,X9] :
( class_Rings_Ocomm__semiring__1(X9)
=> hAPP(hAPP(c_Power_Opower__class_Opower(X9),X6),hAPP(c_Nat_OSuc,X13)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X9),X6),hAPP(hAPP(c_Power_Opower__class_Opower(X9),X6),X13)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I35_J) ).
fof(fact_power__Suc,axiom,
! [X10,X8,X9] :
( class_Power_Opower(X9)
=> hAPP(hAPP(c_Power_Opower__class_Opower(X9),X8),hAPP(c_Nat_OSuc,X10)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X9),X8),hAPP(hAPP(c_Power_Opower__class_Opower(X9),X8),X10)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__Suc) ).
fof(fact_nat__mult__eq__cancel1,axiom,
! [X14,X35,X39] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X39)
=> ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X39),X35) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X39),X14)
<=> X35 = X14 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__mult__eq__cancel1) ).
fof(fact_mod__smult__right,axiom,
! [X33,X6,X8,X9] :
( class_Fields_Ofield(X9)
=> ( X8 != c_Groups_Ozero__class_Ozero(X9)
=> c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(X9),X6,hAPP(hAPP(c_Polynomial_Osmult(X9),X8),X33)) = c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(X9),X6,X33) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__smult__right) ).
fof(fact_order__less__trans,axiom,
! [X32,X33,X6,X9] :
( class_Orderings_Opreorder(X9)
=> ( c_Orderings_Oord__class_Oless(X9,X6,X33)
=> ( c_Orderings_Oord__class_Oless(X9,X33,X32)
=> c_Orderings_Oord__class_Oless(X9,X6,X32) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__less__trans) ).
fof(fact_xt1_I10_J,axiom,
! [X32,X6,X33,X9] :
( class_Orderings_Oorder(X9)
=> ( c_Orderings_Oord__class_Oless(X9,X33,X6)
=> ( c_Orderings_Oord__class_Oless(X9,X32,X33)
=> c_Orderings_Oord__class_Oless(X9,X32,X6) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_xt1_I10_J) ).
fof(fact_mod__poly__less,axiom,
! [X33,X6,X9] :
( class_Fields_Ofield(X9)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(X9,X6),c_Polynomial_Odegree(X9,X33))
=> c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(X9),X6,X33) = X6 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__poly__less) ).
fof(fact_dvd__imp__mod__0,axiom,
! [X21,X8,X9] :
( class_Divides_Osemiring__div(X9)
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X9),X8),X21))
=> c_Divides_Odiv__class_Omod(X9,X21,X8) = c_Groups_Ozero__class_Ozero(X9) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__imp__mod__0) ).
fof(fact_dvd__eq__mod__eq__0,axiom,
! [X25,X11,X5] :
( class_Divides_Osemiring__div(X5)
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X5),X11),X25))
<=> c_Divides_Odiv__class_Omod(X5,X25,X11) = c_Groups_Ozero__class_Ozero(X5) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__eq__mod__eq__0) ).
fof(fact_pCons__def,axiom,
! [X4,X11,X5] :
( class_Groups_Ozero(X5)
=> hAPP(hAPP(c_Polynomial_OpCons(X5),X11),X4) = c_Polynomial_OAbs__poly(X5,c_Nat_Onat_Onat__case(X5,X11,c_Polynomial_Ocoeff(X5,X4))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pCons__def) ).
fof(fact_nat__lt__two__imp__zero__or__one,axiom,
! [X6] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X6,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))
=> ( X6 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X6 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__lt__two__imp__zero__or__one) ).
fof(fact_nonzero__minus__divide__divide,axiom,
! [X8,X21,X9] :
( class_Rings_Odivision__ring(X9)
=> ( X21 != c_Groups_Ozero__class_Ozero(X9)
=> hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X9),hAPP(c_Groups_Ouminus__class_Ouminus(X9),X8)),hAPP(c_Groups_Ouminus__class_Ouminus(X9),X21)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X9),X8),X21) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nonzero__minus__divide__divide) ).
fof(fact_inverse__positive__imp__positive,axiom,
! [X8,X9] :
( class_Fields_Olinordered__field(X9)
=> ( c_Orderings_Oord__class_Oless(X9,c_Groups_Ozero__class_Ozero(X9),hAPP(c_Rings_Oinverse__class_Oinverse(X9),X8))
=> ( X8 != c_Groups_Ozero__class_Ozero(X9)
=> c_Orderings_Oord__class_Oless(X9,c_Groups_Ozero__class_Ozero(X9),X8) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inverse__positive__imp__positive) ).
fof(fact_inverse__negative__imp__negative,axiom,
! [X8,X9] :
( class_Fields_Olinordered__field(X9)
=> ( c_Orderings_Oord__class_Oless(X9,hAPP(c_Rings_Oinverse__class_Oinverse(X9),X8),c_Groups_Ozero__class_Ozero(X9))
=> ( X8 != c_Groups_Ozero__class_Ozero(X9)
=> c_Orderings_Oord__class_Oless(X9,X8,c_Groups_Ozero__class_Ozero(X9)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inverse__negative__imp__negative) ).
fof(fact_degree__synthetic__div,axiom,
! [X23,X7,X9] :
( class_Rings_Ocomm__semiring__0(X9)
=> c_Polynomial_Odegree(X9,c_Polynomial_Osynthetic__div(X9,X7,X23)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),c_Polynomial_Odegree(X9,X7)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_degree__synthetic__div) ).
fof(fact_of__nat__less__imp__less,axiom,
! [X10,X12,X9] :
( class_Rings_Olinordered__semidom(X9)
=> ( c_Orderings_Oord__class_Oless(X9,c_Nat_Osemiring__1__class_Oof__nat(X9,X12),c_Nat_Osemiring__1__class_Oof__nat(X9,X10))
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X12,X10) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_of__nat__less__imp__less) ).
fof(fact_of__nat__less__iff,axiom,
! [X14,X35,X5] :
( class_Rings_Olinordered__semidom(X5)
=> ( c_Orderings_Oord__class_Oless(X5,c_Nat_Osemiring__1__class_Oof__nat(X5,X35),c_Nat_Osemiring__1__class_Oof__nat(X5,X14))
<=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X35,X14) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_of__nat__less__iff) ).
fof(fact_mult__Suc,axiom,
! [X10,X12] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,X12)),X10) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X10),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X12),X10)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__Suc) ).
fof(fact_less__imp__diff__less,axiom,
! [X10,X36,X40] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X40,X36)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X40),X10),X36) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__imp__diff__less) ).
fof(fact_termination__basic__simps_I1_J,axiom,
! [X32,X33,X6] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X6,X33)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X6,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X33),X32)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_termination__basic__simps_I1_J) ).
fof(fact_trans__less__add1,axiom,
! [X12,X40,X42] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X42,X40)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X42,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X40),X12)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_trans__less__add1) ).
fof(fact_termination__basic__simps_I2_J,axiom,
! [X33,X32,X6] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X6,X32)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X6,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X33),X32)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_termination__basic__simps_I2_J) ).
fof(fact_trans__less__add2,axiom,
! [X12,X40,X42] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X42,X40)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X42,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X12),X40)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_trans__less__add2) ).
fof(fact_diff__add__inverse,axiom,
! [X12,X10] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X10),X12)),X10) = X12,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__add__inverse) ).
fof(fact_diff__add__inverse2,axiom,
! [X10,X12] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X12),X10)),X10) = X12,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__add__inverse2) ).
fof(fact_minus__divide__divide,axiom,
! [X21,X8,X9] :
( class_Fields_Ofield__inverse__zero(X9)
=> hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X9),hAPP(c_Groups_Ouminus__class_Ouminus(X9),X8)),hAPP(c_Groups_Ouminus__class_Ouminus(X9),X21)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X9),X8),X21) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__divide__divide) ).
fof(fact_minus__mult__minus,axiom,
! [X21,X8,X9] :
( class_Rings_Oring(X9)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X9),hAPP(c_Groups_Ouminus__class_Ouminus(X9),X8)),hAPP(c_Groups_Ouminus__class_Ouminus(X9),X21)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X9),X8),X21) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__mult__minus) ).
fof(fact_minus__mult__commute,axiom,
! [X21,X8,X9] :
( class_Rings_Oring(X9)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X9),hAPP(c_Groups_Ouminus__class_Ouminus(X9),X8)),X21) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X9),X8),hAPP(c_Groups_Ouminus__class_Ouminus(X9),X21)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__mult__commute) ).
fof(fact_negative__zless__0,axiom,
! [X10] : c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,hAPP(c_Nat_OSuc,X10))),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_negative__zless__0) ).
fof(fact_nonzero__minus__divide__right,axiom,
! [X8,X21,X9] :
( class_Rings_Odivision__ring(X9)
=> ( X21 != c_Groups_Ozero__class_Ozero(X9)
=> hAPP(c_Groups_Ouminus__class_Ouminus(X9),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X9),X8),X21)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X9),X8),hAPP(c_Groups_Ouminus__class_Ouminus(X9),X21)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nonzero__minus__divide__right) ).
fof(fact_neg__less__0__iff__less,axiom,
! [X11,X5] :
( class_Groups_Oordered__ab__group__add(X5)
=> ( c_Orderings_Oord__class_Oless(X5,hAPP(c_Groups_Ouminus__class_Ouminus(X5),X11),c_Groups_Ozero__class_Ozero(X5))
<=> c_Orderings_Oord__class_Oless(X5,c_Groups_Ozero__class_Ozero(X5),X11) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_neg__less__0__iff__less) ).
fof(fact_inverse__positive__iff__positive,axiom,
! [X11,X5] :
( class_Fields_Olinordered__field__inverse__zero(X5)
=> ( c_Orderings_Oord__class_Oless(X5,c_Groups_Ozero__class_Ozero(X5),hAPP(c_Rings_Oinverse__class_Oinverse(X5),X11))
<=> c_Orderings_Oord__class_Oless(X5,c_Groups_Ozero__class_Ozero(X5),X11) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inverse__positive__iff__positive) ).
fof(fact_inverse__negative__iff__negative,axiom,
! [X11,X5] :
( class_Fields_Olinordered__field__inverse__zero(X5)
=> ( c_Orderings_Oord__class_Oless(X5,hAPP(c_Rings_Oinverse__class_Oinverse(X5),X11),c_Groups_Ozero__class_Ozero(X5))
<=> c_Orderings_Oord__class_Oless(X5,X11,c_Groups_Ozero__class_Ozero(X5)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inverse__negative__iff__negative) ).
fof(fact_neg__0__less__iff__less,axiom,
! [X11,X5] :
( class_Groups_Oordered__ab__group__add(X5)
=> ( c_Orderings_Oord__class_Oless(X5,c_Groups_Ozero__class_Ozero(X5),hAPP(c_Groups_Ouminus__class_Ouminus(X5),X11))
<=> c_Orderings_Oord__class_Oless(X5,X11,c_Groups_Ozero__class_Ozero(X5)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_neg__0__less__iff__less) ).
fof(fact_mod__mod__trivial,axiom,
! [X21,X8,X9] :
( class_Divides_Osemiring__div(X9)
=> c_Divides_Odiv__class_Omod(X9,c_Divides_Odiv__class_Omod(X9,X8,X21),X21) = c_Divides_Odiv__class_Omod(X9,X8,X21) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__mod__trivial) ).
fof(fact_mult__right_Ominus,axiom,
! [X6,X44,X9] :
( class_RealVector_Oreal__normed__algebra(X9)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X9),X44),hAPP(c_Groups_Ouminus__class_Ouminus(X9),X6)) = hAPP(c_Groups_Ouminus__class_Ouminus(X9),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X9),X44),X6)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__right_Ominus) ).
fof(fact_mult_Ominus__right,axiom,
! [X21,X8,X9] :
( class_RealVector_Oreal__normed__algebra(X9)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X9),X8),hAPP(c_Groups_Ouminus__class_Ouminus(X9),X21)) = hAPP(c_Groups_Ouminus__class_Ouminus(X9),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X9),X8),X21)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult_Ominus__right) ).
fof(fact_minus__divide__right,axiom,
! [X21,X8,X9] :
( class_Fields_Ofield__inverse__zero(X9)
=> hAPP(c_Groups_Ouminus__class_Ouminus(X9),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X9),X8),X21)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X9),X8),hAPP(c_Groups_Ouminus__class_Ouminus(X9),X21)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__divide__right) ).
fof(fact_minus__mult__right,axiom,
! [X21,X8,X9] :
( class_Rings_Oring(X9)
=> hAPP(c_Groups_Ouminus__class_Ouminus(X9),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X9),X8),X21)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X9),X8),hAPP(c_Groups_Ouminus__class_Ouminus(X9),X21)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__mult__right) ).
fof(fact_dvd__0__left,axiom,
! [X8,X9] :
( class_Rings_Ocomm__semiring__1(X9)
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X9),c_Groups_Ozero__class_Ozero(X9)),X8))
=> X8 = c_Groups_Ozero__class_Ozero(X9) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__0__left) ).
fof(fact_mod__add__self1,axiom,
! [X8,X21,X9] :
( class_Divides_Osemiring__div(X9)
=> c_Divides_Odiv__class_Omod(X9,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X9),X21),X8),X21) = c_Divides_Odiv__class_Omod(X9,X8,X21) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__add__self1) ).
fof(fact_mod__add__self2,axiom,
! [X21,X8,X9] :
( class_Divides_Osemiring__div(X9)
=> c_Divides_Odiv__class_Omod(X9,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X9),X8),X21),X21) = c_Divides_Odiv__class_Omod(X9,X8,X21) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__add__self2) ).
fof(fact_pos__poly__mult,axiom,
! [X13,X7,X9] :
( class_Rings_Olinordered__idom(X9)
=> ( c_Polynomial_Opos__poly(X9,X7)
=> ( c_Polynomial_Opos__poly(X9,X13)
=> c_Polynomial_Opos__poly(X9,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X9)),X7),X13)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pos__poly__mult) ).
fof(fact_pos__poly__add,axiom,
! [X13,X7,X9] :
( class_Rings_Olinordered__idom(X9)
=> ( c_Polynomial_Opos__poly(X9,X7)
=> ( c_Polynomial_Opos__poly(X9,X13)
=> c_Polynomial_Opos__poly(X9,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X9)),X7),X13)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pos__poly__add) ).
fof(fact_Nat__Transfer_Otransfer__int__nat__functions_I2_J,axiom,
! [X33,X6] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,X6)),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,X33)) = c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X6),X33)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__int__nat__functions_I2_J) ).
fof(fact_zmult__int,axiom,
! [X10,X12] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,X12)),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,X10)) = c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X12),X10)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zmult__int) ).
fof(fact_Nat__Transfer_Otransfer__int__nat__functions_I1_J,axiom,
! [X33,X6] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,X6)),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,X33)) = c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X6),X33)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__int__nat__functions_I1_J) ).
fof(fact_zadd__int,axiom,
! [X10,X12] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,X12)),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,X10)) = c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X12),X10)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zadd__int) ).
fof(fact_zmult__zminus,axiom,
! [X51,X32] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X32)),X51) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X32),X51)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zmult__zminus) ).
fof(fact_int__mult,axiom,
! [X10,X12] : c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X12),X10)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,X12)),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,X10)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_int__mult) ).
fof(fact_of__nat__power,axiom,
! [X10,X12,X9] :
( class_Rings_Osemiring__1(X9)
=> c_Nat_Osemiring__1__class_Oof__nat(X9,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X12),X10)) = hAPP(hAPP(c_Power_Opower__class_Opower(X9),c_Nat_Osemiring__1__class_Oof__nat(X9,X12)),X10) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_of__nat__power) ).
fof(fact_Divides_Otransfer__int__nat__functions_I2_J,axiom,
! [X33,X6] : c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,X6),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,X33)) = c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X6,X33)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Divides_Otransfer__int__nat__functions_I2_J) ).
fof(fact_zmod__int,axiom,
! [X21,X8] : c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X8,X21)) = c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,X8),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,X21)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zmod__int) ).
fof(fact_neg__less__nonneg,axiom,
! [X11,X5] :
( class_Groups_Olinordered__ab__group__add(X5)
=> ( c_Orderings_Oord__class_Oless(X5,hAPP(c_Groups_Ouminus__class_Ouminus(X5),X11),X11)
<=> c_Orderings_Oord__class_Oless(X5,c_Groups_Ozero__class_Ozero(X5),X11) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_neg__less__nonneg) ).
fof(fact_less__minus__self__iff,axiom,
! [X11,X5] :
( class_Rings_Olinordered__idom(X5)
=> ( c_Orderings_Oord__class_Oless(X5,X11,hAPP(c_Groups_Ouminus__class_Ouminus(X5),X11))
<=> c_Orderings_Oord__class_Oless(X5,X11,c_Groups_Ozero__class_Ozero(X5)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__minus__self__iff) ).
fof(fact_mult__left__idem,axiom,
! [X21,X8,X9] :
( class_Lattices_Oab__semigroup__idem__mult(X9)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X9),X8),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X9),X8),X21)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X9),X8),X21) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__left__idem) ).
fof(fact_dvd__1__left,axiom,
! [X36] : hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X36)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__1__left) ).
fof(fact_fun__Compl__def,axiom,
! [X27,X59,X15,X5] :
( class_Groups_Ouminus(X5)
=> hAPP(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X15,X5)),X59),X27) = hAPP(c_Groups_Ouminus__class_Ouminus(X5),hAPP(X59,X27)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fun__Compl__def) ).
fof(fact_uminus__apply,axiom,
! [X27,X59,X15,X5] :
( class_Groups_Ouminus(X5)
=> hAPP(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X15,X5)),X59),X27) = hAPP(c_Groups_Ouminus__class_Ouminus(X5),hAPP(X59,X27)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_uminus__apply) ).
fof(fact_Nat__Transfer_Otransfer__int__nat__relations_I2_J,axiom,
! [X28,X27] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,X27),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,X28))
<=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X27,X28) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__int__nat__relations_I2_J) ).
fof(fact_zless__int,axiom,
! [X14,X35] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,X35),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,X14))
<=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X35,X14) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zless__int) ).
fof(fact_Suc__less__eq,axiom,
! [X14,X35] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(c_Nat_OSuc,X35),hAPP(c_Nat_OSuc,X14))
<=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X35,X14) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__less__eq) ).
fof(fact_Suc__less__SucD,axiom,
! [X10,X12] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(c_Nat_OSuc,X12),hAPP(c_Nat_OSuc,X10))
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X12,X10) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__less__SucD) ).
fof(fact_zero__less__two,axiom,
! [X9] :
( class_Rings_Olinordered__semidom(X9)
=> c_Orderings_Oord__class_Oless(X9,c_Groups_Ozero__class_Ozero(X9),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X9),c_Groups_Oone__class_Oone(X9)),c_Groups_Oone__class_Oone(X9))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__less__two) ).
fof(fact_mult__Suc__right,axiom,
! [X10,X12] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X12),hAPP(c_Nat_OSuc,X10)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X12),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X12),X10)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__Suc__right) ).
fof(fact_coeff__pCons,axiom,
! [X4,X11,X5] :
( class_Groups_Ozero(X5)
=> c_Polynomial_Ocoeff(X5,hAPP(hAPP(c_Polynomial_OpCons(X5),X11),X4)) = c_Nat_Onat_Onat__case(X5,X11,c_Polynomial_Ocoeff(X5,X4)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_coeff__pCons) ).
fof(fact_less__Suc__eq__0__disj,axiom,
! [X14,X35] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X35,hAPP(c_Nat_OSuc,X14))
<=> ( X35 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ? [X90] :
( X35 = hAPP(c_Nat_OSuc,X90)
& c_Orderings_Oord__class_Oless(tc_Nat_Onat,X90,X14) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__Suc__eq__0__disj) ).
fof(fact_negative__imp__inverse__negative,axiom,
! [X8,X9] :
( class_Fields_Olinordered__field(X9)
=> ( c_Orderings_Oord__class_Oless(X9,X8,c_Groups_Ozero__class_Ozero(X9))
=> c_Orderings_Oord__class_Oless(X9,hAPP(c_Rings_Oinverse__class_Oinverse(X9),X8),c_Groups_Ozero__class_Ozero(X9)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_negative__imp__inverse__negative) ).
fof(fact_positive__imp__inverse__positive,axiom,
! [X8,X9] :
( class_Fields_Olinordered__field(X9)
=> ( c_Orderings_Oord__class_Oless(X9,c_Groups_Ozero__class_Ozero(X9),X8)
=> c_Orderings_Oord__class_Oless(X9,c_Groups_Ozero__class_Ozero(X9),hAPP(c_Rings_Oinverse__class_Oinverse(X9),X8)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_positive__imp__inverse__positive) ).
fof(fact_of__nat__0__less__iff,axiom,
! [X14,X5] :
( class_Rings_Olinordered__semidom(X5)
=> ( c_Orderings_Oord__class_Oless(X5,c_Groups_Ozero__class_Ozero(X5),c_Nat_Osemiring__1__class_Oof__nat(X5,X14))
<=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X14) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_of__nat__0__less__iff) ).
fof(fact_negD,axiom,
! [X6] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X6,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
=> ? [X49] : X6 = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,hAPP(c_Nat_OSuc,X49))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_negD) ).
fof(fact_Suc__diff__1,axiom,
! [X10] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X10)
=> hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X10),c_Groups_Oone__class_Oone(tc_Nat_Onat))) = X10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__diff__1) ).
fof(fact_Suc__pred_H,axiom,
! [X10] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X10)
=> X10 = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X10),c_Groups_Oone__class_Oone(tc_Nat_Onat))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__pred_H) ).
fof(fact_dvdI,axiom,
! [X36,X21,X8,X9] :
( class_Rings_Odvd(X9)
=> ( X8 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X9),X21),X36)
=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X9),X21),X8)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvdI) ).
fof(fact_less__imp__of__nat__less,axiom,
! [X10,X12,X9] :
( class_Rings_Olinordered__semidom(X9)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X12,X10)
=> c_Orderings_Oord__class_Oless(X9,c_Nat_Osemiring__1__class_Oof__nat(X9,X12),c_Nat_Osemiring__1__class_Oof__nat(X9,X10)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__imp__of__nat__less) ).
fof(fact_square__eq__iff,axiom,
! [X25,X11,X5] :
( class_Rings_Oidom(X5)
=> ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X11),X11) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X25),X25)
<=> ( X11 = X25
| X11 = hAPP(c_Groups_Ouminus__class_Ouminus(X5),X25) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_square__eq__iff) ).
fof(fact_Nat__Transfer_Otransfer__int__nat__functions_I4_J,axiom,
! [X10,X6] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,X6)),X10) = c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X6),X10)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__int__nat__functions_I4_J) ).
fof(fact_zpower__int,axiom,
! [X10,X12] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,X12)),X10) = c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X12),X10)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zpower__int) ).
fof(fact_add__Suc,axiom,
! [X10,X12] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_OSuc,X12)),X10) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X12),X10)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__Suc) ).
fof(fact_int__power,axiom,
! [X10,X12] : c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X12),X10)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,X12)),X10),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_int__power) ).
fof(fact_nat__less__cases,axiom,
! [X68,X14,X35] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X35,X14)
=> hBOOL(hAPP(hAPP(X68,X14),X35)) )
=> ( ( X35 = X14
=> hBOOL(hAPP(hAPP(X68,X14),X35)) )
=> ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X14,X35)
=> hBOOL(hAPP(hAPP(X68,X14),X35)) )
=> hBOOL(hAPP(hAPP(X68,X14),X35)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__less__cases) ).
fof(fact_poly__mod__minus__right,axiom,
! [X33,X6,X9] :
( class_Fields_Ofield(X9)
=> c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(X9),X6,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X9)),X33)) = c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(X9),X6,X33) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_poly__mod__minus__right) ).
fof(fact_Suc__mono,axiom,
! [X10,X12] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X12,X10)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(c_Nat_OSuc,X12),hAPP(c_Nat_OSuc,X10)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__mono) ).
fof(fact_synthetic__div__unique__lemma,axiom,
! [X8,X7,X23,X9] :
( class_Rings_Ocomm__semiring__0(X9)
=> ( hAPP(hAPP(c_Polynomial_Osmult(X9),X23),X7) = hAPP(hAPP(c_Polynomial_OpCons(X9),X8),X7)
=> X7 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X9)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_synthetic__div__unique__lemma) ).
fof(fact_inverse__divide,axiom,
! [X21,X8,X9] :
( class_Fields_Ofield__inverse__zero(X9)
=> hAPP(c_Rings_Oinverse__class_Oinverse(X9),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X9),X8),X21)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X9),X21),X8) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inverse__divide) ).
fof(fact_minus__diff__eq,axiom,
! [X21,X8,X9] :
( class_Groups_Oab__group__add(X9)
=> hAPP(c_Groups_Ouminus__class_Ouminus(X9),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X9),X8),X21)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(X9),X21),X8) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__diff__eq) ).
fof(fact_zero__less__int__conv,axiom,
! [X14] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,X14))
<=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X14) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__less__int__conv) ).
fof(fact_monom__eq__iff,axiom,
! [X25,X14,X11,X5] :
( class_Groups_Ozero(X5)
=> ( c_Polynomial_Omonom(X5,X11,X14) = c_Polynomial_Omonom(X5,X25,X14)
<=> X11 = X25 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_monom__eq__iff) ).
fof(fact_comm__ring__1__class_Onormalizing__ring__rules_I1_J,axiom,
! [X6,X9] :
( class_Rings_Ocomm__ring__1(X9)
=> hAPP(c_Groups_Ouminus__class_Ouminus(X9),X6) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X9),hAPP(c_Groups_Ouminus__class_Ouminus(X9),c_Groups_Oone__class_Oone(X9))),X6) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__ring__1__class_Onormalizing__ring__rules_I1_J) ).
fof(fact_poly__gcd__minus__left,axiom,
! [X33,X6,X9] :
( class_Fields_Ofield(X9)
=> c_Polynomial_Opoly__gcd(X9,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X9)),X6),X33) = c_Polynomial_Opoly__gcd(X9,X6,X33) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_poly__gcd__minus__left) ).
fof(fact_poly__gcd__minus__right,axiom,
! [X33,X6,X9] :
( class_Fields_Ofield(X9)
=> c_Polynomial_Opoly__gcd(X9,X6,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X9)),X33)) = c_Polynomial_Opoly__gcd(X9,X6,X33) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_poly__gcd__minus__right) ).
fof(fact_order__root,axiom,
! [X11,X4,X5] :
( class_Rings_Oidom(X5)
=> ( hAPP(c_Polynomial_Opoly(X5,X4),X11) = c_Groups_Ozero__class_Ozero(X5)
<=> ( X4 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X5))
| c_Polynomial_Oorder(X5,X11,X4) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__root) ).
fof(fact_diff__eq__diff__eq,axiom,
! [X30,X31,X25,X11,X5] :
( class_Groups_Oab__group__add(X5)
=> ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(X5),X11),X25) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(X5),X31),X30)
=> ( X11 = X25
<=> X31 = X30 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__eq__diff__eq) ).
fof(fact_less__add__one,axiom,
! [X8,X9] :
( class_Rings_Olinordered__semidom(X9)
=> c_Orderings_Oord__class_Oless(X9,X8,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X9),X8),c_Groups_Oone__class_Oone(X9))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__add__one) ).
fof(fact_coeff__eq__0,axiom,
! [X10,X7,X9] :
( class_Groups_Ozero(X9)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(X9,X7),X10)
=> hAPP(c_Polynomial_Ocoeff(X9,X7),X10) = c_Groups_Ozero__class_Ozero(X9) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_coeff__eq__0) ).
fof(fact_less__Suc__eq,axiom,
! [X14,X35] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X35,hAPP(c_Nat_OSuc,X14))
<=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X35,X14)
| X35 = X14 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__Suc__eq) ).
fof(fact_zmod__zminus1__not__zero,axiom,
! [X76,X36] :
( c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X36),X76) != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
=> c_Divides_Odiv__class_Omod(tc_Int_Oint,X36,X76) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zmod__zminus1__not__zero) ).
fof(fact_zmod__zminus2__not__zero,axiom,
! [X76,X36] :
( c_Divides_Odiv__class_Omod(tc_Int_Oint,X36,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X76)) != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
=> c_Divides_Odiv__class_Omod(tc_Int_Oint,X36,X76) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zmod__zminus2__not__zero) ).
fof(fact_Suc__lessI,axiom,
! [X10,X12] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X12,X10)
=> ( hAPP(c_Nat_OSuc,X12) != X10
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(c_Nat_OSuc,X12),X10) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__lessI) ).
fof(fact_pCons__eq__iff,axiom,
! [X24,X25,X4,X11,X5] :
( class_Groups_Ozero(X5)
=> ( hAPP(hAPP(c_Polynomial_OpCons(X5),X11),X4) = hAPP(hAPP(c_Polynomial_OpCons(X5),X25),X24)
<=> ( X11 = X25
& X4 = X24 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pCons__eq__iff) ).
fof(fact_add__right__imp__eq,axiom,
! [X23,X8,X21,X9] :
( class_Groups_Ocancel__semigroup__add(X9)
=> ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X9),X21),X8) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X9),X23),X8)
=> X21 = X23 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__right__imp__eq) ).
fof(fact_add__right__cancel,axiom,
! [X31,X11,X25,X5] :
( class_Groups_Ocancel__semigroup__add(X5)
=> ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X25),X11) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X31),X11)
<=> X25 = X31 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__right__cancel) ).
fof(fact_add__imp__eq,axiom,
! [X23,X21,X8,X9] :
( class_Groups_Ocancel__ab__semigroup__add(X9)
=> ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X9),X8),X21) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X9),X8),X23)
=> X21 = X23 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__imp__eq) ).
fof(fact_add__left__imp__eq,axiom,
! [X23,X21,X8,X9] :
( class_Groups_Ocancel__semigroup__add(X9)
=> ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X9),X8),X21) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X9),X8),X23)
=> X21 = X23 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__left__imp__eq) ).
fof(fact_add__left__cancel,axiom,
! [X31,X25,X11,X5] :
( class_Groups_Ocancel__semigroup__add(X5)
=> ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X11),X25) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X11),X31)
<=> X25 = X31 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__left__cancel) ).
fof(fact_degree__pCons__eq__if,axiom,
! [X8,X7,X9] :
( class_Groups_Ozero(X9)
=> ( ( X7 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X9))
=> c_Polynomial_Odegree(X9,hAPP(hAPP(c_Polynomial_OpCons(X9),X8),X7)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( X7 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X9))
=> c_Polynomial_Odegree(X9,hAPP(hAPP(c_Polynomial_OpCons(X9),X8),X7)) = hAPP(c_Nat_OSuc,c_Polynomial_Odegree(X9,X7)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_degree__pCons__eq__if) ).
fof(fact_degree__pCons__eq,axiom,
! [X8,X7,X9] :
( class_Groups_Ozero(X9)
=> ( X7 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X9))
=> c_Polynomial_Odegree(X9,hAPP(hAPP(c_Polynomial_OpCons(X9),X8),X7)) = hAPP(c_Nat_OSuc,c_Polynomial_Odegree(X9,X7)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_degree__pCons__eq) ).
fof(fact_Suc__lessD,axiom,
! [X10,X12] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(c_Nat_OSuc,X12),X10)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X12,X10) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__lessD) ).
fof(fact_mod__div__trivial,axiom,
! [X21,X8,X9] :
( class_Divides_Osemiring__div(X9)
=> c_Divides_Odiv__class_Odiv(X9,c_Divides_Odiv__class_Omod(X9,X8,X21),X21) = c_Groups_Ozero__class_Ozero(X9) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__div__trivial) ).
fof(fact_add__Suc__right,axiom,
! [X10,X12] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X12),hAPP(c_Nat_OSuc,X10)) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X12),X10)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__Suc__right) ).
fof(fact_div__mult__self1__is__id,axiom,
! [X8,X21,X9] :
( class_Divides_Osemiring__div(X9)
=> ( X21 != c_Groups_Ozero__class_Ozero(X9)
=> c_Divides_Odiv__class_Odiv(X9,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X9),X21),X8),X21) = X8 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_div__mult__self1__is__id) ).
fof(fact_div__mult__self2__is__id,axiom,
! [X8,X21,X9] :
( class_Divides_Osemiring__div(X9)
=> ( X21 != c_Groups_Ozero__class_Ozero(X9)
=> c_Divides_Odiv__class_Odiv(X9,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X9),X8),X21),X21) = X8 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_div__mult__self2__is__id) ).
fof(fact_zdiv__zminus__zminus,axiom,
! [X21,X8] : c_Divides_Odiv__class_Odiv(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X8),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X21)) = c_Divides_Odiv__class_Odiv(tc_Int_Oint,X8,X21),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zdiv__zminus__zminus) ).
fof(fact_zdiv__zminus2,axiom,
! [X21,X8] : c_Divides_Odiv__class_Odiv(tc_Int_Oint,X8,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X21)) = c_Divides_Odiv__class_Odiv(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X8),X21),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zdiv__zminus2) ).
fof(fact_pos__zmult__eq__1__iff,axiom,
! [X14,X35] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X35)
=> ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X35),X14) = c_Groups_Oone__class_Oone(tc_Int_Oint)
<=> ( X35 = c_Groups_Oone__class_Oone(tc_Int_Oint)
& X14 = c_Groups_Oone__class_Oone(tc_Int_Oint) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pos__zmult__eq__1__iff) ).
fof(fact_mod__mult__self1__is__0,axiom,
! [X8,X21,X9] :
( class_Divides_Osemiring__div(X9)
=> c_Divides_Odiv__class_Omod(X9,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X9),X21),X8),X21) = c_Groups_Ozero__class_Ozero(X9) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__mult__self1__is__0) ).
fof(fact_mod__mult__self2__is__0,axiom,
! [X21,X8,X9] :
( class_Divides_Osemiring__div(X9)
=> c_Divides_Odiv__class_Omod(X9,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X9),X8),X21),X21) = c_Groups_Ozero__class_Ozero(X9) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__mult__self2__is__0) ).
fof(fact_diff__less__Suc,axiom,
! [X10,X12] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X12),X10),hAPP(c_Nat_OSuc,X12)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__less__Suc) ).
fof(fact_degree__pCons__0,axiom,
! [X8,X9] :
( class_Groups_Ozero(X9)
=> c_Polynomial_Odegree(X9,hAPP(hAPP(c_Polynomial_OpCons(X9),X8),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X9)))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_degree__pCons__0) ).
fof(fact_nat__dvd__1__iff__1,axiom,
! [X35] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X35),c_Groups_Oone__class_Oone(tc_Nat_Onat)))
<=> X35 = c_Groups_Oone__class_Oone(tc_Nat_Onat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__dvd__1__iff__1) ).
fof(fact_diff__Suc__Suc,axiom,
! [X10,X12] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,X12)),hAPP(c_Nat_OSuc,X10)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X12),X10),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__Suc__Suc) ).
fof(fact_add__Suc__shift,axiom,
! [X10,X12] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_OSuc,X12)),X10) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X12),hAPP(c_Nat_OSuc,X10)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__Suc__shift) ).
fof(fact_zmod__eq__0__iff,axiom,
! [X30,X35] :
( c_Divides_Odiv__class_Omod(tc_Int_Oint,X35,X30) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
<=> ? [X77] : X35 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X30),X77) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zmod__eq__0__iff) ).
fof(fact_mod__eq__0__iff,axiom,
! [X30,X35] :
( c_Divides_Odiv__class_Omod(tc_Nat_Onat,X35,X30) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
<=> ? [X77] : X35 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X30),X77) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__eq__0__iff) ).
fof(fact_less__SucI,axiom,
! [X10,X12] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X12,X10)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X12,hAPP(c_Nat_OSuc,X10)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__SucI) ).
fof(fact_zmod__zdiv__trivial,axiom,
! [X21,X8] : c_Divides_Odiv__class_Odiv(tc_Int_Oint,c_Divides_Odiv__class_Omod(tc_Int_Oint,X8,X21),X21) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zmod__zdiv__trivial) ).
fof(fact_nat__case__Suc,axiom,
! [X61,X56,X57,X5] : hAPP(c_Nat_Onat_Onat__case(X5,X57,X56),hAPP(c_Nat_OSuc,X61)) = hAPP(X56,X61),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__case__Suc) ).
fof(fact_diffs0__imp__equal,axiom,
! [X10,X12] :
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X12),X10) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X10),X12) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> X12 = X10 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diffs0__imp__equal) ).
fof(fact_negative__zle,axiom,
! [X12,X10] : c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,X10)),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,X12)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_negative__zle) ).
fof(fact_divide__eq__eq,axiom,
! [X11,X31,X25,X5] :
( class_Fields_Ofield__inverse__zero(X5)
=> ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X5),X25),X31) = X11
<=> ( ( X31 != c_Groups_Ozero__class_Ozero(X5)
=> X25 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X11),X31) )
& ( X31 = c_Groups_Ozero__class_Ozero(X5)
=> X11 = c_Groups_Ozero__class_Ozero(X5) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide__eq__eq) ).
fof(fact_eq__divide__eq,axiom,
! [X31,X25,X11,X5] :
( class_Fields_Ofield__inverse__zero(X5)
=> ( X11 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X5),X25),X31)
<=> ( ( X31 != c_Groups_Ozero__class_Ozero(X5)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X11),X31) = X25 )
& ( X31 = c_Groups_Ozero__class_Ozero(X5)
=> X11 = c_Groups_Ozero__class_Ozero(X5) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_eq__divide__eq) ).
fof(fact_diff__poly__code_I1_J,axiom,
! [X13,X9] :
( class_Groups_Oab__group__add(X9)
=> hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X9)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X9))),X13) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X9)),X13) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__poly__code_I1_J) ).
fof(fact_mult__cancel2,axiom,
! [X14,X39,X35] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X35),X39) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X14),X39)
<=> ( X35 = X14
| X39 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__cancel2) ).
fof(fact_nat__mult__eq__cancel__disj,axiom,
! [X14,X35,X39] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X39),X35) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X39),X14)
<=> ( X39 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X35 = X14 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__mult__eq__cancel__disj) ).
fof(fact_mult__cancel1,axiom,
! [X14,X35,X39] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X39),X35) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X39),X14)
<=> ( X35 = X14
| X39 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__cancel1) ).
fof(fact_divide__eq__imp,axiom,
! [X8,X21,X23,X9] :
( class_Rings_Odivision__ring(X9)
=> ( X23 != c_Groups_Ozero__class_Ozero(X9)
=> ( X21 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X9),X8),X23)
=> hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X9),X21),X23) = X8 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide__eq__imp) ).
fof(fact_nonzero__divide__eq__eq,axiom,
! [X11,X25,X31,X5] :
( class_Rings_Odivision__ring(X5)
=> ( X31 != c_Groups_Ozero__class_Ozero(X5)
=> ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X5),X25),X31) = X11
<=> X25 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X11),X31) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nonzero__divide__eq__eq) ).
fof(fact_nonzero__eq__divide__eq,axiom,
! [X25,X11,X31,X5] :
( class_Rings_Odivision__ring(X5)
=> ( X31 != c_Groups_Ozero__class_Ozero(X5)
=> ( X11 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X5),X25),X31)
<=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X11),X31) = X25 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nonzero__eq__divide__eq) ).
fof(fact_eq__divide__imp,axiom,
! [X21,X8,X23,X9] :
( class_Rings_Odivision__ring(X9)
=> ( X23 != c_Groups_Ozero__class_Ozero(X9)
=> ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X9),X8),X23) = X21
=> X8 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X9),X21),X23) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_eq__divide__imp) ).
fof(fact_diff__minus__eq__add,axiom,
! [X21,X8,X9] :
( class_Groups_Ogroup__add(X9)
=> hAPP(hAPP(c_Groups_Ominus__class_Ominus(X9),X8),hAPP(c_Groups_Ouminus__class_Ouminus(X9),X21)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X9),X8),X21) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__minus__eq__add) ).
fof(fact_divide__inverse,axiom,
! [X21,X8,X9] :
( class_Rings_Odivision__ring(X9)
=> hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X9),X8),X21) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X9),X8),hAPP(c_Rings_Oinverse__class_Oinverse(X9),X21)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide__inverse) ).
fof(fact_field__divide__inverse,axiom,
! [X21,X8,X9] :
( class_Fields_Ofield(X9)
=> hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X9),X8),X21) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X9),X8),hAPP(c_Rings_Oinverse__class_Oinverse(X9),X21)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_field__divide__inverse) ).
fof(fact_diff__def,axiom,
! [X21,X8,X9] :
( class_Groups_Ogroup__add(X9)
=> hAPP(hAPP(c_Groups_Ominus__class_Ominus(X9),X8),X21) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X9),X8),hAPP(c_Groups_Ouminus__class_Ouminus(X9),X21)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__def) ).
fof(fact_ab__diff__minus,axiom,
! [X21,X8,X9] :
( class_Groups_Oab__group__add(X9)
=> hAPP(hAPP(c_Groups_Ominus__class_Ominus(X9),X8),X21) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X9),X8),hAPP(c_Groups_Ouminus__class_Ouminus(X9),X21)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ab__diff__minus) ).
fof(fact_comm__ring__1__class_Onormalizing__ring__rules_I2_J,axiom,
! [X33,X6,X9] :
( class_Rings_Ocomm__ring__1(X9)
=> hAPP(hAPP(c_Groups_Ominus__class_Ominus(X9),X6),X33) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X9),X6),hAPP(c_Groups_Ouminus__class_Ouminus(X9),X33)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__ring__1__class_Onormalizing__ring__rules_I2_J) ).
fof(fact_nat__add__right__cancel,axiom,
! [X14,X39,X35] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X35),X39) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X14),X39)
<=> X35 = X14 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__add__right__cancel) ).
fof(fact_nat__add__left__cancel,axiom,
! [X14,X35,X39] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X39),X35) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X39),X14)
<=> X35 = X14 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__add__left__cancel) ).
fof(fact_left__inverse,axiom,
! [X8,X9] :
( class_Rings_Odivision__ring(X9)
=> ( X8 != c_Groups_Ozero__class_Ozero(X9)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X9),hAPP(c_Rings_Oinverse__class_Oinverse(X9),X8)),X8) = c_Groups_Oone__class_Oone(X9) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_left__inverse) ).
fof(fact_field__inverse,axiom,
! [X8,X9] :
( class_Fields_Ofield(X9)
=> ( X8 != c_Groups_Ozero__class_Ozero(X9)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X9),hAPP(c_Rings_Oinverse__class_Oinverse(X9),X8)),X8) = c_Groups_Oone__class_Oone(X9) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_field__inverse) ).
fof(fact_degree__smult__eq,axiom,
! [X7,X8,X9] :
( class_Rings_Oidom(X9)
=> ( ( X8 = c_Groups_Ozero__class_Ozero(X9)
=> c_Polynomial_Odegree(X9,hAPP(hAPP(c_Polynomial_Osmult(X9),X8),X7)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( X8 != c_Groups_Ozero__class_Ozero(X9)
=> c_Polynomial_Odegree(X9,hAPP(hAPP(c_Polynomial_Osmult(X9),X8),X7)) = c_Polynomial_Odegree(X9,X7) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_degree__smult__eq) ).
fof(fact_degree__offset__poly,axiom,
! [X48,X7,X9] :
( class_Rings_Ocomm__semiring__0(X9)
=> c_Polynomial_Odegree(X9,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X9,X7,X48)) = c_Polynomial_Odegree(X9,X7) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_degree__offset__poly) ).
fof(fact_left__minus,axiom,
! [X8,X9] :
( class_Groups_Ogroup__add(X9)
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(X9),hAPP(c_Groups_Ouminus__class_Ouminus(X9),X8)),X8) = c_Groups_Ozero__class_Ozero(X9) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_left__minus) ).
fof(fact_ab__left__minus,axiom,
! [X8,X9] :
( class_Groups_Oab__group__add(X9)
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(X9),hAPP(c_Groups_Ouminus__class_Ouminus(X9),X8)),X8) = c_Groups_Ozero__class_Ozero(X9) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ab__left__minus) ).
fof(fact_diff__add__0,axiom,
! [X12,X10] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X10),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X10),X12)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__add__0) ).
fof(fact_one__dvd,axiom,
! [X8,X9] :
( class_Rings_Ocomm__semiring__1(X9)
=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X9),c_Groups_Oone__class_Oone(X9)),X8)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_one__dvd) ).
fof(fact_mod__less,axiom,
! [X10,X12] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X12,X10)
=> c_Divides_Odiv__class_Omod(tc_Nat_Onat,X12,X10) = X12 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__less) ).
fof(fact_LeastI__ex,axiom,
! [X68,X5] :
( class_Orderings_Owellorder(X5)
=> ( ? [X74] : hBOOL(hAPP(X68,X74))
=> hBOOL(hAPP(X68,c_Orderings_Oord__class_OLeast(X5,X68))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_LeastI__ex) ).
fof(fact_LeastI,axiom,
! [X39,X68,X5] :
( class_Orderings_Owellorder(X5)
=> ( hBOOL(hAPP(X68,X39))
=> hBOOL(hAPP(X68,c_Orderings_Oord__class_OLeast(X5,X68))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_LeastI) ).
fof(fact_monom__0,axiom,
! [X8,X9] :
( class_Groups_Ozero(X9)
=> c_Polynomial_Omonom(X9,X8,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(hAPP(c_Polynomial_OpCons(X9),X8),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X9))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_monom__0) ).
fof(fact_degree__monom__eq,axiom,
! [X10,X8,X9] :
( class_Groups_Ozero(X9)
=> ( X8 != c_Groups_Ozero__class_Ozero(X9)
=> c_Polynomial_Odegree(X9,c_Polynomial_Omonom(X9,X8,X10)) = X10 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_degree__monom__eq) ).
fof(fact_of__nat__Suc,axiom,
! [X12,X9] :
( class_Rings_Osemiring__1(X9)
=> c_Nat_Osemiring__1__class_Oof__nat(X9,hAPP(c_Nat_OSuc,X12)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X9),c_Groups_Oone__class_Oone(X9)),c_Nat_Osemiring__1__class_Oof__nat(X9,X12)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_of__nat__Suc) ).
fof(fact_less__Suc0,axiom,
! [X14] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X14,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
<=> X14 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__Suc0) ).
fof(fact_mult__poly__0__left,axiom,
! [X13,X9] :
( class_Rings_Ocomm__semiring__0(X9)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X9)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X9))),X13) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X9)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__poly__0__left) ).
fof(fact_add__is__1,axiom,
! [X14,X35] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X35),X14) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
<=> ( ( X35 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
& X14 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
| ( X35 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& X14 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__is__1) ).
fof(fact_one__is__add,axiom,
! [X14,X35] :
( hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X35),X14)
<=> ( ( X35 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
& X14 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
| ( X35 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& X14 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_one__is__add) ).
fof(fact_nonzero__inverse__minus__eq,axiom,
! [X8,X9] :
( class_Rings_Odivision__ring(X9)
=> ( X8 != c_Groups_Ozero__class_Ozero(X9)
=> hAPP(c_Rings_Oinverse__class_Oinverse(X9),hAPP(c_Groups_Ouminus__class_Ouminus(X9),X8)) = hAPP(c_Groups_Ouminus__class_Ouminus(X9),hAPP(c_Rings_Oinverse__class_Oinverse(X9),X8)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nonzero__inverse__minus__eq) ).
fof(fact_leading__coeff__0__iff,axiom,
! [X4,X5] :
( class_Groups_Ozero(X5)
=> ( hAPP(c_Polynomial_Ocoeff(X5,X4),c_Polynomial_Odegree(X5,X4)) = c_Groups_Ozero__class_Ozero(X5)
<=> X4 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X5)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_leading__coeff__0__iff) ).
fof(fact_leading__coeff__neq__0,axiom,
! [X7,X9] :
( class_Groups_Ozero(X9)
=> ( X7 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X9))
=> hAPP(c_Polynomial_Ocoeff(X9,X7),c_Polynomial_Odegree(X9,X7)) != c_Groups_Ozero__class_Ozero(X9) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_leading__coeff__neq__0) ).
fof(fact_square__eq__1__iff,axiom,
! [X27,X5] :
( class_Rings_Oring__1__no__zero__divisors(X5)
=> ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X27),X27) = c_Groups_Oone__class_Oone(X5)
<=> ( X27 = c_Groups_Oone__class_Oone(X5)
| X27 = hAPP(c_Groups_Ouminus__class_Ouminus(X5),c_Groups_Oone__class_Oone(X5)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_square__eq__1__iff) ).
fof(fact_ext,axiom,
! [X1,X2] :
( ! [X3] : hAPP(X2,X3) = hAPP(X1,X3)
=> X2 = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ext) ).
fof(fact_dvd__0__right,axiom,
! [X8,X9] :
( class_Rings_Ocomm__semiring__1(X9)
=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X9),X8),c_Groups_Ozero__class_Ozero(X9))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__0__right) ).
fof(fact_synthetic__div__eq__0__iff,axiom,
! [X31,X4,X5] :
( class_Rings_Ocomm__semiring__0(X5)
=> ( c_Polynomial_Osynthetic__div(X5,X4,X31) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X5))
<=> c_Polynomial_Odegree(X5,X4) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_synthetic__div__eq__0__iff) ).
fof(fact_nat__case__0,axiom,
! [X56,X57,X5] : hAPP(c_Nat_Onat_Onat__case(X5,X57,X56),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X57,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__case__0) ).
fof(fact_diff__int__def__symmetric,axiom,
! [X51,X32] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X32),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X51)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X32),X51),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__int__def__symmetric) ).
fof(fact_diff__int__def,axiom,
! [X51,X32] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X32),X51) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X32),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X51)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__int__def) ).
fof(fact_inverse__minus__eq,axiom,
! [X8,X9] :
( class_Rings_Odivision__ring__inverse__zero(X9)
=> hAPP(c_Rings_Oinverse__class_Oinverse(X9),hAPP(c_Groups_Ouminus__class_Ouminus(X9),X8)) = hAPP(c_Groups_Ouminus__class_Ouminus(X9),hAPP(c_Rings_Oinverse__class_Oinverse(X9),X8)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inverse__minus__eq) ).
fof(fact_power__eq__0__iff,axiom,
! [X14,X11,X5] :
( ( class_Power_Opower(X5)
& class_Rings_Omult__zero(X5)
& class_Rings_Ono__zero__divisors(X5)
& class_Rings_Ozero__neq__one(X5) )
=> ( hAPP(hAPP(c_Power_Opower__class_Opower(X5),X11),X14) = c_Groups_Ozero__class_Ozero(X5)
<=> ( X11 = c_Groups_Ozero__class_Ozero(X5)
& X14 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__eq__0__iff) ).
fof(fact_smult__eq__0__iff,axiom,
! [X4,X11,X5] :
( class_Rings_Oidom(X5)
=> ( hAPP(hAPP(c_Polynomial_Osmult(X5),X11),X4) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X5))
<=> ( X11 = c_Groups_Ozero__class_Ozero(X5)
| X4 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X5)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_smult__eq__0__iff) ).
fof(fact_add__poly__code_I1_J,axiom,
! [X13,X9] :
( class_Groups_Ocomm__monoid__add(X9)
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X9)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X9))),X13) = X13 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__poly__code_I1_J) ).
fof(fact_poly__gcd__zero__iff,axiom,
! [X28,X27,X5] :
( class_Fields_Ofield(X5)
=> ( c_Polynomial_Opoly__gcd(X5,X27,X28) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X5))
<=> ( X27 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X5))
& X28 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X5)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_poly__gcd__zero__iff) ).
fof(fact_offset__poly__eq__0__iff,axiom,
! [X50,X4,X5] :
( class_Rings_Ocomm__semiring__0(X5)
=> ( c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X5,X4,X50) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X5))
<=> X4 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X5)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_offset__poly__eq__0__iff) ).
fof(fact_power__Suc__0,axiom,
! [X10] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X10) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__Suc__0) ).
fof(fact_linorder__neq__iff,axiom,
! [X28,X27,X5] :
( class_Orderings_Olinorder(X5)
=> ( X27 != X28
<=> ( c_Orderings_Oord__class_Oless(X5,X27,X28)
| c_Orderings_Oord__class_Oless(X5,X28,X27) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_linorder__neq__iff) ).
fof(fact_linorder__less__linear,axiom,
! [X33,X6,X9] :
( class_Orderings_Olinorder(X9)
=> ( c_Orderings_Oord__class_Oless(X9,X6,X33)
| X6 = X33
| c_Orderings_Oord__class_Oless(X9,X33,X6) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_linorder__less__linear) ).
fof(fact_constant__def,axiom,
! [X2,X15,X5] :
( c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(X5,X15,X2)
<=> ! [X3,X16] : hAPP(X2,X3) = hAPP(X2,X16) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_constant__def) ).
fof(fact_nat__power__eq__Suc__0__iff,axiom,
! [X35,X27] :
( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X27),X35) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
<=> ( X35 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X27 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__power__eq__Suc__0__iff) ).
fof(fact_inverse__unique,axiom,
! [X21,X8,X9] :
( class_Rings_Odivision__ring(X9)
=> ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X9),X8),X21) = c_Groups_Oone__class_Oone(X9)
=> hAPP(c_Rings_Oinverse__class_Oinverse(X9),X8) = X21 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inverse__unique) ).
fof(fact_minus__unique,axiom,
! [X21,X8,X9] :
( class_Groups_Ogroup__add(X9)
=> ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X9),X8),X21) = c_Groups_Ozero__class_Ozero(X9)
=> hAPP(c_Groups_Ouminus__class_Ouminus(X9),X8) = X21 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__unique) ).
fof(fact_eq__neg__iff__add__eq__0,axiom,
! [X25,X11,X5] :
( class_Groups_Ogroup__add(X5)
=> ( X11 = hAPP(c_Groups_Ouminus__class_Ouminus(X5),X25)
<=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X11),X25) = c_Groups_Ozero__class_Ozero(X5) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_eq__neg__iff__add__eq__0) ).
fof(fact_add__eq__0__iff,axiom,
! [X28,X27,X5] :
( class_Groups_Ogroup__add(X5)
=> ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X27),X28) = c_Groups_Ozero__class_Ozero(X5)
<=> X28 = hAPP(c_Groups_Ouminus__class_Ouminus(X5),X27) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__eq__0__iff) ).
fof(fact_pCons__eq__0__iff,axiom,
! [X4,X11,X5] :
( class_Groups_Ozero(X5)
=> ( hAPP(hAPP(c_Polynomial_OpCons(X5),X11),X4) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X5))
<=> ( X11 = c_Groups_Ozero__class_Ozero(X5)
& X4 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X5)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pCons__eq__0__iff) ).
fof(fact_poly__gcd_Ocommute,axiom,
! [X21,X8,X9] :
( class_Fields_Ofield(X9)
=> c_Polynomial_Opoly__gcd(X9,X8,X21) = c_Polynomial_Opoly__gcd(X9,X21,X8) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_poly__gcd_Ocommute) ).
fof(fact_zero__poly__def,axiom,
! [X5] :
( class_Groups_Ozero(X5)
=> c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X5)) = c_Polynomial_OAbs__poly(X5,hAPP(c_COMBK(X5,tc_Nat_Onat),c_Groups_Ozero__class_Ozero(X5))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__poly__def) ).
fof(fact_mult__eq__1__iff,axiom,
! [X14,X35] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X35),X14) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
<=> ( X35 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
& X14 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__eq__1__iff) ).
fof(fact_monom__eq__0__iff,axiom,
! [X14,X11,X5] :
( class_Groups_Ozero(X5)
=> ( c_Polynomial_Omonom(X5,X11,X14) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X5))
<=> X11 = c_Groups_Ozero__class_Ozero(X5) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_monom__eq__0__iff) ).
fof(fact_dvd__refl,axiom,
! [X8,X9] :
( class_Rings_Ocomm__semiring__1(X9)
=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X9),X8),X8)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__refl) ).
fof(fact_zadd__zminus__inverse2,axiom,
! [X32] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X32)),X32) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zadd__zminus__inverse2) ).
fof(fact_mult__poly__0__right,axiom,
! [X7,X9] :
( class_Rings_Ocomm__semiring__0(X9)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X9)),X7),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X9))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X9)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__poly__0__right) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J,axiom,
! [X21,X8,X9] :
( class_Rings_Ocomm__semiring__1(X9)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X9),X8),X21) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X9),X21),X8) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J,axiom,
! [X23,X8,X9] :
( class_Rings_Ocomm__semiring__1(X9)
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(X9),X8),X23) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X9),X23),X8) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J) ).
fof(fact_int__Suc,axiom,
! [X12] : c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,hAPP(c_Nat_OSuc,X12)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,X12)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_int__Suc) ).
fof(fact_pos__poly__total,axiom,
! [X7,X9] :
( class_Rings_Olinordered__idom(X9)
=> ( X7 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X9))
| c_Polynomial_Opos__poly(X9,X7)
| c_Polynomial_Opos__poly(X9,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X9)),X7)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pos__poly__total) ).
fof(fact_zless__linear,axiom,
! [X33,X6] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X6,X33)
| X6 = X33
| c_Orderings_Oord__class_Oless(tc_Int_Oint,X33,X6) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zless__linear) ).
fof(fact_nat__neq__iff,axiom,
! [X14,X35] :
( X35 != X14
<=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X35,X14)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X14,X35) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__neq__iff) ).
fof(fact_poly__gcd__0__0,axiom,
! [X9] :
( class_Fields_Ofield(X9)
=> c_Polynomial_Opoly__gcd(X9,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X9)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X9))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X9)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_poly__gcd__0__0) ).
fof(fact_gr0__conv__Suc,axiom,
! [X14] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X14)
<=> ? [X91] : X14 = hAPP(c_Nat_OSuc,X91) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_gr0__conv__Suc) ).
fof(fact_right__inverse,axiom,
! [X8,X9] :
( class_Rings_Odivision__ring(X9)
=> ( X8 != c_Groups_Ozero__class_Ozero(X9)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X9),X8),hAPP(c_Rings_Oinverse__class_Oinverse(X9),X8)) = c_Groups_Oone__class_Oone(X9) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_right__inverse) ).
fof(fact_gcd__lcm__complete__lattice__nat_Obot__least,axiom,
! [X6] : hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X6)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_gcd__lcm__complete__lattice__nat_Obot__least) ).
fof(fact_mult__eq__0__iff,axiom,
! [X25,X11,X5] :
( class_Rings_Oring__no__zero__divisors(X5)
=> ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X11),X25) = c_Groups_Ozero__class_Ozero(X5)
<=> ( X11 = c_Groups_Ozero__class_Ozero(X5)
| X25 = c_Groups_Ozero__class_Ozero(X5) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__eq__0__iff) ).
fof(fact_no__zero__divisors,axiom,
! [X21,X8,X9] :
( class_Rings_Ono__zero__divisors(X9)
=> ( X8 != c_Groups_Ozero__class_Ozero(X9)
=> ( X21 != c_Groups_Ozero__class_Ozero(X9)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X9),X8),X21) != c_Groups_Ozero__class_Ozero(X9) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_no__zero__divisors) ).
fof(fact_divisors__zero,axiom,
! [X21,X8,X9] :
( class_Rings_Ono__zero__divisors(X9)
=> ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X9),X8),X21) = c_Groups_Ozero__class_Ozero(X9)
=> ( X8 = c_Groups_Ozero__class_Ozero(X9)
| X21 = c_Groups_Ozero__class_Ozero(X9) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divisors__zero) ).
fof(fact_power__0__Suc,axiom,
! [X10,X9] :
( ( class_Power_Opower(X9)
& class_Rings_Osemiring__0(X9) )
=> hAPP(hAPP(c_Power_Opower__class_Opower(X9),c_Groups_Ozero__class_Ozero(X9)),hAPP(c_Nat_OSuc,X10)) = c_Groups_Ozero__class_Ozero(X9) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__0__Suc) ).
fof(fact_right__inverse__eq,axiom,
! [X11,X25,X5] :
( class_Rings_Odivision__ring(X5)
=> ( X25 != c_Groups_Ozero__class_Ozero(X5)
=> ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X5),X11),X25) = c_Groups_Oone__class_Oone(X5)
<=> X11 = X25 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_right__inverse__eq) ).
fof(fact_diff__poly__code_I2_J,axiom,
! [X7,X9] :
( class_Groups_Oab__group__add(X9)
=> hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X9)),X7),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X9))) = X7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__poly__code_I2_J) ).
fof(fact_add__poly__code_I2_J,axiom,
! [X7,X9] :
( class_Groups_Ocomm__monoid__add(X9)
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X9)),X7),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X9))) = X7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__poly__code_I2_J) ).
fof(fact_right__minus,axiom,
! [X8,X9] :
( class_Groups_Ogroup__add(X9)
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(X9),X8),hAPP(c_Groups_Ouminus__class_Ouminus(X9),X8)) = c_Groups_Ozero__class_Ozero(X9) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_right__minus) ).
fof(fact_field__power__not__zero,axiom,
! [X10,X8,X9] :
( class_Rings_Oring__1__no__zero__divisors(X9)
=> ( X8 != c_Groups_Ozero__class_Ozero(X9)
=> hAPP(hAPP(c_Power_Opower__class_Opower(X9),X8),X10) != c_Groups_Ozero__class_Ozero(X9) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_field__power__not__zero) ).
fof(fact_double__eq__0__iff,axiom,
! [X11,X5] :
( class_Groups_Olinordered__ab__group__add(X5)
=> ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X11),X11) = c_Groups_Ozero__class_Ozero(X5)
<=> X11 = c_Groups_Ozero__class_Ozero(X5) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_double__eq__0__iff) ).
fof(fact_double__zero__sym,axiom,
! [X11,X5] :
( class_Groups_Olinordered__ab__group__add(X5)
=> ( c_Groups_Ozero__class_Ozero(X5) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X11),X11)
<=> X11 = c_Groups_Ozero__class_Ozero(X5) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_double__zero__sym) ).
fof(fact_gcd__lcm__complete__lattice__nat_Otop__greatest,axiom,
! [X6] : hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X6),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_gcd__lcm__complete__lattice__nat_Otop__greatest) ).
fof(fact_pCons__0__0,axiom,
! [X9] :
( class_Groups_Ozero(X9)
=> hAPP(hAPP(c_Polynomial_OpCons(X9),c_Groups_Ozero__class_Ozero(X9)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X9))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X9)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pCons__0__0) ).
fof(fact_one__poly__def,axiom,
! [X9] :
( class_Rings_Ocomm__semiring__1(X9)
=> c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(X9)) = hAPP(hAPP(c_Polynomial_OpCons(X9),c_Groups_Oone__class_Oone(X9)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X9))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_one__poly__def) ).
fof(fact_poly__zero,axiom,
! [X4,X5] :
( ( class_Int_Oring__char__0(X5)
& class_Rings_Oidom(X5) )
=> ( c_Polynomial_Opoly(X5,X4) = c_Polynomial_Opoly(X5,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X5)))
<=> X4 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X5)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_poly__zero) ).
fof(fact_right__minus__eq,axiom,
! [X25,X11,X5] :
( class_Groups_Ogroup__add(X5)
=> ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(X5),X11),X25) = c_Groups_Ozero__class_Ozero(X5)
<=> X11 = X25 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_right__minus__eq) ).
fof(fact_eq__iff__diff__eq__0,axiom,
! [X25,X11,X5] :
( class_Groups_Oab__group__add(X5)
=> ( X11 = X25
<=> hAPP(hAPP(c_Groups_Ominus__class_Ominus(X5),X11),X25) = c_Groups_Ozero__class_Ozero(X5) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_eq__iff__diff__eq__0) ).
fof(fact_dvd_Oeq__refl,axiom,
! [X33,X6] :
( X6 = X33
=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X6),X33)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd_Oeq__refl) ).
fof(fact_degree__minus,axiom,
! [X7,X9] :
( class_Groups_Oab__group__add(X9)
=> c_Polynomial_Odegree(X9,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X9)),X7)) = c_Polynomial_Odegree(X9,X7) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_degree__minus) ).
fof(fact_nonzero__inverse__eq__divide,axiom,
! [X8,X9] :
( class_Rings_Odivision__ring(X9)
=> ( X8 != c_Groups_Ozero__class_Ozero(X9)
=> hAPP(c_Rings_Oinverse__class_Oinverse(X9),X8) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X9),c_Groups_Oone__class_Oone(X9)),X8) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nonzero__inverse__eq__divide) ).
fof(fact_order__less__imp__not__eq2,axiom,
! [X33,X6,X9] :
( class_Orderings_Oorder(X9)
=> ( c_Orderings_Oord__class_Oless(X9,X6,X33)
=> X33 != X6 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__less__imp__not__eq2) ).
fof(fact_order__less__imp__not__eq,axiom,
! [X33,X6,X9] :
( class_Orderings_Oorder(X9)
=> ( c_Orderings_Oord__class_Oless(X9,X6,X33)
=> X6 != X33 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__less__imp__not__eq) ).
fof(fact_less__imp__neq,axiom,
! [X33,X6,X9] :
( class_Orderings_Oorder(X9)
=> ( c_Orderings_Oord__class_Oless(X9,X6,X33)
=> X6 != X33 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__imp__neq) ).
fof(fact_add__0__iff,axiom,
! [X11,X25,X5] :
( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X5)
=> ( X25 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X25),X11)
<=> X11 = c_Groups_Ozero__class_Ozero(X5) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__0__iff) ).
fof(fact_diff__Suc__1,axiom,
! [X10] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,X10)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X10,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__Suc__1) ).
fof(fact_neq0__conv,axiom,
! [X14] :
( X14 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
<=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X14) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_neq0__conv) ).
fof(fact_dvd_Oorder__refl,axiom,
! [X6] : hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X6),X6)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd_Oorder__refl) ).
fof(fact_coeff__1,axiom,
! [X10,X9] :
( class_Rings_Ocomm__semiring__1(X9)
=> ( ( X10 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> hAPP(c_Polynomial_Ocoeff(X9,c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(X9))),X10) = c_Groups_Oone__class_Oone(X9) )
& ( X10 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> hAPP(c_Polynomial_Ocoeff(X9,c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(X9))),X10) = c_Groups_Ozero__class_Ozero(X9) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_coeff__1) ).
fof(help_c__COMBK__1,axiom,
! [X99,X98,X5,X9] : hAPP(hAPP(c_COMBK(X9,X5),X98),X99) = X98,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__COMBK__1) ).
fof(fact_zmult__commute,axiom,
! [X51,X32] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X32),X51) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X51),X32),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zmult__commute) ).
fof(fact_nat__mult__commute,axiom,
! [X10,X12] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X12),X10) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X10),X12),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__mult__commute) ).
fof(fact_zadd__commute,axiom,
! [X51,X32] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X32),X51) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X51),X32),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zadd__commute) ).
fof(fact_nat__add__commute,axiom,
! [X10,X12] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X12),X10) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X10),X12),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__add__commute) ).
fof(fact_diff__0,axiom,
! [X8,X9] :
( class_Groups_Ogroup__add(X9)
=> hAPP(hAPP(c_Groups_Ominus__class_Ominus(X9),c_Groups_Ozero__class_Ozero(X9)),X8) = hAPP(c_Groups_Ouminus__class_Ouminus(X9),X8) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__0) ).
fof(fact_inverse__eq__divide,axiom,
! [X8,X9] :
( class_Rings_Odivision__ring(X9)
=> hAPP(c_Rings_Oinverse__class_Oinverse(X9),X8) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X9),c_Groups_Oone__class_Oone(X9)),X8) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inverse__eq__divide) ).
fof(fact_field__class_Onormalizing__field__rules_I2_J,axiom,
! [X8,X9] :
( class_Fields_Ofield(X9)
=> hAPP(c_Rings_Oinverse__class_Oinverse(X9),X8) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X9),c_Groups_Oone__class_Oone(X9)),X8) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_field__class_Onormalizing__field__rules_I2_J) ).
fof(fact_poly__gcd__1__left,axiom,
! [X33,X9] :
( class_Fields_Ofield(X9)
=> c_Polynomial_Opoly__gcd(X9,c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(X9)),X33) = c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(X9)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_poly__gcd__1__left) ).
fof(fact_synthetic__div__0,axiom,
! [X23,X9] :
( class_Rings_Ocomm__semiring__0(X9)
=> c_Polynomial_Osynthetic__div(X9,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X9)),X23) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X9)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_synthetic__div__0) ).
fof(fact_offset__poly__0,axiom,
! [X48,X9] :
( class_Rings_Ocomm__semiring__0(X9)
=> c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X9,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X9)),X48) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X9)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_offset__poly__0) ).
fof(fact_pcompose__0,axiom,
! [X13,X9] :
( class_Rings_Ocomm__semiring__0(X9)
=> c_Polynomial_Opcompose(X9,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X9)),X13) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X9)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pcompose__0) ).
fof(fact_poly__gcd__1__right,axiom,
! [X6,X9] :
( class_Fields_Ofield(X9)
=> c_Polynomial_Opoly__gcd(X9,X6,c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(X9))) = c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(X9)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_poly__gcd__1__right) ).
fof(fact_gr__implies__not0,axiom,
! [X10,X12] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X12,X10)
=> X10 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_gr__implies__not0) ).
fof(fact_power__0__left,axiom,
! [X10,X9] :
( ( class_Power_Opower(X9)
& class_Rings_Osemiring__0(X9) )
=> ( ( X10 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> hAPP(hAPP(c_Power_Opower__class_Opower(X9),c_Groups_Ozero__class_Ozero(X9)),X10) = c_Groups_Oone__class_Oone(X9) )
& ( X10 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> hAPP(hAPP(c_Power_Opower__class_Opower(X9),c_Groups_Ozero__class_Ozero(X9)),X10) = c_Groups_Ozero__class_Ozero(X9) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__0__left) ).
fof(fact_smult__0__right,axiom,
! [X8,X9] :
( class_Rings_Ocomm__semiring__0(X9)
=> hAPP(hAPP(c_Polynomial_Osmult(X9),X8),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X9))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X9)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_smult__0__right) ).
fof(fact_coeff__0,axiom,
! [X10,X9] :
( class_Groups_Ozero(X9)
=> hAPP(c_Polynomial_Ocoeff(X9,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X9))),X10) = c_Groups_Ozero__class_Ozero(X9) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_coeff__0) ).
fof(fact_poly__1,axiom,
! [X6,X9] :
( class_Rings_Ocomm__semiring__1(X9)
=> hAPP(c_Polynomial_Opoly(X9,c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(X9))),X6) = c_Groups_Oone__class_Oone(X9) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_poly__1) ).
fof(fact_poly__0,axiom,
! [X6,X9] :
( class_Rings_Ocomm__semiring__0(X9)
=> hAPP(c_Polynomial_Opoly(X9,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X9))),X6) = c_Groups_Ozero__class_Ozero(X9) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_poly__0) ).
fof(fact_less__not__refl3,axiom,
! [X88,X89] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X89,X88)
=> X89 != X88 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__not__refl3) ).
fof(fact_less__not__refl2,axiom,
! [X12,X10] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X10,X12)
=> X12 != X10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__not__refl2) ).
fof(fact_negative__eq__positive,axiom,
! [X35,X14] :
( hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,X14)) = c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,X35)
<=> ( X14 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& X35 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_negative__eq__positive) ).
fof(fact_mod__1,axiom,
! [X12] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,X12,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__1) ).
fof(fact_mult__is__0,axiom,
! [X14,X35] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X35),X14) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
<=> ( X35 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X14 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__is__0) ).
fof(fact_nonzero__inverse__eq__imp__eq,axiom,
! [X21,X8,X9] :
( class_Rings_Odivision__ring(X9)
=> ( hAPP(c_Rings_Oinverse__class_Oinverse(X9),X8) = hAPP(c_Rings_Oinverse__class_Oinverse(X9),X21)
=> ( X8 != c_Groups_Ozero__class_Ozero(X9)
=> ( X21 != c_Groups_Ozero__class_Ozero(X9)
=> X8 = X21 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nonzero__inverse__eq__imp__eq) ).
fof(fact_mult__eq__self__implies__10,axiom,
! [X10,X12] :
( X12 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X12),X10)
=> ( X10 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| X12 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__eq__self__implies__10) ).
fof(fact_smult__0__left,axiom,
! [X7,X9] :
( class_Rings_Ocomm__semiring__0(X9)
=> hAPP(hAPP(c_Polynomial_Osmult(X9),c_Groups_Ozero__class_Ozero(X9)),X7) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X9)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_smult__0__left) ).
fof(fact_nat__mult__eq__1__iff,axiom,
! [X14,X35] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X35),X14) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
<=> ( X35 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
& X14 = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__mult__eq__1__iff) ).
fof(fact_add__is__0,axiom,
! [X14,X35] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X35),X14) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
<=> ( X35 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& X14 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__is__0) ).
fof(fact_nat__1__eq__mult__iff,axiom,
! [X14,X35] :
( c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X35),X14)
<=> ( X35 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
& X14 = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__1__eq__mult__iff) ).
fof(fact_zero__less__Suc,axiom,
! [X10] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Nat_OSuc,X10)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__less__Suc) ).
fof(fact_monom__eq__0,axiom,
! [X10,X9] :
( class_Groups_Ozero(X9)
=> c_Polynomial_Omonom(X9,c_Groups_Ozero__class_Ozero(X9),X10) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X9)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_monom__eq__0) ).
fof(fact_power__power__power,axiom,
! [X5] :
( class_Power_Opower(X5)
=> c_Power_Opower__class_Opower(X5) = c_Power_Opower_Opower(X5,c_Groups_Oone__class_Oone(X5),c_Groups_Otimes__class_Otimes(X5)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__power__power) ).
fof(fact_add__eq__self__zero,axiom,
! [X10,X12] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X12),X10) = X12
=> X10 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__eq__self__zero) ).
fof(fact_lessI,axiom,
! [X10] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,X10,hAPP(c_Nat_OSuc,X10)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_lessI) ).
fof(fact_divide_Ozero,axiom,
! [X33,X9] :
( class_RealVector_Oreal__normed__field(X9)
=> hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X9),c_Groups_Ozero__class_Ozero(X9)),X33) = c_Groups_Ozero__class_Ozero(X9) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide_Ozero) ).
fof(fact_divide__zero__left,axiom,
! [X8,X9] :
( class_Rings_Odivision__ring(X9)
=> hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X9),c_Groups_Ozero__class_Ozero(X9)),X8) = c_Groups_Ozero__class_Ozero(X9) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide__zero__left) ).
fof(fact_power__one,axiom,
! [X10,X9] :
( class_Groups_Omonoid__mult(X9)
=> hAPP(hAPP(c_Power_Opower__class_Opower(X9),c_Groups_Oone__class_Oone(X9)),X10) = c_Groups_Oone__class_Oone(X9) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__one) ).
fof(fact_mult_Ozero__left,axiom,
! [X21,X9] :
( class_RealVector_Oreal__normed__algebra(X9)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X9),c_Groups_Ozero__class_Ozero(X9)),X21) = c_Groups_Ozero__class_Ozero(X9) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult_Ozero__left) ).
fof(fact_mult__left_Ozero,axiom,
! [X33,X9] :
( class_RealVector_Oreal__normed__algebra(X9)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X9),c_Groups_Ozero__class_Ozero(X9)),X33) = c_Groups_Ozero__class_Ozero(X9) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__left_Ozero) ).
fof(fact_mult__zero__left,axiom,
! [X8,X9] :
( class_Rings_Omult__zero(X9)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X9),c_Groups_Ozero__class_Ozero(X9)),X8) = c_Groups_Ozero__class_Ozero(X9) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__zero__left) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I9_J,axiom,
! [X8,X9] :
( class_Rings_Ocomm__semiring__1(X9)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X9),c_Groups_Ozero__class_Ozero(X9)),X8) = c_Groups_Ozero__class_Ozero(X9) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I9_J) ).
fof(fact_zero__less__one,axiom,
! [X9] :
( class_Rings_Olinordered__semidom(X9)
=> c_Orderings_Oord__class_Oless(X9,c_Groups_Ozero__class_Ozero(X9),c_Groups_Oone__class_Oone(X9)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__less__one) ).
fof(fact_inverse__eq__iff__eq,axiom,
! [X25,X11,X5] :
( class_Rings_Odivision__ring__inverse__zero(X5)
=> ( hAPP(c_Rings_Oinverse__class_Oinverse(X5),X11) = hAPP(c_Rings_Oinverse__class_Oinverse(X5),X25)
<=> X11 = X25 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inverse__eq__iff__eq) ).
fof(fact_inverse__eq__imp__eq,axiom,
! [X21,X8,X9] :
( class_Rings_Odivision__ring__inverse__zero(X9)
=> ( hAPP(c_Rings_Oinverse__class_Oinverse(X9),X8) = hAPP(c_Rings_Oinverse__class_Oinverse(X9),X21)
=> X8 = X21 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inverse__eq__imp__eq) ).
fof(fact_compl__eq__compl__iff,axiom,
! [X28,X27,X5] :
( class_Lattices_Oboolean__algebra(X5)
=> ( hAPP(c_Groups_Ouminus__class_Ouminus(X5),X27) = hAPP(c_Groups_Ouminus__class_Ouminus(X5),X28)
<=> X27 = X28 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_compl__eq__compl__iff) ).
fof(fact_neg__equal__iff__equal,axiom,
! [X25,X11,X5] :
( class_Groups_Ogroup__add(X5)
=> ( hAPP(c_Groups_Ouminus__class_Ouminus(X5),X11) = hAPP(c_Groups_Ouminus__class_Ouminus(X5),X25)
<=> X11 = X25 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_neg__equal__iff__equal) ).
fof(fact_smult__1__left,axiom,
! [X7,X9] :
( class_Rings_Ocomm__semiring__1(X9)
=> hAPP(hAPP(c_Polynomial_Osmult(X9),c_Groups_Oone__class_Oone(X9)),X7) = X7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_smult__1__left) ).
fof(fact_mult__1,axiom,
! [X8,X9] :
( class_Groups_Ocomm__monoid__mult(X9)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X9),c_Groups_Oone__class_Oone(X9)),X8) = X8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__1) ).
fof(fact_mult__1__left,axiom,
! [X8,X9] :
( class_Groups_Omonoid__mult(X9)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X9),c_Groups_Oone__class_Oone(X9)),X8) = X8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__1__left) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J,axiom,
! [X8,X9] :
( class_Rings_Ocomm__semiring__1(X9)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X9),c_Groups_Oone__class_Oone(X9)),X8) = X8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J) ).
fof(fact_add__0__left,axiom,
! [X8,X9] :
( class_Groups_Omonoid__add(X9)
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(X9),c_Groups_Ozero__class_Ozero(X9)),X8) = X8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__0__left) ).
fof(fact_add__0,axiom,
! [X8,X9] :
( class_Groups_Ocomm__monoid__add(X9)
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(X9),c_Groups_Ozero__class_Ozero(X9)),X8) = X8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__0) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J,axiom,
! [X8,X9] :
( class_Rings_Ocomm__semiring__1(X9)
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(X9),c_Groups_Ozero__class_Ozero(X9)),X8) = X8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J) ).
fof(fact_divide__self__if,axiom,
! [X8,X9] :
( class_Rings_Odivision__ring__inverse__zero(X9)
=> ( ( X8 = c_Groups_Ozero__class_Ozero(X9)
=> hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X9),X8),X8) = c_Groups_Ozero__class_Ozero(X9) )
& ( X8 != c_Groups_Ozero__class_Ozero(X9)
=> hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X9),X8),X8) = c_Groups_Oone__class_Oone(X9) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide__self__if) ).
fof(fact_nonzero__inverse__inverse__eq,axiom,
! [X8,X9] :
( class_Rings_Odivision__ring(X9)
=> ( X8 != c_Groups_Ozero__class_Ozero(X9)
=> hAPP(c_Rings_Oinverse__class_Oinverse(X9),hAPP(c_Rings_Oinverse__class_Oinverse(X9),X8)) = X8 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nonzero__inverse__inverse__eq) ).
fof(fact_div__0,axiom,
! [X8,X9] :
( class_Divides_Osemiring__div(X9)
=> c_Divides_Odiv__class_Odiv(X9,c_Groups_Ozero__class_Ozero(X9),X8) = c_Groups_Ozero__class_Ozero(X9) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_div__0) ).
fof(fact_mod__0,axiom,
! [X8,X9] :
( class_Divides_Osemiring__div(X9)
=> c_Divides_Odiv__class_Omod(X9,c_Groups_Ozero__class_Ozero(X9),X8) = c_Groups_Ozero__class_Ozero(X9) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__0) ).
fof(fact_div__by__0,axiom,
! [X8,X9] :
( class_Divides_Osemiring__div(X9)
=> c_Divides_Odiv__class_Odiv(X9,X8,c_Groups_Ozero__class_Ozero(X9)) = c_Groups_Ozero__class_Ozero(X9) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_div__by__0) ).
fof(fact_mod__by__1,axiom,
! [X8,X9] :
( class_Divides_Osemiring__div(X9)
=> c_Divides_Odiv__class_Omod(X9,X8,c_Groups_Oone__class_Oone(X9)) = c_Groups_Ozero__class_Ozero(X9) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__by__1) ).
fof(fact_psize__def,axiom,
! [X7,X9] :
( class_Groups_Ozero(X9)
=> ( ( X7 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X9))
=> c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(X9,X7) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( X7 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X9))
=> c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(X9,X7) = hAPP(c_Nat_OSuc,c_Polynomial_Odegree(X9,X7)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_psize__def) ).
fof(fact_div__self,axiom,
! [X8,X9] :
( class_Divides_Osemiring__div(X9)
=> ( X8 != c_Groups_Ozero__class_Ozero(X9)
=> c_Divides_Odiv__class_Odiv(X9,X8,X8) = c_Groups_Oone__class_Oone(X9) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_div__self) ).
fof(fact_divide__zero,axiom,
! [X8,X9] :
( class_Rings_Odivision__ring__inverse__zero(X9)
=> hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X9),X8),c_Groups_Ozero__class_Ozero(X9)) = c_Groups_Ozero__class_Ozero(X9) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide__zero) ).
fof(fact_mult_Ozero__right,axiom,
! [X8,X9] :
( class_RealVector_Oreal__normed__algebra(X9)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X9),X8),c_Groups_Ozero__class_Ozero(X9)) = c_Groups_Ozero__class_Ozero(X9) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult_Ozero__right) ).
fof(fact_mult__right_Ozero,axiom,
! [X6,X9] :
( class_RealVector_Oreal__normed__algebra(X9)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X9),X6),c_Groups_Ozero__class_Ozero(X9)) = c_Groups_Ozero__class_Ozero(X9) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__right_Ozero) ).
fof(fact_mult__zero__right,axiom,
! [X8,X9] :
( class_Rings_Omult__zero(X9)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X9),X8),c_Groups_Ozero__class_Ozero(X9)) = c_Groups_Ozero__class_Ozero(X9) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__zero__right) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J,axiom,
! [X8,X9] :
( class_Rings_Ocomm__semiring__1(X9)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X9),X8),c_Groups_Ozero__class_Ozero(X9)) = c_Groups_Ozero__class_Ozero(X9) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J) ).
fof(fact_divide__self,axiom,
! [X8,X9] :
( class_Rings_Odivision__ring(X9)
=> ( X8 != c_Groups_Ozero__class_Ozero(X9)
=> hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X9),X8),X8) = c_Groups_Oone__class_Oone(X9) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide__self) ).
fof(fact_div__by__1,axiom,
! [X8,X9] :
( class_Divides_Osemiring__div(X9)
=> c_Divides_Odiv__class_Odiv(X9,X8,c_Groups_Oone__class_Oone(X9)) = X8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_div__by__1) ).
fof(fact_mod__by__0,axiom,
! [X8,X9] :
( class_Divides_Osemiring__div(X9)
=> c_Divides_Odiv__class_Omod(X9,X8,c_Groups_Ozero__class_Ozero(X9)) = X8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__by__0) ).
fof(fact_minus__poly__code_I1_J,axiom,
! [X9] :
( class_Groups_Oab__group__add(X9)
=> hAPP(c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X9)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X9))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X9)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__poly__code_I1_J) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I32_J,axiom,
! [X6,X9] :
( class_Rings_Ocomm__semiring__1(X9)
=> hAPP(hAPP(c_Power_Opower__class_Opower(X9),X6),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(X9) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I32_J) ).
fof(fact_power__0,axiom,
! [X8,X9] :
( class_Power_Opower(X9)
=> hAPP(hAPP(c_Power_Opower__class_Opower(X9),X8),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(X9) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__0) ).
fof(fact_divide__1,axiom,
! [X8,X9] :
( class_Rings_Odivision__ring(X9)
=> hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X9),X8),c_Groups_Oone__class_Oone(X9)) = X8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide__1) ).
fof(fact_diff__0__right,axiom,
! [X8,X9] :
( class_Groups_Ogroup__add(X9)
=> hAPP(hAPP(c_Groups_Ominus__class_Ominus(X9),X8),c_Groups_Ozero__class_Ozero(X9)) = X8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__0__right) ).
fof(fact_mult_Ocomm__neutral,axiom,
! [X8,X9] :
( class_Groups_Ocomm__monoid__mult(X9)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X9),X8),c_Groups_Oone__class_Oone(X9)) = X8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult_Ocomm__neutral) ).
fof(fact_mult__1__right,axiom,
! [X8,X9] :
( class_Groups_Omonoid__mult(X9)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X9),X8),c_Groups_Oone__class_Oone(X9)) = X8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__1__right) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J,axiom,
! [X8,X9] :
( class_Rings_Ocomm__semiring__1(X9)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X9),X8),c_Groups_Oone__class_Oone(X9)) = X8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J) ).
fof(fact_add__0__right,axiom,
! [X8,X9] :
( class_Groups_Omonoid__add(X9)
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(X9),X8),c_Groups_Ozero__class_Ozero(X9)) = X8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__0__right) ).
fof(fact_add_Ocomm__neutral,axiom,
! [X8,X9] :
( class_Groups_Ocomm__monoid__add(X9)
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(X9),X8),c_Groups_Ozero__class_Ozero(X9)) = X8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add_Ocomm__neutral) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J,axiom,
! [X8,X9] :
( class_Rings_Ocomm__semiring__1(X9)
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(X9),X8),c_Groups_Ozero__class_Ozero(X9)) = X8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J) ).
fof(fact_inverse__inverse__eq,axiom,
! [X8,X9] :
( class_Rings_Odivision__ring__inverse__zero(X9)
=> hAPP(c_Rings_Oinverse__class_Oinverse(X9),hAPP(c_Rings_Oinverse__class_Oinverse(X9),X8)) = X8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inverse__inverse__eq) ).
fof(fact_double__compl,axiom,
! [X6,X9] :
( class_Lattices_Oboolean__algebra(X9)
=> hAPP(c_Groups_Ouminus__class_Ouminus(X9),hAPP(c_Groups_Ouminus__class_Ouminus(X9),X6)) = X6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_double__compl) ).
fof(fact_minus__minus,axiom,
! [X8,X9] :
( class_Groups_Ogroup__add(X9)
=> hAPP(c_Groups_Ouminus__class_Ouminus(X9),hAPP(c_Groups_Ouminus__class_Ouminus(X9),X8)) = X8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__minus) ).
fof(fact_mod__self,axiom,
! [X8,X9] :
( class_Divides_Osemiring__div(X9)
=> c_Divides_Odiv__class_Omod(X9,X8,X8) = c_Groups_Ozero__class_Ozero(X9) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__self) ).
fof(fact_Suc__eq__plus1__left,axiom,
! [X10] : hAPP(c_Nat_OSuc,X10) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X10),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__eq__plus1__left) ).
fof(fact_power__one__right,axiom,
! [X8,X9] :
( class_Groups_Omonoid__mult(X9)
=> hAPP(hAPP(c_Power_Opower__class_Opower(X9),X8),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__one__right) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J,axiom,
! [X6,X9] :
( class_Rings_Ocomm__semiring__1(X9)
=> hAPP(hAPP(c_Power_Opower__class_Opower(X9),X6),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J) ).
fof(fact_diff__self,axiom,
! [X8,X9] :
( class_Groups_Ogroup__add(X9)
=> hAPP(hAPP(c_Groups_Ominus__class_Ominus(X9),X8),X8) = c_Groups_Ozero__class_Ozero(X9) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__self) ).
fof(fact_minus__equation__iff,axiom,
! [X25,X11,X5] :
( class_Groups_Ogroup__add(X5)
=> ( hAPP(c_Groups_Ouminus__class_Ouminus(X5),X11) = X25
<=> hAPP(c_Groups_Ouminus__class_Ouminus(X5),X25) = X11 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__equation__iff) ).
fof(fact_equation__minus__iff,axiom,
! [X25,X11,X5] :
( class_Groups_Ogroup__add(X5)
=> ( X11 = hAPP(c_Groups_Ouminus__class_Ouminus(X5),X25)
<=> X25 = hAPP(c_Groups_Ouminus__class_Ouminus(X5),X11) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_equation__minus__iff) ).
fof(fact_order__refl,axiom,
! [X6,X9] :
( class_Orderings_Opreorder(X9)
=> c_Orderings_Oord__class_Oless__eq(X9,X6,X6) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__refl) ).
fof(fact_Suc__eq__plus1,axiom,
! [X10] : hAPP(c_Nat_OSuc,X10) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X10),c_Groups_Oone__class_Oone(tc_Nat_Onat)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__eq__plus1) ).
fof(fact_poly__eq__iff,axiom,
! [X24,X4,X5] :
( ( class_Int_Oring__char__0(X5)
& class_Rings_Oidom(X5) )
=> ( c_Polynomial_Opoly(X5,X4) = c_Polynomial_Opoly(X5,X24)
<=> X4 = X24 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_poly__eq__iff) ).
fof(fact_mult__idem,axiom,
! [X6,X9] :
( class_Lattices_Oab__semigroup__idem__mult(X9)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X9),X6),X6) = X6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__idem) ).
fof(fact_times_Oidem,axiom,
! [X8,X9] :
( class_Lattices_Oab__semigroup__idem__mult(X9)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X9),X8),X8) = X8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_times_Oidem) ).
fof(fact_gr0I,axiom,
! [X10] :
( X10 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X10) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_gr0I) ).
fof(fact_zdiv__self,axiom,
! [X8] :
( X8 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
=> c_Divides_Odiv__class_Odiv(tc_Int_Oint,X8,X8) = c_Groups_Oone__class_Oone(tc_Int_Oint) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zdiv__self) ).
fof(fact_zdiv__zero,axiom,
! [X21] : c_Divides_Odiv__class_Odiv(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X21) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zdiv__zero) ).
fof(fact_zmod__zero,axiom,
! [X21] : c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X21) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zmod__zero) ).
fof(fact_DIVISION__BY__ZERO,axiom,
! [X8] :
( c_Divides_Odiv__class_Odiv(tc_Int_Oint,X8,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
& c_Divides_Odiv__class_Omod(tc_Int_Oint,X8,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = X8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_DIVISION__BY__ZERO) ).
fof(fact_zmod__self,axiom,
! [X8] : c_Divides_Odiv__class_Omod(tc_Int_Oint,X8,X8) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zmod__self) ).
fof(fact_diff__0__eq__0,axiom,
! [X10] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X10) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__0__eq__0) ).
fof(fact_mult__0,axiom,
! [X10] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X10) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__0) ).
fof(fact_of__nat__eq__iff,axiom,
! [X14,X35,X5] :
( class_Nat_Osemiring__char__0(X5)
=> ( c_Nat_Osemiring__1__class_Oof__nat(X5,X35) = c_Nat_Osemiring__1__class_Oof__nat(X5,X14)
<=> X35 = X14 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_of__nat__eq__iff) ).
fof(fact_coeff__inject,axiom,
! [X28,X27,X5] :
( class_Groups_Ozero(X5)
=> ( c_Polynomial_Ocoeff(X5,X27) = c_Polynomial_Ocoeff(X5,X28)
<=> X27 = X28 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_coeff__inject) ).
fof(fact_zmult__1,axiom,
! [X32] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X32) = X32,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zmult__1) ).
fof(fact_nat__mult__1,axiom,
! [X10] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X10) = X10,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__mult__1) ).
fof(fact_zadd__0,axiom,
! [X32] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X32) = X32,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zadd__0) ).
fof(fact_plus__nat_Oadd__0,axiom,
! [X10] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X10) = X10,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_plus__nat_Oadd__0) ).
fof(fact_mult__0__right,axiom,
! [X12] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X12),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__0__right) ).
fof(fact_neg__0__equal__iff__equal,axiom,
! [X11,X5] :
( class_Groups_Ogroup__add(X5)
=> ( c_Groups_Ozero__class_Ozero(X5) = hAPP(c_Groups_Ouminus__class_Ouminus(X5),X11)
<=> c_Groups_Ozero__class_Ozero(X5) = X11 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_neg__0__equal__iff__equal) ).
fof(fact_inverse__eq__1__iff,axiom,
! [X27,X5] :
( class_Fields_Ofield__inverse__zero(X5)
=> ( hAPP(c_Rings_Oinverse__class_Oinverse(X5),X27) = c_Groups_Oone__class_Oone(X5)
<=> X27 = c_Groups_Oone__class_Oone(X5) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inverse__eq__1__iff) ).
fof(fact_nonzero__imp__inverse__nonzero,axiom,
! [X8,X9] :
( class_Rings_Odivision__ring(X9)
=> ( X8 != c_Groups_Ozero__class_Ozero(X9)
=> hAPP(c_Rings_Oinverse__class_Oinverse(X9),X8) != c_Groups_Ozero__class_Ozero(X9) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nonzero__imp__inverse__nonzero) ).
fof(fact_inverse__zero__imp__zero,axiom,
! [X8,X9] :
( class_Rings_Odivision__ring(X9)
=> ( hAPP(c_Rings_Oinverse__class_Oinverse(X9),X8) = c_Groups_Ozero__class_Ozero(X9)
=> X8 = c_Groups_Ozero__class_Ozero(X9) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inverse__zero__imp__zero) ).
fof(fact_inverse__nonzero__iff__nonzero,axiom,
! [X11,X5] :
( class_Rings_Odivision__ring__inverse__zero(X5)
=> ( hAPP(c_Rings_Oinverse__class_Oinverse(X5),X11) = c_Groups_Ozero__class_Ozero(X5)
<=> X11 = c_Groups_Ozero__class_Ozero(X5) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inverse__nonzero__iff__nonzero) ).
fof(fact_neg__equal__0__iff__equal,axiom,
! [X11,X5] :
( class_Groups_Ogroup__add(X5)
=> ( hAPP(c_Groups_Ouminus__class_Ouminus(X5),X11) = c_Groups_Ozero__class_Ozero(X5)
<=> X11 = c_Groups_Ozero__class_Ozero(X5) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_neg__equal__0__iff__equal) ).
fof(fact_minus__nat_Odiff__0,axiom,
! [X12] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X12),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X12,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__nat_Odiff__0) ).
fof(fact_zmult__1__right,axiom,
! [X32] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X32),c_Groups_Oone__class_Oone(tc_Int_Oint)) = X32,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zmult__1__right) ).
fof(fact_nat__mult__1__right,axiom,
! [X10] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X10),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X10,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__mult__1__right) ).
fof(fact_zadd__0__right,axiom,
! [X32] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X32),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = X32,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zadd__0__right) ).
fof(fact_Nat_Oadd__0__right,axiom,
! [X12] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X12),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X12,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nat_Oadd__0__right) ).
fof(fact_zminus__zminus,axiom,
! [X32] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X32)) = X32,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zminus__zminus) ).
fof(fact_diff__self__eq__0,axiom,
! [X12] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X12),X12) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__self__eq__0) ).
fof(fact_coeff__inverse,axiom,
! [X27,X5] :
( class_Groups_Ozero(X5)
=> c_Polynomial_OAbs__poly(X5,c_Polynomial_Ocoeff(X5,X27)) = X27 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_coeff__inverse) ).
fof(help_c__fequal__2,axiom,
! [X28,X27] :
( X27 != X28
| hBOOL(hAPP(c_fequal(X27),X28)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__fequal__2) ).
fof(fact_neg__equal__zero,axiom,
! [X11,X5] :
( class_Groups_Olinordered__ab__group__add(X5)
=> ( hAPP(c_Groups_Ouminus__class_Ouminus(X5),X11) = X11
<=> X11 = c_Groups_Ozero__class_Ozero(X5) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_neg__equal__zero) ).
fof(fact_equal__neg__zero,axiom,
! [X11,X5] :
( class_Groups_Olinordered__ab__group__add(X5)
=> ( X11 = hAPP(c_Groups_Ouminus__class_Ouminus(X5),X11)
<=> X11 = c_Groups_Ozero__class_Ozero(X5) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_equal__neg__zero) ).
fof(fact_psize__eq__0__iff,axiom,
! [X4,X5] :
( class_Groups_Ozero(X5)
=> ( c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(X5,X4) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
<=> X4 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X5)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_psize__eq__0__iff) ).
fof(fact_degree__1,axiom,
! [X9] :
( class_Rings_Ocomm__semiring__1(X9)
=> c_Polynomial_Odegree(X9,c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(X9))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_degree__1) ).
fof(fact_degree__0,axiom,
! [X9] :
( class_Groups_Ozero(X9)
=> c_Polynomial_Odegree(X9,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X9))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_degree__0) ).
fof(fact_int__int__eq,axiom,
! [X14,X35] :
( c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,X35) = c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,X14)
<=> X35 = X14 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_int__int__eq) ).
fof(fact_Nat__Transfer_Otransfer__int__nat__relations_I1_J,axiom,
! [X28,X27] :
( c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,X27) = c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,X28)
<=> X27 = X28 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__int__nat__relations_I1_J) ).
fof(fact_Suc__inject,axiom,
! [X33,X6] :
( hAPP(c_Nat_OSuc,X6) = hAPP(c_Nat_OSuc,X33)
=> X6 = X33 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__inject) ).
fof(fact_nat_Oinject,axiom,
! [X60,X61] :
( hAPP(c_Nat_OSuc,X61) = hAPP(c_Nat_OSuc,X60)
<=> X61 = X60 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat_Oinject) ).
fof(fact_inverse__1,axiom,
! [X9] :
( class_Rings_Odivision__ring(X9)
=> hAPP(c_Rings_Oinverse__class_Oinverse(X9),c_Groups_Oone__class_Oone(X9)) = c_Groups_Oone__class_Oone(X9) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inverse__1) ).
fof(fact_field__inverse__zero,axiom,
! [X9] :
( class_Fields_Ofield__inverse__zero(X9)
=> hAPP(c_Rings_Oinverse__class_Oinverse(X9),c_Groups_Ozero__class_Ozero(X9)) = c_Groups_Ozero__class_Ozero(X9) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_field__inverse__zero) ).
fof(fact_inverse__zero,axiom,
! [X9] :
( class_Rings_Odivision__ring__inverse__zero(X9)
=> hAPP(c_Rings_Oinverse__class_Oinverse(X9),c_Groups_Ozero__class_Ozero(X9)) = c_Groups_Ozero__class_Ozero(X9) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inverse__zero) ).
fof(fact_minus__zero,axiom,
! [X9] :
( class_Groups_Ogroup__add(X9)
=> hAPP(c_Groups_Ouminus__class_Ouminus(X9),c_Groups_Ozero__class_Ozero(X9)) = c_Groups_Ozero__class_Ozero(X9) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__zero) ).
fof(arity_fun__Orderings_Oord,axiom,
! [X97,X96] :
( class_Orderings_Oord(X96)
=> class_Orderings_Oord(tc_fun(X97,X96)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_fun__Orderings_Oord) ).
fof(arity_fun__Orderings_Oorder,axiom,
! [X97,X96] :
( class_Orderings_Oorder(X96)
=> class_Orderings_Oorder(tc_fun(X97,X96)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_fun__Orderings_Oorder) ).
fof(arity_fun__Orderings_Opreorder,axiom,
! [X97,X96] :
( class_Orderings_Opreorder(X96)
=> class_Orderings_Opreorder(tc_fun(X97,X96)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_fun__Orderings_Opreorder) ).
fof(arity_fun__Groups_Ouminus,axiom,
! [X97,X96] :
( class_Groups_Ouminus(X96)
=> class_Groups_Ouminus(tc_fun(X97,X96)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_fun__Groups_Ouminus) ).
fof(arity_fun__Lattices_Oboolean__algebra,axiom,
! [X97,X96] :
( class_Lattices_Oboolean__algebra(X96)
=> class_Lattices_Oboolean__algebra(tc_fun(X97,X96)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_fun__Lattices_Oboolean__algebra) ).
fof(arity_fun__Groups_Ominus,axiom,
! [X97,X96] :
( class_Groups_Ominus(X96)
=> class_Groups_Ominus(tc_fun(X97,X96)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_fun__Groups_Ominus) ).
fof(fact_of__nat__1,axiom,
! [X9] :
( class_Rings_Osemiring__1(X9)
=> c_Nat_Osemiring__1__class_Oof__nat(X9,c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(X9) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_of__nat__1) ).
fof(fact_of__nat__0,axiom,
! [X9] :
( class_Rings_Osemiring__1(X9)
=> c_Nat_Osemiring__1__class_Oof__nat(X9,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(X9) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_of__nat__0) ).
fof(fact_int__eq__0__conv,axiom,
! [X14] :
( c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,X14) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
<=> X14 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_int__eq__0__conv) ).
fof(fact_Suc__neq__Zero,axiom,
! [X12] : hAPP(c_Nat_OSuc,X12) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__neq__Zero) ).
fof(fact_nat_Osimps_I3_J,axiom,
! [X63] : hAPP(c_Nat_OSuc,X63) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat_Osimps_I3_J) ).
fof(fact_Suc__not__Zero,axiom,
! [X12] : hAPP(c_Nat_OSuc,X12) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__not__Zero) ).
fof(fact_Zero__neq__Suc,axiom,
! [X12] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,X12),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Zero__neq__Suc) ).
fof(fact_nat_Osimps_I2_J,axiom,
! [X62] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,X62),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat_Osimps_I2_J) ).
fof(fact_Zero__not__Suc,axiom,
! [X12] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,X12),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Zero__not__Suc) ).
fof(fact_Suc__n__not__n,axiom,
! [X10] : hAPP(c_Nat_OSuc,X10) != X10,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__n__not__n) ).
fof(fact_n__not__Suc__n,axiom,
! [X10] : X10 != hAPP(c_Nat_OSuc,X10),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_n__not__Suc__n) ).
fof(help_c__COMBI__1,axiom,
! [X98,X9] : hAPP(c_COMBI(X9),X98) = X98,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__COMBI__1) ).
fof(fact_one__neq__zero,axiom,
! [X9] :
( class_Rings_Ozero__neq__one(X9)
=> c_Groups_Oone__class_Oone(X9) != c_Groups_Ozero__class_Ozero(X9) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_one__neq__zero) ).
fof(fact_zero__neq__one,axiom,
! [X9] :
( class_Rings_Ozero__neq__one(X9)
=> c_Groups_Ozero__class_Ozero(X9) != c_Groups_Oone__class_Oone(X9) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__neq__one) ).
fof(arity_Polynomial__Opoly__Groups_Ocancel__comm__monoid__add,axiom,
! [X96] :
( class_Groups_Ocancel__comm__monoid__add(X96)
=> class_Groups_Ocancel__comm__monoid__add(tc_Polynomial_Opoly(X96)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Ocancel__comm__monoid__add) ).
fof(arity_Polynomial__Opoly__Rings_Oordered__ring,axiom,
! [X96] :
( class_Rings_Olinordered__idom(X96)
=> class_Rings_Oordered__ring(tc_Polynomial_Opoly(X96)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Oordered__ring) ).
fof(arity_Polynomial__Opoly__Orderings_Oord,axiom,
! [X96] :
( class_Rings_Olinordered__idom(X96)
=> class_Orderings_Oord(tc_Polynomial_Opoly(X96)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Orderings_Oord) ).
fof(arity_Polynomial__Opoly__Orderings_Oorder,axiom,
! [X96] :
( class_Rings_Olinordered__idom(X96)
=> class_Orderings_Oorder(tc_Polynomial_Opoly(X96)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Orderings_Oorder) ).
fof(arity_Polynomial__Opoly__Orderings_Olinorder,axiom,
! [X96] :
( class_Rings_Olinordered__idom(X96)
=> class_Orderings_Olinorder(tc_Polynomial_Opoly(X96)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Orderings_Olinorder) ).
fof(arity_Polynomial__Opoly__Orderings_Opreorder,axiom,
! [X96] :
( class_Rings_Olinordered__idom(X96)
=> class_Orderings_Opreorder(tc_Polynomial_Opoly(X96)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Orderings_Opreorder) ).
fof(arity_Polynomial__Opoly__Groups_Oordered__cancel__ab__semigroup__add,axiom,
! [X96] :
( class_Rings_Olinordered__idom(X96)
=> class_Groups_Oordered__cancel__ab__semigroup__add(tc_Polynomial_Opoly(X96)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Oordered__cancel__ab__semigroup__add) ).
fof(arity_Polynomial__Opoly__Groups_Oordered__ab__semigroup__add__imp__le,axiom,
! [X96] :
( class_Rings_Olinordered__idom(X96)
=> class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Polynomial_Opoly(X96)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Oordered__ab__semigroup__add__imp__le) ).
fof(arity_Polynomial__Opoly__Groups_Oordered__ab__group__add,axiom,
! [X96] :
( class_Rings_Olinordered__idom(X96)
=> class_Groups_Oordered__ab__group__add(tc_Polynomial_Opoly(X96)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Oordered__ab__group__add) ).
fof(arity_Polynomial__Opoly__Rings_Olinordered__idom,axiom,
! [X96] :
( class_Rings_Olinordered__idom(X96)
=> class_Rings_Olinordered__idom(tc_Polynomial_Opoly(X96)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Olinordered__idom) ).
fof(arity_Polynomial__Opoly__Groups_Oordered__comm__monoid__add,axiom,
! [X96] :
( class_Rings_Olinordered__idom(X96)
=> class_Groups_Oordered__comm__monoid__add(tc_Polynomial_Opoly(X96)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Oordered__comm__monoid__add) ).
fof(arity_Polynomial__Opoly__Rings_Olinordered__ring,axiom,
! [X96] :
( class_Rings_Olinordered__idom(X96)
=> class_Rings_Olinordered__ring(tc_Polynomial_Opoly(X96)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Olinordered__ring) ).
fof(arity_Polynomial__Opoly__Rings_Olinordered__semiring__strict,axiom,
! [X96] :
( class_Rings_Olinordered__idom(X96)
=> class_Rings_Olinordered__semiring__strict(tc_Polynomial_Opoly(X96)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Olinordered__semiring__strict) ).
fof(arity_Polynomial__Opoly__Rings_Olinordered__comm__semiring__strict,axiom,
! [X96] :
( class_Rings_Olinordered__idom(X96)
=> class_Rings_Olinordered__comm__semiring__strict(tc_Polynomial_Opoly(X96)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Olinordered__comm__semiring__strict) ).
fof(arity_Polynomial__Opoly__Rings_Olinordered__semidom,axiom,
! [X96] :
( class_Rings_Olinordered__idom(X96)
=> class_Rings_Olinordered__semidom(tc_Polynomial_Opoly(X96)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Olinordered__semidom) ).
fof(arity_Polynomial__Opoly__Rings_Osemiring__1,axiom,
! [X96] :
( class_Rings_Ocomm__semiring__1(X96)
=> class_Rings_Osemiring__1(tc_Polynomial_Opoly(X96)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Osemiring__1) ).
fof(arity_Polynomial__Opoly__Nat_Osemiring__char__0,axiom,
! [X96] :
( class_Rings_Olinordered__idom(X96)
=> class_Nat_Osemiring__char__0(tc_Polynomial_Opoly(X96)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Nat_Osemiring__char__0) ).
fof(arity_Polynomial__Opoly__Divides_Oring__div,axiom,
! [X96] :
( class_Fields_Ofield(X96)
=> class_Divides_Oring__div(tc_Polynomial_Opoly(X96)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Divides_Oring__div) ).
fof(arity_Polynomial__Opoly__Divides_Osemiring__div,axiom,
! [X96] :
( class_Fields_Ofield(X96)
=> class_Divides_Osemiring__div(tc_Polynomial_Opoly(X96)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Divides_Osemiring__div) ).
fof(arity_Polynomial__Opoly__Rings_Odvd,axiom,
! [X96] :
( class_Rings_Ocomm__semiring__1(X96)
=> class_Rings_Odvd(tc_Polynomial_Opoly(X96)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Odvd) ).
fof(arity_Polynomial__Opoly__Groups_Ouminus,axiom,
! [X96] :
( class_Groups_Oab__group__add(X96)
=> class_Groups_Ouminus(tc_Polynomial_Opoly(X96)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Ouminus) ).
fof(arity_Polynomial__Opoly__Groups_Ominus,axiom,
! [X96] :
( class_Groups_Oab__group__add(X96)
=> class_Groups_Ominus(tc_Polynomial_Opoly(X96)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Ominus) ).
fof(arity_Polynomial__Opoly__Rings_Oring__1,axiom,
! [X96] :
( class_Rings_Ocomm__ring__1(X96)
=> class_Rings_Oring__1(tc_Polynomial_Opoly(X96)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Oring__1) ).
fof(arity_Polynomial__Opoly__Rings_Oring,axiom,
! [X96] :
( class_Rings_Ocomm__ring(X96)
=> class_Rings_Oring(tc_Polynomial_Opoly(X96)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Oring) ).
fof(arity_Polynomial__Opoly__Groups_Ogroup__add,axiom,
! [X96] :
( class_Groups_Oab__group__add(X96)
=> class_Groups_Ogroup__add(tc_Polynomial_Opoly(X96)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Ogroup__add) ).
fof(arity_Polynomial__Opoly__Rings_Ocomm__ring,axiom,
! [X96] :
( class_Rings_Ocomm__ring(X96)
=> class_Rings_Ocomm__ring(tc_Polynomial_Opoly(X96)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Ocomm__ring) ).
fof(arity_Polynomial__Opoly__Groups_Oab__group__add,axiom,
! [X96] :
( class_Groups_Oab__group__add(X96)
=> class_Groups_Oab__group__add(tc_Polynomial_Opoly(X96)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Oab__group__add) ).
fof(arity_Polynomial__Opoly__Rings_Oring__no__zero__divisors,axiom,
! [X96] :
( class_Rings_Oidom(X96)
=> class_Rings_Oring__no__zero__divisors(tc_Polynomial_Opoly(X96)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Oring__no__zero__divisors) ).
fof(arity_Polynomial__Opoly__Rings_Ocomm__ring__1,axiom,
! [X96] :
( class_Rings_Ocomm__ring__1(X96)
=> class_Rings_Ocomm__ring__1(tc_Polynomial_Opoly(X96)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Ocomm__ring__1) ).
fof(arity_Polynomial__Opoly__Rings_Osemiring,axiom,
! [X96] :
( class_Rings_Ocomm__semiring__0(X96)
=> class_Rings_Osemiring(tc_Polynomial_Opoly(X96)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Osemiring) ).
fof(arity_Polynomial__Opoly__Rings_Ocomm__semiring,axiom,
! [X96] :
( class_Rings_Ocomm__semiring__0(X96)
=> class_Rings_Ocomm__semiring(tc_Polynomial_Opoly(X96)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Ocomm__semiring) ).
fof(arity_Polynomial__Opoly__Groups_Olinordered__ab__group__add,axiom,
! [X96] :
( class_Rings_Olinordered__idom(X96)
=> class_Groups_Olinordered__ab__group__add(tc_Polynomial_Opoly(X96)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Olinordered__ab__group__add) ).
fof(arity_Polynomial__Opoly__Groups_Omonoid__add,axiom,
! [X96] :
( class_Groups_Ocomm__monoid__add(X96)
=> class_Groups_Omonoid__add(tc_Polynomial_Opoly(X96)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Omonoid__add) ).
fof(arity_Polynomial__Opoly__Groups_Oone,axiom,
! [X96] :
( class_Rings_Ocomm__semiring__1(X96)
=> class_Groups_Oone(tc_Polynomial_Opoly(X96)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Oone) ).
fof(arity_Polynomial__Opoly__Groups_Ocancel__ab__semigroup__add,axiom,
! [X96] :
( class_Groups_Ocancel__comm__monoid__add(X96)
=> class_Groups_Ocancel__ab__semigroup__add(tc_Polynomial_Opoly(X96)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Ocancel__ab__semigroup__add) ).
fof(arity_Polynomial__Opoly__Groups_Ocancel__semigroup__add,axiom,
! [X96] :
( class_Groups_Ocancel__comm__monoid__add(X96)
=> class_Groups_Ocancel__semigroup__add(tc_Polynomial_Opoly(X96)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Ocancel__semigroup__add) ).
fof(arity_Polynomial__Opoly__Groups_Oab__semigroup__add,axiom,
! [X96] :
( class_Groups_Ocomm__monoid__add(X96)
=> class_Groups_Oab__semigroup__add(tc_Polynomial_Opoly(X96)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Oab__semigroup__add) ).
fof(arity_Polynomial__Opoly__Groups_Oab__semigroup__mult,axiom,
! [X96] :
( class_Rings_Ocomm__semiring__0(X96)
=> class_Groups_Oab__semigroup__mult(tc_Polynomial_Opoly(X96)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Oab__semigroup__mult) ).
fof(arity_Polynomial__Opoly__Rings_Olinordered__ring__strict,axiom,
! [X96] :
( class_Rings_Olinordered__idom(X96)
=> class_Rings_Olinordered__ring__strict(tc_Polynomial_Opoly(X96)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Olinordered__ring__strict) ).
fof(arity_Polynomial__Opoly__Groups_Ocomm__monoid__mult,axiom,
! [X96] :
( class_Rings_Ocomm__semiring__1(X96)
=> class_Groups_Ocomm__monoid__mult(tc_Polynomial_Opoly(X96)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Ocomm__monoid__mult) ).
fof(arity_Polynomial__Opoly__Rings_Oring__1__no__zero__divisors,axiom,
! [X96] :
( class_Rings_Oidom(X96)
=> class_Rings_Oring__1__no__zero__divisors(tc_Polynomial_Opoly(X96)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Oring__1__no__zero__divisors) ).
fof(arity_Polynomial__Opoly__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct,axiom,
! [X96] :
( class_Rings_Oidom(X96)
=> class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Polynomial_Opoly(X96)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct) ).
fof(arity_Polynomial__Opoly__Int_Oring__char__0,axiom,
! [X96] :
( class_Rings_Olinordered__idom(X96)
=> class_Int_Oring__char__0(tc_Polynomial_Opoly(X96)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Int_Oring__char__0) ).
fof(arity_Polynomial__Opoly__Groups_Ocomm__monoid__add,axiom,
! [X96] :
( class_Groups_Ocomm__monoid__add(X96)
=> class_Groups_Ocomm__monoid__add(tc_Polynomial_Opoly(X96)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Ocomm__monoid__add) ).
fof(arity_Polynomial__Opoly__Rings_Ozero__neq__one,axiom,
! [X96] :
( class_Rings_Ocomm__semiring__1(X96)
=> class_Rings_Ozero__neq__one(tc_Polynomial_Opoly(X96)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Ozero__neq__one) ).
fof(arity_Polynomial__Opoly__Rings_Ono__zero__divisors,axiom,
! [X96] :
( class_Rings_Oidom(X96)
=> class_Rings_Ono__zero__divisors(tc_Polynomial_Opoly(X96)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Ono__zero__divisors) ).
fof(arity_Polynomial__Opoly__Rings_Omult__zero,axiom,
! [X96] :
( class_Rings_Ocomm__semiring__0(X96)
=> class_Rings_Omult__zero(tc_Polynomial_Opoly(X96)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Omult__zero) ).
fof(arity_Polynomial__Opoly__Groups_Omonoid__mult,axiom,
! [X96] :
( class_Rings_Ocomm__semiring__1(X96)
=> class_Groups_Omonoid__mult(tc_Polynomial_Opoly(X96)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Omonoid__mult) ).
fof(arity_Polynomial__Opoly__Rings_Ocomm__semiring__1,axiom,
! [X96] :
( class_Rings_Ocomm__semiring__1(X96)
=> class_Rings_Ocomm__semiring__1(tc_Polynomial_Opoly(X96)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Ocomm__semiring__1) ).
fof(arity_Polynomial__Opoly__Rings_Osemiring__0,axiom,
! [X96] :
( class_Rings_Ocomm__semiring__0(X96)
=> class_Rings_Osemiring__0(tc_Polynomial_Opoly(X96)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Osemiring__0) ).
fof(arity_Polynomial__Opoly__Power_Opower,axiom,
! [X96] :
( class_Rings_Ocomm__semiring__1(X96)
=> class_Power_Opower(tc_Polynomial_Opoly(X96)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Power_Opower) ).
fof(arity_Polynomial__Opoly__Rings_Ocomm__semiring__0,axiom,
! [X96] :
( class_Rings_Ocomm__semiring__0(X96)
=> class_Rings_Ocomm__semiring__0(tc_Polynomial_Opoly(X96)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Ocomm__semiring__0) ).
fof(arity_Polynomial__Opoly__Groups_Ozero,axiom,
! [X96] :
( class_Groups_Ozero(X96)
=> class_Groups_Ozero(tc_Polynomial_Opoly(X96)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Ozero) ).
fof(arity_Polynomial__Opoly__Rings_Oidom,axiom,
! [X96] :
( class_Rings_Oidom(X96)
=> class_Rings_Oidom(tc_Polynomial_Opoly(X96)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Oidom) ).
fof(clrel_Rings_Oidom__Groups_Ocancel__comm__monoid__add,axiom,
! [X95] :
( class_Rings_Oidom(X95)
=> class_Groups_Ocancel__comm__monoid__add(X95) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clrel_Rings_Oidom__Groups_Ocancel__comm__monoid__add) ).
fof(clrel_Rings_Oidom__Rings_Osemiring__1,axiom,
! [X95] :
( class_Rings_Oidom(X95)
=> class_Rings_Osemiring__1(X95) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clrel_Rings_Oidom__Rings_Osemiring__1) ).
fof(clrel_Rings_Oidom__Rings_Odvd,axiom,
! [X95] :
( class_Rings_Oidom(X95)
=> class_Rings_Odvd(X95) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clrel_Rings_Oidom__Rings_Odvd) ).
fof(clrel_Rings_Oidom__Groups_Ouminus,axiom,
! [X95] :
( class_Rings_Oidom(X95)
=> class_Groups_Ouminus(X95) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clrel_Rings_Oidom__Groups_Ouminus) ).
fof(clrel_Rings_Oidom__Groups_Ominus,axiom,
! [X95] :
( class_Rings_Oidom(X95)
=> class_Groups_Ominus(X95) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clrel_Rings_Oidom__Groups_Ominus) ).
fof(clrel_Rings_Oidom__Rings_Oring__1,axiom,
! [X95] :
( class_Rings_Oidom(X95)
=> class_Rings_Oring__1(X95) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clrel_Rings_Oidom__Rings_Oring__1) ).
fof(clrel_Rings_Oidom__Rings_Oring,axiom,
! [X95] :
( class_Rings_Oidom(X95)
=> class_Rings_Oring(X95) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clrel_Rings_Oidom__Rings_Oring) ).
fof(clrel_Rings_Oidom__Groups_Ogroup__add,axiom,
! [X95] :
( class_Rings_Oidom(X95)
=> class_Groups_Ogroup__add(X95) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clrel_Rings_Oidom__Groups_Ogroup__add) ).
fof(clrel_Rings_Oidom__Rings_Ocomm__ring,axiom,
! [X95] :
( class_Rings_Oidom(X95)
=> class_Rings_Ocomm__ring(X95) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clrel_Rings_Oidom__Rings_Ocomm__ring) ).
fof(clrel_Rings_Oidom__Groups_Oab__group__add,axiom,
! [X95] :
( class_Rings_Oidom(X95)
=> class_Groups_Oab__group__add(X95) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clrel_Rings_Oidom__Groups_Oab__group__add) ).
fof(clrel_Rings_Oidom__Rings_Oring__no__zero__divisors,axiom,
! [X95] :
( class_Rings_Oidom(X95)
=> class_Rings_Oring__no__zero__divisors(X95) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clrel_Rings_Oidom__Rings_Oring__no__zero__divisors) ).
fof(clrel_Rings_Oidom__Rings_Ocomm__ring__1,axiom,
! [X95] :
( class_Rings_Oidom(X95)
=> class_Rings_Ocomm__ring__1(X95) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clrel_Rings_Oidom__Rings_Ocomm__ring__1) ).
fof(clrel_Rings_Oidom__Rings_Osemiring,axiom,
! [X95] :
( class_Rings_Oidom(X95)
=> class_Rings_Osemiring(X95) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clrel_Rings_Oidom__Rings_Osemiring) ).
fof(clrel_Rings_Oidom__Rings_Ocomm__semiring,axiom,
! [X95] :
( class_Rings_Oidom(X95)
=> class_Rings_Ocomm__semiring(X95) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clrel_Rings_Oidom__Rings_Ocomm__semiring) ).
fof(clrel_Rings_Oidom__Groups_Omonoid__add,axiom,
! [X95] :
( class_Rings_Oidom(X95)
=> class_Groups_Omonoid__add(X95) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clrel_Rings_Oidom__Groups_Omonoid__add) ).
fof(clrel_Rings_Oidom__Groups_Oone,axiom,
! [X95] :
( class_Rings_Oidom(X95)
=> class_Groups_Oone(X95) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clrel_Rings_Oidom__Groups_Oone) ).
fof(clrel_Rings_Oidom__Groups_Ocancel__ab__semigroup__add,axiom,
! [X95] :
( class_Rings_Oidom(X95)
=> class_Groups_Ocancel__ab__semigroup__add(X95) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clrel_Rings_Oidom__Groups_Ocancel__ab__semigroup__add) ).
fof(clrel_Rings_Oidom__Groups_Ocancel__semigroup__add,axiom,
! [X95] :
( class_Rings_Oidom(X95)
=> class_Groups_Ocancel__semigroup__add(X95) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clrel_Rings_Oidom__Groups_Ocancel__semigroup__add) ).
fof(clrel_Rings_Oidom__Groups_Oab__semigroup__add,axiom,
! [X95] :
( class_Rings_Oidom(X95)
=> class_Groups_Oab__semigroup__add(X95) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clrel_Rings_Oidom__Groups_Oab__semigroup__add) ).
fof(clrel_Rings_Oidom__Groups_Oab__semigroup__mult,axiom,
! [X95] :
( class_Rings_Oidom(X95)
=> class_Groups_Oab__semigroup__mult(X95) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clrel_Rings_Oidom__Groups_Oab__semigroup__mult) ).
fof(clrel_Rings_Oidom__Groups_Ocomm__monoid__mult,axiom,
! [X95] :
( class_Rings_Oidom(X95)
=> class_Groups_Ocomm__monoid__mult(X95) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clrel_Rings_Oidom__Groups_Ocomm__monoid__mult) ).
fof(clrel_Rings_Oidom__Rings_Oring__1__no__zero__divisors,axiom,
! [X95] :
( class_Rings_Oidom(X95)
=> class_Rings_Oring__1__no__zero__divisors(X95) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clrel_Rings_Oidom__Rings_Oring__1__no__zero__divisors) ).
fof(clrel_Rings_Oidom__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct,axiom,
! [X95] :
( class_Rings_Oidom(X95)
=> class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X95) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clrel_Rings_Oidom__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct) ).
fof(clrel_Rings_Oidom__Groups_Ocomm__monoid__add,axiom,
! [X95] :
( class_Rings_Oidom(X95)
=> class_Groups_Ocomm__monoid__add(X95) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clrel_Rings_Oidom__Groups_Ocomm__monoid__add) ).
fof(clrel_Rings_Oidom__Rings_Ozero__neq__one,axiom,
! [X95] :
( class_Rings_Oidom(X95)
=> class_Rings_Ozero__neq__one(X95) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clrel_Rings_Oidom__Rings_Ozero__neq__one) ).
fof(clrel_Rings_Oidom__Rings_Ono__zero__divisors,axiom,
! [X95] :
( class_Rings_Oidom(X95)
=> class_Rings_Ono__zero__divisors(X95) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clrel_Rings_Oidom__Rings_Ono__zero__divisors) ).
fof(clrel_Rings_Oidom__Rings_Omult__zero,axiom,
! [X95] :
( class_Rings_Oidom(X95)
=> class_Rings_Omult__zero(X95) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clrel_Rings_Oidom__Rings_Omult__zero) ).
fof(clrel_Rings_Oidom__Groups_Omonoid__mult,axiom,
! [X95] :
( class_Rings_Oidom(X95)
=> class_Groups_Omonoid__mult(X95) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clrel_Rings_Oidom__Groups_Omonoid__mult) ).
fof(clrel_Rings_Oidom__Rings_Ocomm__semiring__1,axiom,
! [X95] :
( class_Rings_Oidom(X95)
=> class_Rings_Ocomm__semiring__1(X95) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clrel_Rings_Oidom__Rings_Ocomm__semiring__1) ).
fof(clrel_Rings_Oidom__Rings_Osemiring__0,axiom,
! [X95] :
( class_Rings_Oidom(X95)
=> class_Rings_Osemiring__0(X95) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clrel_Rings_Oidom__Rings_Osemiring__0) ).
fof(clrel_Rings_Oidom__Power_Opower,axiom,
! [X95] :
( class_Rings_Oidom(X95)
=> class_Power_Opower(X95) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clrel_Rings_Oidom__Power_Opower) ).
fof(clrel_Rings_Oidom__Rings_Ocomm__semiring__0,axiom,
! [X95] :
( class_Rings_Oidom(X95)
=> class_Rings_Ocomm__semiring__0(X95) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clrel_Rings_Oidom__Rings_Ocomm__semiring__0) ).
fof(clrel_Rings_Oidom__Groups_Ozero,axiom,
! [X95] :
( class_Rings_Oidom(X95)
=> class_Groups_Ozero(X95) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clrel_Rings_Oidom__Groups_Ozero) ).
fof(fact_int__0__less__1,axiom,
c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_int__0__less__1) ).
fof(fact_int__Suc0__eq__1,axiom,
c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = c_Groups_Oone__class_Oone(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_int__Suc0__eq__1) ).
fof(fact_zminus__0,axiom,
hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zminus__0) ).
fof(fact_int__1,axiom,
c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_int__1) ).
fof(fact_int__0,axiom,
c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_int__0) ).
fof(fact_transfer__int__nat__numerals_I2_J,axiom,
c_Groups_Oone__class_Oone(tc_Int_Oint) = c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Nat_Onat)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_transfer__int__nat__numerals_I2_J) ).
fof(fact_One__nat__def,axiom,
c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_One__nat__def) ).
fof(fact_transfer__int__nat__numerals_I1_J,axiom,
c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_transfer__int__nat__numerals_I1_J) ).
fof(fact_int__0__neq__1,axiom,
c_Groups_Ozero__class_Ozero(tc_Int_Oint) != c_Groups_Oone__class_Oone(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_int__0__neq__1) ).
fof(arity_Int__Oint__Groups_Ocancel__comm__monoid__add,axiom,
class_Groups_Ocancel__comm__monoid__add(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Ocancel__comm__monoid__add) ).
fof(arity_Nat__Onat__Groups_Ocancel__comm__monoid__add,axiom,
class_Groups_Ocancel__comm__monoid__add(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Ocancel__comm__monoid__add) ).
fof(arity_Int__Oint__Rings_Oordered__ring,axiom,
class_Rings_Oordered__ring(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Oordered__ring) ).
fof(arity_HOL__Obool__Orderings_Oord,axiom,
class_Orderings_Oord(tc_HOL_Obool),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_HOL__Obool__Orderings_Oord) ).
fof(arity_Int__Oint__Orderings_Oord,axiom,
class_Orderings_Oord(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Orderings_Oord) ).
fof(arity_Nat__Onat__Orderings_Oord,axiom,
class_Orderings_Oord(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Orderings_Oord) ).
fof(arity_HOL__Obool__Orderings_Oorder,axiom,
class_Orderings_Oorder(tc_HOL_Obool),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_HOL__Obool__Orderings_Oorder) ).
fof(arity_Int__Oint__Orderings_Oorder,axiom,
class_Orderings_Oorder(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Orderings_Oorder) ).
fof(arity_Nat__Onat__Orderings_Oorder,axiom,
class_Orderings_Oorder(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Orderings_Oorder) ).
fof(arity_Int__Oint__Orderings_Olinorder,axiom,
class_Orderings_Olinorder(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Orderings_Olinorder) ).
fof(arity_Nat__Onat__Orderings_Olinorder,axiom,
class_Orderings_Olinorder(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Orderings_Olinorder) ).
fof(arity_HOL__Obool__Orderings_Opreorder,axiom,
class_Orderings_Opreorder(tc_HOL_Obool),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_HOL__Obool__Orderings_Opreorder) ).
fof(arity_Int__Oint__Orderings_Opreorder,axiom,
class_Orderings_Opreorder(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Orderings_Opreorder) ).
fof(arity_Nat__Onat__Orderings_Opreorder,axiom,
class_Orderings_Opreorder(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Orderings_Opreorder) ).
fof(arity_Int__Oint__Groups_Oordered__cancel__ab__semigroup__add,axiom,
class_Groups_Oordered__cancel__ab__semigroup__add(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Oordered__cancel__ab__semigroup__add) ).
fof(arity_Nat__Onat__Groups_Oordered__cancel__ab__semigroup__add,axiom,
class_Groups_Oordered__cancel__ab__semigroup__add(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Oordered__cancel__ab__semigroup__add) ).
fof(arity_Int__Oint__Groups_Oordered__ab__semigroup__add__imp__le,axiom,
class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Oordered__ab__semigroup__add__imp__le) ).
fof(arity_Nat__Onat__Groups_Oordered__ab__semigroup__add__imp__le,axiom,
class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Oordered__ab__semigroup__add__imp__le) ).
fof(arity_Int__Oint__Groups_Oordered__ab__group__add,axiom,
class_Groups_Oordered__ab__group__add(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Oordered__ab__group__add) ).
fof(arity_Int__Oint__Rings_Olinordered__idom,axiom,
class_Rings_Olinordered__idom(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Olinordered__idom) ).
fof(arity_Int__Oint__Groups_Oordered__comm__monoid__add,axiom,
class_Groups_Oordered__comm__monoid__add(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Oordered__comm__monoid__add) ).
fof(arity_Nat__Onat__Groups_Oordered__comm__monoid__add,axiom,
class_Groups_Oordered__comm__monoid__add(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Oordered__comm__monoid__add) ).
fof(arity_Int__Oint__Rings_Olinordered__ring,axiom,
class_Rings_Olinordered__ring(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Olinordered__ring) ).
fof(arity_Int__Oint__Rings_Olinordered__semiring__strict,axiom,
class_Rings_Olinordered__semiring__strict(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Olinordered__semiring__strict) ).
fof(arity_Nat__Onat__Rings_Olinordered__semiring__strict,axiom,
class_Rings_Olinordered__semiring__strict(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Olinordered__semiring__strict) ).
fof(arity_Int__Oint__Rings_Olinordered__comm__semiring__strict,axiom,
class_Rings_Olinordered__comm__semiring__strict(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Olinordered__comm__semiring__strict) ).
fof(arity_Nat__Onat__Rings_Olinordered__comm__semiring__strict,axiom,
class_Rings_Olinordered__comm__semiring__strict(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Olinordered__comm__semiring__strict) ).
fof(arity_Int__Oint__Rings_Olinordered__semidom,axiom,
class_Rings_Olinordered__semidom(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Olinordered__semidom) ).
fof(arity_Nat__Onat__Rings_Olinordered__semidom,axiom,
class_Rings_Olinordered__semidom(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Olinordered__semidom) ).
fof(arity_Int__Oint__Rings_Osemiring__1,axiom,
class_Rings_Osemiring__1(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Osemiring__1) ).
fof(arity_Nat__Onat__Rings_Osemiring__1,axiom,
class_Rings_Osemiring__1(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Osemiring__1) ).
fof(arity_Int__Oint__Nat_Osemiring__char__0,axiom,
class_Nat_Osemiring__char__0(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Nat_Osemiring__char__0) ).
fof(arity_Nat__Onat__Nat_Osemiring__char__0,axiom,
class_Nat_Osemiring__char__0(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Nat_Osemiring__char__0) ).
fof(arity_Int__Oint__Divides_Oring__div,axiom,
class_Divides_Oring__div(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Divides_Oring__div) ).
fof(arity_Int__Oint__Divides_Osemiring__div,axiom,
class_Divides_Osemiring__div(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Divides_Osemiring__div) ).
fof(arity_Nat__Onat__Divides_Osemiring__div,axiom,
class_Divides_Osemiring__div(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Divides_Osemiring__div) ).
fof(arity_Nat__Onat__Orderings_Owellorder,axiom,
class_Orderings_Owellorder(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Orderings_Owellorder) ).
fof(arity_Int__Oint__Rings_Odvd,axiom,
class_Rings_Odvd(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Odvd) ).
fof(arity_Nat__Onat__Rings_Odvd,axiom,
class_Rings_Odvd(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Odvd) ).
fof(arity_HOL__Obool__Groups_Ouminus,axiom,
class_Groups_Ouminus(tc_HOL_Obool),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_HOL__Obool__Groups_Ouminus) ).
fof(arity_Int__Oint__Groups_Ouminus,axiom,
class_Groups_Ouminus(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Ouminus) ).
fof(arity_HOL__Obool__Lattices_Oboolean__algebra,axiom,
class_Lattices_Oboolean__algebra(tc_HOL_Obool),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_HOL__Obool__Lattices_Oboolean__algebra) ).
fof(arity_HOL__Obool__Groups_Ominus,axiom,
class_Groups_Ominus(tc_HOL_Obool),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_HOL__Obool__Groups_Ominus) ).
fof(arity_Int__Oint__Groups_Ominus,axiom,
class_Groups_Ominus(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Ominus) ).
fof(arity_Nat__Onat__Groups_Ominus,axiom,
class_Groups_Ominus(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Ominus) ).
fof(arity_Int__Oint__Rings_Oring__1,axiom,
class_Rings_Oring__1(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Oring__1) ).
fof(arity_Int__Oint__Rings_Oring,axiom,
class_Rings_Oring(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Oring) ).
fof(arity_Int__Oint__Groups_Ogroup__add,axiom,
class_Groups_Ogroup__add(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Ogroup__add) ).
fof(arity_Int__Oint__Rings_Ocomm__ring,axiom,
class_Rings_Ocomm__ring(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Ocomm__ring) ).
fof(arity_Int__Oint__Groups_Oab__group__add,axiom,
class_Groups_Oab__group__add(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Oab__group__add) ).
fof(arity_Int__Oint__Rings_Oring__no__zero__divisors,axiom,
class_Rings_Oring__no__zero__divisors(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Oring__no__zero__divisors) ).
fof(arity_Int__Oint__Rings_Ocomm__ring__1,axiom,
class_Rings_Ocomm__ring__1(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Ocomm__ring__1) ).
fof(arity_Int__Oint__Rings_Osemiring,axiom,
class_Rings_Osemiring(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Osemiring) ).
fof(arity_Nat__Onat__Rings_Osemiring,axiom,
class_Rings_Osemiring(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Osemiring) ).
fof(arity_Int__Oint__Rings_Ocomm__semiring,axiom,
class_Rings_Ocomm__semiring(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Ocomm__semiring) ).
fof(arity_Nat__Onat__Rings_Ocomm__semiring,axiom,
class_Rings_Ocomm__semiring(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Ocomm__semiring) ).
fof(arity_Int__Oint__Groups_Olinordered__ab__group__add,axiom,
class_Groups_Olinordered__ab__group__add(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Olinordered__ab__group__add) ).
fof(arity_Int__Oint__Groups_Omonoid__add,axiom,
class_Groups_Omonoid__add(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Omonoid__add) ).
fof(arity_Nat__Onat__Groups_Omonoid__add,axiom,
class_Groups_Omonoid__add(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Omonoid__add) ).
fof(arity_Int__Oint__Groups_Oone,axiom,
class_Groups_Oone(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Oone) ).
fof(arity_Nat__Onat__Groups_Oone,axiom,
class_Groups_Oone(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Oone) ).
fof(arity_Int__Oint__Groups_Ocancel__ab__semigroup__add,axiom,
class_Groups_Ocancel__ab__semigroup__add(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Ocancel__ab__semigroup__add) ).
fof(arity_Nat__Onat__Groups_Ocancel__ab__semigroup__add,axiom,
class_Groups_Ocancel__ab__semigroup__add(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Ocancel__ab__semigroup__add) ).
fof(arity_Int__Oint__Groups_Ocancel__semigroup__add,axiom,
class_Groups_Ocancel__semigroup__add(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Ocancel__semigroup__add) ).
fof(arity_Nat__Onat__Groups_Ocancel__semigroup__add,axiom,
class_Groups_Ocancel__semigroup__add(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Ocancel__semigroup__add) ).
fof(arity_Int__Oint__Groups_Oab__semigroup__add,axiom,
class_Groups_Oab__semigroup__add(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Oab__semigroup__add) ).
fof(arity_Nat__Onat__Groups_Oab__semigroup__add,axiom,
class_Groups_Oab__semigroup__add(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Oab__semigroup__add) ).
fof(arity_Int__Oint__Groups_Oab__semigroup__mult,axiom,
class_Groups_Oab__semigroup__mult(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Oab__semigroup__mult) ).
fof(arity_Nat__Onat__Groups_Oab__semigroup__mult,axiom,
class_Groups_Oab__semigroup__mult(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Oab__semigroup__mult) ).
fof(arity_Int__Oint__Rings_Olinordered__ring__strict,axiom,
class_Rings_Olinordered__ring__strict(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Olinordered__ring__strict) ).
fof(arity_Int__Oint__Groups_Ocomm__monoid__mult,axiom,
class_Groups_Ocomm__monoid__mult(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Ocomm__monoid__mult) ).
fof(arity_Nat__Onat__Groups_Ocomm__monoid__mult,axiom,
class_Groups_Ocomm__monoid__mult(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Ocomm__monoid__mult) ).
fof(arity_Int__Oint__Rings_Oring__1__no__zero__divisors,axiom,
class_Rings_Oring__1__no__zero__divisors(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Oring__1__no__zero__divisors) ).
fof(arity_Int__Oint__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct,axiom,
class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct) ).
fof(arity_Nat__Onat__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct,axiom,
class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct) ).
fof(arity_Int__Oint__Int_Oring__char__0,axiom,
class_Int_Oring__char__0(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Int_Oring__char__0) ).
fof(arity_Int__Oint__Groups_Ocomm__monoid__add,axiom,
class_Groups_Ocomm__monoid__add(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Ocomm__monoid__add) ).
fof(arity_Nat__Onat__Groups_Ocomm__monoid__add,axiom,
class_Groups_Ocomm__monoid__add(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Ocomm__monoid__add) ).
fof(arity_Int__Oint__Rings_Ozero__neq__one,axiom,
class_Rings_Ozero__neq__one(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Ozero__neq__one) ).
fof(arity_Nat__Onat__Rings_Ozero__neq__one,axiom,
class_Rings_Ozero__neq__one(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Ozero__neq__one) ).
fof(arity_Int__Oint__Rings_Ono__zero__divisors,axiom,
class_Rings_Ono__zero__divisors(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Ono__zero__divisors) ).
fof(arity_Nat__Onat__Rings_Ono__zero__divisors,axiom,
class_Rings_Ono__zero__divisors(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Ono__zero__divisors) ).
fof(arity_Int__Oint__Rings_Omult__zero,axiom,
class_Rings_Omult__zero(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Omult__zero) ).
fof(arity_Nat__Onat__Rings_Omult__zero,axiom,
class_Rings_Omult__zero(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Omult__zero) ).
fof(arity_Int__Oint__Groups_Omonoid__mult,axiom,
class_Groups_Omonoid__mult(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Omonoid__mult) ).
fof(arity_Nat__Onat__Groups_Omonoid__mult,axiom,
class_Groups_Omonoid__mult(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Omonoid__mult) ).
fof(arity_Int__Oint__Rings_Ocomm__semiring__1,axiom,
class_Rings_Ocomm__semiring__1(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Ocomm__semiring__1) ).
fof(arity_Nat__Onat__Rings_Ocomm__semiring__1,axiom,
class_Rings_Ocomm__semiring__1(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Ocomm__semiring__1) ).
fof(arity_Int__Oint__Rings_Osemiring__0,axiom,
class_Rings_Osemiring__0(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Osemiring__0) ).
fof(arity_Nat__Onat__Rings_Osemiring__0,axiom,
class_Rings_Osemiring__0(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Osemiring__0) ).
fof(arity_Int__Oint__Power_Opower,axiom,
class_Power_Opower(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Power_Opower) ).
fof(arity_Nat__Onat__Power_Opower,axiom,
class_Power_Opower(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Power_Opower) ).
fof(arity_Int__Oint__Rings_Ocomm__semiring__0,axiom,
class_Rings_Ocomm__semiring__0(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Ocomm__semiring__0) ).
fof(arity_Nat__Onat__Rings_Ocomm__semiring__0,axiom,
class_Rings_Ocomm__semiring__0(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Ocomm__semiring__0) ).
fof(arity_Int__Oint__Groups_Ozero,axiom,
class_Groups_Ozero(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Ozero) ).
fof(arity_Nat__Onat__Groups_Ozero,axiom,
class_Groups_Ozero(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Ozero) ).
fof(arity_Int__Oint__Rings_Oidom,axiom,
class_Rings_Oidom(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Oidom) ).
fof(tfree_0,hypothesis,
class_Rings_Oidom(t_a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tfree_0) ).
fof(i_0_1179,plain,
! [X28,X27,X2,X5] :
( class_Orderings_Oorder(X5)
=> ( c_Orderings_Oorder_Ostrict__mono(tc_Nat_Onat,X5,hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool,c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),X2)
=> ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X27),X28))
& ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X28),X27)) )
=> c_Orderings_Oord__class_Oless(X5,hAPP(X2,X27),hAPP(X2,X28)) ) ) ),
inference(fof_simplification,[status(thm)],[fact_dvd_Ostrict__monoD]) ).
fof(i_0_1180,plain,
! [X8,X7,X9] :
( class_Rings_Oidom(X9)
=> ( X7 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X9))
=> ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X9)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(X9)),hAPP(hAPP(c_Polynomial_OpCons(X9),hAPP(c_Groups_Ouminus__class_Ouminus(X9),X8)),hAPP(hAPP(c_Polynomial_OpCons(X9),c_Groups_Oone__class_Oone(X9)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X9))))),hAPP(c_Nat_OSuc,c_Polynomial_Oorder(X9,X8,X7)))),X7)) ) ),
inference(fof_simplification,[status(thm)],[fact_order__2]) ).
fof(i_0_1181,plain,
! [X8,X7,X9] :
( class_Rings_Oidom(X9)
=> ( X7 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X9))
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X9)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(X9)),hAPP(hAPP(c_Polynomial_OpCons(X9),hAPP(c_Groups_Ouminus__class_Ouminus(X9),X8)),hAPP(hAPP(c_Polynomial_OpCons(X9),c_Groups_Oone__class_Oone(X9)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X9))))),c_Polynomial_Oorder(X9,X8,X7))),X7))
& ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X9)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(X9)),hAPP(hAPP(c_Polynomial_OpCons(X9),hAPP(c_Groups_Ouminus__class_Ouminus(X9),X8)),hAPP(hAPP(c_Polynomial_OpCons(X9),c_Groups_Oone__class_Oone(X9)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X9))))),hAPP(c_Nat_OSuc,c_Polynomial_Oorder(X9,X8,X7)))),X7)) ) ) ),
inference(fof_simplification,[status(thm)],[fact_order]) ).
fof(i_0_1182,negated_conjecture,
~ ? [X66,X103] :
( X103 != c_Groups_Ozero__class_Ozero(t_a)
& X66 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& ? [X77] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(t_a,X77)),X66)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(t_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)))
& ! [X104] : hAPP(c_Polynomial_Opoly(t_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),X104) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(t_a),hAPP(c_Polynomial_Opoly(t_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),c_Groups_Ozero__class_Ozero(t_a))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),hAPP(hAPP(c_Power_Opower__class_Opower(t_a),X104),X66)),hAPP(c_Polynomial_Opoly(t_a,hAPP(hAPP(c_Polynomial_OpCons(t_a),X103),X77)),X104))) ) ),
inference(assume_negation,[status(cth)],[conj_0]) ).
fof(i_0_1183,plain,
! [X33,X6,X9] :
( class_Rings_Olinordered__ring(X9)
=> ~ c_Orderings_Oord__class_Oless(X9,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X9),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X9),X6),X6)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X9),X33),X33)),c_Groups_Ozero__class_Ozero(X9)) ),
inference(fof_simplification,[status(thm)],[fact_not__sum__squares__lt__zero]) ).
fof(i_0_1184,plain,
! [X14,X68] :
( hBOOL(hAPP(X68,X14))
=> ( ~ hBOOL(hAPP(X68,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
=> c_Orderings_Oord__class_OLeast(tc_Nat_Onat,X68) = hAPP(c_Nat_OSuc,c_Orderings_Oord__class_OLeast(tc_Nat_Onat,hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_Nat_Onat),X68),c_Nat_OSuc))) ) ),
inference(fof_simplification,[status(thm)],[fact_Least__Suc]) ).
fof(i_0_1185,plain,
! [X11,X31,X25,X5] :
( class_Fields_Olinordered__field__inverse__zero(X5)
=> ( c_Orderings_Oord__class_Oless(X5,hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X5),X25),X31),X11)
<=> ( ( c_Orderings_Oord__class_Oless(X5,c_Groups_Ozero__class_Ozero(X5),X31)
=> c_Orderings_Oord__class_Oless(X5,X25,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X11),X31)) )
& ( ~ c_Orderings_Oord__class_Oless(X5,c_Groups_Ozero__class_Ozero(X5),X31)
=> ( ( c_Orderings_Oord__class_Oless(X5,X31,c_Groups_Ozero__class_Ozero(X5))
=> c_Orderings_Oord__class_Oless(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X11),X31),X25) )
& ( ~ c_Orderings_Oord__class_Oless(X5,X31,c_Groups_Ozero__class_Ozero(X5))
=> c_Orderings_Oord__class_Oless(X5,c_Groups_Ozero__class_Ozero(X5),X11) ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[fact_divide__less__eq]) ).
fof(i_0_1186,plain,
! [X31,X25,X11,X5] :
( class_Fields_Olinordered__field__inverse__zero(X5)
=> ( c_Orderings_Oord__class_Oless(X5,X11,hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X5),X25),X31))
<=> ( ( c_Orderings_Oord__class_Oless(X5,c_Groups_Ozero__class_Ozero(X5),X31)
=> c_Orderings_Oord__class_Oless(X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X11),X31),X25) )
& ( ~ c_Orderings_Oord__class_Oless(X5,c_Groups_Ozero__class_Ozero(X5),X31)
=> ( ( c_Orderings_Oord__class_Oless(X5,X31,c_Groups_Ozero__class_Ozero(X5))
=> c_Orderings_Oord__class_Oless(X5,X25,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X11),X31)) )
& ( ~ c_Orderings_Oord__class_Oless(X5,X31,c_Groups_Ozero__class_Ozero(X5))
=> c_Orderings_Oord__class_Oless(X5,X11,c_Groups_Ozero__class_Ozero(X5)) ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[fact_less__divide__eq]) ).
fof(i_0_1187,plain,
! [X25,X11,X68] :
( hBOOL(hAPP(X68,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X11),X25)))
<=> ~ ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X11,X25)
& ~ hBOOL(hAPP(X68,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) )
| ? [X93] :
( X11 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X25),X93)
& ~ hBOOL(hAPP(X68,X93)) ) ) ),
inference(fof_simplification,[status(thm)],[fact_nat__diff__split__asm]) ).
fof(i_0_1188,plain,
! [X32,X33,X6] :
( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X6),X33))
& ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X33),X6)) )
=> ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X33),X32))
& ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X32),X33)) )
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X6),X32))
& ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X32),X6)) ) ) ),
inference(fof_simplification,[status(thm)],[fact_dvd_Oless__trans]) ).
fof(i_0_1189,plain,
! [X32,X33,X6] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X6),X33))
=> ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X33),X32))
& ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X32),X33)) )
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X6),X32))
& ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X32),X6)) ) ) ),
inference(fof_simplification,[status(thm)],[fact_dvd_Ole__less__trans]) ).
fof(i_0_1190,plain,
! [X32,X33,X6] :
( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X6),X33))
& ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X33),X6)) )
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X33),X32))
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X6),X32))
& ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X32),X6)) ) ) ),
inference(fof_simplification,[status(thm)],[fact_dvd_Oless__le__trans]) ).
fof(i_0_1191,plain,
! [X10,X12] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X12)
=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X12,X10)
=> ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X10),X12)) ) ),
inference(fof_simplification,[status(thm)],[fact_zdvd__not__zless]) ).
fof(i_0_1192,plain,
! [X10,X12] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X12)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X12,X10)
=> ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X10),X12)) ) ),
inference(fof_simplification,[status(thm)],[fact_nat__dvd__not__less]) ).
fof(i_0_1193,plain,
! [X28,X27] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X27),X28))
<=> ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X27),X28))
& ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X28),X27)) )
| X27 = X28 ) ),
inference(fof_simplification,[status(thm)],[fact_dvd_Ole__less]) ).
fof(i_0_1194,plain,
! [X28,X27] :
( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X27),X28))
& ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X28),X27)) )
<=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X27),X28))
& X27 != X28 ) ),
inference(fof_simplification,[status(thm)],[fact_dvd_Oless__le]) ).
fof(i_0_1195,plain,
! [X21,X8] :
( X8 != X21
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X8),X21))
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X8),X21))
& ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X21),X8)) ) ) ),
inference(fof_simplification,[status(thm)],[fact_dvd_Oneq__le__trans]) ).
fof(i_0_1196,plain,
! [X33,X6] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X6),X33))
=> ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X6),X33))
& ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X33),X6)) )
| X6 = X33 ) ),
inference(fof_simplification,[status(thm)],[fact_dvd_Ole__imp__less__or__eq]) ).
fof(i_0_1197,plain,
! [X21,X8] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X8),X21))
=> ( X8 != X21
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X8),X21))
& ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X21),X8)) ) ) ),
inference(fof_simplification,[status(thm)],[fact_dvd_Ole__neq__trans]) ).
fof(i_0_1198,plain,
! [X8,X9] :
( class_Rings_Olinordered__ring(X9)
=> ~ c_Orderings_Oord__class_Oless(X9,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X9),X8),X8),c_Groups_Ozero__class_Ozero(X9)) ),
inference(fof_simplification,[status(thm)],[fact_not__square__less__zero]) ).
fof(i_0_1199,plain,
! [X10,X12] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X12,X10)
=> c_Divides_Odiv__class_Omod(tc_Nat_Onat,X12,X10) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X12),X10),X10) ),
inference(fof_simplification,[status(thm)],[fact_mod__geq]) ).
fof(i_0_1200,plain,
! [X10,X12] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X12,X10)
=> c_Divides_Odiv__class_Omod(tc_Nat_Onat,X12,X10) = X12 )
& ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X12,X10)
=> c_Divides_Odiv__class_Omod(tc_Nat_Onat,X12,X10) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X12),X10),X10) ) ),
inference(fof_simplification,[status(thm)],[fact_mod__if]) ).
fof(i_0_1201,plain,
! [X12,X10] : ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,X10),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,X12))),
inference(fof_simplification,[status(thm)],[fact_not__int__zless__negative]) ).
fof(i_0_1202,plain,
! [X40,X42] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X42),X40),X42),
inference(fof_simplification,[status(thm)],[fact_not__add__less1]) ).
fof(i_0_1203,plain,
! [X42,X40] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X40),X42),X42),
inference(fof_simplification,[status(thm)],[fact_not__add__less2]) ).
fof(i_0_1204,plain,
! [X14,X35] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X35,X14)
<=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X14,hAPP(c_Nat_OSuc,X35)) ),
inference(fof_simplification,[status(thm)],[fact_not__less__eq]) ).
fof(i_0_1205,plain,
! [X10,X12] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X12,X10)
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X10),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X12),X10)) = X12 ),
inference(fof_simplification,[status(thm)],[fact_add__diff__inverse]) ).
fof(i_0_1206,plain,
! [X68,X39,X5] :
( class_Orderings_Owellorder(X5)
=> ( c_Orderings_Oord__class_Oless(X5,X39,c_Orderings_Oord__class_OLeast(X5,X68))
=> ~ hBOOL(hAPP(X68,X39)) ) ),
inference(fof_simplification,[status(thm)],[fact_not__less__Least]) ).
fof(i_0_1207,plain,
! [X8,X21,X9] :
( class_Orderings_Oorder(X9)
=> ( c_Orderings_Oord__class_Oless(X9,X21,X8)
=> ~ c_Orderings_Oord__class_Oless(X9,X8,X21) ) ),
inference(fof_simplification,[status(thm)],[fact_xt1_I9_J]) ).
fof(i_0_1208,plain,
! [X28,X27,X5] :
( class_Orderings_Olinorder(X5)
=> ( ~ c_Orderings_Oord__class_Oless(X5,X27,X28)
<=> ( c_Orderings_Oord__class_Oless(X5,X28,X27)
| X27 = X28 ) ) ),
inference(fof_simplification,[status(thm)],[fact_not__less__iff__gr__or__eq]) ).
fof(i_0_1209,plain,
! [X33,X6,X9] :
( class_Orderings_Opreorder(X9)
=> ( c_Orderings_Oord__class_Oless(X9,X6,X33)
=> ~ c_Orderings_Oord__class_Oless(X9,X33,X6) ) ),
inference(fof_simplification,[status(thm)],[fact_order__less__asym]) ).
fof(i_0_1210,plain,
! [X21,X8,X9] :
( class_Orderings_Opreorder(X9)
=> ( c_Orderings_Oord__class_Oless(X9,X8,X21)
=> ~ c_Orderings_Oord__class_Oless(X9,X21,X8) ) ),
inference(fof_simplification,[status(thm)],[fact_order__less__asym_H]) ).
fof(i_0_1211,plain,
! [X33,X6,X9] :
( class_Orderings_Opreorder(X9)
=> ( c_Orderings_Oord__class_Oless(X9,X6,X33)
=> ~ c_Orderings_Oord__class_Oless(X9,X33,X6) ) ),
inference(fof_simplification,[status(thm)],[fact_order__less__imp__not__less]) ).
fof(i_0_1212,plain,
! [X33,X6,X9] :
( class_Orderings_Opreorder(X9)
=> ( c_Orderings_Oord__class_Oless(X9,X6,X33)
=> ~ c_Orderings_Oord__class_Oless(X9,X33,X6) ) ),
inference(fof_simplification,[status(thm)],[fact_order__less__not__sym]) ).
fof(i_0_1213,plain,
! [X35,X14] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X14,X35)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X14,hAPP(c_Nat_OSuc,X35))
<=> X14 = X35 ) ),
inference(fof_simplification,[status(thm)],[fact_not__less__less__Suc__eq]) ).
fof(i_0_1214,plain,
! [X12,X10] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X10,X12)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X10,hAPP(c_Nat_OSuc,X12))
=> X12 = X10 ) ),
inference(fof_simplification,[status(thm)],[fact_less__antisym]) ).
fof(i_0_1215,plain,
! [X10,X12] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X12,hAPP(c_Nat_OSuc,X10))
=> ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X12,X10)
=> X12 = X10 ) ),
inference(fof_simplification,[status(thm)],[fact_less__SucE]) ).
fof(i_0_1216,plain,
! [X6,X9] :
( class_Rings_Olinordered__idom(X9)
=> ( ( X6 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X9))
=> c_Groups_Osgn__class_Osgn(tc_Polynomial_Opoly(X9),X6) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X9)) )
& ( X6 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X9))
=> ( ( c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(X9),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X9)),X6)
=> c_Groups_Osgn__class_Osgn(tc_Polynomial_Opoly(X9),X6) = c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(X9)) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(X9),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X9)),X6)
=> c_Groups_Osgn__class_Osgn(tc_Polynomial_Opoly(X9),X6) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X9)),c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(X9))) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[fact_sgn__poly__def]) ).
fof(i_0_1217,plain,
( class_Rings_Oidom(t_a)
=> ~ c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(t_a,t_a,c_Polynomial_Opoly(t_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)))) ),
inference(fof_simplification,[status(thm)],[fact__C0_C]) ).
fof(i_0_1218,plain,
! [X12,X9] :
( class_Rings_Olinordered__semidom(X9)
=> ~ c_Orderings_Oord__class_Oless(X9,c_Nat_Osemiring__1__class_Oof__nat(X9,X12),c_Groups_Ozero__class_Ozero(X9)) ),
inference(fof_simplification,[status(thm)],[fact_of__nat__less__0__iff]) ).
fof(i_0_1219,plain,
! [X36] : ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,X36),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),
inference(fof_simplification,[status(thm)],[fact_int__less__0__conv]) ).
fof(i_0_1220,plain,
! [X101,X68] :
( ~ hBOOL(hAPP(hAPP(c_fconj,X68),X101))
| hBOOL(X68) ),
inference(fof_simplification,[status(thm)],[help_c__fconj__2]) ).
fof(i_0_1221,plain,
! [X101,X68] :
( ~ hBOOL(hAPP(hAPP(c_fconj,X68),X101))
| hBOOL(X101) ),
inference(fof_simplification,[status(thm)],[help_c__fconj__3]) ).
fof(i_0_1222,plain,
! [X33,X6,X9] :
( class_Orderings_Olinorder(X9)
=> ( ~ c_Orderings_Oord__class_Oless(X9,X6,X33)
=> ( X6 != X33
=> c_Orderings_Oord__class_Oless(X9,X33,X6) ) ) ),
inference(fof_simplification,[status(thm)],[fact_linorder__cases]) ).
fof(i_0_1223,plain,
! [X33,X6,X9] :
( class_Orderings_Olinorder(X9)
=> ( X6 != X33
=> ( ~ c_Orderings_Oord__class_Oless(X9,X6,X33)
=> c_Orderings_Oord__class_Oless(X9,X33,X6) ) ) ),
inference(fof_simplification,[status(thm)],[fact_linorder__neqE]) ).
fof(i_0_1224,plain,
! [X27,X28,X5] :
( class_Orderings_Olinorder(X5)
=> ( ~ c_Orderings_Oord__class_Oless(X5,X28,X27)
=> ( ~ c_Orderings_Oord__class_Oless(X5,X27,X28)
<=> X27 = X28 ) ) ),
inference(fof_simplification,[status(thm)],[fact_linorder__antisym__conv3]) ).
fof(i_0_1225,plain,
! [X33,X6,X9] :
( class_Rings_Olinordered__idom(X9)
=> ( X6 != X33
=> ( ~ c_Orderings_Oord__class_Oless(X9,X6,X33)
=> c_Orderings_Oord__class_Oless(X9,X33,X6) ) ) ),
inference(fof_simplification,[status(thm)],[fact_linorder__neqE__linordered__idom]) ).
fof(i_0_1226,plain,
( class_Rings_Oidom(t_a)
=> ~ c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(t_a,t_a,c_Polynomial_Opoly(t_a,v_p)) ),
inference(fof_simplification,[status(thm)],[fact_assms]) ).
fof(i_0_1227,plain,
! [X9] :
( class_Rings_Olinordered__semidom(X9)
=> ~ c_Orderings_Oord__class_Oless(X9,c_Groups_Oone__class_Oone(X9),c_Groups_Ozero__class_Ozero(X9)) ),
inference(fof_simplification,[status(thm)],[fact_not__one__less__zero]) ).
fof(i_0_1228,plain,
! [X33,X6] :
( X6 != X33
=> ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X6,X33)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X33,X6) ) ),
inference(fof_simplification,[status(thm)],[fact_linorder__neqE__nat]) ).
fof(i_0_1229,plain,
! [X6,X9] :
( class_Orderings_Opreorder(X9)
=> ~ c_Orderings_Oord__class_Oless(X9,X6,X6) ),
inference(fof_simplification,[status(thm)],[fact_order__less__irrefl]) ).
fof(i_0_1230,plain,
! [X101,X68] :
( ~ hBOOL(X68)
| ~ hBOOL(X101)
| hBOOL(hAPP(hAPP(c_fconj,X68),X101)) ),
inference(fof_simplification,[status(thm)],[help_c__fconj__1]) ).
fof(i_0_1231,plain,
! [X10] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X10,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(fof_simplification,[status(thm)],[fact_not__less0]) ).
fof(i_0_1232,plain,
! [X10] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X10,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(fof_simplification,[status(thm)],[fact_less__nat__zero__code]) ).
fof(i_0_1233,plain,
! [X10] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X10,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(fof_simplification,[status(thm)],[fact_less__zeroE]) ).
fof(i_0_1234,plain,
! [X10] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X10,X10),
inference(fof_simplification,[status(thm)],[fact_less__irrefl__nat]) ).
fof(i_0_1235,plain,
! [X10] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X10,X10),
inference(fof_simplification,[status(thm)],[fact_less__not__refl]) ).
fof(i_0_1236,plain,
! [X28,X27] :
( ~ hBOOL(hAPP(c_fequal(X27),X28))
| X27 = X28 ),
inference(fof_simplification,[status(thm)],[help_c__fequal__1]) ).
fof(i_0_1237,plain,
! [X9] :
( class_Rings_Olinordered__idom(X9)
=> ~ c_Polynomial_Opos__poly(X9,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X9))) ),
inference(fof_simplification,[status(thm)],[fact_not__pos__poly__0]) ).
fof(i_0_1238,plain,
! [X68] :
( ~ hBOOL(hAPP(c_fNot,X68))
| ~ hBOOL(X68) ),
inference(fof_simplification,[status(thm)],[help_c__fNot__1]) ).
fof(i_0_1239,plain,
! [X68] :
( hBOOL(X68)
| hBOOL(hAPP(c_fNot,X68)) ),
inference(fof_simplification,[status(thm)],[help_c__fNot__2]) ).
fof(i_0_1240,plain,
! [X4454,X4455,X4456] :
( ~ class_Rings_Oidom(X4456)
| c_Polynomial_Oorder(X4456,X4455,X4454) = c_Orderings_Oord__class_OLeast(tc_Nat_Onat,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot),hAPP(c_COMBC(tc_Nat_Onat,tc_Polynomial_Opoly(X4456),tc_HOL_Obool,hAPP(hAPP(c_COMBB(tc_Polynomial_Opoly(X4456),tc_fun(tc_Polynomial_Opoly(X4456),tc_HOL_Obool),tc_Nat_Onat),c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X4456))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Polynomial_Opoly(X4456),tc_Nat_Onat),hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(X4456)),hAPP(hAPP(c_Polynomial_OpCons(X4456),hAPP(c_Groups_Ouminus__class_Ouminus(X4456),X4455)),hAPP(hAPP(c_Polynomial_OpCons(X4456),c_Groups_Oone__class_Oone(X4456)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4456)))))),c_Nat_OSuc))),X4454))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__def])]) ).
fof(i_0_1241,plain,
! [X3555,X3556,X3557] :
( ~ class_Rings_Ocomm__semiring__0(X3557)
| c_Polynomial_Opcompose(X3557,X3556,X3555) = c_Polynomial_Opoly__rec(tc_Polynomial_Opoly(X3557),X3557,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3557)),hAPP(hAPP(c_COMBB(tc_fun(tc_Polynomial_Opoly(X3557),tc_Polynomial_Opoly(X3557)),tc_fun(tc_Polynomial_Opoly(X3557),tc_fun(tc_Polynomial_Opoly(X3557),tc_Polynomial_Opoly(X3557))),X3557),c_COMBK(tc_fun(tc_Polynomial_Opoly(X3557),tc_Polynomial_Opoly(X3557)),tc_Polynomial_Opoly(X3557))),hAPP(c_COMBC(X3557,tc_fun(tc_Polynomial_Opoly(X3557),tc_Polynomial_Opoly(X3557)),tc_fun(tc_Polynomial_Opoly(X3557),tc_Polynomial_Opoly(X3557)),hAPP(hAPP(c_COMBB(tc_fun(tc_Polynomial_Opoly(X3557),tc_Polynomial_Opoly(X3557)),tc_fun(tc_fun(tc_Polynomial_Opoly(X3557),tc_Polynomial_Opoly(X3557)),tc_fun(tc_Polynomial_Opoly(X3557),tc_Polynomial_Opoly(X3557))),X3557),c_COMBB(tc_Polynomial_Opoly(X3557),tc_Polynomial_Opoly(X3557),tc_Polynomial_Opoly(X3557))),hAPP(hAPP(c_COMBB(tc_Polynomial_Opoly(X3557),tc_fun(tc_Polynomial_Opoly(X3557),tc_Polynomial_Opoly(X3557)),X3557),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X3557))),hAPP(c_COMBC(X3557,tc_Polynomial_Opoly(X3557),tc_Polynomial_Opoly(X3557),c_Polynomial_OpCons(X3557)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3557)))))),hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X3557)),X3555))),X3556) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pcompose__def])]) ).
fof(i_0_1242,plain,
! [X3680,X3681,X3682] :
( ~ class_Rings_Ocomm__semiring__0(X3682)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X3682)),X3681),X3680) = c_Polynomial_Opoly__rec(tc_Polynomial_Opoly(X3682),X3682,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3682)),hAPP(hAPP(c_COMBB(tc_fun(tc_Polynomial_Opoly(X3682),tc_Polynomial_Opoly(X3682)),tc_fun(tc_Polynomial_Opoly(X3682),tc_fun(tc_Polynomial_Opoly(X3682),tc_Polynomial_Opoly(X3682))),X3682),c_COMBK(tc_fun(tc_Polynomial_Opoly(X3682),tc_Polynomial_Opoly(X3682)),tc_Polynomial_Opoly(X3682))),hAPP(c_COMBC(X3682,tc_fun(tc_Polynomial_Opoly(X3682),tc_Polynomial_Opoly(X3682)),tc_fun(tc_Polynomial_Opoly(X3682),tc_Polynomial_Opoly(X3682)),hAPP(hAPP(c_COMBB(tc_fun(tc_Polynomial_Opoly(X3682),tc_Polynomial_Opoly(X3682)),tc_fun(tc_fun(tc_Polynomial_Opoly(X3682),tc_Polynomial_Opoly(X3682)),tc_fun(tc_Polynomial_Opoly(X3682),tc_Polynomial_Opoly(X3682))),X3682),c_COMBB(tc_Polynomial_Opoly(X3682),tc_Polynomial_Opoly(X3682),tc_Polynomial_Opoly(X3682))),hAPP(hAPP(c_COMBB(tc_Polynomial_Opoly(X3682),tc_fun(tc_Polynomial_Opoly(X3682),tc_Polynomial_Opoly(X3682)),X3682),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X3682))),hAPP(c_COMBC(X3682,tc_Polynomial_Opoly(X3682),tc_Polynomial_Opoly(X3682),c_Polynomial_Osmult(X3682)),X3680)))),hAPP(c_Polynomial_OpCons(X3682),c_Groups_Ozero__class_Ozero(X3682)))),X3681) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_times__poly__def])]) ).
fof(i_0_1243,plain,
! [X5806,X5807,X5808,X5809] :
( ~ class_Orderings_Oorder(X5809)
| ~ c_Orderings_Oorder_Ostrict__mono(tc_Nat_Onat,X5809,hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool,c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),X5808)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X5807),X5806))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X5806),X5807))
| c_Orderings_Oord__class_Oless(X5809,hAPP(X5808,X5807),hAPP(X5808,X5806)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1179])]) ).
fof(i_0_1244,plain,
! [X5849,X5850] :
( ~ class_Orderings_Oorder(X5850)
| ~ c_Orderings_Oorder_Ostrict__mono(tc_Nat_Onat,X5850,hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool,c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),X5849)
| c_Orderings_Oorder_Omono(tc_Nat_Onat,X5850,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X5849) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvd_Ostrict__mono__mono])]) ).
fof(i_0_1245,plain,
! [X3624,X3625,X3626] :
( ~ class_Rings_Ocomm__semiring__0(X3626)
| c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X3626,X3625,X3624) = c_Polynomial_Opoly__rec(tc_Polynomial_Opoly(X3626),X3626,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3626)),hAPP(hAPP(c_COMBB(tc_fun(tc_Polynomial_Opoly(X3626),tc_Polynomial_Opoly(X3626)),tc_fun(tc_Polynomial_Opoly(X3626),tc_fun(tc_Polynomial_Opoly(X3626),tc_Polynomial_Opoly(X3626))),X3626),c_COMBK(tc_fun(tc_Polynomial_Opoly(X3626),tc_Polynomial_Opoly(X3626)),tc_Polynomial_Opoly(X3626))),hAPP(hAPP(c_COMBB(tc_fun(tc_Polynomial_Opoly(X3626),tc_Polynomial_Opoly(X3626)),tc_fun(tc_Polynomial_Opoly(X3626),tc_Polynomial_Opoly(X3626)),X3626),hAPP(c_COMBS(tc_Polynomial_Opoly(X3626),tc_Polynomial_Opoly(X3626),tc_Polynomial_Opoly(X3626)),hAPP(hAPP(c_COMBB(tc_Polynomial_Opoly(X3626),tc_fun(tc_Polynomial_Opoly(X3626),tc_Polynomial_Opoly(X3626)),tc_Polynomial_Opoly(X3626)),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X3626))),hAPP(c_Polynomial_Osmult(X3626),X3624)))),c_Polynomial_OpCons(X3626))),X3625) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_offset__poly__def])]) ).
fof(i_0_1246,plain,
! [X4852,X4853,X4854,X4855] :
( ~ class_Fields_Ofield(X4855)
| X4854 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4855))
| c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(X4855),hAPP(hAPP(c_Polynomial_OpCons(X4855),X4853),X4852),X4854) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X4855)),hAPP(hAPP(c_Polynomial_OpCons(X4855),X4853),c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(X4855),X4852,X4854))),hAPP(hAPP(c_Polynomial_Osmult(X4855),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4855),hAPP(c_Polynomial_Ocoeff(X4855,hAPP(hAPP(c_Polynomial_OpCons(X4855),X4853),c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(X4855),X4852,X4854))),c_Polynomial_Odegree(X4855,X4854))),hAPP(c_Polynomial_Ocoeff(X4855,X4854),c_Polynomial_Odegree(X4855,X4854)))),X4854)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__pCons])]) ).
fof(i_0_1247,plain,
! [X3879,X3880,X3881] :
( ~ class_Groups_Ozero(X3881)
| c_Polynomial_Omonom(X3881,X3880,X3879) = c_Polynomial_OAbs__poly(X3881,hAPP(c_COMBC(tc_Nat_Onat,X3881,X3881,hAPP(c_COMBC(tc_Nat_Onat,X3881,tc_fun(X3881,X3881),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X3881,tc_fun(X3881,X3881)),tc_Nat_Onat),c_If(X3881)),c_fequal(X3879))),X3880)),c_Groups_Ozero__class_Ozero(X3881))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_monom__def])]) ).
fof(i_0_1248,plain,
! [X4211,X4212,X4213] :
( ~ class_Rings_Oidom(X4213)
| X4212 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4213))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X4213)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(X4213)),hAPP(hAPP(c_Polynomial_OpCons(X4213),hAPP(c_Groups_Ouminus__class_Ouminus(X4213),X4211)),hAPP(hAPP(c_Polynomial_OpCons(X4213),c_Groups_Oone__class_Oone(X4213)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4213))))),hAPP(c_Nat_OSuc,c_Polynomial_Oorder(X4213,X4211,X4212)))),X4212)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1180])]) ).
fof(i_0_1249,plain,
! [X4214,X4215,X4216] :
( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X4216)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(X4216)),hAPP(hAPP(c_Polynomial_OpCons(X4216),hAPP(c_Groups_Ouminus__class_Ouminus(X4216),X4214)),hAPP(hAPP(c_Polynomial_OpCons(X4216),c_Groups_Oone__class_Oone(X4216)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4216))))),c_Polynomial_Oorder(X4216,X4214,X4215))),X4215))
| X4215 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4216))
| ~ class_Rings_Oidom(X4216) )
& ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X4216)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(X4216)),hAPP(hAPP(c_Polynomial_OpCons(X4216),hAPP(c_Groups_Ouminus__class_Ouminus(X4216),X4214)),hAPP(hAPP(c_Polynomial_OpCons(X4216),c_Groups_Oone__class_Oone(X4216)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4216))))),hAPP(c_Nat_OSuc,c_Polynomial_Oorder(X4216,X4214,X4215)))),X4215))
| X4215 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4216))
| ~ class_Rings_Oidom(X4216) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1181])])]) ).
fof(i_0_1250,plain,
! [X4220,X4221,X4222] :
( ~ class_Rings_Oidom(X4222)
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X4222)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(X4222)),hAPP(hAPP(c_Polynomial_OpCons(X4222),hAPP(c_Groups_Ouminus__class_Ouminus(X4222),X4221)),hAPP(hAPP(c_Polynomial_OpCons(X4222),c_Groups_Oone__class_Oone(X4222)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4222))))),c_Polynomial_Oorder(X4222,X4221,X4220))),X4220)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__1])]) ).
fof(i_0_1251,plain,
! [X5077,X5078,X5079,X5080,X5081,X5082] :
( ~ class_RealVector_Oreal__normed__field(X5082)
| ~ c_Deriv_Oderiv(X5082,X5081,X5080,X5079)
| ~ c_Deriv_Oderiv(X5082,X5078,X5080,X5077)
| hAPP(X5078,X5080) = c_Groups_Ozero__class_Ozero(X5082)
| c_Deriv_Oderiv(X5082,hAPP(hAPP(c_COMBS(X5082,X5082,X5082),hAPP(hAPP(c_COMBB(X5082,tc_fun(X5082,X5082),X5082),c_Rings_Oinverse__class_Odivide(X5082)),X5081)),X5078),X5080,hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X5082),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X5082),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5082),X5079),hAPP(X5078,X5080))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5082),hAPP(X5081,X5080)),X5077))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5082),hAPP(X5078,X5080)),hAPP(X5078,X5080)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_DERIV__divide])]) ).
fof(i_0_1252,plain,
! [X4856,X4857,X4858,X4859,X4860,X4861] :
( ~ class_RealVector_Oreal__normed__field(X4861)
| ~ c_Deriv_Oderiv(X4861,X4860,X4859,X4858)
| ~ c_Deriv_Oderiv(X4861,X4857,X4859,X4856)
| hAPP(X4857,X4859) = c_Groups_Ozero__class_Ozero(X4861)
| c_Deriv_Oderiv(X4861,hAPP(hAPP(c_COMBS(X4861,X4861,X4861),hAPP(hAPP(c_COMBB(X4861,tc_fun(X4861,X4861),X4861),c_Rings_Oinverse__class_Odivide(X4861)),X4860)),X4857),X4859,hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4861),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X4861),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4861),X4858),hAPP(X4857,X4859))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4861),X4856),hAPP(X4860,X4859)))),hAPP(hAPP(c_Power_Opower__class_Opower(X4861),hAPP(X4857,X4859)),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_DERIV__quotient])]) ).
fof(i_0_1253,plain,
! [X3845,X3846,X3847,X3848,X3849] :
( ~ class_RealVector_Oreal__normed__algebra(X3849)
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(X3849),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3849),X3848),X3847)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3849),X3846),X3845)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X3849),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X3849),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3849),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X3849),X3848),X3846)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X3849),X3847),X3845))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3849),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X3849),X3848),X3846)),X3845))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3849),X3846),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X3849),X3847),X3845))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult_Oprod__diff__prod])]) ).
fof(i_0_1254,plain,
! [X3569,X3570,X3571,X3572,X3573,X3574] :
( ~ class_Groups_Ozero(X3574)
| c_Polynomial_Opoly__rec(X3573,X3574,X3572,X3571,hAPP(hAPP(c_Polynomial_OpCons(X3574),X3570),X3569)) = hAPP(hAPP(hAPP(X3571,X3570),X3569),hAPP(hAPP(hAPP(c_If(X3573),hAPP(c_fequal(X3569),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3574)))),X3572),c_Polynomial_Opoly__rec(X3573,X3574,X3572,X3571,X3569))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_poly__rec_Osimps])]) ).
fof(i_0_1255,plain,
! [X4862,X4863,X4864,X4865,X4866] :
( ~ class_RealVector_Oreal__normed__field(X4866)
| ~ c_Deriv_Oderiv(X4866,X4865,X4864,X4863)
| c_Deriv_Oderiv(X4866,hAPP(c_COMBC(X4866,tc_Nat_Onat,X4866,hAPP(hAPP(c_COMBB(X4866,tc_fun(tc_Nat_Onat,X4866),X4866),c_Power_Opower__class_Opower(X4866)),X4865)),X4862),X4864,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4866),c_Nat_Osemiring__1__class_Oof__nat(X4866,X4862)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4866),X4863),hAPP(hAPP(c_Power_Opower__class_Opower(X4866),hAPP(X4865,X4864)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X4862),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_DERIV__power])]) ).
fof(i_0_1256,negated_conjecture,
! [X6193,X6194,X6195] :
( X6194 = c_Groups_Ozero__class_Ozero(t_a)
| X6193 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(t_a,X6195)),X6193)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) != c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(t_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)))
| hAPP(c_Polynomial_Opoly(t_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),esk21_3(X6193,X6194,X6195)) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(t_a),hAPP(c_Polynomial_Opoly(t_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),c_Groups_Ozero__class_Ozero(t_a))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),hAPP(hAPP(c_Power_Opower__class_Opower(t_a),esk21_3(X6193,X6194,X6195)),X6193)),hAPP(c_Polynomial_Opoly(t_a,hAPP(hAPP(c_Polynomial_OpCons(t_a),X6194),X6195)),esk21_3(X6193,X6194,X6195)))) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1182])])])]) ).
fof(i_0_1257,plain,
! [X4867,X4868,X4869,X4870,X4871] :
( ~ class_RealVector_Oreal__normed__field(X4871)
| ~ c_Deriv_Oderiv(X4871,X4870,X4869,X4868)
| c_Deriv_Oderiv(X4871,hAPP(c_COMBC(X4871,tc_Nat_Onat,X4871,hAPP(hAPP(c_COMBB(X4871,tc_fun(tc_Nat_Onat,X4871),X4871),c_Power_Opower__class_Opower(X4871)),X4870)),hAPP(c_Nat_OSuc,X4867)),X4869,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4871),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4871),c_Groups_Oone__class_Oone(X4871)),c_Nat_Osemiring__1__class_Oof__nat(X4871,X4867))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4871),X4868),hAPP(hAPP(c_Power_Opower__class_Opower(X4871),hAPP(X4870,X4869)),X4867)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_DERIV__power__Suc])]) ).
fof(i_0_1258,plain,
! [X5089,X5090,X5091,X5092,X5093,X5094,X5095] :
( ~ class_Fields_Ofield(X5095)
| ~ c_Polynomial_Opdivmod__rel(X5095,X5094,X5093,X5092,X5091)
| X5093 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X5095))
| X5090 != hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X5095),hAPP(c_Polynomial_Ocoeff(X5095,hAPP(hAPP(c_Polynomial_OpCons(X5095),X5089),X5091)),c_Polynomial_Odegree(X5095,X5093))),hAPP(c_Polynomial_Ocoeff(X5095,X5093),c_Polynomial_Odegree(X5095,X5093)))
| c_Polynomial_Opdivmod__rel(X5095,hAPP(hAPP(c_Polynomial_OpCons(X5095),X5089),X5094),X5093,hAPP(hAPP(c_Polynomial_OpCons(X5095),X5090),X5092),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X5095)),hAPP(hAPP(c_Polynomial_OpCons(X5095),X5089),X5091)),hAPP(hAPP(c_Polynomial_Osmult(X5095),X5090),X5093))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pdivmod__rel__pCons])]) ).
fof(i_0_1259,plain,
! [X5083,X5084,X5085,X5086] :
( ~ class_RealVector_Oreal__normed__field(X5086)
| X5085 = c_Groups_Ozero__class_Ozero(X5086)
| X5084 = c_Groups_Ozero__class_Ozero(X5086)
| hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X5086),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X5086),hAPP(c_Rings_Oinverse__class_Oinverse(X5086),X5085)),hAPP(c_Rings_Oinverse__class_Oinverse(X5086),X5084))),X5083) = hAPP(c_Groups_Ouminus__class_Ouminus(X5086),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5086),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5086),hAPP(c_Rings_Oinverse__class_Oinverse(X5086),X5085)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X5086),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X5086),X5085),X5084)),X5083))),hAPP(c_Rings_Oinverse__class_Oinverse(X5086),X5084))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_DERIV__inverse__lemma])]) ).
fof(i_0_1260,plain,
! [X5068,X5069,X5070,X5071,X5072,X5073] :
( ~ class_RealVector_Oreal__field(X5073)
| hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X5073),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X5073),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5073),X5072),X5071)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5073),X5070),X5069))),X5068) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5073),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5073),X5072),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X5073),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X5073),X5071),X5069)),X5068))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5073),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X5073),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X5073),X5072),X5070)),X5068)),X5069)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_DERIV__mult__lemma])]) ).
fof(i_0_1261,plain,
! [X3892,X3893,X3894] :
( ~ class_Rings_Ocomm__ring__1(X3894)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X3894)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X3894)),hAPP(hAPP(c_Polynomial_OpCons(X3894),hAPP(c_Groups_Ouminus__class_Ouminus(X3894),X3893)),hAPP(hAPP(c_Polynomial_OpCons(X3894),c_Groups_Oone__class_Oone(X3894)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3894))))),c_Polynomial_Osynthetic__div(X3894,X3892,X3893))),hAPP(hAPP(c_Polynomial_OpCons(X3894),hAPP(c_Polynomial_Opoly(X3894,X3892),X3893)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3894)))) = X3892 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_synthetic__div__correct_H])]) ).
fof(i_0_1262,plain,
! [X5153,X5154,X5155,X5156,X5157,X5158,X5159,X5160] :
( ~ class_Fields_Ofield(X5160)
| ~ c_Polynomial_Opdivmod__rel(X5160,X5159,X5158,X5157,X5156)
| ~ c_Polynomial_Opdivmod__rel(X5160,X5157,X5155,X5154,X5153)
| c_Polynomial_Opdivmod__rel(X5160,X5159,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X5160)),X5158),X5155),X5154,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X5160)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X5160)),X5158),X5153)),X5156)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pdivmod__rel__mult])]) ).
fof(i_0_1263,plain,
! [X4636,X4637,X4638,X4639,X4640,X4641] :
( ~ class_RealVector_Oreal__normed__field(X4641)
| ~ c_Deriv_Oderiv(X4641,X4640,X4639,X4638)
| ~ c_Deriv_Oderiv(X4641,X4637,X4639,X4636)
| c_Deriv_Oderiv(X4641,hAPP(hAPP(c_COMBS(X4641,X4641,X4641),hAPP(hAPP(c_COMBB(X4641,tc_fun(X4641,X4641),X4641),c_Groups_Oplus__class_Oplus(X4641)),X4640)),hAPP(hAPP(c_COMBB(X4641,X4641,X4641),c_Groups_Ouminus__class_Ouminus(X4641)),X4637)),X4639,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4641),X4638),hAPP(c_Groups_Ouminus__class_Ouminus(X4641),X4636))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_DERIV__add__minus])]) ).
fof(i_0_1264,plain,
! [X4630,X4631,X4632,X4633,X4634,X4635] :
( ~ class_RealVector_Oreal__normed__field(X4635)
| ~ c_Deriv_Oderiv(X4635,X4634,X4633,X4632)
| ~ c_Deriv_Oderiv(X4635,X4631,X4633,X4630)
| c_Deriv_Oderiv(X4635,hAPP(hAPP(c_COMBS(X4635,X4635,X4635),hAPP(hAPP(c_COMBB(X4635,tc_fun(X4635,X4635),X4635),c_Groups_Otimes__class_Otimes(X4635)),X4634)),X4631),X4633,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4635),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4635),hAPP(X4634,X4633)),X4630)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4635),X4632),hAPP(X4631,X4633)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_DERIV__mult_H])]) ).
fof(i_0_1265,plain,
! [X4624,X4625,X4626,X4627,X4628,X4629] :
( ~ class_RealVector_Oreal__normed__field(X4629)
| ~ c_Deriv_Oderiv(X4629,X4628,X4627,X4626)
| ~ c_Deriv_Oderiv(X4629,X4625,X4627,X4624)
| c_Deriv_Oderiv(X4629,hAPP(hAPP(c_COMBS(X4629,X4629,X4629),hAPP(hAPP(c_COMBB(X4629,tc_fun(X4629,X4629),X4629),c_Groups_Otimes__class_Otimes(X4629)),X4628)),X4625),X4627,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4629),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4629),X4626),hAPP(X4625,X4627))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4629),X4624),hAPP(X4628,X4627)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_DERIV__mult])]) ).
fof(i_0_1266,plain,
! [X4642,X4643,X4644,X4645] :
( ~ class_RealVector_Oreal__normed__field(X4645)
| ~ c_Deriv_Oderiv(X4645,X4644,X4643,X4642)
| hAPP(X4644,X4643) = c_Groups_Ozero__class_Ozero(X4645)
| c_Deriv_Oderiv(X4645,hAPP(hAPP(c_COMBB(X4645,X4645,X4645),c_Rings_Oinverse__class_Oinverse(X4645)),X4644),X4643,hAPP(c_Groups_Ouminus__class_Ouminus(X4645),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4645),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4645),hAPP(c_Rings_Oinverse__class_Oinverse(X4645),hAPP(X4644,X4643))),X4642)),hAPP(c_Rings_Oinverse__class_Oinverse(X4645),hAPP(X4644,X4643))))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_DERIV__inverse_H])]) ).
fof(i_0_1267,plain,
! [X6009,X6010,X6011,X6012] :
( ~ class_Divides_Osemiring__div(X6012)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X6012),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X6012),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6012),c_Divides_Odiv__class_Odiv(X6012,X6011,X6010)),X6010)),c_Divides_Odiv__class_Omod(X6012,X6011,X6010))),X6009) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X6012),X6011),X6009) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_div__mod__equality])]) ).
fof(i_0_1268,plain,
! [X4403,X4404,X4405,X4406,X4407,X4408] :
( ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X4406),X4405),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4406),X4407),X4403)))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X4406),X4405),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4406),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X4406),X4407),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4406),X4408),X4404))),X4403)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X4406),X4405),X4404))
| ~ class_Rings_Ocomm__ring(X4406)
| ~ class_Rings_Odvd(X4406) )
& ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X4406),X4405),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4406),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X4406),X4407),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4406),X4408),X4404))),X4403)))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X4406),X4405),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4406),X4407),X4403)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X4406),X4405),X4404))
| ~ class_Rings_Ocomm__ring(X4406)
| ~ class_Rings_Odvd(X4406) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__period_I3_J])])])]) ).
fof(i_0_1269,plain,
! [X4397,X4398,X4399,X4400,X4401,X4402] :
( ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X4400),X4399),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4400),X4401),X4397)))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X4400),X4399),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4400),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X4400),X4401),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4400),X4402),X4398))),X4397)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X4400),X4399),X4398))
| ~ class_Rings_Ocomm__ring(X4400)
| ~ class_Rings_Odvd(X4400) )
& ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X4400),X4399),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4400),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X4400),X4401),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4400),X4402),X4398))),X4397)))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X4400),X4399),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4400),X4401),X4397)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X4400),X4399),X4398))
| ~ class_Rings_Ocomm__ring(X4400)
| ~ class_Rings_Odvd(X4400) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__period_I4_J])])])]) ).
fof(i_0_1270,plain,
! [X5945,X5946,X5947] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X5947,X5946)),X5946)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X5947,X5946))),X5945) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X5947),X5945),
inference(variable_rename,[status(thm)],[fact_zdiv__zmod__equality2]) ).
fof(i_0_1271,plain,
! [X4876,X4877,X4878,X4879,X4880] :
( ~ class_RealVector_Oreal__normed__field(X4880)
| ~ c_Deriv_Oderiv(X4880,X4879,X4878,X4877)
| c_Deriv_Oderiv(X4880,hAPP(c_COMBC(X4880,X4880,X4880,hAPP(hAPP(c_COMBB(X4880,tc_fun(X4880,X4880),X4880),c_Rings_Oinverse__class_Odivide(X4880)),X4879)),X4876),X4878,hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4880),X4877),X4876)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_DERIV__cdivide])]) ).
fof(i_0_1272,plain,
! [X4605,X4606,X4607,X4608,X4609,X4610] :
( ~ class_RealVector_Oreal__normed__field(X4610)
| ~ c_Deriv_Oderiv(X4610,X4609,X4608,X4607)
| ~ c_Deriv_Oderiv(X4610,X4606,X4608,X4605)
| c_Deriv_Oderiv(X4610,hAPP(hAPP(c_COMBS(X4610,X4610,X4610),hAPP(hAPP(c_COMBB(X4610,tc_fun(X4610,X4610),X4610),c_Groups_Ominus__class_Ominus(X4610)),X4609)),X4606),X4608,hAPP(hAPP(c_Groups_Ominus__class_Ominus(X4610),X4607),X4605)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_DERIV__diff])]) ).
fof(i_0_1273,plain,
! [X4599,X4600,X4601,X4602,X4603,X4604] :
( ~ class_RealVector_Oreal__normed__field(X4604)
| ~ c_Deriv_Oderiv(X4604,X4603,X4602,X4601)
| ~ c_Deriv_Oderiv(X4604,X4600,X4602,X4599)
| c_Deriv_Oderiv(X4604,hAPP(hAPP(c_COMBS(X4604,X4604,X4604),hAPP(hAPP(c_COMBB(X4604,tc_fun(X4604,X4604),X4604),c_Groups_Oplus__class_Oplus(X4604)),X4603)),X4600),X4602,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4604),X4601),X4599)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_DERIV__add])]) ).
fof(i_0_1274,plain,
! [X5670,X5671,X5672,X5673,X5674,X5675] :
( ( ~ c_Orderings_Oord__class_Oless(X5675,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5675),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5675),X5674),X5673)),X5672),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5675),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5675),X5671),X5673)),X5670))
| c_Orderings_Oord__class_Oless(X5675,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5675),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5675),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X5675),X5674),X5671)),X5673)),X5672),X5670)
| ~ class_Rings_Oordered__ring(X5675) )
& ( ~ c_Orderings_Oord__class_Oless(X5675,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5675),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5675),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X5675),X5674),X5671)),X5673)),X5672),X5670)
| c_Orderings_Oord__class_Oless(X5675,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5675),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5675),X5674),X5673)),X5672),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5675),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5675),X5671),X5673)),X5670))
| ~ class_Rings_Oordered__ring(X5675) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__add__iff1])])]) ).
fof(i_0_1275,plain,
! [X5664,X5665,X5666,X5667,X5668,X5669] :
( ( ~ c_Orderings_Oord__class_Oless(X5669,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5669),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5669),X5668),X5667)),X5666),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5669),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5669),X5665),X5667)),X5664))
| c_Orderings_Oord__class_Oless(X5669,X5666,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5669),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5669),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X5669),X5665),X5668)),X5667)),X5664))
| ~ class_Rings_Oordered__ring(X5669) )
& ( ~ c_Orderings_Oord__class_Oless(X5669,X5666,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5669),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5669),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X5669),X5665),X5668)),X5667)),X5664))
| c_Orderings_Oord__class_Oless(X5669,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5669),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5669),X5668),X5667)),X5666),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5669),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5669),X5665),X5667)),X5664))
| ~ class_Rings_Oordered__ring(X5669) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__add__iff2])])]) ).
fof(i_0_1276,plain,
! [X4539,X4540,X4541,X4542] :
( ~ class_RealVector_Oreal__normed__field(X4542)
| ~ c_Deriv_Oderiv(X4542,X4541,X4540,X4539)
| hAPP(X4541,X4540) = c_Groups_Ozero__class_Ozero(X4542)
| c_Deriv_Oderiv(X4542,hAPP(hAPP(c_COMBB(X4542,X4542,X4542),c_Rings_Oinverse__class_Oinverse(X4542)),X4541),X4540,hAPP(c_Groups_Ouminus__class_Ouminus(X4542),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4542),X4539),hAPP(c_Rings_Oinverse__class_Oinverse(X4542),hAPP(hAPP(c_Power_Opower__class_Opower(X4542),hAPP(X4541,X4540)),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_DERIV__inverse__fun])]) ).
fof(i_0_1277,plain,
! [X4439,X4440,X4441,X4442,X4443] :
( ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X4443),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X4441),X4440)))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X4443),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X4441),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X4439),X4442))),X4440)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X4443),X4442)) )
& ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X4443),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X4441),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X4439),X4442))),X4440)))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X4443),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X4441),X4440)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X4443),X4442)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zdvd__period])])]) ).
fof(i_0_1278,plain,
! [X4457,X4458,X4459,X4460] :
( ( X4458 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4460))
| X4457 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4460))
| X4458 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4460))
| c_Polynomial_Opoly__gcd(X4460,X4458,X4457) = X4459
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X4460)),esk7_4(X4457,X4458,X4459,X4460)),X4458))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X4460)),X4459),X4457))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X4460)),X4459),X4458))
| ~ class_Fields_Ofield(X4460) )
& ( hAPP(c_Polynomial_Ocoeff(X4460,X4459),c_Polynomial_Odegree(X4460,X4459)) != c_Groups_Oone__class_Oone(X4460)
| X4458 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4460))
| c_Polynomial_Opoly__gcd(X4460,X4458,X4457) = X4459
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X4460)),esk7_4(X4457,X4458,X4459,X4460)),X4458))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X4460)),X4459),X4457))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X4460)),X4459),X4458))
| ~ class_Fields_Ofield(X4460) )
& ( X4458 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4460))
| X4457 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4460))
| X4457 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4460))
| c_Polynomial_Opoly__gcd(X4460,X4458,X4457) = X4459
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X4460)),esk7_4(X4457,X4458,X4459,X4460)),X4458))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X4460)),X4459),X4457))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X4460)),X4459),X4458))
| ~ class_Fields_Ofield(X4460) )
& ( hAPP(c_Polynomial_Ocoeff(X4460,X4459),c_Polynomial_Odegree(X4460,X4459)) != c_Groups_Oone__class_Oone(X4460)
| X4457 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4460))
| c_Polynomial_Opoly__gcd(X4460,X4458,X4457) = X4459
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X4460)),esk7_4(X4457,X4458,X4459,X4460)),X4458))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X4460)),X4459),X4457))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X4460)),X4459),X4458))
| ~ class_Fields_Ofield(X4460) )
& ( X4458 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4460))
| X4457 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4460))
| hAPP(c_Polynomial_Ocoeff(X4460,X4459),c_Polynomial_Odegree(X4460,X4459)) != c_Groups_Ozero__class_Ozero(X4460)
| c_Polynomial_Opoly__gcd(X4460,X4458,X4457) = X4459
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X4460)),esk7_4(X4457,X4458,X4459,X4460)),X4458))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X4460)),X4459),X4457))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X4460)),X4459),X4458))
| ~ class_Fields_Ofield(X4460) )
& ( hAPP(c_Polynomial_Ocoeff(X4460,X4459),c_Polynomial_Odegree(X4460,X4459)) != c_Groups_Oone__class_Oone(X4460)
| hAPP(c_Polynomial_Ocoeff(X4460,X4459),c_Polynomial_Odegree(X4460,X4459)) != c_Groups_Ozero__class_Ozero(X4460)
| c_Polynomial_Opoly__gcd(X4460,X4458,X4457) = X4459
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X4460)),esk7_4(X4457,X4458,X4459,X4460)),X4458))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X4460)),X4459),X4457))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X4460)),X4459),X4458))
| ~ class_Fields_Ofield(X4460) )
& ( X4458 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4460))
| X4457 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4460))
| X4458 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4460))
| c_Polynomial_Opoly__gcd(X4460,X4458,X4457) = X4459
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X4460)),esk7_4(X4457,X4458,X4459,X4460)),X4457))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X4460)),X4459),X4457))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X4460)),X4459),X4458))
| ~ class_Fields_Ofield(X4460) )
& ( hAPP(c_Polynomial_Ocoeff(X4460,X4459),c_Polynomial_Odegree(X4460,X4459)) != c_Groups_Oone__class_Oone(X4460)
| X4458 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4460))
| c_Polynomial_Opoly__gcd(X4460,X4458,X4457) = X4459
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X4460)),esk7_4(X4457,X4458,X4459,X4460)),X4457))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X4460)),X4459),X4457))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X4460)),X4459),X4458))
| ~ class_Fields_Ofield(X4460) )
& ( X4458 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4460))
| X4457 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4460))
| X4457 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4460))
| c_Polynomial_Opoly__gcd(X4460,X4458,X4457) = X4459
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X4460)),esk7_4(X4457,X4458,X4459,X4460)),X4457))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X4460)),X4459),X4457))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X4460)),X4459),X4458))
| ~ class_Fields_Ofield(X4460) )
& ( hAPP(c_Polynomial_Ocoeff(X4460,X4459),c_Polynomial_Odegree(X4460,X4459)) != c_Groups_Oone__class_Oone(X4460)
| X4457 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4460))
| c_Polynomial_Opoly__gcd(X4460,X4458,X4457) = X4459
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X4460)),esk7_4(X4457,X4458,X4459,X4460)),X4457))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X4460)),X4459),X4457))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X4460)),X4459),X4458))
| ~ class_Fields_Ofield(X4460) )
& ( X4458 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4460))
| X4457 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4460))
| hAPP(c_Polynomial_Ocoeff(X4460,X4459),c_Polynomial_Odegree(X4460,X4459)) != c_Groups_Ozero__class_Ozero(X4460)
| c_Polynomial_Opoly__gcd(X4460,X4458,X4457) = X4459
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X4460)),esk7_4(X4457,X4458,X4459,X4460)),X4457))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X4460)),X4459),X4457))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X4460)),X4459),X4458))
| ~ class_Fields_Ofield(X4460) )
& ( hAPP(c_Polynomial_Ocoeff(X4460,X4459),c_Polynomial_Odegree(X4460,X4459)) != c_Groups_Oone__class_Oone(X4460)
| hAPP(c_Polynomial_Ocoeff(X4460,X4459),c_Polynomial_Odegree(X4460,X4459)) != c_Groups_Ozero__class_Ozero(X4460)
| c_Polynomial_Opoly__gcd(X4460,X4458,X4457) = X4459
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X4460)),esk7_4(X4457,X4458,X4459,X4460)),X4457))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X4460)),X4459),X4457))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X4460)),X4459),X4458))
| ~ class_Fields_Ofield(X4460) )
& ( X4458 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4460))
| X4457 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4460))
| X4458 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4460))
| c_Polynomial_Opoly__gcd(X4460,X4458,X4457) = X4459
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X4460)),esk7_4(X4457,X4458,X4459,X4460)),X4459))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X4460)),X4459),X4457))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X4460)),X4459),X4458))
| ~ class_Fields_Ofield(X4460) )
& ( hAPP(c_Polynomial_Ocoeff(X4460,X4459),c_Polynomial_Odegree(X4460,X4459)) != c_Groups_Oone__class_Oone(X4460)
| X4458 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4460))
| c_Polynomial_Opoly__gcd(X4460,X4458,X4457) = X4459
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X4460)),esk7_4(X4457,X4458,X4459,X4460)),X4459))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X4460)),X4459),X4457))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X4460)),X4459),X4458))
| ~ class_Fields_Ofield(X4460) )
& ( X4458 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4460))
| X4457 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4460))
| X4457 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4460))
| c_Polynomial_Opoly__gcd(X4460,X4458,X4457) = X4459
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X4460)),esk7_4(X4457,X4458,X4459,X4460)),X4459))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X4460)),X4459),X4457))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X4460)),X4459),X4458))
| ~ class_Fields_Ofield(X4460) )
& ( hAPP(c_Polynomial_Ocoeff(X4460,X4459),c_Polynomial_Odegree(X4460,X4459)) != c_Groups_Oone__class_Oone(X4460)
| X4457 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4460))
| c_Polynomial_Opoly__gcd(X4460,X4458,X4457) = X4459
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X4460)),esk7_4(X4457,X4458,X4459,X4460)),X4459))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X4460)),X4459),X4457))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X4460)),X4459),X4458))
| ~ class_Fields_Ofield(X4460) )
& ( X4458 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4460))
| X4457 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4460))
| hAPP(c_Polynomial_Ocoeff(X4460,X4459),c_Polynomial_Odegree(X4460,X4459)) != c_Groups_Ozero__class_Ozero(X4460)
| c_Polynomial_Opoly__gcd(X4460,X4458,X4457) = X4459
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X4460)),esk7_4(X4457,X4458,X4459,X4460)),X4459))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X4460)),X4459),X4457))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X4460)),X4459),X4458))
| ~ class_Fields_Ofield(X4460) )
& ( hAPP(c_Polynomial_Ocoeff(X4460,X4459),c_Polynomial_Odegree(X4460,X4459)) != c_Groups_Oone__class_Oone(X4460)
| hAPP(c_Polynomial_Ocoeff(X4460,X4459),c_Polynomial_Odegree(X4460,X4459)) != c_Groups_Ozero__class_Ozero(X4460)
| c_Polynomial_Opoly__gcd(X4460,X4458,X4457) = X4459
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X4460)),esk7_4(X4457,X4458,X4459,X4460)),X4459))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X4460)),X4459),X4457))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X4460)),X4459),X4458))
| ~ class_Fields_Ofield(X4460) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_poly__gcd__unique])])])]) ).
fof(i_0_1279,plain,
! [X3560,X3561,X3562,X3563,X3564,X3565] :
( ~ class_Groups_Ozero(X3565)
| hAPP(hAPP(hAPP(X3564,c_Groups_Ozero__class_Ozero(X3565)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3565))),X3563) != X3563
| c_Polynomial_Opoly__rec(X3562,X3565,X3563,X3564,hAPP(hAPP(c_Polynomial_OpCons(X3565),X3561),X3560)) = hAPP(hAPP(hAPP(X3564,X3561),X3560),c_Polynomial_Opoly__rec(X3562,X3565,X3563,X3564,X3560)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_poly__rec__pCons])]) ).
fof(i_0_1280,plain,
! [X4223,X4224,X4225] :
( ( hAPP(c_Polynomial_Opoly(X4225,X4224),X4223) != c_Groups_Ozero__class_Ozero(X4225)
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X4225)),hAPP(hAPP(c_Polynomial_OpCons(X4225),hAPP(c_Groups_Ouminus__class_Ouminus(X4225),X4223)),hAPP(hAPP(c_Polynomial_OpCons(X4225),c_Groups_Oone__class_Oone(X4225)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4225))))),X4224))
| ~ class_Rings_Oidom(X4225) )
& ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X4225)),hAPP(hAPP(c_Polynomial_OpCons(X4225),hAPP(c_Groups_Ouminus__class_Ouminus(X4225),X4223)),hAPP(hAPP(c_Polynomial_OpCons(X4225),c_Groups_Oone__class_Oone(X4225)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4225))))),X4224))
| hAPP(c_Polynomial_Opoly(X4225,X4224),X4223) = c_Groups_Ozero__class_Ozero(X4225)
| ~ class_Rings_Oidom(X4225) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_poly__eq__0__iff__dvd])])]) ).
fof(i_0_1281,plain,
! [X5120,X5121,X5122,X5123,X5124,X5125,X5126] :
( ( X5123 = X5121
| ~ c_Polynomial_Opdivmod__rel(X5126,X5125,X5124,X5121,X5120)
| ~ c_Polynomial_Opdivmod__rel(X5126,X5125,X5124,X5123,X5122)
| ~ class_Fields_Ofield(X5126) )
& ( X5122 = X5120
| ~ c_Polynomial_Opdivmod__rel(X5126,X5125,X5124,X5121,X5120)
| ~ c_Polynomial_Opdivmod__rel(X5126,X5125,X5124,X5123,X5122)
| ~ class_Fields_Ofield(X5126) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pdivmod__rel__unique])])]) ).
fof(i_0_1282,plain,
! [X5134,X5135,X5136,X5137,X5138,X5139,X5140] :
( ~ class_Fields_Ofield(X5140)
| ~ c_Polynomial_Opdivmod__rel(X5140,X5139,X5138,X5137,X5136)
| ~ c_Polynomial_Opdivmod__rel(X5140,X5139,X5138,X5135,X5134)
| X5137 = X5135 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pdivmod__rel__unique__div])]) ).
fof(i_0_1283,plain,
! [X5127,X5128,X5129,X5130,X5131,X5132,X5133] :
( ~ class_Fields_Ofield(X5133)
| ~ c_Polynomial_Opdivmod__rel(X5133,X5132,X5131,X5130,X5129)
| ~ c_Polynomial_Opdivmod__rel(X5133,X5132,X5131,X5128,X5127)
| X5129 = X5127 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pdivmod__rel__unique__mod])]) ).
fof(i_0_1284,plain,
! [X3566,X3567,X3568] :
( ~ class_Rings_Ocomm__semiring__1(X3568)
| hAPP(c_Polynomial_Ocoeff(X3568,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(X3568)),hAPP(hAPP(c_Polynomial_OpCons(X3568),X3567),hAPP(hAPP(c_Polynomial_OpCons(X3568),c_Groups_Oone__class_Oone(X3568)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3568))))),X3566)),X3566) = c_Groups_Oone__class_Oone(X3568) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_coeff__linear__power])]) ).
fof(i_0_1285,plain,
! [X3736,X3737,X3738] :
( ~ class_Groups_Oab__group__add(X3738)
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X3738)),X3737),X3736) = c_Polynomial_OAbs__poly(X3738,hAPP(hAPP(c_COMBS(tc_Nat_Onat,X3738,X3738),hAPP(hAPP(c_COMBB(X3738,tc_fun(X3738,X3738),tc_Nat_Onat),c_Groups_Ominus__class_Ominus(X3738)),c_Polynomial_Ocoeff(X3738,X3737))),c_Polynomial_Ocoeff(X3738,X3736))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_minus__poly__def])]) ).
fof(i_0_1286,plain,
! [X3699,X3700,X3701] :
( ~ class_Groups_Ocomm__monoid__add(X3701)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X3701)),X3700),X3699) = c_Polynomial_OAbs__poly(X3701,hAPP(hAPP(c_COMBS(tc_Nat_Onat,X3701,X3701),hAPP(hAPP(c_COMBB(X3701,tc_fun(X3701,X3701),tc_Nat_Onat),c_Groups_Oplus__class_Oplus(X3701)),c_Polynomial_Ocoeff(X3701,X3700))),c_Polynomial_Ocoeff(X3701,X3699))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_plus__poly__def])]) ).
fof(i_0_1287,plain,
! [X5161,X5162,X5163,X5164,X5165,X5166] :
( ~ class_Fields_Ofield(X5166)
| X5165 = c_Groups_Ozero__class_Ozero(X5166)
| ~ c_Polynomial_Opdivmod__rel(X5166,X5164,X5163,X5162,X5161)
| c_Polynomial_Opdivmod__rel(X5166,X5164,hAPP(hAPP(c_Polynomial_Osmult(X5166),X5165),X5163),hAPP(hAPP(c_Polynomial_Osmult(X5166),hAPP(c_Rings_Oinverse__class_Oinverse(X5166),X5165)),X5162),X5161) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pdivmod__rel__smult__right])]) ).
fof(i_0_1288,plain,
! [X5114,X5115,X5116,X5117,X5118,X5119] :
( ~ class_Fields_Ofield(X5119)
| ~ c_Polynomial_Opdivmod__rel(X5119,X5118,X5117,X5116,X5115)
| c_Polynomial_Opdivmod__rel(X5119,hAPP(hAPP(c_Polynomial_Osmult(X5119),X5114),X5118),X5117,hAPP(hAPP(c_Polynomial_Osmult(X5119),X5114),X5116),hAPP(hAPP(c_Polynomial_Osmult(X5119),X5114),X5115)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pdivmod__rel__smult__left])]) ).
fof(i_0_1289,plain,
! [X6013,X6014,X6015,X6016] :
( ~ class_Divides_Osemiring__div(X6016)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X6016),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X6016),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6016),X6015),c_Divides_Odiv__class_Odiv(X6016,X6014,X6015))),c_Divides_Odiv__class_Omod(X6016,X6014,X6015))),X6013) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X6016),X6014),X6013) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_div__mod__equality2])]) ).
fof(i_0_1290,plain,
! [X5978,X5979,X5980] : c_Divides_Odiv__class_Odiv(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X5980),X5979),X5978) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X5980,X5978)),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X5979,X5978))),c_Divides_Odiv__class_Odiv(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,X5980,X5978)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X5979,X5978)),X5978)),
inference(variable_rename,[status(thm)],[fact_zdiv__zadd1__eq]) ).
fof(i_0_1291,plain,
! [X5948,X5949,X5950] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X5950),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X5949,X5950))),c_Divides_Odiv__class_Omod(tc_Int_Oint,X5949,X5950))),X5948) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X5949),X5948),
inference(variable_rename,[status(thm)],[fact_zdiv__zmod__equality]) ).
fof(i_0_1292,plain,
! [X4226,X4227,X4228] :
( ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X4228)),hAPP(hAPP(c_Polynomial_OpCons(X4228),X4227),hAPP(hAPP(c_Polynomial_OpCons(X4228),c_Groups_Oone__class_Oone(X4228)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4228))))),X4226))
| hAPP(c_Polynomial_Opoly(X4228,X4226),hAPP(c_Groups_Ouminus__class_Ouminus(X4228),X4227)) = c_Groups_Ozero__class_Ozero(X4228)
| ~ class_Rings_Oidom(X4228) )
& ( hAPP(c_Polynomial_Opoly(X4228,X4226),hAPP(c_Groups_Ouminus__class_Ouminus(X4228),X4227)) != c_Groups_Ozero__class_Ozero(X4228)
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X4228)),hAPP(hAPP(c_Polynomial_OpCons(X4228),X4227),hAPP(hAPP(c_Polynomial_OpCons(X4228),c_Groups_Oone__class_Oone(X4228)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4228))))),X4226))
| ~ class_Rings_Oidom(X4228) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvd__iff__poly__eq__0])])]) ).
fof(i_0_1293,plain,
! [X5173,X5174,X5175,X5176,X5177] :
( ( X5176 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X5177)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X5177)),X5174),X5175)),X5173)
| ~ c_Polynomial_Opdivmod__rel(X5177,X5176,X5175,X5174,X5173)
| ~ class_Fields_Ofield(X5177) )
& ( X5175 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X5177))
| X5174 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X5177))
| ~ c_Polynomial_Opdivmod__rel(X5177,X5176,X5175,X5174,X5173)
| ~ class_Fields_Ofield(X5177) )
& ( X5175 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X5177))
| X5173 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X5177))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(X5177,X5173),c_Polynomial_Odegree(X5177,X5175))
| ~ c_Polynomial_Opdivmod__rel(X5177,X5176,X5175,X5174,X5173)
| ~ class_Fields_Ofield(X5177) )
& ( X5175 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X5177))
| X5175 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X5177))
| X5176 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X5177)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X5177)),X5174),X5175)),X5173)
| c_Polynomial_Opdivmod__rel(X5177,X5176,X5175,X5174,X5173)
| ~ class_Fields_Ofield(X5177) )
& ( X5173 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X5177))
| X5175 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X5177))
| X5176 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X5177)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X5177)),X5174),X5175)),X5173)
| c_Polynomial_Opdivmod__rel(X5177,X5176,X5175,X5174,X5173)
| ~ class_Fields_Ofield(X5177) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(X5177,X5173),c_Polynomial_Odegree(X5177,X5175))
| X5175 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X5177))
| X5176 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X5177)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X5177)),X5174),X5175)),X5173)
| c_Polynomial_Opdivmod__rel(X5177,X5176,X5175,X5174,X5173)
| ~ class_Fields_Ofield(X5177) )
& ( X5175 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X5177))
| X5174 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X5177))
| X5176 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X5177)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X5177)),X5174),X5175)),X5173)
| c_Polynomial_Opdivmod__rel(X5177,X5176,X5175,X5174,X5173)
| ~ class_Fields_Ofield(X5177) )
& ( X5173 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X5177))
| X5174 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X5177))
| X5176 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X5177)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X5177)),X5174),X5175)),X5173)
| c_Polynomial_Opdivmod__rel(X5177,X5176,X5175,X5174,X5173)
| ~ class_Fields_Ofield(X5177) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(X5177,X5173),c_Polynomial_Odegree(X5177,X5175))
| X5174 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X5177))
| X5176 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X5177)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X5177)),X5174),X5175)),X5173)
| c_Polynomial_Opdivmod__rel(X5177,X5176,X5175,X5174,X5173)
| ~ class_Fields_Ofield(X5177) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pdivmod__rel__def])])]) ).
fof(i_0_1294,plain,
! [X4389,X4390,X4391] :
( ~ class_Rings_Odivision__ring(X4391)
| X4390 = c_Groups_Ozero__class_Ozero(X4391)
| X4389 = c_Groups_Ozero__class_Ozero(X4391)
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(X4391),hAPP(c_Rings_Oinverse__class_Oinverse(X4391),X4390)),hAPP(c_Rings_Oinverse__class_Oinverse(X4391),X4389)) = hAPP(c_Groups_Ouminus__class_Ouminus(X4391),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4391),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4391),hAPP(c_Rings_Oinverse__class_Oinverse(X4391),X4390)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X4391),X4390),X4389))),hAPP(c_Rings_Oinverse__class_Oinverse(X4391),X4389))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Deriv_Oinverse__diff__inverse])]) ).
fof(i_0_1295,plain,
! [X3833,X3834,X3835,X3836,X3837,X3838] :
( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X3838),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3838),X3837),X3836)),X3835) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(X3838),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3838),X3834),X3836)),X3833)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X3838),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3838),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X3838),X3837),X3834)),X3836)),X3835) = X3833
| ~ class_Rings_Oring(X3838) )
& ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X3838),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3838),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X3838),X3837),X3834)),X3836)),X3835) != X3833
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X3838),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3838),X3837),X3836)),X3835) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X3838),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3838),X3834),X3836)),X3833)
| ~ class_Rings_Oring(X3838) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_eq__add__iff1])])]) ).
fof(i_0_1296,plain,
! [X3839,X3840,X3841,X3842,X3843,X3844] :
( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X3844),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3844),X3843),X3842)),X3841) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(X3844),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3844),X3840),X3842)),X3839)
| X3841 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X3844),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3844),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X3844),X3840),X3843)),X3842)),X3839)
| ~ class_Rings_Oring(X3844) )
& ( X3841 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(X3844),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3844),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X3844),X3840),X3843)),X3842)),X3839)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X3844),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3844),X3843),X3842)),X3841) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X3844),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3844),X3840),X3842)),X3839)
| ~ class_Rings_Oring(X3844) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_eq__add__iff2])])]) ).
fof(i_0_1297,plain,
! [X5055,X5056,X5057,X5058,X5059] :
( ~ class_Fields_Ofield(X5059)
| X5058 = c_Groups_Ozero__class_Ozero(X5059)
| X5057 = c_Groups_Ozero__class_Ozero(X5059)
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(X5059),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X5059),X5056),X5058)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X5059),X5055),X5057)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X5059),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X5059),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5059),X5056),X5057)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5059),X5055),X5058))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5059),X5058),X5057)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__frac__eq])]) ).
fof(i_0_1298,plain,
! [X5050,X5051,X5052,X5053,X5054] :
( ~ class_Fields_Ofield(X5054)
| X5053 = c_Groups_Ozero__class_Ozero(X5054)
| X5052 = c_Groups_Ozero__class_Ozero(X5054)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5054),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X5054),X5051),X5053)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X5054),X5050),X5052)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X5054),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5054),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5054),X5051),X5052)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5054),X5050),X5053))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5054),X5053),X5052)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__frac__eq])]) ).
fof(i_0_1299,plain,
! [X5141,X5142,X5143,X5144,X5145] :
( ~ class_Fields_Ofield(X5145)
| ~ c_Polynomial_Opdivmod__rel(X5145,X5144,X5143,X5142,X5141)
| c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(X5145),X5144,X5143) = X5141 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__poly__eq])]) ).
fof(i_0_1300,plain,
! [X5102,X5103,X5104,X5105] :
( ( X5103 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X5105))
| ~ c_Polynomial_Opdivmod__rel(X5105,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X5105)),X5104,X5103,X5102)
| ~ class_Fields_Ofield(X5105) )
& ( X5102 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X5105))
| ~ c_Polynomial_Opdivmod__rel(X5105,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X5105)),X5104,X5103,X5102)
| ~ class_Fields_Ofield(X5105) )
& ( X5103 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X5105))
| X5102 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X5105))
| c_Polynomial_Opdivmod__rel(X5105,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X5105)),X5104,X5103,X5102)
| ~ class_Fields_Ofield(X5105) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pdivmod__rel__0__iff])])]) ).
fof(i_0_1301,plain,
! [X5106,X5107,X5108,X5109] :
( ( X5107 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X5109))
| ~ c_Polynomial_Opdivmod__rel(X5109,X5108,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X5109)),X5107,X5106)
| ~ class_Fields_Ofield(X5109) )
& ( X5106 = X5108
| ~ c_Polynomial_Opdivmod__rel(X5109,X5108,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X5109)),X5107,X5106)
| ~ class_Fields_Ofield(X5109) )
& ( X5107 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X5109))
| X5106 != X5108
| c_Polynomial_Opdivmod__rel(X5109,X5108,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X5109)),X5107,X5106)
| ~ class_Fields_Ofield(X5109) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pdivmod__rel__by__0__iff])])]) ).
fof(i_0_1302,plain,
! [X6035,X6036,X6037,X6038,X6039] :
( ( ~ hBOOL(hAPP(hAPP(X6036,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X6035,X6037)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X6035,X6037)))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X6039)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X6039,X6037)
| X6035 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X6037),X6038)),X6039)
| hBOOL(hAPP(hAPP(X6036,X6038),X6039))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X6037) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),esk20_3(X6035,X6036,X6037))
| hBOOL(hAPP(hAPP(X6036,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X6035,X6037)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X6035,X6037)))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X6037) )
& ( c_Orderings_Oord__class_Oless(tc_Int_Oint,esk20_3(X6035,X6036,X6037),X6037)
| hBOOL(hAPP(hAPP(X6036,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X6035,X6037)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X6035,X6037)))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X6037) )
& ( X6035 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X6037),esk19_3(X6035,X6036,X6037))),esk20_3(X6035,X6036,X6037))
| hBOOL(hAPP(hAPP(X6036,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X6035,X6037)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X6035,X6037)))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X6037) )
& ( ~ hBOOL(hAPP(hAPP(X6036,esk19_3(X6035,X6036,X6037)),esk20_3(X6035,X6036,X6037)))
| hBOOL(hAPP(hAPP(X6036,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X6035,X6037)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X6035,X6037)))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X6037) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_split__pos__lemma])])])])]) ).
fof(i_0_1303,plain,
! [X3709,X3710,X3711] :
( ~ class_Rings_Ocomm__semiring__1(X3711)
| c_Polynomial_Odegree(X3711,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(X3711)),hAPP(hAPP(c_Polynomial_OpCons(X3711),X3710),hAPP(hAPP(c_Polynomial_OpCons(X3711),c_Groups_Oone__class_Oone(X3711)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3711))))),X3709)) = X3709 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_degree__linear__power])]) ).
fof(i_0_1304,plain,
! [X3493,X3494,X3495,X3496,X3497] :
( ~ class_Rings_Osemiring(X3497)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X3497),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3497),X3496),X3495)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X3497),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3497),X3494),X3495)),X3493)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X3497),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3497),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X3497),X3496),X3494)),X3495)),X3493) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_combine__common__factor])]) ).
fof(i_0_1305,plain,
! [X6026,X6027,X6028] :
( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X6028)
| c_Divides_Odiv__class_Omod(tc_Int_Oint,X6027,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X6026),X6028)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X6026),c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X6027,X6026),X6028))),c_Divides_Odiv__class_Omod(tc_Int_Oint,X6027,X6026)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zmod__zmult2__eq])]) ).
fof(i_0_1306,plain,
! [X6052,X6053,X6054] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,X6054,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X6053),X6052)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X6053),c_Divides_Odiv__class_Omod(tc_Nat_Onat,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X6054,X6053),X6052))),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X6054,X6053)),
inference(variable_rename,[status(thm)],[fact_mod__mult2__eq]) ).
fof(i_0_1307,plain,
! [X4554,X4555,X4556,X4557,X4558,X4559] :
( ~ class_RealVector_Oreal__normed__field(X4559)
| ~ c_Deriv_Oderiv(X4559,X4558,hAPP(X4557,X4556),X4555)
| ~ c_Deriv_Oderiv(X4559,X4557,X4556,X4554)
| c_Deriv_Oderiv(X4559,hAPP(hAPP(c_COMBB(X4559,X4559,X4559),X4558),X4557),X4556,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4559),X4555),X4554)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_DERIV__chain2])]) ).
fof(i_0_1308,plain,
! [X4560,X4561,X4562,X4563,X4564,X4565] :
( ~ class_RealVector_Oreal__normed__field(X4565)
| ~ c_Deriv_Oderiv(X4565,X4564,X4563,X4562)
| ~ c_Deriv_Oderiv(X4565,X4561,hAPP(X4564,X4563),X4560)
| c_Deriv_Oderiv(X4565,hAPP(hAPP(c_COMBB(X4565,X4565,X4565),X4561),X4564),X4563,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4565),X4560),X4562)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_DERIV__chain_H])]) ).
fof(i_0_1309,plain,
! [X3498,X3499,X3500,X3501] :
( ~ class_Rings_Ocomm__ring__1(X3501)
| hAPP(c_Polynomial_Opoly(X3501,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X3501)),c_Polynomial_Omonom(X3501,c_Groups_Oone__class_Oone(X3501),X3500)),X3499)),X3498) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3501),hAPP(hAPP(c_Power_Opower__class_Opower(X3501),X3498),X3500)),hAPP(c_Polynomial_Opoly(X3501,X3499),X3498)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_poly__replicate__append])]) ).
fof(i_0_1310,plain,
! [X5972,X5973,X5974,X5975] :
( ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X5975),c_Divides_Odiv__class_Odiv(X5975,X5973,X5974)),c_Divides_Odiv__class_Odiv(X5975,X5972,X5974)))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X5975),X5973),X5972))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X5975),X5974),X5972))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X5975),X5974),X5973))
| ~ class_Divides_Osemiring__div(X5975) )
& ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X5975),X5973),X5972))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X5975),c_Divides_Odiv__class_Odiv(X5975,X5973,X5974)),c_Divides_Odiv__class_Odiv(X5975,X5972,X5974)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X5975),X5974),X5972))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X5975),X5974),X5973))
| ~ class_Divides_Osemiring__div(X5975) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_div__dvd__div])])]) ).
fof(i_0_1311,plain,
! [X3466,X3467,X3468,X3469] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3469),X3468)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3467),X3468)),X3466)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3469),X3467)),X3468)),X3466),
inference(variable_rename,[status(thm)],[fact_left__add__mult__distrib]) ).
fof(i_0_1312,plain,
! [X5797,X5798,X5799,X5800] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X5800)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X5799,X5798)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X5798),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X5797,X5800))),X5799),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X5798),X5800)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__lemma])]) ).
fof(i_0_1313,plain,
! [X4409,X4410,X4411,X4412,X4414] :
( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X4411),X4409),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4411),esk5_3(X4409,X4410,X4411)),c_Groups_Ozero__class_Ozero(X4411))))
| ~ hBOOL(hAPP(X4410,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4411),X4409),X4412)))
| ~ class_Rings_Odvd(X4411)
| ~ class_Rings_Osemiring__0(X4411) )
& ( hBOOL(hAPP(X4410,esk5_3(X4409,X4410,X4411)))
| ~ hBOOL(hAPP(X4410,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4411),X4409),X4412)))
| ~ class_Rings_Odvd(X4411)
| ~ class_Rings_Osemiring__0(X4411) )
& ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X4411),X4409),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4411),X4414),c_Groups_Ozero__class_Ozero(X4411))))
| ~ hBOOL(hAPP(X4410,X4414))
| hBOOL(hAPP(X4410,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4411),X4409),esk6_3(X4409,X4410,X4411))))
| ~ class_Rings_Odvd(X4411)
| ~ class_Rings_Osemiring__0(X4411) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_unity__coeff__ex])])])])]) ).
fof(i_0_1314,plain,
! [X3887,X3888,X3889,X3890,X3891] :
( ~ class_Rings_Oring(X3891)
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(X3891),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3891),X3890),X3889)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3891),X3888),X3887)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X3891),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3891),X3890),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X3891),X3889),X3887))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3891),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X3891),X3890),X3888)),X3887)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__diff__mult])]) ).
fof(i_0_1315,plain,
! [X5951,X5952,X5953] : c_Divides_Odiv__class_Odiv(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X5953),X5952),X5951) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X5953),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X5952,X5951))),c_Divides_Odiv__class_Odiv(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X5953),c_Divides_Odiv__class_Omod(tc_Int_Oint,X5952,X5951)),X5951)),
inference(variable_rename,[status(thm)],[fact_zdiv__zmult1__eq]) ).
fof(i_0_1316,plain,
! [X6055,X6056,X6057] : c_Divides_Odiv__class_Odiv(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X6057),X6056),X6055) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X6057),c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X6056,X6055))),c_Divides_Odiv__class_Odiv(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X6057),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X6056,X6055)),X6055)),
inference(variable_rename,[status(thm)],[fact_div__mult1__eq]) ).
fof(i_0_1317,plain,
! [X3687,X3688,X3689,X3690] :
( ~ class_Groups_Ozero(X3690)
| hAPP(hAPP(hAPP(X3689,c_Groups_Ozero__class_Ozero(X3690)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3690))),X3688) != X3688
| c_Polynomial_Opoly__rec(X3687,X3690,X3688,X3689,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3690))) = X3688 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_poly__rec__0])]) ).
fof(i_0_1318,plain,
! [X4394,X4395,X4396] :
( ~ class_Fields_Ofield(X4396)
| X4395 = c_Groups_Ozero__class_Ozero(X4396)
| X4394 = c_Groups_Ozero__class_Ozero(X4396)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4396),hAPP(c_Rings_Oinverse__class_Oinverse(X4396),X4395)),hAPP(c_Rings_Oinverse__class_Oinverse(X4396),X4394)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4396),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4396),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4396),X4395),X4394)),hAPP(c_Rings_Oinverse__class_Oinverse(X4396),X4395))),hAPP(c_Rings_Oinverse__class_Oinverse(X4396),X4394)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inverse__add])]) ).
fof(i_0_1319,plain,
! [X6049,X6050,X6051] :
( ~ class_Fields_Ofield(X6051)
| c_Polynomial_Opdivmod__rel(X6051,X6050,X6049,c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(X6051),X6050,X6049),c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(X6051),X6050,X6049)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pdivmod__rel])]) ).
fof(i_0_1320,plain,
! [X4566,X4567,X4568,X4569,X4570] :
( ~ class_RealVector_Oreal__normed__field(X4570)
| ~ c_Deriv_Oderiv(X4570,X4569,X4568,X4567)
| c_Deriv_Oderiv(X4570,hAPP(hAPP(c_COMBB(X4570,X4570,X4570),hAPP(c_Groups_Otimes__class_Otimes(X4570),X4566)),X4569),X4568,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4570),X4566),X4567)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_DERIV__cmult])]) ).
fof(i_0_1321,plain,
! [X5087,X5088] :
( ~ class_Rings_Osemiring__1(X5088)
| c_Nat_Osemiring__1__class_Oof__nat(X5088,X5087) = c_Nat_Osemiring__1__class_Oof__nat__aux(X5088,hAPP(c_COMBC(X5088,X5088,X5088,c_Groups_Oplus__class_Oplus(X5088)),c_Groups_Oone__class_Oone(X5088)),X5087,c_Groups_Ozero__class_Ozero(X5088)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_semiring__1__class_Oof__nat__code])]) ).
fof(i_0_1322,plain,
! [X5110,X5111] :
( ~ class_Fields_Ofield(X5111)
| c_Polynomial_Opdivmod__rel(X5111,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X5111)),X5110,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X5111)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X5111))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pdivmod__rel__0])]) ).
fof(i_0_1323,plain,
! [X4341,X4342,X4343,X4344] :
( ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X4344),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4344),X4343),X4342)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4344),X4343),X4341)))
| X4343 = c_Groups_Ozero__class_Ozero(X4344)
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X4344),X4342),X4341))
| ~ class_Rings_Oidom(X4344) )
& ( X4343 != c_Groups_Ozero__class_Ozero(X4344)
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X4344),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4344),X4343),X4342)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4344),X4343),X4341)))
| ~ class_Rings_Oidom(X4344) )
& ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X4344),X4342),X4341))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X4344),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4344),X4343),X4342)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4344),X4343),X4341)))
| ~ class_Rings_Oidom(X4344) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvd__mult__cancel__left])])]) ).
fof(i_0_1324,plain,
! [X4345,X4346,X4347,X4348] :
( ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X4348),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4348),X4347),X4346)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4348),X4345),X4346)))
| X4346 = c_Groups_Ozero__class_Ozero(X4348)
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X4348),X4347),X4345))
| ~ class_Rings_Oidom(X4348) )
& ( X4346 != c_Groups_Ozero__class_Ozero(X4348)
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X4348),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4348),X4347),X4346)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4348),X4345),X4346)))
| ~ class_Rings_Oidom(X4348) )
& ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X4348),X4347),X4345))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X4348),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4348),X4347),X4346)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4348),X4345),X4346)))
| ~ class_Rings_Oidom(X4348) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvd__mult__cancel__right])])]) ).
fof(i_0_1325,plain,
! [X5112,X5113] :
( ~ class_Fields_Ofield(X5113)
| c_Polynomial_Opdivmod__rel(X5113,X5112,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X5113)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X5113)),X5112) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pdivmod__rel__by__0])]) ).
fof(i_0_1326,plain,
! [X5660,X5661,X5662] :
( ( ~ c_Orderings_Oord__class_Oless(X5662,c_Groups_Ozero__class_Ozero(X5662),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5662),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5662),X5661),X5661)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5662),X5660),X5660)))
| X5661 != c_Groups_Ozero__class_Ozero(X5662)
| X5660 != c_Groups_Ozero__class_Ozero(X5662)
| ~ class_Rings_Olinordered__ring__strict(X5662) )
& ( X5661 = c_Groups_Ozero__class_Ozero(X5662)
| c_Orderings_Oord__class_Oless(X5662,c_Groups_Ozero__class_Ozero(X5662),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5662),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5662),X5661),X5661)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5662),X5660),X5660)))
| ~ class_Rings_Olinordered__ring__strict(X5662) )
& ( X5660 = c_Groups_Ozero__class_Ozero(X5662)
| c_Orderings_Oord__class_Oless(X5662,c_Groups_Ozero__class_Ozero(X5662),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5662),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5662),X5661),X5661)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5662),X5660),X5660)))
| ~ class_Rings_Olinordered__ring__strict(X5662) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sum__squares__gt__zero__iff])])]) ).
fof(i_0_1327,plain,
! [X5064,X5065,X5066,X5067] :
( ~ class_Fields_Ofield(X5067)
| X5066 = c_Groups_Ozero__class_Ozero(X5067)
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(X5067),X5065),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X5067),X5064),X5066)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X5067),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X5067),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5067),X5066),X5065)),X5064)),X5066) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__divide__eq__iff])]) ).
fof(i_0_1328,plain,
! [X5038,X5039,X5040,X5041] :
( ~ class_Fields_Ofield(X5041)
| X5040 = c_Groups_Ozero__class_Ozero(X5041)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5041),X5039),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X5041),X5038),X5040)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X5041),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5041),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5041),X5040),X5039)),X5038)),X5040) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__divide__eq__iff])]) ).
fof(i_0_1329,plain,
! [X5657,X5658,X5659] :
( ~ class_Rings_Olinordered__ring(X5659)
| ~ c_Orderings_Oord__class_Oless(X5659,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5659),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5659),X5658),X5658)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5659),X5657),X5657)),c_Groups_Ozero__class_Ozero(X5659)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1183])]) ).
fof(i_0_1330,plain,
! [X6017,X6018,X6019] :
( ~ class_Divides_Osemiring__div(X6019)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X6019),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6019),c_Divides_Odiv__class_Odiv(X6019,X6018,X6017)),X6017)),c_Divides_Odiv__class_Omod(X6019,X6018,X6017)) = X6018 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__div__equality])]) ).
fof(i_0_1331,plain,
! [X4613,X4614,X4615,X4616] :
( ~ class_RealVector_Oreal__normed__field(X4616)
| ~ c_Deriv_Oderiv(X4616,X4615,X4614,X4613)
| c_Deriv_Oderiv(X4616,hAPP(hAPP(c_COMBB(X4616,X4616,X4616),c_Groups_Ouminus__class_Ouminus(X4616)),X4615),X4614,hAPP(c_Groups_Ouminus__class_Ouminus(X4616),X4613)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_DERIV__minus])]) ).
fof(i_0_1332,plain,
! [X4203,X4204,X4205] :
( ~ class_Rings_Ocomm__ring__1(X4205)
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(X4205),hAPP(hAPP(c_Power_Opower__class_Opower(X4205),X4204),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))),hAPP(hAPP(c_Power_Opower__class_Opower(X4205),X4203),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4205),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X4205),X4204),X4203)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4205),X4204),X4203)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_realpow__two__diff])]) ).
fof(i_0_1333,plain,
! [X4378,X4379,X4380] :
( ~ class_Rings_Odivision__ring(X4380)
| X4379 = c_Groups_Ozero__class_Ozero(X4380)
| X4378 = c_Groups_Ozero__class_Ozero(X4380)
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(X4380),hAPP(c_Rings_Oinverse__class_Oinverse(X4380),X4379)),hAPP(c_Rings_Oinverse__class_Oinverse(X4380),X4378)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4380),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4380),hAPP(c_Rings_Oinverse__class_Oinverse(X4380),X4379)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X4380),X4378),X4379))),hAPP(c_Rings_Oinverse__class_Oinverse(X4380),X4378)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_division__ring__inverse__diff])]) ).
fof(i_0_1334,plain,
! [X4375,X4376,X4377] :
( ~ class_Rings_Odivision__ring(X4377)
| X4376 = c_Groups_Ozero__class_Ozero(X4377)
| X4375 = c_Groups_Ozero__class_Ozero(X4377)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4377),hAPP(c_Rings_Oinverse__class_Oinverse(X4377),X4376)),hAPP(c_Rings_Oinverse__class_Oinverse(X4377),X4375)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4377),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4377),hAPP(c_Rings_Oinverse__class_Oinverse(X4377),X4376)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4377),X4376),X4375))),hAPP(c_Rings_Oinverse__class_Oinverse(X4377),X4375)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_division__ring__inverse__add])]) ).
fof(i_0_1335,plain,
! [X3620,X3621,X3622,X3623] :
( ~ class_Rings_Ocomm__semiring__0(X3623)
| c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X3623,hAPP(hAPP(c_Polynomial_OpCons(X3623),X3622),X3621),X3620) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X3623)),hAPP(hAPP(c_Polynomial_Osmult(X3623),X3620),c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X3623,X3621,X3620))),hAPP(hAPP(c_Polynomial_OpCons(X3623),X3622),c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X3623,X3621,X3620))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_offset__poly__pCons])]) ).
fof(i_0_1336,plain,
! [X5747,X5748,X5749] :
( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X5749),X5748)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X5749),X5747)))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X5749)
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X5748),X5747)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvd__mult__cancel])]) ).
fof(i_0_1337,plain,
! [X5744,X5745,X5746] :
( ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X5746),X5745)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X5746),X5744)))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X5745),X5744))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X5746) )
& ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X5745),X5744))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X5746),X5745)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X5746),X5744)))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X5746) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__mult__dvd__cancel1])])]) ).
fof(i_0_1338,plain,
! [X3282,X3283,X3284,X3285,X3286] :
( ( X3285 = X3284
| X3283 = X3282
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X3286),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3286),X3285),X3283)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3286),X3284),X3282)) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(X3286),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3286),X3285),X3282)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3286),X3284),X3283))
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X3286) )
& ( X3285 != X3284
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X3286),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3286),X3285),X3283)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3286),X3284),X3282)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X3286),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3286),X3285),X3282)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3286),X3284),X3283))
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X3286) )
& ( X3283 != X3282
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X3286),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3286),X3285),X3283)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3286),X3284),X3282)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X3286),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3286),X3285),X3282)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3286),X3284),X3283))
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X3286) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_crossproduct__noteq])])]) ).
fof(i_0_1339,plain,
! [X3269,X3270,X3271,X3272,X3273] :
( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X3273),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3273),X3272),X3271)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3273),X3270),X3269)) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(X3273),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3273),X3272),X3269)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3273),X3270),X3271))
| X3272 = X3270
| X3271 = X3269
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X3273) )
& ( X3272 != X3270
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X3273),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3273),X3272),X3271)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3273),X3270),X3269)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X3273),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3273),X3272),X3269)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3273),X3270),X3271))
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X3273) )
& ( X3271 != X3269
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X3273),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3273),X3272),X3271)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3273),X3270),X3269)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X3273),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3273),X3272),X3269)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3273),X3270),X3271))
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X3273) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_crossproduct__eq])])]) ).
fof(i_0_1340,plain,
! [X4546,X4547] :
( ~ class_RealVector_Oreal__normed__field(X4547)
| X4546 = c_Groups_Ozero__class_Ozero(X4547)
| c_Deriv_Oderiv(X4547,c_Rings_Oinverse__class_Oinverse(X4547),X4546,hAPP(c_Groups_Ouminus__class_Ouminus(X4547),hAPP(hAPP(c_Power_Opower__class_Opower(X4547),hAPP(c_Rings_Oinverse__class_Oinverse(X4547),X4546)),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_DERIV__inverse])]) ).
fof(i_0_1341,plain,
! [X4433,X4434,X4435] :
( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X4435),X4434)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X4435),X4433)))
| X4435 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X4434),X4433)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zdvd__mult__cancel])]) ).
fof(i_0_1342,plain,
! [X4430,X4431,X4432] :
( ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X4431),X4430))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X4432),X4431)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X4432),X4430)))
| X4432 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
& ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X4432),X4431)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X4432),X4430)))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X4431),X4430))
| X4432 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zdvd__mono])])]) ).
fof(i_0_1343,plain,
! [X4445,X4446,X4447] :
( ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4447),X4446)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4447),X4445)))
| X4447 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X4446),X4445)) )
& ( X4447 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4447),X4446)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4447),X4445))) )
& ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X4446),X4445))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4447),X4446)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4447),X4445))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__mult__dvd__cancel__disj])])]) ).
fof(i_0_1344,plain,
! [X4536,X4537,X4538] :
( ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X4537),X4538)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X4536),X4538)))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X4537),X4536))
| X4538 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X4537),X4536))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X4537),X4538)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X4536),X4538)))
| X4538 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pow__divides__eq__int])])]) ).
fof(i_0_1345,plain,
! [X4533,X4534,X4535] :
( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X4535),X4534)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X4533),X4534)))
| X4534 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X4535),X4533)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pow__divides__pow__int])]) ).
fof(i_0_1346,plain,
! [X4465,X4466,X4467] :
( ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X4466),X4467)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X4465),X4467)))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X4466),X4465))
| X4467 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X4466),X4465))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X4466),X4467)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X4465),X4467)))
| X4467 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pow__divides__eq__nat])])]) ).
fof(i_0_1347,plain,
! [X4462,X4463,X4464] :
( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X4464),X4463)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X4462),X4463)))
| X4463 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X4464),X4462)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pow__divides__pow__nat])]) ).
fof(i_0_1348,plain,
! [X4436,X4437,X4438] :
( ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X4438),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X4437),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X4438),X4436))))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X4438),X4437)) )
& ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X4438),X4437))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X4438),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X4437),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X4438),X4436)))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zdvd__reduce])]) ).
fof(i_0_1349,plain,
! [X6169,X6170,X6171,X6172,X6173,X6174] : hAPP(hAPP(c_COMBC(X6174,X6173,X6172,X6171),X6170),X6169) = hAPP(hAPP(X6171,X6169),X6170),
inference(variable_rename,[status(thm)],[help_c__COMBC__1]) ).
fof(i_0_1350,plain,
! [X4531,X4532] :
( ~ hBOOL(hAPP(X4532,X4531))
| hBOOL(hAPP(X4532,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| c_Orderings_Oord__class_OLeast(tc_Nat_Onat,X4532) = hAPP(c_Nat_OSuc,c_Orderings_Oord__class_OLeast(tc_Nat_Onat,hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_Nat_Onat),X4532),c_Nat_OSuc))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1184])]) ).
fof(i_0_1351,plain,
! [X4268,X4269,X4270,X4271,X4272] :
( ~ class_Rings_Ocomm__semiring__1(X4272)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X4272),X4271),X4270))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X4272),X4269),X4268))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X4272),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4272),X4271),X4269)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4272),X4270),X4268))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__dvd__mono])]) ).
fof(i_0_1352,plain,
! [X4385,X4386,X4387,X4388] :
( ( X4387 != c_Groups_Ozero__class_Ozero(X4388)
| X4385 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4388))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X4388)),hAPP(hAPP(c_Polynomial_Osmult(X4388),X4387),X4386)),X4385))
| ~ class_Fields_Ofield(X4388) )
& ( X4387 = c_Groups_Ozero__class_Ozero(X4388)
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X4388)),X4386),X4385))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X4388)),hAPP(hAPP(c_Polynomial_Osmult(X4388),X4387),X4386)),X4385))
| ~ class_Fields_Ofield(X4388) )
& ( X4387 != c_Groups_Ozero__class_Ozero(X4388)
| X4387 = c_Groups_Ozero__class_Ozero(X4388)
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X4388)),hAPP(hAPP(c_Polynomial_Osmult(X4388),X4387),X4386)),X4385))
| ~ class_Fields_Ofield(X4388) )
& ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X4388)),X4386),X4385))
| X4387 = c_Groups_Ozero__class_Ozero(X4388)
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X4388)),hAPP(hAPP(c_Polynomial_Osmult(X4388),X4387),X4386)),X4385))
| ~ class_Fields_Ofield(X4388) )
& ( X4387 != c_Groups_Ozero__class_Ozero(X4388)
| X4385 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4388))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X4388)),hAPP(hAPP(c_Polynomial_Osmult(X4388),X4387),X4386)),X4385))
| ~ class_Fields_Ofield(X4388) )
& ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X4388)),X4386),X4385))
| X4385 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4388))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X4388)),hAPP(hAPP(c_Polynomial_Osmult(X4388),X4387),X4386)),X4385))
| ~ class_Fields_Ofield(X4388) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_smult__dvd__iff])])]) ).
fof(i_0_1353,plain,
! [X4725,X4726,X4727] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4727),X4726)),X4725)),X4726) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,X4725),X4726),
inference(variable_rename,[status(thm)],[fact_mod__mult__self4]) ).
fof(i_0_1354,plain,
! [X4325,X4326,X4327,X4328] :
( ~ class_Rings_Ocomm__semiring__1(X4328)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X4328)),hAPP(hAPP(c_Polynomial_Osmult(X4328),X4327),X4326)),X4325))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X4328)),X4326),X4325)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_smult__dvd__cancel])]) ).
fof(i_0_1355,plain,
! [X5787,X5788,X5789,X5790,X5791,X5792,X5793,X5794] :
( ( X5787 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hBOOL(hAPP(X5789,X5788))
| ~ hBOOL(hAPP(X5789,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X5788,X5787))) )
& ( X5787 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X5791,X5787)
| X5788 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X5787),X5790)),X5791)
| hBOOL(hAPP(X5789,X5791))
| ~ hBOOL(hAPP(X5789,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X5788,X5787))) )
& ( X5792 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X5792 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hBOOL(hAPP(X5794,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X5793,X5792))) )
& ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,esk16_3(X5792,X5793,X5794),X5792)
| X5792 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hBOOL(hAPP(X5794,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X5793,X5792))) )
& ( X5793 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X5792),esk15_3(X5792,X5793,X5794))),esk16_3(X5792,X5793,X5794))
| X5792 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hBOOL(hAPP(X5794,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X5793,X5792))) )
& ( ~ hBOOL(hAPP(X5794,esk16_3(X5792,X5793,X5794)))
| X5792 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hBOOL(hAPP(X5794,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X5793,X5792))) )
& ( X5792 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(X5794,X5793))
| hBOOL(hAPP(X5794,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X5793,X5792))) )
& ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,esk16_3(X5792,X5793,X5794),X5792)
| ~ hBOOL(hAPP(X5794,X5793))
| hBOOL(hAPP(X5794,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X5793,X5792))) )
& ( X5793 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X5792),esk15_3(X5792,X5793,X5794))),esk16_3(X5792,X5793,X5794))
| ~ hBOOL(hAPP(X5794,X5793))
| hBOOL(hAPP(X5794,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X5793,X5792))) )
& ( ~ hBOOL(hAPP(X5794,esk16_3(X5792,X5793,X5794)))
| ~ hBOOL(hAPP(X5794,X5793))
| hBOOL(hAPP(X5794,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X5793,X5792))) ) ),
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)],[fact_split__mod])])])])])]) ).
fof(i_0_1356,plain,
! [X3876,X3877,X3878] :
( ~ class_Rings_Ocomm__semiring__0(X3878)
| hAPP(c_Polynomial_Ocoeff(X3878,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X3878)),X3877),X3876)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Polynomial_Odegree(X3878,X3877)),c_Polynomial_Odegree(X3878,X3876))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3878),hAPP(c_Polynomial_Ocoeff(X3878,X3877),c_Polynomial_Odegree(X3878,X3877))),hAPP(c_Polynomial_Ocoeff(X3878,X3876),c_Polynomial_Odegree(X3878,X3876))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_coeff__mult__degree__sum])]) ).
fof(i_0_1357,plain,
! [X3575,X3576,X3577,X3578] :
( ~ class_Rings_Ocomm__semiring__0(X3578)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X3578)),hAPP(hAPP(c_Polynomial_OpCons(X3578),X3577),X3576)),X3575) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X3578)),hAPP(hAPP(c_Polynomial_Osmult(X3578),X3577),X3575)),hAPP(hAPP(c_Polynomial_OpCons(X3578),c_Groups_Ozero__class_Ozero(X3578)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X3578)),X3576),X3575))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__pCons__left])]) ).
fof(i_0_1358,plain,
! [X5923,X5924,X5925,X5926,X5927] :
( ~ class_Divides_Osemiring__div(X5927)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X5927),X5926),X5925))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X5927),X5924),X5923))
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5927),c_Divides_Odiv__class_Odiv(X5927,X5925,X5926)),c_Divides_Odiv__class_Odiv(X5927,X5923,X5924)) = c_Divides_Odiv__class_Odiv(X5927,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5927),X5925),X5923),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5927),X5926),X5924)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_div__mult__div__if__dvd])]) ).
fof(i_0_1359,plain,
! [X4809,X4810,X4811,X4812] :
( ~ class_Divides_Oring__div(X4812)
| c_Divides_Odiv__class_Omod(X4812,hAPP(hAPP(c_Groups_Ominus__class_Ominus(X4812),X4811),X4810),X4809) = c_Divides_Odiv__class_Omod(X4812,hAPP(hAPP(c_Groups_Ominus__class_Ominus(X4812),c_Divides_Odiv__class_Omod(X4812,X4811,X4809)),c_Divides_Odiv__class_Omod(X4812,X4810,X4809)),X4809) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__diff__eq])]) ).
fof(i_0_1360,plain,
! [X4759,X4760,X4761,X4762] :
( ~ class_Divides_Osemiring__div(X4762)
| c_Divides_Odiv__class_Omod(X4762,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4762),X4761),X4760),X4759) = c_Divides_Odiv__class_Omod(X4762,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4762),c_Divides_Odiv__class_Omod(X4762,X4761,X4759)),c_Divides_Odiv__class_Omod(X4762,X4760,X4759)),X4759) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__mult__eq])]) ).
fof(i_0_1361,plain,
! [X4785,X4786,X4787,X4788] :
( ~ class_Divides_Osemiring__div(X4788)
| c_Divides_Odiv__class_Omod(X4788,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4788),X4787),X4786),X4785) = c_Divides_Odiv__class_Omod(X4788,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4788),c_Divides_Odiv__class_Omod(X4788,X4787,X4785)),c_Divides_Odiv__class_Omod(X4788,X4786,X4785)),X4785) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__add__eq])]) ).
fof(i_0_1362,plain,
! [X5722,X5723,X5724] :
( ~ class_Fields_Olinordered__field(X5724)
| ~ c_Orderings_Oord__class_Oless(X5724,X5723,X5722)
| c_Orderings_Oord__class_Oless(X5724,hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X5724),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5724),X5723),X5722)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5724),c_Groups_Oone__class_Oone(X5724)),c_Groups_Oone__class_Oone(X5724))),X5722) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_gt__half__sum])]) ).
fof(i_0_1363,plain,
! [X5725,X5726,X5727] :
( ~ class_Fields_Olinordered__field(X5727)
| ~ c_Orderings_Oord__class_Oless(X5727,X5726,X5725)
| c_Orderings_Oord__class_Oless(X5727,X5726,hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X5727),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5727),X5726),X5725)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5727),c_Groups_Oone__class_Oone(X5727)),c_Groups_Oone__class_Oone(X5727)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__half__sum])]) ).
fof(i_0_1364,plain,
! [X5060,X5061,X5062,X5063] :
( ~ class_Fields_Ofield(X5063)
| X5062 = c_Groups_Ozero__class_Ozero(X5063)
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(X5063),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X5063),X5061),X5062)),X5060) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X5063),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X5063),X5061),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5063),X5062),X5060))),X5062) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divide__diff__eq__iff])]) ).
fof(i_0_1365,plain,
! [X5046,X5047,X5048,X5049] :
( ~ class_Fields_Ofield(X5049)
| X5048 = c_Groups_Ozero__class_Ozero(X5049)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5049),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X5049),X5047),X5048)),X5046) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X5049),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5049),X5047),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5049),X5048),X5046))),X5048) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divide__add__eq__iff])]) ).
fof(i_0_1366,plain,
! [X5042,X5043,X5044,X5045] :
( ~ class_Fields_Ofield__inverse__zero(X5045)
| X5044 = c_Groups_Ozero__class_Ozero(X5045)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5045),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X5045),X5043),X5044)),X5042) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X5045),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5045),X5043),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5045),X5042),X5044))),X5044) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__frac__num])]) ).
fof(i_0_1367,plain,
! [X3197,X3198,X3199,X3200,X3201] :
( ~ class_Rings_Ocomm__semiring__1(X3201)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3201),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3201),X3200),X3199)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3201),X3198),X3197)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3201),X3198),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3201),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3201),X3200),X3199)),X3197)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J])]) ).
fof(i_0_1368,plain,
! [X5835] :
( ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X5835)),X5835),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| c_Orderings_Oord__class_Oless(tc_Int_Oint,X5835,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X5835,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X5835)),X5835),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_odd__less__0])]) ).
fof(i_0_1369,plain,
! [X4260,X4261,X4262,X4263] :
( ~ class_Rings_Ocomm__semiring__1(X4263)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X4263),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4263),X4262),X4261)),X4260))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X4263),X4262),X4260)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvd__mult__left])]) ).
fof(i_0_1370,plain,
! [X4256,X4257,X4258,X4259] :
( ~ class_Rings_Ocomm__semiring__1(X4259)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X4259),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4259),X4258),X4257)),X4256))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X4259),X4257),X4256)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvd__mult__right])]) ).
fof(i_0_1371,plain,
! [X3374,X3375,X3376,X3377] :
( ~ class_Rings_Ocomm__semiring__0(X3377)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X3377)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X3377)),X3376),X3375)),X3374) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X3377)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X3377)),X3376),X3374)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X3377)),X3375),X3374)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__poly__add__left])]) ).
fof(i_0_1372,plain,
! [X4182,X4183,X4184] :
( ~ class_Rings_Oring__1(X4184)
| hAPP(hAPP(c_Power_Opower__class_Opower(X4184),hAPP(c_Groups_Ouminus__class_Ouminus(X4184),X4183)),X4182) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4184),hAPP(hAPP(c_Power_Opower__class_Opower(X4184),hAPP(c_Groups_Ouminus__class_Ouminus(X4184),c_Groups_Oone__class_Oone(X4184))),X4182)),hAPP(hAPP(c_Power_Opower__class_Opower(X4184),X4183),X4182)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__minus])]) ).
fof(i_0_1373,plain,
! [X3579,X3580,X3581,X3582] :
( ~ class_Rings_Ocomm__semiring__0(X3582)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X3582)),X3581),hAPP(hAPP(c_Polynomial_OpCons(X3582),X3580),X3579)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X3582)),hAPP(hAPP(c_Polynomial_Osmult(X3582),X3580),X3581)),hAPP(hAPP(c_Polynomial_OpCons(X3582),c_Groups_Ozero__class_Ozero(X3582)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X3582)),X3581),X3579))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__pCons__right])]) ).
fof(i_0_1374,plain,
! [X4315,X4316,X4317,X4318] :
( ~ class_Rings_Ocomm__semiring__1(X4318)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X4318),X4317),X4316))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X4318),hAPP(hAPP(c_Power_Opower__class_Opower(X4318),X4317),X4315)),hAPP(hAPP(c_Power_Opower__class_Opower(X4318),X4316),X4315))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvd__power__same])]) ).
fof(i_0_1375,plain,
! [X3462,X3463,X3464,X3465] :
( ~ class_Rings_Ocomm__semiring__0(X3465)
| c_Polynomial_Opcompose(X3465,hAPP(hAPP(c_Polynomial_OpCons(X3465),X3464),X3463),X3462) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X3465)),hAPP(hAPP(c_Polynomial_OpCons(X3465),X3464),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3465)))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X3465)),X3462),c_Polynomial_Opcompose(X3465,X3463,X3462))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pcompose__pCons])]) ).
fof(i_0_1376,plain,
! [X5928,X5929,X5930,X5931] :
( ~ class_Divides_Osemiring__div(X5931)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X5931),X5930),X5929))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X5931),X5930),X5928))
| c_Divides_Odiv__class_Odiv(X5931,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5931),X5929),X5928),X5930) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5931),c_Divides_Odiv__class_Odiv(X5931,X5929,X5930)),c_Divides_Odiv__class_Odiv(X5931,X5928,X5930)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_div__add])]) ).
fof(i_0_1377,plain,
! [X4337,X4338,X4339,X4340] :
( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X4340)),X4339),X4338))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X4340)),X4339),c_Polynomial_Opoly__gcd(X4340,X4338,X4337)))
| ~ class_Fields_Ofield(X4340) )
& ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X4340)),X4339),X4337))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X4340)),X4339),c_Polynomial_Opoly__gcd(X4340,X4338,X4337)))
| ~ class_Fields_Ofield(X4340) )
& ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X4340)),X4339),X4338))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X4340)),X4339),X4337))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X4340)),X4339),c_Polynomial_Opoly__gcd(X4340,X4338,X4337)))
| ~ class_Fields_Ofield(X4340) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvd__poly__gcd__iff])])]) ).
fof(i_0_1378,plain,
! [X4333,X4334,X4335,X4336] :
( ~ class_Fields_Ofield(X4336)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X4336)),X4335),X4334))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X4336)),X4335),X4333))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X4336)),X4335),c_Polynomial_Opoly__gcd(X4336,X4334,X4333))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_poly__gcd__greatest])]) ).
fof(i_0_1379,plain,
! [X5034,X5035,X5036,X5037] :
( ~ class_Fields_Ofield__inverse__zero(X5037)
| X5036 = c_Groups_Ozero__class_Ozero(X5037)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5037),X5035),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X5037),X5034),X5036)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X5037),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5037),X5034),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5037),X5035),X5036))),X5036) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__num__frac])]) ).
fof(i_0_1380,plain,
! [X4364,X4365,X4366,X4367] :
( ~ class_Fields_Ofield(X4367)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X4367)),X4366),X4365))
| X4364 = c_Groups_Ozero__class_Ozero(X4367)
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X4367)),hAPP(hAPP(c_Polynomial_Osmult(X4367),X4364),X4366)),X4365)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_smult__dvd])]) ).
fof(i_0_1381,plain,
! [X4105,X4106,X4107,X4108,X4109] : hAPP(hAPP(c_Power_Opower_Opower(X4109,X4108,X4107),X4106),hAPP(c_Nat_OSuc,X4105)) = hAPP(hAPP(X4107,X4106),hAPP(hAPP(c_Power_Opower_Opower(X4109,X4108,X4107),X4106),X4105)),
inference(variable_rename,[status(thm)],[fact_power_Opower_Opower__Suc]) ).
fof(i_0_1382,plain,
! [X5785,X5786] :
( ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X5785),X5786)),X5786))
| X5785 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X5786) )
& ( X5785 != c_Groups_Oone__class_Oone(tc_Nat_Onat)
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X5785),X5786)),X5786))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X5786) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvd__mult__cancel2])])]) ).
fof(i_0_1383,plain,
! [X5783,X5784] :
( ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X5784),X5783)),X5784))
| X5783 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X5784) )
& ( X5783 != c_Groups_Oone__class_Oone(tc_Nat_Onat)
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X5784),X5783)),X5784))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X5784) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvd__mult__cancel1])])]) ).
fof(i_0_1384,plain,
! [X6023,X6024,X6025] :
( ~ class_Divides_Osemiring__div(X6025)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X6025),c_Divides_Odiv__class_Omod(X6025,X6024,X6023)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6025),c_Divides_Odiv__class_Odiv(X6025,X6024,X6023)),X6023)) = X6024 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_semiring__div__class_Omod__div__equality_H])]) ).
fof(i_0_1385,plain,
! [X6020,X6021,X6022] :
( ~ class_Divides_Osemiring__div(X6022)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X6022),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6022),X6021),c_Divides_Odiv__class_Odiv(X6022,X6020,X6021))),c_Divides_Odiv__class_Omod(X6022,X6020,X6021)) = X6020 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__div__equality2])]) ).
fof(i_0_1386,plain,
! [X3756,X3757,X3758,X3759,X3760] :
( ~ class_Groups_Oab__group__add(X3760)
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X3760)),hAPP(hAPP(c_Polynomial_OpCons(X3760),X3759),X3758)),hAPP(hAPP(c_Polynomial_OpCons(X3760),X3757),X3756)) = hAPP(hAPP(c_Polynomial_OpCons(X3760),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X3760),X3759),X3757)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X3760)),X3758),X3756)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__pCons])]) ).
fof(i_0_1387,plain,
! [X3315,X3316,X3317,X3318,X3319] :
( ~ class_Groups_Ocomm__monoid__add(X3319)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X3319)),hAPP(hAPP(c_Polynomial_OpCons(X3319),X3318),X3317)),hAPP(hAPP(c_Polynomial_OpCons(X3319),X3316),X3315)) = hAPP(hAPP(c_Polynomial_OpCons(X3319),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X3319),X3318),X3316)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X3319)),X3317),X3315)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__pCons])]) ).
fof(i_0_1388,plain,
! [X5181,X5182,X5183] :
( ~ class_Groups_Omonoid__mult(X5183)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X5182)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5183),hAPP(hAPP(c_Power_Opower__class_Opower(X5183),X5181),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X5182),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),X5181) = hAPP(hAPP(c_Power_Opower__class_Opower(X5183),X5181),X5182) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_realpow__minus__mult])]) ).
fof(i_0_1389,plain,
! [X4588,X4589,X4590,X4591,X4592] :
( ~ class_RealVector_Oreal__normed__field(X4592)
| ~ c_Deriv_Oderiv(X4592,X4591,X4590,X4589)
| ~ c_Deriv_Oderiv(X4592,X4591,X4590,X4588)
| X4589 = X4588 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_DERIV__unique])]) ).
fof(i_0_1390,plain,
! [X4840,X4841,X4842,X4843] :
( ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X4843),X4842),c_Divides_Odiv__class_Omod(X4843,X4840,X4841)))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X4843),X4842),X4840))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X4843),X4842),X4841))
| ~ class_Divides_Osemiring__div(X4843) )
& ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X4843),X4842),X4840))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X4843),X4842),c_Divides_Odiv__class_Omod(X4843,X4840,X4841)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X4843),X4842),X4841))
| ~ class_Divides_Osemiring__div(X4843) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvd__mod__iff])])]) ).
fof(i_0_1391,plain,
! [X4828,X4829,X4830,X4831] :
( ~ class_Divides_Osemiring__div(X4831)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X4831),X4830),c_Divides_Odiv__class_Omod(X4831,X4829,X4828)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X4831),X4830),X4828))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X4831),X4830),X4829)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvd__mod__imp__dvd])]) ).
fof(i_0_1392,plain,
! [X3702,X3703,X3704] :
( ~ class_Rings_Ocomm__semiring__0(X3704)
| hAPP(hAPP(c_Polynomial_Osmult(X3704),X3703),X3702) = c_Polynomial_OAbs__poly(X3704,hAPP(hAPP(c_COMBB(X3704,X3704,tc_Nat_Onat),hAPP(c_Groups_Otimes__class_Otimes(X3704),X3703)),c_Polynomial_Ocoeff(X3704,X3702))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_smult__def])]) ).
fof(i_0_1393,plain,
! [X5680,X5681,X5682,X5683] :
( ( ~ c_Orderings_Oord__class_Oless(X5683,c_Groups_Ozero__class_Ozero(X5683),X5681)
| c_Orderings_Oord__class_Oless(X5683,X5682,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5683),X5680),X5681))
| ~ c_Orderings_Oord__class_Oless(X5683,hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X5683),X5682),X5681),X5680)
| ~ class_Fields_Olinordered__field__inverse__zero(X5683) )
& ( ~ c_Orderings_Oord__class_Oless(X5683,X5681,c_Groups_Ozero__class_Ozero(X5683))
| c_Orderings_Oord__class_Oless(X5683,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5683),X5680),X5681),X5682)
| c_Orderings_Oord__class_Oless(X5683,c_Groups_Ozero__class_Ozero(X5683),X5681)
| ~ c_Orderings_Oord__class_Oless(X5683,hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X5683),X5682),X5681),X5680)
| ~ class_Fields_Olinordered__field__inverse__zero(X5683) )
& ( c_Orderings_Oord__class_Oless(X5683,X5681,c_Groups_Ozero__class_Ozero(X5683))
| c_Orderings_Oord__class_Oless(X5683,c_Groups_Ozero__class_Ozero(X5683),X5680)
| c_Orderings_Oord__class_Oless(X5683,c_Groups_Ozero__class_Ozero(X5683),X5681)
| ~ c_Orderings_Oord__class_Oless(X5683,hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X5683),X5682),X5681),X5680)
| ~ class_Fields_Olinordered__field__inverse__zero(X5683) )
& ( ~ c_Orderings_Oord__class_Oless(X5683,c_Groups_Ozero__class_Ozero(X5683),X5681)
| c_Orderings_Oord__class_Oless(X5683,c_Groups_Ozero__class_Ozero(X5683),X5681)
| c_Orderings_Oord__class_Oless(X5683,hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X5683),X5682),X5681),X5680)
| ~ class_Fields_Olinordered__field__inverse__zero(X5683) )
& ( ~ c_Orderings_Oord__class_Oless(X5683,X5681,c_Groups_Ozero__class_Ozero(X5683))
| c_Orderings_Oord__class_Oless(X5683,X5681,c_Groups_Ozero__class_Ozero(X5683))
| c_Orderings_Oord__class_Oless(X5683,c_Groups_Ozero__class_Ozero(X5683),X5681)
| c_Orderings_Oord__class_Oless(X5683,hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X5683),X5682),X5681),X5680)
| ~ class_Fields_Olinordered__field__inverse__zero(X5683) )
& ( ~ c_Orderings_Oord__class_Oless(X5683,c_Groups_Ozero__class_Ozero(X5683),X5680)
| c_Orderings_Oord__class_Oless(X5683,X5681,c_Groups_Ozero__class_Ozero(X5683))
| c_Orderings_Oord__class_Oless(X5683,c_Groups_Ozero__class_Ozero(X5683),X5681)
| c_Orderings_Oord__class_Oless(X5683,hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X5683),X5682),X5681),X5680)
| ~ class_Fields_Olinordered__field__inverse__zero(X5683) )
& ( ~ c_Orderings_Oord__class_Oless(X5683,X5681,c_Groups_Ozero__class_Ozero(X5683))
| ~ c_Orderings_Oord__class_Oless(X5683,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5683),X5680),X5681),X5682)
| c_Orderings_Oord__class_Oless(X5683,c_Groups_Ozero__class_Ozero(X5683),X5681)
| c_Orderings_Oord__class_Oless(X5683,hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X5683),X5682),X5681),X5680)
| ~ class_Fields_Olinordered__field__inverse__zero(X5683) )
& ( ~ c_Orderings_Oord__class_Oless(X5683,c_Groups_Ozero__class_Ozero(X5683),X5680)
| ~ c_Orderings_Oord__class_Oless(X5683,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5683),X5680),X5681),X5682)
| c_Orderings_Oord__class_Oless(X5683,c_Groups_Ozero__class_Ozero(X5683),X5681)
| c_Orderings_Oord__class_Oless(X5683,hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X5683),X5682),X5681),X5680)
| ~ class_Fields_Olinordered__field__inverse__zero(X5683) )
& ( ~ c_Orderings_Oord__class_Oless(X5683,c_Groups_Ozero__class_Ozero(X5683),X5681)
| ~ c_Orderings_Oord__class_Oless(X5683,X5682,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5683),X5680),X5681))
| c_Orderings_Oord__class_Oless(X5683,hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X5683),X5682),X5681),X5680)
| ~ class_Fields_Olinordered__field__inverse__zero(X5683) )
& ( ~ c_Orderings_Oord__class_Oless(X5683,X5681,c_Groups_Ozero__class_Ozero(X5683))
| c_Orderings_Oord__class_Oless(X5683,X5681,c_Groups_Ozero__class_Ozero(X5683))
| ~ c_Orderings_Oord__class_Oless(X5683,X5682,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5683),X5680),X5681))
| c_Orderings_Oord__class_Oless(X5683,hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X5683),X5682),X5681),X5680)
| ~ class_Fields_Olinordered__field__inverse__zero(X5683) )
& ( ~ c_Orderings_Oord__class_Oless(X5683,c_Groups_Ozero__class_Ozero(X5683),X5680)
| c_Orderings_Oord__class_Oless(X5683,X5681,c_Groups_Ozero__class_Ozero(X5683))
| ~ c_Orderings_Oord__class_Oless(X5683,X5682,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5683),X5680),X5681))
| c_Orderings_Oord__class_Oless(X5683,hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X5683),X5682),X5681),X5680)
| ~ class_Fields_Olinordered__field__inverse__zero(X5683) )
& ( ~ c_Orderings_Oord__class_Oless(X5683,X5681,c_Groups_Ozero__class_Ozero(X5683))
| ~ c_Orderings_Oord__class_Oless(X5683,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5683),X5680),X5681),X5682)
| ~ c_Orderings_Oord__class_Oless(X5683,X5682,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5683),X5680),X5681))
| c_Orderings_Oord__class_Oless(X5683,hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X5683),X5682),X5681),X5680)
| ~ class_Fields_Olinordered__field__inverse__zero(X5683) )
& ( ~ c_Orderings_Oord__class_Oless(X5683,c_Groups_Ozero__class_Ozero(X5683),X5680)
| ~ c_Orderings_Oord__class_Oless(X5683,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5683),X5680),X5681),X5682)
| ~ c_Orderings_Oord__class_Oless(X5683,X5682,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5683),X5680),X5681))
| c_Orderings_Oord__class_Oless(X5683,hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X5683),X5682),X5681),X5680)
| ~ class_Fields_Olinordered__field__inverse__zero(X5683) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1185])])]) ).
fof(i_0_1394,plain,
! [X5676,X5677,X5678,X5679] :
( ( ~ c_Orderings_Oord__class_Oless(X5679,c_Groups_Ozero__class_Ozero(X5679),X5676)
| c_Orderings_Oord__class_Oless(X5679,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5679),X5678),X5676),X5677)
| ~ c_Orderings_Oord__class_Oless(X5679,X5678,hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X5679),X5677),X5676))
| ~ class_Fields_Olinordered__field__inverse__zero(X5679) )
& ( ~ c_Orderings_Oord__class_Oless(X5679,X5676,c_Groups_Ozero__class_Ozero(X5679))
| c_Orderings_Oord__class_Oless(X5679,X5677,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5679),X5678),X5676))
| c_Orderings_Oord__class_Oless(X5679,c_Groups_Ozero__class_Ozero(X5679),X5676)
| ~ c_Orderings_Oord__class_Oless(X5679,X5678,hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X5679),X5677),X5676))
| ~ class_Fields_Olinordered__field__inverse__zero(X5679) )
& ( c_Orderings_Oord__class_Oless(X5679,X5676,c_Groups_Ozero__class_Ozero(X5679))
| c_Orderings_Oord__class_Oless(X5679,X5678,c_Groups_Ozero__class_Ozero(X5679))
| c_Orderings_Oord__class_Oless(X5679,c_Groups_Ozero__class_Ozero(X5679),X5676)
| ~ c_Orderings_Oord__class_Oless(X5679,X5678,hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X5679),X5677),X5676))
| ~ class_Fields_Olinordered__field__inverse__zero(X5679) )
& ( ~ c_Orderings_Oord__class_Oless(X5679,c_Groups_Ozero__class_Ozero(X5679),X5676)
| c_Orderings_Oord__class_Oless(X5679,c_Groups_Ozero__class_Ozero(X5679),X5676)
| c_Orderings_Oord__class_Oless(X5679,X5678,hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X5679),X5677),X5676))
| ~ class_Fields_Olinordered__field__inverse__zero(X5679) )
& ( ~ c_Orderings_Oord__class_Oless(X5679,X5676,c_Groups_Ozero__class_Ozero(X5679))
| c_Orderings_Oord__class_Oless(X5679,X5676,c_Groups_Ozero__class_Ozero(X5679))
| c_Orderings_Oord__class_Oless(X5679,c_Groups_Ozero__class_Ozero(X5679),X5676)
| c_Orderings_Oord__class_Oless(X5679,X5678,hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X5679),X5677),X5676))
| ~ class_Fields_Olinordered__field__inverse__zero(X5679) )
& ( ~ c_Orderings_Oord__class_Oless(X5679,X5678,c_Groups_Ozero__class_Ozero(X5679))
| c_Orderings_Oord__class_Oless(X5679,X5676,c_Groups_Ozero__class_Ozero(X5679))
| c_Orderings_Oord__class_Oless(X5679,c_Groups_Ozero__class_Ozero(X5679),X5676)
| c_Orderings_Oord__class_Oless(X5679,X5678,hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X5679),X5677),X5676))
| ~ class_Fields_Olinordered__field__inverse__zero(X5679) )
& ( ~ c_Orderings_Oord__class_Oless(X5679,X5676,c_Groups_Ozero__class_Ozero(X5679))
| ~ c_Orderings_Oord__class_Oless(X5679,X5677,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5679),X5678),X5676))
| c_Orderings_Oord__class_Oless(X5679,c_Groups_Ozero__class_Ozero(X5679),X5676)
| c_Orderings_Oord__class_Oless(X5679,X5678,hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X5679),X5677),X5676))
| ~ class_Fields_Olinordered__field__inverse__zero(X5679) )
& ( ~ c_Orderings_Oord__class_Oless(X5679,X5678,c_Groups_Ozero__class_Ozero(X5679))
| ~ c_Orderings_Oord__class_Oless(X5679,X5677,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5679),X5678),X5676))
| c_Orderings_Oord__class_Oless(X5679,c_Groups_Ozero__class_Ozero(X5679),X5676)
| c_Orderings_Oord__class_Oless(X5679,X5678,hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X5679),X5677),X5676))
| ~ class_Fields_Olinordered__field__inverse__zero(X5679) )
& ( ~ c_Orderings_Oord__class_Oless(X5679,c_Groups_Ozero__class_Ozero(X5679),X5676)
| ~ c_Orderings_Oord__class_Oless(X5679,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5679),X5678),X5676),X5677)
| c_Orderings_Oord__class_Oless(X5679,X5678,hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X5679),X5677),X5676))
| ~ class_Fields_Olinordered__field__inverse__zero(X5679) )
& ( ~ c_Orderings_Oord__class_Oless(X5679,X5676,c_Groups_Ozero__class_Ozero(X5679))
| c_Orderings_Oord__class_Oless(X5679,X5676,c_Groups_Ozero__class_Ozero(X5679))
| ~ c_Orderings_Oord__class_Oless(X5679,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5679),X5678),X5676),X5677)
| c_Orderings_Oord__class_Oless(X5679,X5678,hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X5679),X5677),X5676))
| ~ class_Fields_Olinordered__field__inverse__zero(X5679) )
& ( ~ c_Orderings_Oord__class_Oless(X5679,X5678,c_Groups_Ozero__class_Ozero(X5679))
| c_Orderings_Oord__class_Oless(X5679,X5676,c_Groups_Ozero__class_Ozero(X5679))
| ~ c_Orderings_Oord__class_Oless(X5679,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5679),X5678),X5676),X5677)
| c_Orderings_Oord__class_Oless(X5679,X5678,hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X5679),X5677),X5676))
| ~ class_Fields_Olinordered__field__inverse__zero(X5679) )
& ( ~ c_Orderings_Oord__class_Oless(X5679,X5676,c_Groups_Ozero__class_Ozero(X5679))
| ~ c_Orderings_Oord__class_Oless(X5679,X5677,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5679),X5678),X5676))
| ~ c_Orderings_Oord__class_Oless(X5679,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5679),X5678),X5676),X5677)
| c_Orderings_Oord__class_Oless(X5679,X5678,hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X5679),X5677),X5676))
| ~ class_Fields_Olinordered__field__inverse__zero(X5679) )
& ( ~ c_Orderings_Oord__class_Oless(X5679,X5678,c_Groups_Ozero__class_Ozero(X5679))
| ~ c_Orderings_Oord__class_Oless(X5679,X5677,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5679),X5678),X5676))
| ~ c_Orderings_Oord__class_Oless(X5679,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5679),X5678),X5676),X5677)
| c_Orderings_Oord__class_Oless(X5679,X5678,hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X5679),X5677),X5676))
| ~ class_Fields_Olinordered__field__inverse__zero(X5679) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1186])])]) ).
fof(i_0_1395,plain,
! [X4747,X4748,X4749,X4750] :
( ~ class_Divides_Osemiring__div(X4750)
| c_Divides_Odiv__class_Omod(X4750,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4750),c_Divides_Odiv__class_Omod(X4750,X4749,X4748)),X4747),X4748) = c_Divides_Odiv__class_Omod(X4750,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4750),X4749),X4747),X4748) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zmod__simps_I4_J])]) ).
fof(i_0_1396,plain,
! [X4777,X4778,X4779,X4780] :
( ~ class_Divides_Osemiring__div(X4780)
| c_Divides_Odiv__class_Omod(X4780,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4780),c_Divides_Odiv__class_Omod(X4780,X4779,X4778)),X4777),X4778) = c_Divides_Odiv__class_Omod(X4780,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4780),X4779),X4777),X4778) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zmod__simps_I1_J])]) ).
fof(i_0_1397,plain,
! [X4813,X4814,X4815,X4816] :
( ~ class_Divides_Oring__div(X4816)
| c_Divides_Odiv__class_Omod(X4816,hAPP(hAPP(c_Groups_Ominus__class_Ominus(X4816),X4815),X4814),X4813) = c_Divides_Odiv__class_Omod(X4816,hAPP(hAPP(c_Groups_Ominus__class_Ominus(X4816),c_Divides_Odiv__class_Omod(X4816,X4815,X4813)),X4814),X4813) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__diff__left__eq])]) ).
fof(i_0_1398,plain,
! [X4763,X4764,X4765,X4766] :
( ~ class_Divides_Osemiring__div(X4766)
| c_Divides_Odiv__class_Omod(X4766,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4766),X4765),X4764),X4763) = c_Divides_Odiv__class_Omod(X4766,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4766),c_Divides_Odiv__class_Omod(X4766,X4765,X4763)),X4764),X4763) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__mult__left__eq])]) ).
fof(i_0_1399,plain,
! [X4789,X4790,X4791,X4792] :
( ~ class_Divides_Osemiring__div(X4792)
| c_Divides_Odiv__class_Omod(X4792,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4792),X4791),X4790),X4789) = c_Divides_Odiv__class_Omod(X4792,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4792),c_Divides_Odiv__class_Omod(X4792,X4791,X4789)),X4790),X4789) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__add__left__eq])]) ).
fof(i_0_1400,plain,
! [X5954,X5955] : X5955 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X5954),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X5955,X5954))),c_Divides_Odiv__class_Omod(tc_Int_Oint,X5955,X5954)),
inference(variable_rename,[status(thm)],[fact_zmod__zdiv__equality]) ).
fof(i_0_1401,plain,
! [X4368,X4369,X4370,X4371] :
( ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X4371)),X4369),hAPP(hAPP(c_Polynomial_Osmult(X4371),X4370),X4368)))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X4371)),X4369),X4368))
| X4370 = c_Groups_Ozero__class_Ozero(X4371)
| ~ class_Fields_Ofield(X4371) )
& ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X4371)),X4369),X4368))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X4371)),X4369),hAPP(hAPP(c_Polynomial_Osmult(X4371),X4370),X4368)))
| X4370 = c_Groups_Ozero__class_Ozero(X4371)
| ~ class_Fields_Ofield(X4371) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvd__smult__iff])])]) ).
fof(i_0_1402,plain,
! [X4360,X4361,X4362,X4363] :
( ~ class_Fields_Ofield(X4363)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X4363)),X4362),hAPP(hAPP(c_Polynomial_Osmult(X4363),X4361),X4360)))
| X4361 = c_Groups_Ozero__class_Ozero(X4363)
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X4363)),X4362),X4360)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvd__smult__cancel])]) ).
fof(i_0_1403,plain,
! [X4229,X4230] :
( ~ class_Fields_Ofield(X4230)
| c_Polynomial_Opoly__gcd(X4230,X4229,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4230))) = hAPP(hAPP(c_Polynomial_Osmult(X4230),hAPP(c_Rings_Oinverse__class_Oinverse(X4230),hAPP(c_Polynomial_Ocoeff(X4230,X4229),c_Polynomial_Odegree(X4230,X4229)))),X4229) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_poly__gcd_Osimps_I1_J])]) ).
fof(i_0_1404,plain,
! [X4543,X4544,X4545] :
( ( X4544 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4545))
| c_Polynomial_Opoly__gcd(X4545,X4543,X4544) = hAPP(hAPP(c_Polynomial_Osmult(X4545),hAPP(c_Rings_Oinverse__class_Oinverse(X4545),hAPP(c_Polynomial_Ocoeff(X4545,X4543),c_Polynomial_Odegree(X4545,X4543)))),X4543)
| ~ class_Fields_Ofield(X4545) )
& ( X4544 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4545))
| c_Polynomial_Opoly__gcd(X4545,X4543,X4544) = c_Polynomial_Opoly__gcd(X4545,X4544,c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(X4545),X4543,X4544))
| ~ class_Fields_Ofield(X4545) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_poly__gcd__code])])]) ).
fof(i_0_1405,plain,
! [X5014,X5015,X5016] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,X5016)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,X5015)),X5014)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X5016),X5015))),X5014),
inference(variable_rename,[status(thm)],[fact_zadd__int__left]) ).
fof(i_0_1406,plain,
! [X4922,X4923,X4924,X4925,X4926] :
( ~ class_Fields_Ofield__inverse__zero(X4926)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4926),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4926),X4925),X4924)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4926),X4923),X4922)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4926),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4926),X4925),X4923)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4926),X4924),X4922)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_times__divide__times__eq])]) ).
fof(i_0_1407,plain,
! [X3895,X3896,X3897,X3898,X3899] :
( ~ class_Groups_Oab__group__add(X3899)
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(X3899),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X3899),X3898),X3897)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X3899),X3896),X3895)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X3899),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X3899),X3898),X3896)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X3899),X3897),X3895)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Deriv_Oadd__diff__add])]) ).
fof(i_0_1408,plain,
! [X3192,X3193,X3194,X3195,X3196] :
( ~ class_Rings_Ocomm__semiring__1(X3196)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3196),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3196),X3195),X3194)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3196),X3193),X3192)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3196),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3196),X3195),X3193)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3196),X3194),X3192)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J])]) ).
fof(i_0_1409,plain,
! [X3226,X3227,X3228,X3229,X3230] :
( ~ class_Rings_Ocomm__semiring__1(X3230)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X3230),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X3230),X3229),X3228)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X3230),X3227),X3226)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X3230),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X3230),X3229),X3227)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X3230),X3228),X3226)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J])]) ).
fof(i_0_1410,plain,
! [X3202,X3203,X3204,X3205,X3206] :
( ~ class_Rings_Ocomm__semiring__1(X3206)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3206),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3206),X3205),X3204)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3206),X3203),X3202)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3206),X3205),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3206),X3204),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3206),X3203),X3202))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I14_J])]) ).
fof(i_0_1411,plain,
! [X4666,X4667,X4668] :
( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X4668),c_Divides_Odiv__class_Omod(tc_Int_Oint,X4667,X4666)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X4668),X4666))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X4668),X4667)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zdvd__zmod__imp__zdvd])]) ).
fof(i_0_1412,plain,
! [X3691,X3692,X3693] :
( ~ class_Rings_Ocomm__semiring__0(X3693)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X3693)),X3692),hAPP(hAPP(c_Polynomial_Osmult(X3693),X3691),c_Polynomial_Osynthetic__div(X3693,X3692,X3691))) = hAPP(hAPP(c_Polynomial_OpCons(X3693),hAPP(c_Polynomial_Opoly(X3693,X3692),X3691)),c_Polynomial_Osynthetic__div(X3693,X3692,X3691)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_synthetic__div__correct])]) ).
fof(i_0_1413,plain,
! [X5616,X5617,X5618] :
( ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,X5618)),X5617),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,X5618)),X5616))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X5617,X5616) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X5617,X5616)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,X5618)),X5617),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,X5618)),X5616)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Suc__mult__less__cancel1])]) ).
fof(i_0_1414,plain,
! [X4372,X4373,X4374] :
( ~ class_Rings_Oidom(X4374)
| hAPP(c_Polynomial_Ocoeff(X4374,X4373),c_Polynomial_Odegree(X4374,X4373)) != hAPP(c_Polynomial_Ocoeff(X4374,X4372),c_Polynomial_Odegree(X4374,X4372))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X4374)),X4373),X4372))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X4374)),X4372),X4373))
| X4373 = X4372 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_poly__dvd__antisym])]) ).
fof(i_0_1415,plain,
! [X5647,X5648,X5649] :
( ~ class_Rings_Oring__1(X5649)
| c_Transcendental_Odiffs(X5649,hAPP(hAPP(c_COMBB(X5649,X5649,tc_Nat_Onat),c_Groups_Ouminus__class_Ouminus(X5649)),X5648),X5647) = hAPP(c_Groups_Ouminus__class_Ouminus(X5649),c_Transcendental_Odiffs(X5649,X5648,X5647)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diffs__minus])]) ).
fof(i_0_1416,plain,
! [X5708,X5709,X5710,X5711] :
( ~ class_Fields_Olinordered__field(X5711)
| ~ c_Orderings_Oord__class_Oless(X5711,X5710,X5709)
| ~ c_Orderings_Oord__class_Oless(X5711,c_Groups_Ozero__class_Ozero(X5711),X5708)
| ~ c_Orderings_Oord__class_Oless(X5711,c_Groups_Ozero__class_Ozero(X5711),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5711),X5709),X5710))
| c_Orderings_Oord__class_Oless(X5711,hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X5711),X5708),X5709),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X5711),X5708),X5710)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divide__strict__left__mono])]) ).
fof(i_0_1417,plain,
! [X5712,X5713,X5714,X5715] :
( ~ class_Fields_Olinordered__field(X5715)
| ~ c_Orderings_Oord__class_Oless(X5715,X5714,X5713)
| ~ c_Orderings_Oord__class_Oless(X5715,X5712,c_Groups_Ozero__class_Ozero(X5715))
| ~ c_Orderings_Oord__class_Oless(X5715,c_Groups_Ozero__class_Ozero(X5715),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5715),X5714),X5713))
| c_Orderings_Oord__class_Oless(X5715,hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X5715),X5712),X5714),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X5715),X5712),X5713)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divide__strict__left__mono__neg])]) ).
fof(i_0_1418,plain,
! [X4672,X4673,X4674] : c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,X4674,X4673)),X4672),X4673) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X4674),X4672),X4673),
inference(variable_rename,[status(thm)],[fact_zdiff__zmod__left]) ).
fof(i_0_1419,plain,
! [X4697,X4698,X4699] : c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,X4699,X4698)),X4697),X4698) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X4699),X4697),X4698),
inference(variable_rename,[status(thm)],[fact_zpower__zmod]) ).
fof(i_0_1420,plain,
! [X5941,X5942,X5943,X5944] :
( ~ class_Divides_Osemiring__div(X5944)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X5944),X5943),X5942))
| hAPP(hAPP(c_Power_Opower__class_Opower(X5944),c_Divides_Odiv__class_Odiv(X5944,X5942,X5943)),X5941) = c_Divides_Odiv__class_Odiv(X5944,hAPP(hAPP(c_Power_Opower__class_Opower(X5944),X5942),X5941),hAPP(hAPP(c_Power_Opower__class_Opower(X5944),X5943),X5941)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_div__power])]) ).
fof(i_0_1421,plain,
! [X4417,X4418,X4419] :
( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X4419),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X4418),X4417)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X4419),X4417))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X4419),X4418)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zdvd__zdiffD])]) ).
fof(i_0_1422,plain,
! [X6031,X6032] :
( ( c_Divides_Odiv__class_Omod(tc_Int_Oint,X6031,X6032) != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| c_Divides_Odiv__class_Odiv(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X6031),X6032) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X6031,X6032))
| X6032 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
& ( c_Divides_Odiv__class_Omod(tc_Int_Oint,X6031,X6032) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| c_Divides_Odiv__class_Odiv(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X6031),X6032) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X6031,X6032))),c_Groups_Oone__class_Oone(tc_Int_Oint))
| X6032 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zdiv__zminus1__eq__if])])]) ).
fof(i_0_1423,plain,
! [X6029,X6030] :
( ( c_Divides_Odiv__class_Omod(tc_Int_Oint,X6029,X6030) != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| c_Divides_Odiv__class_Odiv(tc_Int_Oint,X6029,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X6030)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X6029,X6030))
| X6030 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
& ( c_Divides_Odiv__class_Omod(tc_Int_Oint,X6029,X6030) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| c_Divides_Odiv__class_Odiv(tc_Int_Oint,X6029,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X6030)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X6029,X6030))),c_Groups_Oone__class_Oone(tc_Int_Oint))
| X6030 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zdiv__zminus2__eq__if])])]) ).
fof(i_0_1424,plain,
! [X3885,X3886] :
( ~ class_Rings_Oring__1(X3886)
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(X3886),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3886),X3885),X3885)),c_Groups_Oone__class_Oone(X3886)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3886),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X3886),X3885),c_Groups_Oone__class_Oone(X3886))),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X3886),X3885),c_Groups_Oone__class_Oone(X3886))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_real__squared__diff__one__factored])]) ).
fof(i_0_1425,plain,
! [X4803,X4804,X4805,X4806,X4807,X4808] :
( ~ class_Divides_Oring__div(X4808)
| c_Divides_Odiv__class_Omod(X4808,X4807,X4806) != c_Divides_Odiv__class_Omod(X4808,X4805,X4806)
| c_Divides_Odiv__class_Omod(X4808,X4804,X4806) != c_Divides_Odiv__class_Omod(X4808,X4803,X4806)
| c_Divides_Odiv__class_Omod(X4808,hAPP(hAPP(c_Groups_Ominus__class_Ominus(X4808),X4807),X4804),X4806) = c_Divides_Odiv__class_Omod(X4808,hAPP(hAPP(c_Groups_Ominus__class_Ominus(X4808),X4805),X4803),X4806) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__diff__cong])]) ).
fof(i_0_1426,plain,
! [X4741,X4742,X4743,X4744,X4745,X4746] :
( ~ class_Divides_Osemiring__div(X4746)
| c_Divides_Odiv__class_Omod(X4746,X4745,X4744) != c_Divides_Odiv__class_Omod(X4746,X4743,X4744)
| c_Divides_Odiv__class_Omod(X4746,X4742,X4744) != c_Divides_Odiv__class_Omod(X4746,X4741,X4744)
| c_Divides_Odiv__class_Omod(X4746,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4746),X4745),X4742),X4744) = c_Divides_Odiv__class_Omod(X4746,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4746),X4743),X4741),X4744) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__mult__cong])]) ).
fof(i_0_1427,plain,
! [X4771,X4772,X4773,X4774,X4775,X4776] :
( ~ class_Divides_Osemiring__div(X4776)
| c_Divides_Odiv__class_Omod(X4776,X4775,X4774) != c_Divides_Odiv__class_Omod(X4776,X4773,X4774)
| c_Divides_Odiv__class_Omod(X4776,X4772,X4774) != c_Divides_Odiv__class_Omod(X4776,X4771,X4774)
| c_Divides_Odiv__class_Omod(X4776,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4776),X4775),X4772),X4774) = c_Divides_Odiv__class_Omod(X4776,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4776),X4773),X4771),X4774) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__add__cong])]) ).
fof(i_0_1428,plain,
! [X4832,X4833,X4834,X4835] :
( ~ class_Divides_Osemiring__div(X4835)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X4835),X4834),X4833))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X4835),X4834),X4832))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X4835),X4834),c_Divides_Odiv__class_Omod(X4835,X4833,X4832))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvd__mod])]) ).
fof(i_0_1429,plain,
! [X5772,X5773,X5774] :
( ~ class_Rings_Olinordered__semidom(X5774)
| ~ c_Orderings_Oord__class_Oless(X5774,c_Groups_Ozero__class_Ozero(X5774),X5773)
| ~ c_Orderings_Oord__class_Oless(X5774,X5773,c_Groups_Oone__class_Oone(X5774))
| c_Orderings_Oord__class_Oless(X5774,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5774),X5773),hAPP(hAPP(c_Power_Opower__class_Opower(X5774),X5773),X5772)),hAPP(hAPP(c_Power_Opower__class_Opower(X5774),X5773),X5772)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__Suc__less])]) ).
fof(i_0_1430,plain,
! [X4080,X4081,X4082] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,X4082)),X4081)),hAPP(c_Nat_OSuc,X4080)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X4082),X4081)),X4080),
inference(variable_rename,[status(thm)],[fact_Suc__diff__diff]) ).
fof(i_0_1431,plain,
! [X4303,X4304,X4305,X4306] :
( ~ class_Rings_Ocomm__ring__1(X4306)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X4306),X4305),X4304))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X4306),X4305),X4303))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X4306),X4305),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X4306),X4304),X4303))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvd__diff])]) ).
fof(i_0_1432,plain,
! [X4287,X4288,X4289,X4290] :
( ~ class_Rings_Ocomm__semiring__1(X4290)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X4290),X4289),X4288))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X4290),X4289),X4287))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X4290),X4289),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4290),X4288),X4287))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvd__add])]) ).
fof(i_0_1433,plain,
! [X5758,X5759,X5760,X5761,X5762,X5763,X5764] :
( ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X5759,X5758)
| hBOOL(hAPP(X5760,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ hBOOL(hAPP(X5760,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X5759),X5758))) )
& ( X5759 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X5758),X5761)
| hBOOL(hAPP(X5760,X5761))
| ~ hBOOL(hAPP(X5760,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X5759),X5758))) )
& ( X5763 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X5762),esk14_3(X5762,X5763,X5764))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X5763,X5762)
| hBOOL(hAPP(X5764,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X5763),X5762))) )
& ( ~ hBOOL(hAPP(X5764,esk14_3(X5762,X5763,X5764)))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X5763,X5762)
| hBOOL(hAPP(X5764,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X5763),X5762))) )
& ( X5763 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X5762),esk14_3(X5762,X5763,X5764))
| ~ hBOOL(hAPP(X5764,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| hBOOL(hAPP(X5764,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X5763),X5762))) )
& ( ~ hBOOL(hAPP(X5764,esk14_3(X5762,X5763,X5764)))
| ~ hBOOL(hAPP(X5764,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| hBOOL(hAPP(X5764,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X5763),X5762))) ) ),
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)],[fact_nat__diff__split])])])])])]) ).
fof(i_0_1434,plain,
! [X5750,X5751,X5752,X5753,X5754,X5755,X5756] :
( ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X5751,X5750)
| hBOOL(hAPP(X5752,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ hBOOL(hAPP(X5752,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X5751),X5750))) )
& ( X5751 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X5750),X5753)
| hBOOL(hAPP(X5752,X5753))
| ~ hBOOL(hAPP(X5752,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X5751),X5750))) )
& ( X5755 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X5754),esk13_3(X5754,X5755,X5756))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X5755,X5754)
| hBOOL(hAPP(X5756,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X5755),X5754))) )
& ( ~ hBOOL(hAPP(X5756,esk13_3(X5754,X5755,X5756)))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X5755,X5754)
| hBOOL(hAPP(X5756,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X5755),X5754))) )
& ( X5755 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X5754),esk13_3(X5754,X5755,X5756))
| ~ hBOOL(hAPP(X5756,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| hBOOL(hAPP(X5756,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X5755),X5754))) )
& ( ~ hBOOL(hAPP(X5756,esk13_3(X5754,X5755,X5756)))
| ~ hBOOL(hAPP(X5756,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| hBOOL(hAPP(X5756,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X5755),X5754))) ) ),
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)],[i_0_1187])])])])])]) ).
fof(i_0_1435,plain,
! [X3527,X3528,X3529,X3530,X3531] :
( ~ class_Rings_Ocomm__semiring__0(X3531)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X3531)),c_Polynomial_Omonom(X3531,X3530,X3529)),c_Polynomial_Omonom(X3531,X3528,X3527)) = c_Polynomial_Omonom(X3531,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3531),X3530),X3528),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3529),X3527)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__monom])]) ).
fof(i_0_1436,plain,
! [X3721,X3722,X3723,X3724] :
( ~ class_Rings_Ocomm__ring(X3724)
| hAPP(hAPP(c_Polynomial_Osmult(X3724),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X3724),X3723),X3722)),X3721) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X3724)),hAPP(hAPP(c_Polynomial_Osmult(X3724),X3723),X3721)),hAPP(hAPP(c_Polynomial_Osmult(X3724),X3722),X3721)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_smult__diff__left])]) ).
fof(i_0_1437,plain,
! [X3657,X3658,X3659,X3660] :
( ~ class_Rings_Ocomm__semiring__0(X3660)
| hAPP(hAPP(c_Polynomial_Osmult(X3660),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X3660),X3659),X3658)),X3657) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X3660)),hAPP(hAPP(c_Polynomial_Osmult(X3660),X3659),X3657)),hAPP(hAPP(c_Polynomial_Osmult(X3660),X3658),X3657)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_smult__add__left])]) ).
fof(i_0_1438,plain,
! [X5653,X5654,X5655,X5656] :
( ~ class_Groups_Oab__group__add(X5656)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(X5656,X5655),X5654)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(X5656,X5653),X5654)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(X5656,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X5656)),X5655),X5653)),X5654) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_degree__diff__less])]) ).
fof(i_0_1439,plain,
! [X5643,X5644,X5645,X5646] :
( ~ class_Groups_Ocomm__monoid__add(X5646)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(X5646,X5645),X5644)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(X5646,X5643),X5644)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(X5646,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X5646)),X5645),X5643)),X5644) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_degree__add__less])]) ).
fof(i_0_1440,plain,
! [X3673,X3674,X3675,X3676] :
( ~ class_Rings_Ocomm__semiring__0(X3676)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X3676)),hAPP(hAPP(c_Polynomial_Osmult(X3676),X3675),X3674)),hAPP(hAPP(c_Polynomial_OpCons(X3676),X3673),X3674)) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3676))
| X3674 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3676)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_offset__poly__eq__0__lemma])]) ).
fof(i_0_1441,plain,
! [X4471,X4472,X4473] :
( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X4473),X4471))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X4472),X4471))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X4471),X4472))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X4473),X4472))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X4472),X4473)) )
& ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X4471),X4473))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X4472),X4471))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X4471),X4472))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X4473),X4472))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X4472),X4473)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1188])])]) ).
fof(i_0_1442,plain,
! [X3717,X3718,X3719,X3720] :
( ~ class_Groups_Oab__group__add(X3720)
| hAPP(c_Polynomial_Ocoeff(X3720,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X3720)),X3719),X3718)),X3717) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(X3720),hAPP(c_Polynomial_Ocoeff(X3720,X3719),X3717)),hAPP(c_Polynomial_Ocoeff(X3720,X3718),X3717)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_coeff__diff])]) ).
fof(i_0_1443,plain,
! [X3653,X3654,X3655,X3656] :
( ~ class_Groups_Ocomm__monoid__add(X3656)
| hAPP(c_Polynomial_Ocoeff(X3656,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X3656)),X3655),X3654)),X3653) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X3656),hAPP(c_Polynomial_Ocoeff(X3656,X3655),X3653)),hAPP(c_Polynomial_Ocoeff(X3656,X3654),X3653)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_coeff__add])]) ).
fof(i_0_1444,plain,
! [X3752,X3753,X3754,X3755] :
( ~ class_Rings_Ocomm__ring(X3755)
| hAPP(c_Polynomial_Opoly(X3755,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X3755)),X3754),X3753)),X3752) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(X3755),hAPP(c_Polynomial_Opoly(X3755,X3754),X3752)),hAPP(c_Polynomial_Opoly(X3755,X3753),X3752)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_poly__diff])]) ).
fof(i_0_1445,plain,
! [X3320,X3321,X3322,X3323] :
( ~ class_Rings_Ocomm__semiring__0(X3323)
| hAPP(c_Polynomial_Opoly(X3323,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X3323)),X3322),X3321)),X3320) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3323),hAPP(c_Polynomial_Opoly(X3323,X3322),X3320)),hAPP(c_Polynomial_Opoly(X3323,X3321),X3320)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_poly__mult])]) ).
fof(i_0_1446,plain,
! [X3324,X3325,X3326,X3327] :
( ~ class_Rings_Ocomm__semiring__0(X3327)
| hAPP(c_Polynomial_Opoly(X3327,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X3327)),X3326),X3325)),X3324) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X3327),hAPP(c_Polynomial_Opoly(X3327,X3326),X3324)),hAPP(c_Polynomial_Opoly(X3327,X3325),X3324)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_poly__add])]) ).
fof(i_0_1447,plain,
! [X5884,X5885,X5886,X5887,X5888] :
( ( c_Divides_Odiv__class_Odiv(X5888,X5885,X5887) != c_Divides_Odiv__class_Odiv(X5888,X5884,X5886)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5888),X5885),X5886) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5888),X5887),X5884)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X5888),X5886),X5884))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X5888),X5887),X5885))
| X5886 = c_Groups_Ozero__class_Ozero(X5888)
| X5887 = c_Groups_Ozero__class_Ozero(X5888)
| ~ class_Divides_Osemiring__div(X5888) )
& ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5888),X5885),X5886) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5888),X5887),X5884)
| c_Divides_Odiv__class_Odiv(X5888,X5885,X5887) = c_Divides_Odiv__class_Odiv(X5888,X5884,X5886)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X5888),X5886),X5884))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X5888),X5887),X5885))
| X5886 = c_Groups_Ozero__class_Ozero(X5888)
| X5887 = c_Groups_Ozero__class_Ozero(X5888)
| ~ class_Divides_Osemiring__div(X5888) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvd__div__div__eq__mult])])]) ).
fof(i_0_1448,plain,
! [X4993,X4994,X4995,X4996] :
( ~ class_Fields_Ofield(X4996)
| X4995 = c_Groups_Ozero__class_Ozero(X4996)
| hAPP(hAPP(c_Power_Opower__class_Opower(X4996),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4996),X4994),X4995)),X4993) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4996),hAPP(hAPP(c_Power_Opower__class_Opower(X4996),X4994),X4993)),hAPP(hAPP(c_Power_Opower__class_Opower(X4996),X4995),X4993)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nonzero__power__divide])]) ).
fof(i_0_1449,plain,
! [X3274,X3275,X3276,X3277] :
( ~ class_Rings_Ocomm__semiring__1(X3277)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X3277),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3277),X3276),X3275)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3277),X3274),X3275)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3277),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X3277),X3276),X3274)),X3275) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J])]) ).
fof(i_0_1450,plain,
! [X4899,X4900,X4901,X4902] :
( ~ class_RealVector_Oreal__normed__field(X4902)
| hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4902),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X4902),X4901),X4900)),X4899) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(X4902),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4902),X4901),X4899)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4902),X4900),X4899)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divide_Odiff])]) ).
fof(i_0_1451,plain,
! [X4903,X4904,X4905,X4906] :
( ~ class_Rings_Odivision__ring(X4906)
| hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4906),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X4906),X4905),X4904)),X4903) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(X4906),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4906),X4905),X4903)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4906),X4904),X4903)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__divide__distrib])]) ).
fof(i_0_1452,plain,
! [X4891,X4892,X4893,X4894] :
( ~ class_RealVector_Oreal__normed__field(X4894)
| hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4894),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4894),X4893),X4892)),X4891) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4894),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4894),X4893),X4891)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4894),X4892),X4891)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divide_Oadd])]) ).
fof(i_0_1453,plain,
! [X4895,X4896,X4897,X4898] :
( ~ class_Rings_Odivision__ring(X4898)
| hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4898),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4898),X4897),X4896)),X4895) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4898),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4898),X4897),X4895)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4898),X4896),X4895)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__divide__distrib])]) ).
fof(i_0_1454,plain,
! [X4915,X4916,X4917,X4918] :
( ~ class_Fields_Ofield__inverse__zero(X4918)
| hAPP(hAPP(c_Power_Opower__class_Opower(X4918),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4918),X4917),X4916)),X4915) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4918),hAPP(hAPP(c_Power_Opower__class_Opower(X4918),X4917),X4915)),hAPP(hAPP(c_Power_Opower__class_Opower(X4918),X4916),X4915)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__divide])]) ).
fof(i_0_1455,plain,
! [X3302,X3303,X3304,X3305] :
( ~ class_Groups_Ocomm__monoid__mult(X3305)
| hAPP(hAPP(c_Power_Opower__class_Opower(X3305),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3305),X3304),X3303)),X3302) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3305),hAPP(hAPP(c_Power_Opower__class_Opower(X3305),X3304),X3302)),hAPP(hAPP(c_Power_Opower__class_Opower(X3305),X3303),X3302)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__mult__distrib])]) ).
fof(i_0_1456,plain,
! [X3298,X3299,X3300,X3301] :
( ~ class_Rings_Ocomm__semiring__1(X3301)
| hAPP(hAPP(c_Power_Opower__class_Opower(X3301),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3301),X3300),X3299)),X3298) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3301),hAPP(hAPP(c_Power_Opower__class_Opower(X3301),X3300),X3298)),hAPP(hAPP(c_Power_Opower__class_Opower(X3301),X3299),X3298)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I30_J])]) ).
fof(i_0_1457,plain,
! [X3779,X3780,X3781,X3782] :
( ~ class_RealVector_Oreal__normed__algebra(X3782)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3782),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X3782),X3781),X3780)),X3779) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(X3782),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3782),X3781),X3779)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3782),X3780),X3779)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult_Odiff__left])]) ).
fof(i_0_1458,plain,
! [X3775,X3776,X3777,X3778] :
( ~ class_RealVector_Oreal__normed__algebra(X3778)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3778),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X3778),X3777),X3776)),X3775) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(X3778),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3778),X3777),X3775)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3778),X3776),X3775)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__left_Odiff])]) ).
fof(i_0_1459,plain,
! [X3481,X3482,X3483,X3484] :
( ~ class_Rings_Ocomm__semiring(X3484)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3484),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X3484),X3483),X3482)),X3481) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X3484),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3484),X3483),X3481)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3484),X3482),X3481)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__class_Odistrib])]) ).
fof(i_0_1460,plain,
! [X3489,X3490,X3491,X3492] :
( ~ class_RealVector_Oreal__normed__algebra(X3492)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3492),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X3492),X3491),X3490)),X3489) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X3492),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3492),X3491),X3489)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3492),X3490),X3489)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__left_Oadd])]) ).
fof(i_0_1461,plain,
! [X3485,X3486,X3487,X3488] :
( ~ class_RealVector_Oreal__normed__algebra(X3488)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3488),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X3488),X3487),X3486)),X3485) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X3488),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3488),X3487),X3485)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3488),X3486),X3485)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult_Oadd__left])]) ).
fof(i_0_1462,plain,
! [X3278,X3279,X3280,X3281] :
( ~ class_Rings_Ocomm__semiring__1(X3281)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3281),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X3281),X3280),X3279)),X3278) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X3281),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3281),X3280),X3278)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3281),X3279),X3278)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J])]) ).
fof(i_0_1463,plain,
! [X4095,X4096] :
( ~ class_Groups_Oab__group__add(X4096)
| hAPP(c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X4096)),X4095) = c_Polynomial_OAbs__poly(X4096,hAPP(hAPP(c_COMBB(X4096,X4096,tc_Nat_Onat),c_Groups_Ouminus__class_Ouminus(X4096)),c_Polynomial_Ocoeff(X4096,X4095))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_uminus__poly__def])]) ).
fof(i_0_1464,plain,
! [X4329,X4330,X4331,X4332] :
( ~ class_Rings_Ocomm__semiring__1(X4332)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X4332)),X4331),X4330))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X4332)),X4331),hAPP(hAPP(c_Polynomial_Osmult(X4332),X4329),X4330))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvd__smult])]) ).
fof(i_0_1465,plain,
! [X5956,X5957] : c_Divides_Odiv__class_Omod(tc_Int_Oint,X5957,X5956) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X5957),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X5957,X5956)),X5956)),
inference(variable_rename,[status(thm)],[fact_zmod__zdiv__equality_H]) ).
fof(i_0_1466,plain,
! [X4663,X4664,X4665] :
( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X4665),X4664))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X4665),X4663))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X4665),c_Divides_Odiv__class_Omod(tc_Int_Oint,X4664,X4663))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zdvd__zmod])]) ).
fof(i_0_1467,plain,
! [X5919,X5920,X5921,X5922] :
( ~ class_Divides_Osemiring__div(X5922)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X5922),X5921),X5920))
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5922),c_Divides_Odiv__class_Odiv(X5922,X5920,X5921)),X5919) = c_Divides_Odiv__class_Odiv(X5922,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5922),X5920),X5919),X5921) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvd__div__mult])]) ).
fof(i_0_1468,plain,
! [X4085,X4086,X4087,X4088] :
( ~ class_Rings_Ocomm__ring(X4088)
| hAPP(hAPP(c_Polynomial_Osmult(X4088),X4087),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X4088)),X4086),X4085)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X4088)),hAPP(hAPP(c_Polynomial_Osmult(X4088),X4087),X4086)),hAPP(hAPP(c_Polynomial_Osmult(X4088),X4087),X4085)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_smult__diff__right])]) ).
fof(i_0_1469,plain,
! [X3608,X3609,X3610,X3611] :
( ~ class_Rings_Ocomm__semiring__0(X3611)
| hAPP(hAPP(c_Polynomial_Osmult(X3611),X3610),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X3611)),X3609),X3608)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X3611)),hAPP(hAPP(c_Polynomial_Osmult(X3611),X3610),X3609)),hAPP(hAPP(c_Polynomial_Osmult(X3611),X3610),X3608)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_smult__add__right])]) ).
fof(i_0_1470,plain,
! [X4236,X4237,X4238] :
( ~ class_Fields_Ofield(X4238)
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X4238)),c_Polynomial_Opoly__gcd(X4238,X4237,X4236)),X4237)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_poly__gcd__dvd1])]) ).
fof(i_0_1471,plain,
! [X4233,X4234,X4235] :
( ~ class_Fields_Ofield(X4235)
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X4235)),c_Polynomial_Opoly__gcd(X4235,X4234,X4233)),X4233)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_poly__gcd__dvd2])]) ).
fof(i_0_1472,plain,
! [X5845,X5846,X5847] :
( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X5847,X5846)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X5845)
| c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,X5845)),X5847),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,X5845)),X5846)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zmult__zless__mono2__lemma])]) ).
fof(i_0_1473,plain,
! [X6175,X6176,X6177,X6178,X6179,X6180] : hAPP(hAPP(hAPP(c_COMBS(X6180,X6179,X6178),X6177),X6176),X6175) = hAPP(hAPP(X6177,X6175),hAPP(X6176,X6175)),
inference(variable_rename,[status(thm)],[help_c__COMBS__1]) ).
fof(i_0_1474,plain,
! [X3348,X3349,X3350] :
( ( X3349 = c_Groups_Ozero__class_Ozero(X3350)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X3350),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3350),X3349),X3349)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3350),X3348),X3348)) != c_Groups_Ozero__class_Ozero(X3350)
| ~ class_Rings_Olinordered__ring__strict(X3350) )
& ( X3348 = c_Groups_Ozero__class_Ozero(X3350)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X3350),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3350),X3349),X3349)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3350),X3348),X3348)) != c_Groups_Ozero__class_Ozero(X3350)
| ~ class_Rings_Olinordered__ring__strict(X3350) )
& ( X3349 != c_Groups_Ozero__class_Ozero(X3350)
| X3348 != c_Groups_Ozero__class_Ozero(X3350)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X3350),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3350),X3349),X3349)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3350),X3348),X3348)) = c_Groups_Ozero__class_Ozero(X3350)
| ~ class_Rings_Olinordered__ring__strict(X3350) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sum__squares__eq__zero__iff])])]) ).
fof(i_0_1475,plain,
! [X4426,X4427,X4428] :
( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X4428),X4427))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X4428),X4426))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X4428),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X4427),X4426))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvd__diff__nat])]) ).
fof(i_0_1476,plain,
! [X3715,X3716] :
( ( X3716 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3716),X3715) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( X3716 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3716),X3715) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3715),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X3716),c_Groups_Oone__class_Oone(tc_Nat_Onat))),X3715)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__eq__if])]) ).
fof(i_0_1477,plain,
! [X5719,X5720,X5721] :
( ~ class_Rings_Olinordered__semidom(X5721)
| ~ c_Orderings_Oord__class_Oless(X5721,c_Groups_Oone__class_Oone(X5721),X5720)
| c_Orderings_Oord__class_Oless(X5721,hAPP(hAPP(c_Power_Opower__class_Opower(X5721),X5720),X5719),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5721),X5720),hAPP(hAPP(c_Power_Opower__class_Opower(X5721),X5720),X5719))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__less__power__Suc])]) ).
fof(i_0_1478,plain,
! [X5245,X5246,X5247,X5248] :
( ( ~ c_Orderings_Oord__class_Oless(X5248,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5248),X5247),X5246),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5248),X5247),X5245))
| c_Orderings_Oord__class_Oless(X5248,X5246,X5245)
| ~ c_Orderings_Oord__class_Oless(X5248,c_Groups_Ozero__class_Ozero(X5248),X5247)
| ~ class_Rings_Olinordered__ring__strict(X5248) )
& ( ~ c_Orderings_Oord__class_Oless(X5248,X5246,X5245)
| c_Orderings_Oord__class_Oless(X5248,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5248),X5247),X5246),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5248),X5247),X5245))
| ~ c_Orderings_Oord__class_Oless(X5248,c_Groups_Ozero__class_Ozero(X5248),X5247)
| ~ class_Rings_Olinordered__ring__strict(X5248) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__less__cancel__left__pos])])]) ).
fof(i_0_1479,plain,
! [X5226,X5227,X5228,X5229] :
( ( ~ c_Orderings_Oord__class_Oless(X5229,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5229),X5228),X5227),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5229),X5228),X5226))
| c_Orderings_Oord__class_Oless(X5229,X5226,X5227)
| ~ c_Orderings_Oord__class_Oless(X5229,X5228,c_Groups_Ozero__class_Ozero(X5229))
| ~ class_Rings_Olinordered__ring__strict(X5229) )
& ( ~ c_Orderings_Oord__class_Oless(X5229,X5226,X5227)
| c_Orderings_Oord__class_Oless(X5229,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5229),X5228),X5227),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5229),X5228),X5226))
| ~ c_Orderings_Oord__class_Oless(X5229,X5228,c_Groups_Ozero__class_Ozero(X5229))
| ~ class_Rings_Olinordered__ring__strict(X5229) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__less__cancel__left__neg])])]) ).
fof(i_0_1480,plain,
! [X5288,X5289,X5290,X5291] :
( ( ~ c_Orderings_Oord__class_Oless(X5291,hAPP(hAPP(c_Power_Opower__class_Opower(X5291),X5290),X5289),hAPP(hAPP(c_Power_Opower__class_Opower(X5291),X5290),X5288))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X5289,X5288)
| ~ c_Orderings_Oord__class_Oless(X5291,c_Groups_Oone__class_Oone(X5291),X5290)
| ~ class_Rings_Olinordered__semidom(X5291) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X5289,X5288)
| c_Orderings_Oord__class_Oless(X5291,hAPP(hAPP(c_Power_Opower__class_Opower(X5291),X5290),X5289),hAPP(hAPP(c_Power_Opower__class_Opower(X5291),X5290),X5288))
| ~ c_Orderings_Oord__class_Oless(X5291,c_Groups_Oone__class_Oone(X5291),X5290)
| ~ class_Rings_Olinordered__semidom(X5291) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__strict__increasing__iff])])]) ).
fof(i_0_1481,plain,
! [X5284,X5285,X5286,X5287] :
( ~ class_Rings_Olinordered__semidom(X5287)
| ~ c_Orderings_Oord__class_Oless(X5287,c_Groups_Oone__class_Oone(X5287),X5286)
| ~ c_Orderings_Oord__class_Oless(X5287,hAPP(hAPP(c_Power_Opower__class_Opower(X5287),X5286),X5285),hAPP(hAPP(c_Power_Opower__class_Opower(X5287),X5286),X5284))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X5285,X5284) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__less__imp__less__exp])]) ).
fof(i_0_1482,plain,
! [X3136,X3137,X3138,X3139] :
( ~ class_Rings_Ocomm__semiring__0(X3139)
| hAPP(c_Polynomial_Opoly(X3139,hAPP(hAPP(c_Polynomial_OpCons(X3139),X3138),X3137)),X3136) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X3139),X3138),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3139),X3136),hAPP(c_Polynomial_Opoly(X3139,X3137),X3136))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_poly__pCons])]) ).
fof(i_0_1483,plain,
! [X3761,X3762,X3763,X3764] :
( ~ class_Groups_Oab__group__add(X3764)
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X3764)),c_Polynomial_Omonom(X3764,X3763,X3762)),c_Polynomial_Omonom(X3764,X3761,X3762)) = c_Polynomial_Omonom(X3764,hAPP(hAPP(c_Groups_Ominus__class_Ominus(X3764),X3763),X3761),X3762) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__monom])]) ).
fof(i_0_1484,plain,
! [X3513,X3514,X3515,X3516] :
( ~ class_Groups_Ocomm__monoid__add(X3516)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X3516)),c_Polynomial_Omonom(X3516,X3515,X3514)),c_Polynomial_Omonom(X3516,X3513,X3514)) = c_Polynomial_Omonom(X3516,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X3516),X3515),X3513),X3514) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__monom])]) ).
fof(i_0_1485,plain,
! [X6163,X6164,X6165,X6166,X6167,X6168] : hAPP(hAPP(hAPP(c_COMBB(X6168,X6167,X6166),X6165),X6164),X6163) = hAPP(X6165,hAPP(X6164,X6163)),
inference(variable_rename,[status(thm)],[help_c__COMBB__1]) ).
fof(i_0_1486,plain,
! [X3330,X3331,X3332,X3333] :
( ~ class_Rings_Ocomm__semiring__1(X3333)
| hAPP(c_Polynomial_Opoly(X3333,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(X3333)),X3332),X3331)),X3330) = hAPP(hAPP(c_Power_Opower__class_Opower(X3333),hAPP(c_Polynomial_Opoly(X3333,X3332),X3330)),X3331) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_poly__power])]) ).
fof(i_0_1487,plain,
! [X4704,X4705,X4706] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4706),X4705)),X4704),X4705) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,X4704,X4705),
inference(variable_rename,[status(thm)],[fact_mod__mult__self3]) ).
fof(i_0_1488,plain,
! [X5149,X5150,X5151,X5152] :
( ~ class_Rings_Osemiring__1(X5152)
| c_Nat_Osemiring__1__class_Oof__nat__aux(X5152,X5151,hAPP(c_Nat_OSuc,X5150),X5149) = c_Nat_Osemiring__1__class_Oof__nat__aux(X5152,X5151,X5150,hAPP(X5151,X5149)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__nat__aux_Osimps_I2_J])]) ).
fof(i_0_1489,plain,
! [X3342,X3343,X3344] :
( ~ class_Rings_Ocomm__semiring__1(X3344)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X3344),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3344),X3343),X3342)),X3342) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3344),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X3344),X3343),c_Groups_Oone__class_Oone(X3344))),X3342) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I2_J])]) ).
fof(i_0_1490,plain,
! [X4061,X4062,X4063] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X4063),X4062)),X4061) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X4063),X4061)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X4062),X4061)),
inference(variable_rename,[status(thm)],[fact_zdiff__zmult__distrib]) ).
fof(i_0_1491,plain,
! [X3725,X3726,X3727] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X3727),X3726)),X3725) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X3727),X3725)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X3726),X3725)),
inference(variable_rename,[status(thm)],[fact_zadd__zmult__distrib]) ).
fof(i_0_1492,plain,
! [X3815,X3816,X3817] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X3817),X3816)),X3815) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3817),X3815)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3816),X3815)),
inference(variable_rename,[status(thm)],[fact_diff__mult__distrib]) ).
fof(i_0_1493,plain,
! [X3441,X3442,X3443] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3443),X3442)),X3441) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3443),X3441)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3442),X3441)),
inference(variable_rename,[status(thm)],[fact_add__mult__distrib]) ).
fof(i_0_1494,plain,
! [X5416,X5417,X5418,X5419] :
( ~ class_Rings_Olinordered__semidom(X5419)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X5418,X5417)
| ~ c_Orderings_Oord__class_Oless(X5419,c_Groups_Ozero__class_Ozero(X5419),X5416)
| ~ c_Orderings_Oord__class_Oless(X5419,X5416,c_Groups_Oone__class_Oone(X5419))
| c_Orderings_Oord__class_Oless(X5419,hAPP(hAPP(c_Power_Opower__class_Opower(X5419),X5416),X5417),hAPP(hAPP(c_Power_Opower__class_Opower(X5419),X5416),X5418)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__strict__decreasing])]) ).
fof(i_0_1495,plain,
! [X4494,X4495,X4496] :
( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X4496),X4494))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X4495),X4494))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X4494),X4495))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X4496),X4495)) )
& ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X4494),X4496))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X4495),X4494))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X4494),X4495))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X4496),X4495)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1189])])]) ).
fof(i_0_1496,plain,
! [X4476,X4477,X4478] :
( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X4478),X4476))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X4477),X4476))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X4478),X4477))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X4477),X4478)) )
& ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X4476),X4478))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X4477),X4476))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X4478),X4477))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X4477),X4478)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1190])])]) ).
fof(i_0_1497,plain,
! [X3900,X3901,X3902] :
( ( X3901 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3902))
| X3900 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3902))
| hAPP(c_Polynomial_Ocoeff(X3902,c_Polynomial_Opoly__gcd(X3902,X3901,X3900)),c_Polynomial_Odegree(X3902,c_Polynomial_Opoly__gcd(X3902,X3901,X3900))) = c_Groups_Ozero__class_Ozero(X3902)
| ~ class_Fields_Ofield(X3902) )
& ( X3901 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3902))
| hAPP(c_Polynomial_Ocoeff(X3902,c_Polynomial_Opoly__gcd(X3902,X3901,X3900)),c_Polynomial_Odegree(X3902,c_Polynomial_Opoly__gcd(X3902,X3901,X3900))) = c_Groups_Oone__class_Oone(X3902)
| ~ class_Fields_Ofield(X3902) )
& ( X3900 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3902))
| hAPP(c_Polynomial_Ocoeff(X3902,c_Polynomial_Opoly__gcd(X3902,X3901,X3900)),c_Polynomial_Odegree(X3902,c_Polynomial_Opoly__gcd(X3902,X3901,X3900))) = c_Groups_Oone__class_Oone(X3902)
| ~ class_Fields_Ofield(X3902) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_poly__gcd__monic])])]) ).
fof(i_0_1498,plain,
! [X4722,X4723,X4724] :
( ( c_Divides_Odiv__class_Omod(tc_Int_Oint,X4724,X4723) != c_Divides_Odiv__class_Omod(tc_Int_Oint,X4722,X4723)
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X4723),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X4724),X4722))) )
& ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X4723),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X4724),X4722)))
| c_Divides_Odiv__class_Omod(tc_Int_Oint,X4724,X4723) = c_Divides_Odiv__class_Omod(tc_Int_Oint,X4722,X4723) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zmod__eq__dvd__iff])]) ).
fof(i_0_1499,plain,
! [X4206,X4207] :
( ( X4207 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X4207),X4206) = X4206 )
& ( X4207 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X4207),X4206) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X4207),c_Groups_Oone__class_Oone(tc_Nat_Onat))),X4206)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__eq__if])]) ).
fof(i_0_1500,plain,
! [X5249,X5250,X5251,X5252] :
( ( c_Orderings_Oord__class_Oless(X5252,X5251,c_Groups_Ozero__class_Ozero(X5252))
| c_Orderings_Oord__class_Oless(X5252,c_Groups_Ozero__class_Ozero(X5252),X5251)
| ~ c_Orderings_Oord__class_Oless(X5252,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5252),X5251),X5250),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5252),X5251),X5249))
| ~ class_Rings_Olinordered__ring__strict(X5252) )
& ( c_Orderings_Oord__class_Oless(X5252,X5249,X5250)
| c_Orderings_Oord__class_Oless(X5252,c_Groups_Ozero__class_Ozero(X5252),X5251)
| ~ c_Orderings_Oord__class_Oless(X5252,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5252),X5251),X5250),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5252),X5251),X5249))
| ~ class_Rings_Olinordered__ring__strict(X5252) )
& ( c_Orderings_Oord__class_Oless(X5252,X5251,c_Groups_Ozero__class_Ozero(X5252))
| c_Orderings_Oord__class_Oless(X5252,X5250,X5249)
| ~ c_Orderings_Oord__class_Oless(X5252,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5252),X5251),X5250),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5252),X5251),X5249))
| ~ class_Rings_Olinordered__ring__strict(X5252) )
& ( c_Orderings_Oord__class_Oless(X5252,X5249,X5250)
| c_Orderings_Oord__class_Oless(X5252,X5250,X5249)
| ~ c_Orderings_Oord__class_Oless(X5252,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5252),X5251),X5250),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5252),X5251),X5249))
| ~ class_Rings_Olinordered__ring__strict(X5252) )
& ( ~ c_Orderings_Oord__class_Oless(X5252,c_Groups_Ozero__class_Ozero(X5252),X5251)
| ~ c_Orderings_Oord__class_Oless(X5252,X5250,X5249)
| c_Orderings_Oord__class_Oless(X5252,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5252),X5251),X5250),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5252),X5251),X5249))
| ~ class_Rings_Olinordered__ring__strict(X5252) )
& ( ~ c_Orderings_Oord__class_Oless(X5252,X5251,c_Groups_Ozero__class_Ozero(X5252))
| ~ c_Orderings_Oord__class_Oless(X5252,X5249,X5250)
| c_Orderings_Oord__class_Oless(X5252,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5252),X5251),X5250),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5252),X5251),X5249))
| ~ class_Rings_Olinordered__ring__strict(X5252) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__less__cancel__left__disj])])]) ).
fof(i_0_1501,plain,
! [X5253,X5254,X5255,X5256] :
( ( c_Orderings_Oord__class_Oless(X5256,X5254,c_Groups_Ozero__class_Ozero(X5256))
| c_Orderings_Oord__class_Oless(X5256,c_Groups_Ozero__class_Ozero(X5256),X5254)
| ~ c_Orderings_Oord__class_Oless(X5256,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5256),X5255),X5254),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5256),X5253),X5254))
| ~ class_Rings_Olinordered__ring__strict(X5256) )
& ( c_Orderings_Oord__class_Oless(X5256,X5253,X5255)
| c_Orderings_Oord__class_Oless(X5256,c_Groups_Ozero__class_Ozero(X5256),X5254)
| ~ c_Orderings_Oord__class_Oless(X5256,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5256),X5255),X5254),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5256),X5253),X5254))
| ~ class_Rings_Olinordered__ring__strict(X5256) )
& ( c_Orderings_Oord__class_Oless(X5256,X5254,c_Groups_Ozero__class_Ozero(X5256))
| c_Orderings_Oord__class_Oless(X5256,X5255,X5253)
| ~ c_Orderings_Oord__class_Oless(X5256,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5256),X5255),X5254),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5256),X5253),X5254))
| ~ class_Rings_Olinordered__ring__strict(X5256) )
& ( c_Orderings_Oord__class_Oless(X5256,X5253,X5255)
| c_Orderings_Oord__class_Oless(X5256,X5255,X5253)
| ~ c_Orderings_Oord__class_Oless(X5256,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5256),X5255),X5254),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5256),X5253),X5254))
| ~ class_Rings_Olinordered__ring__strict(X5256) )
& ( ~ c_Orderings_Oord__class_Oless(X5256,c_Groups_Ozero__class_Ozero(X5256),X5254)
| ~ c_Orderings_Oord__class_Oless(X5256,X5255,X5253)
| c_Orderings_Oord__class_Oless(X5256,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5256),X5255),X5254),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5256),X5253),X5254))
| ~ class_Rings_Olinordered__ring__strict(X5256) )
& ( ~ c_Orderings_Oord__class_Oless(X5256,X5254,c_Groups_Ozero__class_Ozero(X5256))
| ~ c_Orderings_Oord__class_Oless(X5256,X5253,X5255)
| c_Orderings_Oord__class_Oless(X5256,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5256),X5255),X5254),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5256),X5253),X5254))
| ~ class_Rings_Olinordered__ring__strict(X5256) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__less__cancel__right__disj])])]) ).
fof(i_0_1502,plain,
! [X4781,X4782,X4783,X4784] :
( ~ class_Divides_Osemiring__div(X4784)
| c_Divides_Odiv__class_Omod(X4784,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4784),X4783),c_Divides_Odiv__class_Omod(X4784,X4782,X4781)),X4781) = c_Divides_Odiv__class_Omod(X4784,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4784),X4783),X4782),X4781) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zmod__simps_I2_J])]) ).
fof(i_0_1503,plain,
! [X4817,X4818,X4819,X4820] :
( ~ class_Divides_Oring__div(X4820)
| c_Divides_Odiv__class_Omod(X4820,hAPP(hAPP(c_Groups_Ominus__class_Ominus(X4820),X4819),X4818),X4817) = c_Divides_Odiv__class_Omod(X4820,hAPP(hAPP(c_Groups_Ominus__class_Ominus(X4820),X4819),c_Divides_Odiv__class_Omod(X4820,X4818,X4817)),X4817) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__diff__right__eq])]) ).
fof(i_0_1504,plain,
! [X4767,X4768,X4769,X4770] :
( ~ class_Divides_Osemiring__div(X4770)
| c_Divides_Odiv__class_Omod(X4770,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4770),X4769),X4768),X4767) = c_Divides_Odiv__class_Omod(X4770,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4770),X4769),c_Divides_Odiv__class_Omod(X4770,X4768,X4767)),X4767) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__mult__right__eq])]) ).
fof(i_0_1505,plain,
! [X4793,X4794,X4795,X4796] :
( ~ class_Divides_Osemiring__div(X4796)
| c_Divides_Odiv__class_Omod(X4796,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4796),X4795),X4794),X4793) = c_Divides_Odiv__class_Omod(X4796,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4796),X4795),c_Divides_Odiv__class_Omod(X4796,X4794,X4793)),X4793) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__add__right__eq])]) ).
fof(i_0_1506,plain,
! [X5994,X5995,X5996,X5997] :
( ~ class_Divides_Osemiring__div(X5997)
| X5996 = c_Groups_Ozero__class_Ozero(X5997)
| c_Divides_Odiv__class_Odiv(X5997,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5997),X5995),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5997),X5996),X5994)),X5996) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5997),X5994),c_Divides_Odiv__class_Odiv(X5997,X5995,X5996)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_div__mult__self2])]) ).
fof(i_0_1507,plain,
! [X5990,X5991,X5992,X5993] :
( ~ class_Divides_Osemiring__div(X5993)
| X5992 = c_Groups_Ozero__class_Ozero(X5993)
| c_Divides_Odiv__class_Odiv(X5993,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5993),X5991),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5993),X5990),X5992)),X5992) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5993),X5990),c_Divides_Odiv__class_Odiv(X5993,X5991,X5992)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_div__mult__self1])]) ).
fof(i_0_1508,plain,
! [X4751,X4752,X4753,X4754] :
( ~ class_Divides_Osemiring__div(X4754)
| c_Divides_Odiv__class_Omod(X4754,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4754),X4753),X4752),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4754),X4751),X4752)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4754),c_Divides_Odiv__class_Omod(X4754,X4753,X4751)),X4752) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__mult__mult2])]) ).
fof(i_0_1509,plain,
! [X4424,X4425] :
( ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X4425),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X4424),X4425)))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X4425),X4424)) )
& ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X4425),X4424))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X4425),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X4424),X4425))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvd__reduce])]) ).
fof(i_0_1510,plain,
! [X4309,X4310,X4311] :
( ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X4311),hAPP(c_Groups_Ouminus__class_Ouminus(X4311),X4310)),X4309))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X4311),X4310),X4309))
| ~ class_Rings_Ocomm__ring__1(X4311) )
& ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X4311),X4310),X4309))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X4311),hAPP(c_Groups_Ouminus__class_Ouminus(X4311),X4310)),X4309))
| ~ class_Rings_Ocomm__ring__1(X4311) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_minus__dvd__iff])])]) ).
fof(i_0_1511,plain,
! [X3634,X3635,X3636,X3637] :
( ~ class_Rings_Ocomm__semiring__0(X3637)
| hAPP(hAPP(c_Polynomial_Osmult(X3637),X3636),hAPP(hAPP(c_Polynomial_OpCons(X3637),X3635),X3634)) = hAPP(hAPP(c_Polynomial_OpCons(X3637),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3637),X3636),X3635)),hAPP(hAPP(c_Polynomial_Osmult(X3637),X3636),X3634)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_smult__pCons])]) ).
fof(i_0_1512,plain,
! [X3787,X3788,X3789,X3790] :
( ~ class_RealVector_Oreal__normed__algebra(X3790)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3790),X3789),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X3790),X3788),X3787)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(X3790),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3790),X3789),X3788)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3790),X3789),X3787)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult_Odiff__right])]) ).
fof(i_0_1513,plain,
! [X3783,X3784,X3785,X3786] :
( ~ class_RealVector_Oreal__normed__algebra(X3786)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3786),X3785),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X3786),X3784),X3783)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(X3786),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3786),X3785),X3784)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3786),X3785),X3783)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__right_Odiff])]) ).
fof(i_0_1514,plain,
! [X3477,X3478,X3479,X3480] :
( ~ class_RealVector_Oreal__normed__algebra(X3480)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3480),X3479),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X3480),X3478),X3477)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X3480),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3480),X3479),X3478)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3480),X3479),X3477)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__right_Oadd])]) ).
fof(i_0_1515,plain,
! [X3473,X3474,X3475,X3476] :
( ~ class_RealVector_Oreal__normed__algebra(X3476)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3476),X3475),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X3476),X3474),X3473)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X3476),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3476),X3475),X3474)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3476),X3475),X3473)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult_Oadd__right])]) ).
fof(i_0_1516,plain,
! [X3287,X3288,X3289,X3290] :
( ~ class_Rings_Ocomm__semiring__1(X3290)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3290),X3289),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X3290),X3288),X3287)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X3290),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3290),X3289),X3288)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3290),X3289),X3287)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I34_J])]) ).
fof(i_0_1517,plain,
! [X3207,X3208,X3209,X3210] :
( ~ class_Rings_Ocomm__semiring__1(X3210)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3210),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3210),X3209),X3208)),X3207) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3210),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3210),X3209),X3207)),X3208) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J])]) ).
fof(i_0_1518,plain,
! [X3231,X3232,X3233,X3234] :
( ~ class_Rings_Ocomm__semiring__1(X3234)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X3234),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X3234),X3233),X3232)),X3231) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X3234),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X3234),X3233),X3231)),X3232) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J])]) ).
fof(i_0_1519,plain,
! [X5876,X5877] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X5877)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X5876)
| c_Divides_Odiv__class_Odiv(tc_Int_Oint,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X5876),X5877),X5876) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X5876),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X5877),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_int__power__div__base])]) ).
fof(i_0_1520,plain,
! [X5632,X5633,X5634] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X5634)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X5634),X5633),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X5634),X5632))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X5633,X5632) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__power__less__imp__less])]) ).
fof(i_0_1521,plain,
! [X5606,X5607,X5608] :
( ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X5608),X5607),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X5608),X5606))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X5607,X5606)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X5608) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X5607,X5606)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X5608),X5607),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X5608),X5606))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X5608) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__mult__less__cancel1])])]) ).
fof(i_0_1522,plain,
! [X3153,X3154,X3155,X3156] :
( ~ class_Rings_Ocomm__semiring__1(X3156)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3156),hAPP(hAPP(c_Power_Opower__class_Opower(X3156),X3155),X3154)),hAPP(hAPP(c_Power_Opower__class_Opower(X3156),X3155),X3153)) = hAPP(hAPP(c_Power_Opower__class_Opower(X3156),X3155),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3154),X3153)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I26_J])]) ).
fof(i_0_1523,plain,
! [X3149,X3150,X3151,X3152] :
( ~ class_Groups_Omonoid__mult(X3152)
| hAPP(hAPP(c_Power_Opower__class_Opower(X3152),X3151),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3150),X3149)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3152),hAPP(hAPP(c_Power_Opower__class_Opower(X3152),X3151),X3150)),hAPP(hAPP(c_Power_Opower__class_Opower(X3152),X3151),X3149)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__add])]) ).
fof(i_0_1524,plain,
! [X5688,X5689,X5690,X5691] :
( ( ~ c_Orderings_Oord__class_Oless(X5691,hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X5691),X5689),X5690),X5688)
| c_Orderings_Oord__class_Oless(X5691,X5689,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5691),X5688),X5690))
| ~ c_Orderings_Oord__class_Oless(X5691,c_Groups_Ozero__class_Ozero(X5691),X5690)
| ~ class_Fields_Olinordered__field(X5691) )
& ( ~ c_Orderings_Oord__class_Oless(X5691,X5689,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5691),X5688),X5690))
| c_Orderings_Oord__class_Oless(X5691,hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X5691),X5689),X5690),X5688)
| ~ c_Orderings_Oord__class_Oless(X5691,c_Groups_Ozero__class_Ozero(X5691),X5690)
| ~ class_Fields_Olinordered__field(X5691) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pos__divide__less__eq])])]) ).
fof(i_0_1525,plain,
! [X5692,X5693,X5694,X5695] :
( ~ class_Fields_Olinordered__field(X5695)
| ~ c_Orderings_Oord__class_Oless(X5695,c_Groups_Ozero__class_Ozero(X5695),X5694)
| ~ c_Orderings_Oord__class_Oless(X5695,X5693,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5695),X5692),X5694))
| c_Orderings_Oord__class_Oless(X5695,hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X5695),X5693),X5694),X5692) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__imp__div__pos__less])]) ).
fof(i_0_1526,plain,
! [X5684,X5685,X5686,X5687] :
( ( ~ c_Orderings_Oord__class_Oless(X5687,X5685,hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X5687),X5684),X5686))
| c_Orderings_Oord__class_Oless(X5687,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5687),X5685),X5686),X5684)
| ~ c_Orderings_Oord__class_Oless(X5687,c_Groups_Ozero__class_Ozero(X5687),X5686)
| ~ class_Fields_Olinordered__field(X5687) )
& ( ~ c_Orderings_Oord__class_Oless(X5687,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5687),X5685),X5686),X5684)
| c_Orderings_Oord__class_Oless(X5687,X5685,hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X5687),X5684),X5686))
| ~ c_Orderings_Oord__class_Oless(X5687,c_Groups_Ozero__class_Ozero(X5687),X5686)
| ~ class_Fields_Olinordered__field(X5687) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pos__less__divide__eq])])]) ).
fof(i_0_1527,plain,
! [X5704,X5705,X5706,X5707] :
( ( ~ c_Orderings_Oord__class_Oless(X5707,hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X5707),X5705),X5706),X5704)
| c_Orderings_Oord__class_Oless(X5707,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5707),X5704),X5706),X5705)
| ~ c_Orderings_Oord__class_Oless(X5707,X5706,c_Groups_Ozero__class_Ozero(X5707))
| ~ class_Fields_Olinordered__field(X5707) )
& ( ~ c_Orderings_Oord__class_Oless(X5707,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5707),X5704),X5706),X5705)
| c_Orderings_Oord__class_Oless(X5707,hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X5707),X5705),X5706),X5704)
| ~ c_Orderings_Oord__class_Oless(X5707,X5706,c_Groups_Ozero__class_Ozero(X5707))
| ~ class_Fields_Olinordered__field(X5707) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_neg__divide__less__eq])])]) ).
fof(i_0_1528,plain,
! [X5696,X5697,X5698,X5699] :
( ~ class_Fields_Olinordered__field(X5699)
| ~ c_Orderings_Oord__class_Oless(X5699,c_Groups_Ozero__class_Ozero(X5699),X5698)
| ~ c_Orderings_Oord__class_Oless(X5699,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5699),X5697),X5698),X5696)
| c_Orderings_Oord__class_Oless(X5699,X5697,hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X5699),X5696),X5698)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__imp__less__div__pos])]) ).
fof(i_0_1529,plain,
! [X5700,X5701,X5702,X5703] :
( ( ~ c_Orderings_Oord__class_Oless(X5703,X5701,hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X5703),X5700),X5702))
| c_Orderings_Oord__class_Oless(X5703,X5700,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5703),X5701),X5702))
| ~ c_Orderings_Oord__class_Oless(X5703,X5702,c_Groups_Ozero__class_Ozero(X5703))
| ~ class_Fields_Olinordered__field(X5703) )
& ( ~ c_Orderings_Oord__class_Oless(X5703,X5700,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5703),X5701),X5702))
| c_Orderings_Oord__class_Oless(X5703,X5701,hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X5703),X5700),X5702))
| ~ c_Orderings_Oord__class_Oless(X5703,X5702,c_Groups_Ozero__class_Ozero(X5703))
| ~ class_Fields_Olinordered__field(X5703) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_neg__less__divide__eq])])]) ).
fof(i_0_1530,plain,
! [X3336,X3337,X3338,X3339,X3340,X3341] :
( ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X3341)
| X3340 = c_Groups_Ozero__class_Ozero(X3341)
| X3339 != X3338
| X3337 = X3336
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X3341),X3339),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3341),X3340),X3337)) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(X3341),X3338),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3341),X3340),X3336)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__scale__eq__noteq])]) ).
fof(i_0_1531,plain,
! [X4669,X4670,X4671] : c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X4671),c_Divides_Odiv__class_Omod(tc_Int_Oint,X4670,X4669)),X4669) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X4671),X4670),X4669),
inference(variable_rename,[status(thm)],[fact_zdiff__zmod__right]) ).
fof(i_0_1532,plain,
! [X4686,X4687,X4688] : c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X4688),c_Divides_Odiv__class_Omod(tc_Int_Oint,X4687,X4686)),X4686) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X4688),X4687),X4686),
inference(variable_rename,[status(thm)],[fact_zmod__simps_I3_J]) ).
fof(i_0_1533,plain,
! [X4683,X4684,X4685] : c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X4685),X4684),X4683) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X4685),c_Divides_Odiv__class_Omod(tc_Int_Oint,X4684,X4683)),X4683),
inference(variable_rename,[status(thm)],[fact_zmod__zmult1__eq]) ).
fof(i_0_1534,plain,
! [X3616,X3617,X3618,X3619] :
( ~ class_Rings_Ocomm__semiring__0(X3619)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X3619)),hAPP(hAPP(c_Polynomial_Osmult(X3619),X3618),X3617)),X3616) = hAPP(hAPP(c_Polynomial_Osmult(X3619),X3618),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X3619)),X3617),X3616)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__smult__left])]) ).
fof(i_0_1535,plain,
! [X5912,X5913,X5914,X5915] :
( ~ class_Divides_Osemiring__div(X5915)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X5915),X5914),X5913))
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5915),X5912),c_Divides_Odiv__class_Odiv(X5915,X5913,X5914)) = c_Divides_Odiv__class_Odiv(X5915,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5915),X5912),X5913),X5914) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_div__mult__swap])]) ).
fof(i_0_1536,plain,
! [X4692,X4693,X4694] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X4694,X4693)),X4692) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4694),X4692),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4693),X4692)),
inference(variable_rename,[status(thm)],[fact_mod__mult__distrib]) ).
fof(i_0_1537,plain,
! [X4277,X4278,X4279,X4280] :
( ~ class_Rings_Ocomm__semiring__1(X4280)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X4280),X4279),X4278))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X4280),X4279),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4280),X4278),X4277))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvd__mult2])]) ).
fof(i_0_1538,plain,
! [X4273,X4274,X4275,X4276] :
( ~ class_Rings_Ocomm__semiring__1(X4276)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X4276),X4275),X4274))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X4276),X4275),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4276),X4273),X4274))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvd__mult])]) ).
fof(i_0_1539,plain,
! [X4998,X4999,X5000] :
( ~ class_Fields_Ofield__inverse__zero(X5000)
| hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X5000),c_Groups_Oone__class_Oone(X5000)),hAPP(hAPP(c_Power_Opower__class_Opower(X5000),X4999),X4998)) = hAPP(hAPP(c_Power_Opower__class_Opower(X5000),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X5000),c_Groups_Oone__class_Oone(X5000)),X4999)),X4998) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__one__over])]) ).
fof(i_0_1540,plain,
! [X3705,X3706,X3707,X3708] :
( ~ class_Rings_Ocomm__semiring__0(X3708)
| c_Polynomial_Osynthetic__div(X3708,hAPP(hAPP(c_Polynomial_OpCons(X3708),X3707),X3706),X3705) = hAPP(hAPP(c_Polynomial_OpCons(X3708),hAPP(c_Polynomial_Opoly(X3708,X3706),X3705)),c_Polynomial_Osynthetic__div(X3708,X3706,X3705)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_synthetic__div__pCons])]) ).
fof(i_0_1541,plain,
! [X3588,X3589,X3590,X3591] :
( ( X3589 != X3588
| hAPP(c_Polynomial_Ocoeff(X3590,X3589),X3591) = hAPP(c_Polynomial_Ocoeff(X3590,X3588),X3591)
| ~ class_Groups_Ozero(X3590) )
& ( hAPP(c_Polynomial_Ocoeff(X3590,X3589),esk4_3(X3588,X3589,X3590)) != hAPP(c_Polynomial_Ocoeff(X3590,X3588),esk4_3(X3588,X3589,X3590))
| X3589 = X3588
| ~ class_Groups_Ozero(X3590) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_expand__poly__eq])])])])]) ).
fof(i_0_1542,plain,
! [X5716,X5717,X5718] :
( ~ class_Rings_Olinordered__semidom(X5718)
| ~ c_Orderings_Oord__class_Oless(X5718,c_Groups_Oone__class_Oone(X5718),X5717)
| c_Orderings_Oord__class_Oless(X5718,c_Groups_Oone__class_Oone(X5718),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5718),X5717),hAPP(hAPP(c_Power_Opower__class_Opower(X5718),X5717),X5716))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__gt1__lemma])]) ).
fof(i_0_1543,plain,
! [X5317,X5318,X5319,X5320] :
( ( ~ c_Orderings_Oord__class_Oless(X5320,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5320),X5319),X5318),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5320),X5317),X5318))
| c_Orderings_Oord__class_Oless(X5320,X5319,X5317)
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X5320) )
& ( ~ c_Orderings_Oord__class_Oless(X5320,X5319,X5317)
| c_Orderings_Oord__class_Oless(X5320,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5320),X5319),X5318),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5320),X5317),X5318))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X5320) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__less__cancel__right])])]) ).
fof(i_0_1544,plain,
! [X5296,X5297,X5298,X5299] :
( ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X5299)
| ~ c_Orderings_Oord__class_Oless(X5299,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5299),X5298),X5297),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5299),X5296),X5297))
| c_Orderings_Oord__class_Oless(X5299,X5298,X5296) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__less__imp__less__right])]) ).
fof(i_0_1545,plain,
! [X5313,X5314,X5315,X5316] :
( ( ~ c_Orderings_Oord__class_Oless(X5316,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5316),X5315),X5314),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5316),X5315),X5313))
| c_Orderings_Oord__class_Oless(X5316,X5314,X5313)
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X5316) )
& ( ~ c_Orderings_Oord__class_Oless(X5316,X5314,X5313)
| c_Orderings_Oord__class_Oless(X5316,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5316),X5315),X5314),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5316),X5315),X5313))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X5316) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__less__cancel__left])])]) ).
fof(i_0_1546,plain,
! [X5292,X5293,X5294,X5295] :
( ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X5295)
| ~ c_Orderings_Oord__class_Oless(X5295,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5295),X5294),X5293),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5295),X5294),X5292))
| c_Orderings_Oord__class_Oless(X5295,X5293,X5292) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__less__imp__less__left])]) ).
fof(i_0_1547,plain,
! [X4192,X4193,X4194,X4195,X4196] :
( ~ class_Groups_Ominus(X4196)
| hAPP(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4195,X4196)),X4194),X4193),X4192) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(X4196),hAPP(X4194,X4192)),hAPP(X4193,X4192)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_minus__apply])]) ).
fof(i_0_1548,plain,
! [X3905,X3906,X3907,X3908,X3909] :
( ~ class_Groups_Ominus(X3909)
| hAPP(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X3908,X3909)),X3907),X3906),X3905) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(X3909),hAPP(X3907,X3905)),hAPP(X3906,X3905)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fun__diff__def])]) ).
fof(i_0_1549,plain,
! [X5171,X5172] :
( ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,X5172)),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,X5171)))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X5172),X5171)) )
& ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X5172),X5171))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,X5172)),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,X5171))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Nat__Transfer_Otransfer__int__nat__relations_I4_J])]) ).
fof(i_0_1550,plain,
! [X5026,X5027] :
( ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X5027),X5026))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,X5027)),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,X5026))) )
& ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,X5027)),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,X5026)))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X5027),X5026)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zdvd__int])]) ).
fof(i_0_1551,plain,
! [X3670,X3671,X3672] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X3672),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3671),X3670)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X3672),X3671)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X3672),X3670)),
inference(variable_rename,[status(thm)],[fact_zpower__zadd__distrib]) ).
fof(i_0_1552,plain,
! [X4058,X4059,X4060] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X4060),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X4059),X4058)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X4060),X4059)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X4060),X4058)),
inference(variable_rename,[status(thm)],[fact_zdiff__zmult__distrib2]) ).
fof(i_0_1553,plain,
! [X3731,X3732,X3733] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X3733),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X3732),X3731)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X3733),X3732)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X3733),X3731)),
inference(variable_rename,[status(thm)],[fact_zadd__zmult__distrib2]) ).
fof(i_0_1554,plain,
! [X3818,X3819,X3820] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3820),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X3819),X3818)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3820),X3819)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3820),X3818)),
inference(variable_rename,[status(thm)],[fact_diff__mult__distrib2]) ).
fof(i_0_1555,plain,
! [X3438,X3439,X3440] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3440),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3439),X3438)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3440),X3439)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3440),X3438)),
inference(variable_rename,[status(thm)],[fact_add__mult__distrib2]) ).
fof(i_0_1556,plain,
! [X3746,X3747,X3748] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X3748),X3747)),X3746) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X3748),X3746)),X3747),
inference(variable_rename,[status(thm)],[fact_diff__commute]) ).
fof(i_0_1557,plain,
! [X4243,X4244,X4245,X4246] :
( ~ class_Rings_Ocomm__semiring__1(X4246)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X4246),X4245),X4244))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X4246),X4244),X4243))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X4246),X4245),X4243)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvd__trans])]) ).
fof(i_0_1558,plain,
! [X3916,X3917,X3918] :
( ( hAPP(hAPP(c_Power_Opower__class_Opower(X3918),X3917),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) != hAPP(hAPP(c_Power_Opower__class_Opower(X3918),X3916),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))
| X3917 = X3916
| X3917 = hAPP(c_Groups_Ouminus__class_Ouminus(X3918),X3916)
| ~ class_Rings_Oidom(X3918) )
& ( X3917 != X3916
| hAPP(hAPP(c_Power_Opower__class_Opower(X3918),X3917),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = hAPP(hAPP(c_Power_Opower__class_Opower(X3918),X3916),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))
| ~ class_Rings_Oidom(X3918) )
& ( X3917 != hAPP(c_Groups_Ouminus__class_Ouminus(X3918),X3916)
| hAPP(hAPP(c_Power_Opower__class_Opower(X3918),X3917),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = hAPP(hAPP(c_Power_Opower__class_Opower(X3918),X3916),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))
| ~ class_Rings_Oidom(X3918) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_realpow__two__disj])])]) ).
fof(i_0_1559,plain,
! [X5527,X5528,X5529,X5530] :
( ~ class_Fields_Olinordered__field(X5530)
| ~ c_Orderings_Oord__class_Oless(X5530,X5529,X5528)
| ~ c_Orderings_Oord__class_Oless(X5530,c_Groups_Ozero__class_Ozero(X5530),X5527)
| c_Orderings_Oord__class_Oless(X5530,hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X5530),X5529),X5527),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X5530),X5528),X5527)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divide__strict__right__mono])]) ).
fof(i_0_1560,plain,
! [X5216,X5217,X5218,X5219] :
( ~ class_Rings_Olinordered__semiring__strict(X5219)
| ~ c_Orderings_Oord__class_Oless(X5219,X5218,X5217)
| ~ c_Orderings_Oord__class_Oless(X5219,c_Groups_Ozero__class_Ozero(X5219),X5216)
| c_Orderings_Oord__class_Oless(X5219,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5219),X5218),X5216),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5219),X5217),X5216)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__strict__right__mono])]) ).
fof(i_0_1561,plain,
! [X5212,X5213,X5214,X5215] :
( ~ class_Rings_Olinordered__semiring__strict(X5215)
| ~ c_Orderings_Oord__class_Oless(X5215,X5214,X5213)
| ~ c_Orderings_Oord__class_Oless(X5215,c_Groups_Ozero__class_Ozero(X5215),X5212)
| c_Orderings_Oord__class_Oless(X5215,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5215),X5212),X5214),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5215),X5212),X5213)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__strict__left__mono])]) ).
fof(i_0_1562,plain,
! [X5208,X5209,X5210,X5211] :
( ~ class_Rings_Olinordered__comm__semiring__strict(X5211)
| ~ c_Orderings_Oord__class_Oless(X5211,X5210,X5209)
| ~ c_Orderings_Oord__class_Oless(X5211,c_Groups_Ozero__class_Ozero(X5211),X5208)
| c_Orderings_Oord__class_Oless(X5211,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5211),X5208),X5210),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5211),X5208),X5209)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__mult__strict__left__mono])]) ).
fof(i_0_1563,plain,
! [X5531,X5532,X5533,X5534] :
( ~ class_Fields_Olinordered__field(X5534)
| ~ c_Orderings_Oord__class_Oless(X5534,X5533,X5532)
| ~ c_Orderings_Oord__class_Oless(X5534,X5531,c_Groups_Ozero__class_Ozero(X5534))
| c_Orderings_Oord__class_Oless(X5534,hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X5534),X5532),X5531),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X5534),X5533),X5531)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divide__strict__right__mono__neg])]) ).
fof(i_0_1564,plain,
! [X5204,X5205,X5206,X5207] :
( ~ class_Rings_Olinordered__ring__strict(X5207)
| ~ c_Orderings_Oord__class_Oless(X5207,X5206,X5205)
| ~ c_Orderings_Oord__class_Oless(X5207,X5204,c_Groups_Ozero__class_Ozero(X5207))
| c_Orderings_Oord__class_Oless(X5207,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5207),X5205),X5204),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5207),X5206),X5204)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__strict__right__mono__neg])]) ).
fof(i_0_1565,plain,
! [X5200,X5201,X5202,X5203] :
( ~ class_Rings_Olinordered__ring__strict(X5203)
| ~ c_Orderings_Oord__class_Oless(X5203,X5202,X5201)
| ~ c_Orderings_Oord__class_Oless(X5203,X5200,c_Groups_Ozero__class_Ozero(X5203))
| c_Orderings_Oord__class_Oless(X5203,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5203),X5200),X5201),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5203),X5200),X5202)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__strict__left__mono__neg])]) ).
fof(i_0_1566,plain,
! [X5280,X5281,X5282,X5283] :
( ~ class_Rings_Olinordered__semidom(X5283)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X5282,X5281)
| ~ c_Orderings_Oord__class_Oless(X5283,c_Groups_Oone__class_Oone(X5283),X5280)
| c_Orderings_Oord__class_Oless(X5283,hAPP(hAPP(c_Power_Opower__class_Opower(X5283),X5280),X5282),hAPP(hAPP(c_Power_Opower__class_Opower(X5283),X5280),X5281)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__strict__increasing])]) ).
fof(i_0_1567,plain,
! [X4420,X4421] :
( ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X4421),X4420))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X4421)),X4420)) )
& ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X4421)),X4420))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X4421),X4420)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_uminus__dvd__conv_I1_J])]) ).
fof(i_0_1568,plain,
! [X3345,X3346,X3347] :
( ~ class_Rings_Ocomm__semiring__1(X3347)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X3347),X3346),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3347),X3345),X3346)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3347),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X3347),X3345),c_Groups_Oone__class_Oone(X3347))),X3346) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I3_J])]) ).
fof(i_0_1569,plain,
! [X5916,X5917,X5918] :
( ~ class_Divides_Osemiring__div(X5918)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X5918),X5917),X5916))
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5918),c_Divides_Odiv__class_Odiv(X5918,X5916,X5917)),X5917) = X5916 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvd__div__mult__self])]) ).
fof(i_0_1570,plain,
! [X5984,X5985,X5986] :
( ~ class_Divides_Osemiring__div(X5986)
| X5985 = c_Groups_Ozero__class_Ozero(X5986)
| c_Divides_Odiv__class_Odiv(X5986,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5986),X5985),X5984),X5985) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5986),c_Divides_Odiv__class_Odiv(X5986,X5984,X5985)),c_Groups_Oone__class_Oone(X5986)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_div__add__self1])]) ).
fof(i_0_1571,plain,
! [X5987,X5988,X5989] :
( ~ class_Divides_Osemiring__div(X5989)
| X5988 = c_Groups_Ozero__class_Ozero(X5989)
| c_Divides_Odiv__class_Odiv(X5989,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5989),X5987),X5988),X5988) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5989),c_Divides_Odiv__class_Odiv(X5989,X5987,X5988)),c_Groups_Oone__class_Oone(X5989)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_div__add__self2])]) ).
fof(i_0_1572,plain,
! [X5300,X5301,X5302,X5303,X5304] :
( ~ class_Groups_Oordered__cancel__ab__semigroup__add(X5304)
| ~ c_Orderings_Oord__class_Oless(X5304,X5303,X5302)
| ~ c_Orderings_Oord__class_Oless(X5304,X5301,X5300)
| c_Orderings_Oord__class_Oless(X5304,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5304),X5303),X5301),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5304),X5302),X5300)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__strict__mono])]) ).
fof(i_0_1573,plain,
! [X5769,X5770,X5771] :
( ~ class_Fields_Ofield(X5771)
| X5770 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X5771))
| c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(X5771),X5769,X5770) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X5771))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(X5771,c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(X5771),X5769,X5770)),c_Polynomial_Odegree(X5771,X5770)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_degree__mod__less])]) ).
fof(i_0_1574,plain,
! [X5739,X5740] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X5740)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X5739)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X5739),X5740)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_one__less__mult])]) ).
fof(i_0_1575,plain,
! [X3694,X3695,X3696,X3697,X3698] :
( ( X3694 = hAPP(c_Polynomial_Opoly(X3698,X3697),X3696)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X3698)),X3697),hAPP(hAPP(c_Polynomial_Osmult(X3698),X3696),X3695)) != hAPP(hAPP(c_Polynomial_OpCons(X3698),X3694),X3695)
| ~ class_Rings_Ocomm__semiring__0(X3698) )
& ( X3695 = c_Polynomial_Osynthetic__div(X3698,X3697,X3696)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X3698)),X3697),hAPP(hAPP(c_Polynomial_Osmult(X3698),X3696),X3695)) != hAPP(hAPP(c_Polynomial_OpCons(X3698),X3694),X3695)
| ~ class_Rings_Ocomm__semiring__0(X3698) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_synthetic__div__unique])])]) ).
fof(i_0_1576,plain,
! [X4755,X4756,X4757,X4758] :
( ~ class_Divides_Osemiring__div(X4758)
| c_Divides_Odiv__class_Omod(X4758,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4758),X4757),X4756),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4758),X4757),X4755)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4758),X4757),c_Divides_Odiv__class_Omod(X4758,X4756,X4755)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__mult__mult1])]) ).
fof(i_0_1577,plain,
! [X4949,X4950,X4951,X4952] :
( ~ class_Fields_Ofield__inverse__zero(X4952)
| X4951 = c_Groups_Ozero__class_Ozero(X4952)
| hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4952),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4952),X4951),X4950)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4952),X4951),X4949)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4952),X4950),X4949) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__divide__mult__cancel__left])]) ).
fof(i_0_1578,plain,
! [X4945,X4946,X4947,X4948] :
( ~ class_Fields_Ofield__inverse__zero(X4948)
| X4947 = c_Groups_Ozero__class_Ozero(X4948)
| hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4948),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4948),X4946),X4947)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4948),X4945),X4947)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4948),X4946),X4945) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__divide__mult__cancel__right])]) ).
fof(i_0_1579,plain,
! [X5601,X5602,X5603] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X5603)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X5603),X5602),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X5603),X5601)) )
& ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X5602,X5601)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X5603),X5602),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X5603),X5601)) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X5603)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X5602,X5601)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X5603),X5602),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X5603),X5601)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__less__cancel1])])]) ).
fof(i_0_1580,plain,
! [X5598,X5599,X5600] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X5599)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X5600),X5599),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X5598),X5599)) )
& ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X5600,X5598)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X5600),X5599),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X5598),X5599)) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X5599)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X5600,X5598)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X5600),X5599),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X5598),X5599)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__less__cancel2])])]) ).
fof(i_0_1581,plain,
! [X4659,X4660,X4661,X4662] :
( ~ class_Divides_Osemiring__div(X4662)
| c_Divides_Odiv__class_Omod(X4662,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4662),X4661),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4662),X4660),X4659)),X4660) = c_Divides_Odiv__class_Omod(X4662,X4661,X4660) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__mult__self2])]) ).
fof(i_0_1582,plain,
! [X4655,X4656,X4657,X4658] :
( ~ class_Divides_Osemiring__div(X4658)
| c_Divides_Odiv__class_Omod(X4658,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4658),X4657),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4658),X4656),X4655)),X4655) = c_Divides_Odiv__class_Omod(X4658,X4657,X4655) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__mult__self1])]) ).
fof(i_0_1583,plain,
! [X5230,X5231,X5232] :
( ~ class_Rings_Olinordered__semiring__strict(X5232)
| ~ c_Orderings_Oord__class_Oless(X5232,c_Groups_Ozero__class_Ozero(X5232),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5232),X5231),X5230))
| ~ c_Orderings_Oord__class_Oless(X5232,c_Groups_Ozero__class_Ozero(X5232),X5230)
| c_Orderings_Oord__class_Oless(X5232,c_Groups_Ozero__class_Ozero(X5232),X5231) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__less__mult__pos2])]) ).
fof(i_0_1584,plain,
! [X5233,X5234,X5235] :
( ~ class_Rings_Olinordered__semiring__strict(X5235)
| ~ c_Orderings_Oord__class_Oless(X5235,c_Groups_Ozero__class_Ozero(X5235),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5235),X5234),X5233))
| ~ c_Orderings_Oord__class_Oless(X5235,c_Groups_Ozero__class_Ozero(X5235),X5234)
| c_Orderings_Oord__class_Oless(X5235,c_Groups_Ozero__class_Ozero(X5235),X5233) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__less__mult__pos])]) ).
fof(i_0_1585,plain,
! [X5383,X5384,X5385] :
( ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X5385),X5384),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X5385),X5383))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X5384,X5383) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X5384,X5383)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X5385),X5384),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X5385),X5383)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__add__left__cancel__less])]) ).
fof(i_0_1586,plain,
! [X3306,X3307,X3308] :
( ~ class_Groups_Omonoid__mult(X3308)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3308),hAPP(hAPP(c_Power_Opower__class_Opower(X3308),X3307),X3306)),X3307) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3308),X3307),hAPP(hAPP(c_Power_Opower__class_Opower(X3308),X3307),X3306)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__commutes])]) ).
fof(i_0_1587,plain,
! [X3384,X3385,X3386,X3387] :
( ~ class_Groups_Oab__semigroup__mult(X3387)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3387),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3387),X3386),X3385)),X3384) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3387),X3386),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3387),X3385),X3384)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ab__semigroup__mult__class_Omult__ac_I1_J])]) ).
fof(i_0_1588,plain,
! [X3211,X3212,X3213,X3214] :
( ~ class_Rings_Ocomm__semiring__1(X3214)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3214),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3214),X3213),X3212)),X3211) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3214),X3213),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3214),X3212),X3211)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J])]) ).
fof(i_0_1589,plain,
! [X3388,X3389,X3390,X3391] :
( ~ class_Groups_Oab__semigroup__add(X3391)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X3391),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X3391),X3390),X3389)),X3388) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X3391),X3390),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X3391),X3389),X3388)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ab__semigroup__add__class_Oadd__ac_I1_J])]) ).
fof(i_0_1590,plain,
! [X3235,X3236,X3237,X3238] :
( ~ class_Rings_Ocomm__semiring__1(X3238)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X3238),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X3238),X3237),X3236)),X3235) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X3238),X3237),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X3238),X3236),X3235)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J])]) ).
fof(i_0_1591,plain,
! [X3600,X3601,X3602,X3603] :
( ~ class_Rings_Ocomm__semiring__0(X3603)
| hAPP(hAPP(c_Polynomial_Osmult(X3603),X3602),hAPP(hAPP(c_Polynomial_Osmult(X3603),X3601),X3600)) = hAPP(hAPP(c_Polynomial_Osmult(X3603),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3603),X3602),X3601)),X3600) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_smult__smult])]) ).
fof(i_0_1592,plain,
! [X4887,X4888,X4889,X4890] :
( ~ class_Rings_Odivision__ring(X4890)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4890),X4889),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4890),X4888),X4887)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4890),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4890),X4889),X4888)),X4887) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_times__divide__eq__right])]) ).
fof(i_0_1593,plain,
! [X3215,X3216,X3217,X3218] :
( ~ class_Rings_Ocomm__semiring__1(X3218)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3218),X3217),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3218),X3216),X3215)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3218),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3218),X3217),X3216)),X3215) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J])]) ).
fof(i_0_1594,plain,
! [X3239,X3240,X3241,X3242] :
( ~ class_Rings_Ocomm__semiring__1(X3242)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X3242),X3241),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X3242),X3240),X3239)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X3242),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X3242),X3241),X3240)),X3239) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J])]) ).
fof(i_0_1595,plain,
! [X3521,X3522,X3523,X3524] :
( ~ class_Rings_Ocomm__semiring__1(X3524)
| hAPP(c_Polynomial_Opoly(X3524,c_Polynomial_Omonom(X3524,X3523,X3522)),X3521) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3524),X3523),hAPP(hAPP(c_Power_Opower__class_Opower(X3524),X3521),X3522)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_poly__monom])]) ).
fof(i_0_1596,plain,
! [X3882,X3883,X3884] :
( ( X3883 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Power_Opower__class_Opower(X3884),X3882),X3883) = c_Groups_Oone__class_Oone(X3884)
| ~ class_Power_Opower(X3884) )
& ( X3883 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Power_Opower__class_Opower(X3884),X3882),X3883) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3884),X3882),hAPP(hAPP(c_Power_Opower__class_Opower(X3884),X3882),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X3883),c_Groups_Oone__class_Oone(tc_Nat_Onat))))
| ~ class_Power_Opower(X3884) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_realpow__num__eq__if])])]) ).
fof(i_0_1597,plain,
! [X5775,X5776,X5777] :
( ~ class_Rings_Olinordered__semidom(X5777)
| ~ c_Orderings_Oord__class_Oless(X5777,c_Groups_Ozero__class_Ozero(X5777),X5776)
| ~ c_Orderings_Oord__class_Oless(X5777,X5776,c_Groups_Oone__class_Oone(X5777))
| c_Orderings_Oord__class_Oless(X5777,hAPP(hAPP(c_Power_Opower__class_Opower(X5777),X5776),hAPP(c_Nat_OSuc,X5775)),c_Groups_Oone__class_Oone(X5777)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__Suc__less__one])]) ).
fof(i_0_1598,plain,
! [X5778,X5779,X5780] :
( ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X5779)
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X5780),X5778),hAPP(hAPP(c_Power_Opower__class_Opower(X5780),X5778),X5779)))
| ~ class_Rings_Ocomm__semiring__1(X5780) )
& ( X5778 != c_Groups_Oone__class_Oone(X5780)
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X5780),X5778),hAPP(hAPP(c_Power_Opower__class_Opower(X5780),X5778),X5779)))
| ~ class_Rings_Ocomm__semiring__1(X5780) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvd__power])])]) ).
fof(i_0_1599,plain,
! [X3170,X3171,X3172,X3173] :
( ~ class_Groups_Omonoid__mult(X3173)
| hAPP(hAPP(c_Power_Opower__class_Opower(X3173),X3172),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3171),X3170)) = hAPP(hAPP(c_Power_Opower__class_Opower(X3173),hAPP(hAPP(c_Power_Opower__class_Opower(X3173),X3172),X3171)),X3170) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__mult])]) ).
fof(i_0_1600,plain,
! [X3166,X3167,X3168,X3169] :
( ~ class_Rings_Ocomm__semiring__1(X3169)
| hAPP(hAPP(c_Power_Opower__class_Opower(X3169),hAPP(hAPP(c_Power_Opower__class_Opower(X3169),X3168),X3167)),X3166) = hAPP(hAPP(c_Power_Opower__class_Opower(X3169),X3168),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3167),X3166)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I31_J])]) ).
fof(i_0_1601,plain,
! [X4821,X4822,X4823] :
( ~ class_Divides_Oring__div(X4823)
| c_Divides_Odiv__class_Omod(X4823,hAPP(c_Groups_Ouminus__class_Ouminus(X4823),X4822),X4821) = c_Divides_Odiv__class_Omod(X4823,hAPP(c_Groups_Ouminus__class_Ouminus(X4823),c_Divides_Odiv__class_Omod(X4823,X4822,X4821)),X4821) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__minus__eq])]) ).
fof(i_0_1602,plain,
! [X5815,X5816,X5817] :
( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X5817,X5816)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X5815)
| c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X5815),X5817),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X5815),X5816)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zmult__zless__mono2])]) ).
fof(i_0_1603,plain,
! [X5595,X5596,X5597] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X5597,X5596)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X5595)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X5597),X5595),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X5596),X5595)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__less__mono1])]) ).
fof(i_0_1604,plain,
! [X5592,X5593,X5594] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X5594,X5593)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X5592)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X5592),X5594),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X5592),X5593)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__less__mono2])]) ).
fof(i_0_1605,plain,
! [X3683,X3684,X3685,X3686] :
( ~ class_Rings_Ocomm__semiring__0(X3686)
| hAPP(c_Polynomial_Opoly(X3686,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X3686,X3685,X3684)),X3683) = hAPP(c_Polynomial_Opoly(X3686,X3685),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X3686),X3684),X3683)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_poly__offset__poly])]) ).
fof(i_0_1606,plain,
! [X5737,X5738] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X5738)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X5737)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X5738,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X5738),X5737)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_n__less__n__mult__m])]) ).
fof(i_0_1607,plain,
! [X5735,X5736] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X5736)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X5735)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X5736,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X5735),X5736)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_n__less__m__mult__n])]) ).
fof(i_0_1608,plain,
! [X4312,X4313,X4314] :
( ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X4314),X4313),hAPP(c_Groups_Ouminus__class_Ouminus(X4314),X4312)))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X4314),X4313),X4312))
| ~ class_Rings_Ocomm__ring__1(X4314) )
& ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X4314),X4313),X4312))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X4314),X4313),hAPP(c_Groups_Ouminus__class_Ouminus(X4314),X4312)))
| ~ class_Rings_Ocomm__ring__1(X4314) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvd__minus__iff])])]) ).
fof(i_0_1609,plain,
! [X5357,X5358,X5359] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X5359,X5358)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X5359,X5357)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X5357),X5358),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X5357),X5359)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__less__mono2])]) ).
fof(i_0_1610,plain,
! [X5370,X5371,X5372,X5373] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X5373,X5372)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X5371,X5370)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X5373),X5371),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X5372),X5370)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__less__mono])]) ).
fof(i_0_1611,plain,
! [X3978] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X3978)),X3978) != c_Groups_Ozero__class_Ozero(tc_Int_Oint),
inference(variable_rename,[status(thm)],[fact_odd__nonzero]) ).
fof(i_0_1612,plain,
! [X6002,X6003] :
( ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X6002,X6003),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X6002)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X6003,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X6002)
| c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X6002,X6003),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X6003,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_neg__imp__zdiv__neg__iff])])]) ).
fof(i_0_1613,plain,
! [X6004,X6005] :
( ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X6004,X6005),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| c_Orderings_Oord__class_Oless(tc_Int_Oint,X6004,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X6005) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X6004,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X6004,X6005),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X6005) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pos__imp__zdiv__neg__iff])])]) ).
fof(i_0_1614,plain,
! [X5938,X5939,X5940] :
( ~ class_Divides_Oring__div(X5940)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X5940),X5939),X5938))
| c_Divides_Odiv__class_Odiv(X5940,hAPP(c_Groups_Ouminus__class_Ouminus(X5940),X5938),X5939) = hAPP(c_Groups_Ouminus__class_Ouminus(X5940),c_Divides_Odiv__class_Odiv(X5940,X5938,X5939)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvd__neg__div])]) ).
fof(i_0_1615,plain,
! [X5935,X5936,X5937] :
( ~ class_Divides_Oring__div(X5937)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X5937),X5936),X5935))
| c_Divides_Odiv__class_Odiv(X5937,X5935,hAPP(c_Groups_Ouminus__class_Ouminus(X5937),X5936)) = hAPP(c_Groups_Ouminus__class_Ouminus(X5937),c_Divides_Odiv__class_Odiv(X5937,X5935,X5936)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvd__div__neg])]) ).
fof(i_0_1616,plain,
! [X4730,X4731] :
( ( c_Divides_Odiv__class_Omod(tc_Int_Oint,X4731,X4730) != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| c_Divides_Odiv__class_Omod(tc_Int_Oint,X4731,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X4730)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
& ( c_Divides_Odiv__class_Omod(tc_Int_Oint,X4731,X4730) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| c_Divides_Odiv__class_Omod(tc_Int_Oint,X4731,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X4730)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,X4731,X4730)),X4730) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zmod__zminus2__eq__if])]) ).
fof(i_0_1617,plain,
! [X4500,X4501,X4502] :
( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X4502),X4501))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X4501),X4500))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X4502),X4500)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvd_Oorder__trans])]) ).
fof(i_0_1618,plain,
! [X4836,X4837,X4838,X4839] :
( ~ class_Divides_Osemiring__div(X4839)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X4839),X4838),X4837))
| c_Divides_Odiv__class_Omod(X4839,c_Divides_Odiv__class_Omod(X4839,X4836,X4837),X4838) = c_Divides_Odiv__class_Omod(X4839,X4836,X4838) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__mod__cancel])]) ).
fof(i_0_1619,plain,
! [X3612,X3613,X3614,X3615] :
( ~ class_Rings_Ocomm__semiring__0(X3615)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X3615)),X3614),hAPP(hAPP(c_Polynomial_Osmult(X3615),X3613),X3612)) = hAPP(hAPP(c_Polynomial_Osmult(X3615),X3613),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X3615)),X3614),X3612)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__smult__right])]) ).
fof(i_0_1620,plain,
! [X3164,X3165] :
( ~ class_Rings_Ocomm__semiring__1(X3165)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X3165),X3164),X3164) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3165),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X3165),c_Groups_Oone__class_Oone(X3165)),c_Groups_Oone__class_Oone(X3165))),X3164) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J])]) ).
fof(i_0_1621,plain,
! [X6006,X6007,X6008] :
( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X6008)
| c_Divides_Odiv__class_Odiv(tc_Int_Oint,X6007,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X6006),X6008)) = c_Divides_Odiv__class_Odiv(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X6007,X6006),X6008) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zdiv__zmult2__eq])]) ).
fof(i_0_1622,plain,
! [X5512,X5513,X5514] :
( ( c_Orderings_Oord__class_Oless(X5514,X5513,c_Groups_Ozero__class_Ozero(X5514))
| c_Orderings_Oord__class_Oless(X5514,c_Groups_Ozero__class_Ozero(X5514),X5513)
| ~ c_Orderings_Oord__class_Oless(X5514,hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X5514),X5513),X5512),c_Groups_Ozero__class_Ozero(X5514))
| ~ class_Fields_Olinordered__field__inverse__zero(X5514) )
& ( c_Orderings_Oord__class_Oless(X5514,c_Groups_Ozero__class_Ozero(X5514),X5512)
| c_Orderings_Oord__class_Oless(X5514,c_Groups_Ozero__class_Ozero(X5514),X5513)
| ~ c_Orderings_Oord__class_Oless(X5514,hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X5514),X5513),X5512),c_Groups_Ozero__class_Ozero(X5514))
| ~ class_Fields_Olinordered__field__inverse__zero(X5514) )
& ( c_Orderings_Oord__class_Oless(X5514,X5513,c_Groups_Ozero__class_Ozero(X5514))
| c_Orderings_Oord__class_Oless(X5514,X5512,c_Groups_Ozero__class_Ozero(X5514))
| ~ c_Orderings_Oord__class_Oless(X5514,hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X5514),X5513),X5512),c_Groups_Ozero__class_Ozero(X5514))
| ~ class_Fields_Olinordered__field__inverse__zero(X5514) )
& ( c_Orderings_Oord__class_Oless(X5514,c_Groups_Ozero__class_Ozero(X5514),X5512)
| c_Orderings_Oord__class_Oless(X5514,X5512,c_Groups_Ozero__class_Ozero(X5514))
| ~ c_Orderings_Oord__class_Oless(X5514,hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X5514),X5513),X5512),c_Groups_Ozero__class_Ozero(X5514))
| ~ class_Fields_Olinordered__field__inverse__zero(X5514) )
& ( ~ c_Orderings_Oord__class_Oless(X5514,c_Groups_Ozero__class_Ozero(X5514),X5513)
| ~ c_Orderings_Oord__class_Oless(X5514,X5512,c_Groups_Ozero__class_Ozero(X5514))
| c_Orderings_Oord__class_Oless(X5514,hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X5514),X5513),X5512),c_Groups_Ozero__class_Ozero(X5514))
| ~ class_Fields_Olinordered__field__inverse__zero(X5514) )
& ( ~ c_Orderings_Oord__class_Oless(X5514,X5513,c_Groups_Ozero__class_Ozero(X5514))
| ~ c_Orderings_Oord__class_Oless(X5514,c_Groups_Ozero__class_Ozero(X5514),X5512)
| c_Orderings_Oord__class_Oless(X5514,hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X5514),X5513),X5512),c_Groups_Ozero__class_Ozero(X5514))
| ~ class_Fields_Olinordered__field__inverse__zero(X5514) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divide__less__0__iff])])]) ).
fof(i_0_1623,plain,
! [X5509,X5510,X5511] :
( ( c_Orderings_Oord__class_Oless(X5511,X5510,c_Groups_Ozero__class_Ozero(X5511))
| c_Orderings_Oord__class_Oless(X5511,c_Groups_Ozero__class_Ozero(X5511),X5510)
| ~ c_Orderings_Oord__class_Oless(X5511,c_Groups_Ozero__class_Ozero(X5511),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X5511),X5510),X5509))
| ~ class_Fields_Olinordered__field__inverse__zero(X5511) )
& ( c_Orderings_Oord__class_Oless(X5511,X5509,c_Groups_Ozero__class_Ozero(X5511))
| c_Orderings_Oord__class_Oless(X5511,c_Groups_Ozero__class_Ozero(X5511),X5510)
| ~ c_Orderings_Oord__class_Oless(X5511,c_Groups_Ozero__class_Ozero(X5511),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X5511),X5510),X5509))
| ~ class_Fields_Olinordered__field__inverse__zero(X5511) )
& ( c_Orderings_Oord__class_Oless(X5511,X5510,c_Groups_Ozero__class_Ozero(X5511))
| c_Orderings_Oord__class_Oless(X5511,c_Groups_Ozero__class_Ozero(X5511),X5509)
| ~ c_Orderings_Oord__class_Oless(X5511,c_Groups_Ozero__class_Ozero(X5511),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X5511),X5510),X5509))
| ~ class_Fields_Olinordered__field__inverse__zero(X5511) )
& ( c_Orderings_Oord__class_Oless(X5511,X5509,c_Groups_Ozero__class_Ozero(X5511))
| c_Orderings_Oord__class_Oless(X5511,c_Groups_Ozero__class_Ozero(X5511),X5509)
| ~ c_Orderings_Oord__class_Oless(X5511,c_Groups_Ozero__class_Ozero(X5511),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X5511),X5510),X5509))
| ~ class_Fields_Olinordered__field__inverse__zero(X5511) )
& ( ~ c_Orderings_Oord__class_Oless(X5511,c_Groups_Ozero__class_Ozero(X5511),X5510)
| ~ c_Orderings_Oord__class_Oless(X5511,c_Groups_Ozero__class_Ozero(X5511),X5509)
| c_Orderings_Oord__class_Oless(X5511,c_Groups_Ozero__class_Ozero(X5511),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X5511),X5510),X5509))
| ~ class_Fields_Olinordered__field__inverse__zero(X5511) )
& ( ~ c_Orderings_Oord__class_Oless(X5511,X5510,c_Groups_Ozero__class_Ozero(X5511))
| ~ c_Orderings_Oord__class_Oless(X5511,X5509,c_Groups_Ozero__class_Ozero(X5511))
| c_Orderings_Oord__class_Oless(X5511,c_Groups_Ozero__class_Ozero(X5511),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X5511),X5510),X5509))
| ~ class_Fields_Olinordered__field__inverse__zero(X5511) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__less__divide__iff])])]) ).
fof(i_0_1624,plain,
! [X4689,X4690,X4691] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4691),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X4690,X4689)) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4691),X4690),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4691),X4689)),
inference(variable_rename,[status(thm)],[fact_mod__mult__distrib2]) ).
fof(i_0_1625,plain,
! [X3596,X3597,X3598,X3599] :
( ~ class_Rings_Ocomm__semiring__0(X3599)
| hAPP(c_Polynomial_Ocoeff(X3599,hAPP(hAPP(c_Polynomial_Osmult(X3599),X3598),X3597)),X3596) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3599),X3598),hAPP(c_Polynomial_Ocoeff(X3599,X3597),X3596)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_coeff__smult])]) ).
fof(i_0_1626,plain,
! [X3641,X3642,X3643,X3644] :
( ~ class_Rings_Ocomm__semiring__0(X3644)
| hAPP(c_Polynomial_Opoly(X3644,hAPP(hAPP(c_Polynomial_Osmult(X3644),X3643),X3642)),X3641) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3644),X3643),hAPP(c_Polynomial_Opoly(X3644,X3642),X3641)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_poly__smult])]) ).
fof(i_0_1627,plain,
! [X3517,X3518,X3519,X3520] :
( ~ class_Rings_Ocomm__semiring__0(X3520)
| hAPP(c_Polynomial_Opoly(X3520,c_Polynomial_Opcompose(X3520,X3519,X3518)),X3517) = hAPP(c_Polynomial_Opoly(X3520,X3519),hAPP(c_Polynomial_Opoly(X3520,X3518),X3517)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_poly__pcompose])]) ).
fof(i_0_1628,plain,
! [X3873,X3874] :
( ( X3874 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X3873),X3874) = c_Groups_Oone__class_Oone(tc_Nat_Onat) )
& ( X3874 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X3873),X3874) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3873),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X3873),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X3874),c_Groups_Oone__class_Oone(tc_Nat_Onat)))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__eq__if])]) ).
fof(i_0_1629,plain,
! [X4675,X4676] : c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,X4676,X4675)),X4675) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X4676),X4675),
inference(variable_rename,[status(thm)],[fact_zminus__zmod]) ).
fof(i_0_1630,plain,
! [X5623,X5624,X5625] :
( ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X5625,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X5624),X5623))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X5625),X5623),X5624) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X5625),X5623),X5624)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X5625,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X5624),X5623)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__diff__conv])]) ).
fof(i_0_1631,plain,
! [X5559,X5560,X5561] :
( ~ class_Fields_Olinordered__field(X5561)
| ~ c_Orderings_Oord__class_Oless(X5561,hAPP(c_Rings_Oinverse__class_Oinverse(X5561),X5560),hAPP(c_Rings_Oinverse__class_Oinverse(X5561),X5559))
| ~ c_Orderings_Oord__class_Oless(X5561,c_Groups_Ozero__class_Ozero(X5561),X5560)
| c_Orderings_Oord__class_Oless(X5561,X5559,X5560) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inverse__less__imp__less])]) ).
fof(i_0_1632,plain,
! [X5562,X5563,X5564] :
( ~ class_Fields_Olinordered__field(X5564)
| ~ c_Orderings_Oord__class_Oless(X5564,hAPP(c_Rings_Oinverse__class_Oinverse(X5564),X5563),hAPP(c_Rings_Oinverse__class_Oinverse(X5564),X5562))
| ~ c_Orderings_Oord__class_Oless(X5564,X5562,c_Groups_Ozero__class_Ozero(X5564))
| c_Orderings_Oord__class_Oless(X5564,X5562,X5563) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inverse__less__imp__less__neg])]) ).
fof(i_0_1633,plain,
! [X4824,X4825,X4826,X4827] :
( ~ class_Divides_Oring__div(X4827)
| c_Divides_Odiv__class_Omod(X4827,X4826,X4825) != c_Divides_Odiv__class_Omod(X4827,X4824,X4825)
| c_Divides_Odiv__class_Omod(X4827,hAPP(c_Groups_Ouminus__class_Ouminus(X4827),X4826),X4825) = c_Divides_Odiv__class_Omod(X4827,hAPP(c_Groups_Ouminus__class_Ouminus(X4827),X4824),X4825) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__minus__cong])]) ).
fof(i_0_1634,plain,
! [X3805,X3806,X3807] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3807),X3806)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3807),X3805)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X3806),X3805),
inference(variable_rename,[status(thm)],[fact_diff__cancel]) ).
fof(i_0_1635,plain,
! [X3802,X3803,X3804] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3804),X3803)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3802),X3803)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X3804),X3802),
inference(variable_rename,[status(thm)],[fact_diff__cancel2]) ).
fof(i_0_1636,plain,
! [X3808,X3809,X3810] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X3810),X3809)),X3808) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X3810),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3809),X3808)),
inference(variable_rename,[status(thm)],[fact_diff__diff__left]) ).
fof(i_0_1637,plain,
! [X3677,X3678,X3679] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X3679),X3678)),X3677) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X3679),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3678),X3677)),
inference(variable_rename,[status(thm)],[fact_zpower__zpower]) ).
fof(i_0_1638,plain,
! [X3728,X3729,X3730] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X3730),X3729)),X3728) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X3730),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X3729),X3728)),
inference(variable_rename,[status(thm)],[fact_zmult__assoc]) ).
fof(i_0_1639,plain,
! [X3371,X3372,X3373] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3373),X3372)),X3371) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3373),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3372),X3371)),
inference(variable_rename,[status(thm)],[fact_nat__mult__assoc]) ).
fof(i_0_1640,plain,
! [X3989,X3990,X3991] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X3991),X3990)),X3989) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X3991),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X3990),X3989)),
inference(variable_rename,[status(thm)],[fact_zadd__assoc]) ).
fof(i_0_1641,plain,
! [X3429,X3430,X3431] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3431),X3430)),X3429) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3431),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3430),X3429)),
inference(variable_rename,[status(thm)],[fact_nat__add__assoc]) ).
fof(i_0_1642,plain,
! [X5521,X5522,X5523] :
( ~ class_Fields_Olinordered__field(X5523)
| ~ c_Orderings_Oord__class_Oless(X5523,X5522,c_Groups_Ozero__class_Ozero(X5523))
| ~ c_Orderings_Oord__class_Oless(X5523,c_Groups_Ozero__class_Ozero(X5523),X5521)
| c_Orderings_Oord__class_Oless(X5523,hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X5523),X5522),X5521),c_Groups_Ozero__class_Ozero(X5523)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divide__neg__pos])]) ).
fof(i_0_1643,plain,
! [X5518,X5519,X5520] :
( ~ class_Fields_Olinordered__field(X5520)
| ~ c_Orderings_Oord__class_Oless(X5520,c_Groups_Ozero__class_Ozero(X5520),X5519)
| ~ c_Orderings_Oord__class_Oless(X5520,X5518,c_Groups_Ozero__class_Ozero(X5520))
| c_Orderings_Oord__class_Oless(X5520,hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X5520),X5519),X5518),c_Groups_Ozero__class_Ozero(X5520)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divide__pos__neg])]) ).
fof(i_0_1644,plain,
! [X5223,X5224,X5225] :
( ~ class_Rings_Olinordered__semiring__strict(X5225)
| ~ c_Orderings_Oord__class_Oless(X5225,X5224,c_Groups_Ozero__class_Ozero(X5225))
| ~ c_Orderings_Oord__class_Oless(X5225,c_Groups_Ozero__class_Ozero(X5225),X5223)
| c_Orderings_Oord__class_Oless(X5225,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5225),X5224),X5223),c_Groups_Ozero__class_Ozero(X5225)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__neg__pos])]) ).
fof(i_0_1645,plain,
! [X5239,X5240,X5241] :
( ~ class_Rings_Olinordered__semiring__strict(X5241)
| ~ c_Orderings_Oord__class_Oless(X5241,c_Groups_Ozero__class_Ozero(X5241),X5240)
| ~ c_Orderings_Oord__class_Oless(X5241,X5239,c_Groups_Ozero__class_Ozero(X5241))
| c_Orderings_Oord__class_Oless(X5241,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5241),X5240),X5239),c_Groups_Ozero__class_Ozero(X5241)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__pos__neg])]) ).
fof(i_0_1646,plain,
! [X5236,X5237,X5238] :
( ~ class_Rings_Olinordered__semiring__strict(X5238)
| ~ c_Orderings_Oord__class_Oless(X5238,c_Groups_Ozero__class_Ozero(X5238),X5237)
| ~ c_Orderings_Oord__class_Oless(X5238,X5236,c_Groups_Ozero__class_Ozero(X5238))
| c_Orderings_Oord__class_Oless(X5238,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5238),X5236),X5237),c_Groups_Ozero__class_Ozero(X5238)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__pos__neg2])]) ).
fof(i_0_1647,plain,
! [X5263,X5264,X5265] :
( ~ class_Groups_Oordered__comm__monoid__add(X5265)
| ~ c_Orderings_Oord__class_Oless(X5265,X5264,c_Groups_Ozero__class_Ozero(X5265))
| ~ c_Orderings_Oord__class_Oless(X5265,X5263,c_Groups_Ozero__class_Ozero(X5265))
| c_Orderings_Oord__class_Oless(X5265,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5265),X5264),X5263),c_Groups_Ozero__class_Ozero(X5265)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__neg__neg])]) ).
fof(i_0_1648,plain,
! [X5501,X5502,X5503] :
( ~ class_Rings_Olinordered__semidom(X5503)
| ~ c_Orderings_Oord__class_Oless(X5503,c_Groups_Oone__class_Oone(X5503),X5502)
| ~ c_Orderings_Oord__class_Oless(X5503,c_Groups_Oone__class_Oone(X5503),X5501)
| c_Orderings_Oord__class_Oless(X5503,c_Groups_Oone__class_Oone(X5503),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5503),X5502),X5501)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__1__mult])]) ).
fof(i_0_1649,plain,
! [X5515,X5516,X5517] :
( ~ class_Fields_Olinordered__field(X5517)
| ~ c_Orderings_Oord__class_Oless(X5517,c_Groups_Ozero__class_Ozero(X5517),X5516)
| ~ c_Orderings_Oord__class_Oless(X5517,c_Groups_Ozero__class_Ozero(X5517),X5515)
| c_Orderings_Oord__class_Oless(X5517,c_Groups_Ozero__class_Ozero(X5517),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X5517),X5516),X5515)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divide__pos__pos])]) ).
fof(i_0_1650,plain,
! [X5242,X5243,X5244] :
( ~ class_Rings_Olinordered__semiring__strict(X5244)
| ~ c_Orderings_Oord__class_Oless(X5244,c_Groups_Ozero__class_Ozero(X5244),X5243)
| ~ c_Orderings_Oord__class_Oless(X5244,c_Groups_Ozero__class_Ozero(X5244),X5242)
| c_Orderings_Oord__class_Oless(X5244,c_Groups_Ozero__class_Ozero(X5244),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5244),X5243),X5242)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__pos__pos])]) ).
fof(i_0_1651,plain,
! [X5266,X5267,X5268] :
( ~ class_Groups_Oordered__comm__monoid__add(X5268)
| ~ c_Orderings_Oord__class_Oless(X5268,c_Groups_Ozero__class_Ozero(X5268),X5267)
| ~ c_Orderings_Oord__class_Oless(X5268,c_Groups_Ozero__class_Ozero(X5268),X5266)
| c_Orderings_Oord__class_Oless(X5268,c_Groups_Ozero__class_Ozero(X5268),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5268),X5267),X5266)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__pos__pos])]) ).
fof(i_0_1652,plain,
! [X5524,X5525,X5526] :
( ~ class_Fields_Olinordered__field(X5526)
| ~ c_Orderings_Oord__class_Oless(X5526,X5525,c_Groups_Ozero__class_Ozero(X5526))
| ~ c_Orderings_Oord__class_Oless(X5526,X5524,c_Groups_Ozero__class_Ozero(X5526))
| c_Orderings_Oord__class_Oless(X5526,c_Groups_Ozero__class_Ozero(X5526),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X5526),X5525),X5524)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divide__neg__neg])]) ).
fof(i_0_1653,plain,
! [X5220,X5221,X5222] :
( ~ class_Rings_Olinordered__ring__strict(X5222)
| ~ c_Orderings_Oord__class_Oless(X5222,X5221,c_Groups_Ozero__class_Ozero(X5222))
| ~ c_Orderings_Oord__class_Oless(X5222,X5220,c_Groups_Ozero__class_Ozero(X5222))
| c_Orderings_Oord__class_Oless(X5222,c_Groups_Ozero__class_Ozero(X5222),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5222),X5221),X5220)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__neg__neg])]) ).
fof(i_0_1654,plain,
! [X4695,X4696] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,X4696),X4695) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X4696,X4695)),X4695),
inference(variable_rename,[status(thm)],[fact_mod__Suc__eq__Suc__mod]) ).
fof(i_0_1655,plain,
! [X5413,X5414,X5415] :
( ~ class_Rings_Olinordered__semidom(X5415)
| ~ c_Orderings_Oord__class_Oless(X5415,c_Groups_Oone__class_Oone(X5415),X5414)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X5413)
| c_Orderings_Oord__class_Oless(X5415,c_Groups_Oone__class_Oone(X5415),hAPP(hAPP(c_Power_Opower__class_Opower(X5415),X5414),X5413)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_one__less__power])]) ).
fof(i_0_1656,plain,
! [X5309,X5310,X5311,X5312] :
( ~ class_Groups_Oordered__cancel__ab__semigroup__add(X5312)
| ~ c_Orderings_Oord__class_Oless(X5312,X5311,X5310)
| c_Orderings_Oord__class_Oless(X5312,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5312),X5311),X5309),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5312),X5310),X5309)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__strict__right__mono])]) ).
fof(i_0_1657,plain,
! [X5305,X5306,X5307,X5308] :
( ~ class_Groups_Oordered__cancel__ab__semigroup__add(X5308)
| ~ c_Orderings_Oord__class_Oless(X5308,X5307,X5306)
| c_Orderings_Oord__class_Oless(X5308,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5308),X5305),X5307),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5308),X5305),X5306)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__strict__left__mono])]) ).
fof(i_0_1658,plain,
! [X5640,X5641,X5642] :
( ~ class_Groups_Ocomm__monoid__add(X5642)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(X5642,X5641),c_Polynomial_Odegree(X5642,X5640))
| c_Polynomial_Odegree(X5642,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X5642)),X5641),X5640)) = c_Polynomial_Odegree(X5642,X5640) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_degree__add__eq__right])]) ).
fof(i_0_1659,plain,
! [X5637,X5638,X5639] :
( ~ class_Groups_Ocomm__monoid__add(X5639)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(X5639,X5638),c_Polynomial_Odegree(X5639,X5637))
| c_Polynomial_Odegree(X5639,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X5639)),X5637),X5638)) = c_Polynomial_Odegree(X5639,X5637) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_degree__add__eq__left])]) ).
fof(i_0_1660,plain,
! [X5801,X5802] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X5802)
| c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X5802),X5801)),X5802) = c_Groups_Oone__class_Oone(tc_Nat_Onat) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Suc__times__mod__eq])]) ).
fof(i_0_1661,plain,
! [X5259,X5260,X5261,X5262] :
( ~ class_Rings_Olinordered__semidom(X5262)
| ~ c_Orderings_Oord__class_Oless(X5262,c_Groups_Ozero__class_Ozero(X5262),X5261)
| ~ c_Orderings_Oord__class_Oless(X5262,X5260,X5259)
| c_Orderings_Oord__class_Oless(X5262,X5260,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5262),X5261),X5259)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pos__add__strict])]) ).
fof(i_0_1662,plain,
! [X4422,X4423] :
( ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X4423),X4422))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X4423),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X4422))) )
& ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X4423),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X4422)))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X4423),X4422)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_uminus__dvd__conv_I2_J])]) ).
fof(i_0_1663,plain,
! [X5580,X5581] :
( ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X5581),X5580))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X5581)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X5580) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X5581)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X5581),X5580)) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X5580)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X5581),X5580)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__gr__0])])]) ).
fof(i_0_1664,plain,
! [X4574,X4575,X4576,X4577] :
( ~ class_Fields_Ofield(X4577)
| c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(X4577),hAPP(hAPP(c_Polynomial_Osmult(X4577),X4576),X4575),X4574) = hAPP(hAPP(c_Polynomial_Osmult(X4577),X4576),c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(X4577),X4575,X4574)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__smult__left])]) ).
fof(i_0_1665,plain,
! [X4158,X4159,X4160] :
( ~ class_Rings_Ocomm__semiring__1(X4160)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4160),hAPP(hAPP(c_Power_Opower__class_Opower(X4160),X4159),X4158)),X4159) = hAPP(hAPP(c_Power_Opower__class_Opower(X4160),X4159),hAPP(c_Nat_OSuc,X4158)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I28_J])]) ).
fof(i_0_1666,plain,
! [X4152,X4153,X4154] :
( ~ class_Groups_Omonoid__mult(X4154)
| hAPP(hAPP(c_Power_Opower__class_Opower(X4154),X4153),hAPP(c_Nat_OSuc,X4152)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4154),hAPP(hAPP(c_Power_Opower__class_Opower(X4154),X4153),X4152)),X4153) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__Suc2])]) ).
fof(i_0_1667,plain,
! [X4551,X4552,X4553] :
( ~ class_RealVector_Oreal__normed__field(X4553)
| c_Deriv_Oderiv(X4553,hAPP(c_COMBK(X4553,X4553),X4552),X4551,c_Groups_Ozero__class_Ozero(X4553)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_DERIV__const])]) ).
fof(i_0_1668,plain,
! [X6000,X6001] :
( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X6001,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X6000)
| c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X6001,X6000),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_div__neg__pos__less0])]) ).
fof(i_0_1669,plain,
! [X5909,X5910,X5911] :
( ~ class_Divides_Osemiring__div(X5911)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X5911),X5910),X5909))
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5911),X5910),c_Divides_Odiv__class_Odiv(X5911,X5909,X5910)) = X5909 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvd__mult__div__cancel])]) ).
fof(i_0_1670,plain,
! [X5998,X5999] :
( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X5999)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X5998)
| c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X5999,X5998),X5999) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_int__div__less__self])]) ).
fof(i_0_1671,plain,
! [X3925,X3926,X3927] :
( ~ class_Groups_Oab__group__add(X3927)
| hAPP(c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X3927)),hAPP(hAPP(c_Polynomial_OpCons(X3927),X3926),X3925)) = hAPP(hAPP(c_Polynomial_OpCons(X3927),hAPP(c_Groups_Ouminus__class_Ouminus(X3927),X3926)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X3927)),X3925)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_minus__poly__code_I2_J])]) ).
fof(i_0_1672,plain,
! [X3922,X3923,X3924] :
( ~ class_Groups_Oab__group__add(X3924)
| hAPP(c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X3924)),hAPP(hAPP(c_Polynomial_OpCons(X3924),X3923),X3922)) = hAPP(hAPP(c_Polynomial_OpCons(X3924),hAPP(c_Groups_Ouminus__class_Ouminus(X3924),X3923)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X3924)),X3922)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_minus__pCons])]) ).
fof(i_0_1673,plain,
! [X3944,X3945,X3946,X3947] :
( ~ class_Fields_Ofield(X3947)
| c_Polynomial_Opoly__gcd(X3947,c_Polynomial_Opoly__gcd(X3947,X3946,X3945),X3944) = c_Polynomial_Opoly__gcd(X3947,X3946,c_Polynomial_Opoly__gcd(X3947,X3945,X3944)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_poly__gcd_Oassoc])]) ).
fof(i_0_1674,plain,
! [X3937,X3938,X3939,X3940] :
( ~ class_Fields_Ofield(X3940)
| c_Polynomial_Opoly__gcd(X3940,X3939,c_Polynomial_Opoly__gcd(X3940,X3938,X3937)) = c_Polynomial_Opoly__gcd(X3940,X3938,c_Polynomial_Opoly__gcd(X3940,X3939,X3937)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_poly__gcd_Oleft__commute])]) ).
fof(i_0_1675,plain,
! [X5178,X5179,X5180] :
( ~ class_Rings_Oring__1(X5180)
| c_Transcendental_Odiffs(X5180,X5179,X5178) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5180),c_Nat_Osemiring__1__class_Oof__nat(X5180,hAPP(c_Nat_OSuc,X5178))),hAPP(X5179,hAPP(c_Nat_OSuc,X5178))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diffs__def])]) ).
fof(i_0_1676,plain,
! [X5864,X5865,X5866] :
( ( ~ c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(X5866),X5865,X5864)
| c_Polynomial_Opos__poly(X5866,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X5866)),X5864),X5865))
| ~ class_Rings_Olinordered__idom(X5866) )
& ( ~ c_Polynomial_Opos__poly(X5866,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X5866)),X5864),X5865))
| c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(X5866),X5865,X5864)
| ~ class_Rings_Olinordered__idom(X5866) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__poly__def])])]) ).
fof(i_0_1677,plain,
! [X5889,X5890,X5891,X5892] :
( ( X5891 != c_Groups_Ozero__class_Ozero(X5892)
| c_Divides_Odiv__class_Odiv(X5892,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5892),X5891),X5890),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5892),X5891),X5889)) = c_Groups_Ozero__class_Ozero(X5892)
| ~ class_Divides_Osemiring__div(X5892) )
& ( X5891 = c_Groups_Ozero__class_Ozero(X5892)
| c_Divides_Odiv__class_Odiv(X5892,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5892),X5891),X5890),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5892),X5891),X5889)) = c_Divides_Odiv__class_Odiv(X5892,X5890,X5889)
| ~ class_Divides_Osemiring__div(X5892) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_div__mult__mult1__if])])]) ).
fof(i_0_1678,plain,
! [X5903,X5904,X5905,X5906] :
( ~ class_Divides_Osemiring__div(X5906)
| X5905 = c_Groups_Ozero__class_Ozero(X5906)
| c_Divides_Odiv__class_Odiv(X5906,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5906),X5905),X5904),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5906),X5905),X5903)) = c_Divides_Odiv__class_Odiv(X5906,X5904,X5903) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_div__mult__mult1])]) ).
fof(i_0_1679,plain,
! [X5899,X5900,X5901,X5902] :
( ~ class_Divides_Osemiring__div(X5902)
| X5901 = c_Groups_Ozero__class_Ozero(X5902)
| c_Divides_Odiv__class_Odiv(X5902,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5902),X5900),X5901),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5902),X5899),X5901)) = c_Divides_Odiv__class_Odiv(X5902,X5900,X5899) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_div__mult__mult2])]) ).
fof(i_0_1680,plain,
! [X5271,X5272] :
( ( ~ c_Orderings_Oord__class_Oless(X5272,c_Groups_Ozero__class_Ozero(X5272),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5272),X5271),X5271))
| c_Orderings_Oord__class_Oless(X5272,c_Groups_Ozero__class_Ozero(X5272),X5271)
| ~ class_Groups_Olinordered__ab__group__add(X5272) )
& ( ~ c_Orderings_Oord__class_Oless(X5272,c_Groups_Ozero__class_Ozero(X5272),X5271)
| c_Orderings_Oord__class_Oless(X5272,c_Groups_Ozero__class_Ozero(X5272),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5272),X5271),X5271))
| ~ class_Groups_Olinordered__ab__group__add(X5272) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__less__double__add__iff__zero__less__single__add])])]) ).
fof(i_0_1681,plain,
! [X5273,X5274] :
( ( ~ c_Orderings_Oord__class_Oless(X5274,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5274),X5273),X5273),c_Groups_Ozero__class_Ozero(X5274))
| c_Orderings_Oord__class_Oless(X5274,X5273,c_Groups_Ozero__class_Ozero(X5274))
| ~ class_Rings_Olinordered__idom(X5274) )
& ( ~ c_Orderings_Oord__class_Oless(X5274,X5273,c_Groups_Ozero__class_Ozero(X5274))
| c_Orderings_Oord__class_Oless(X5274,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5274),X5273),X5273),c_Groups_Ozero__class_Ozero(X5274))
| ~ class_Rings_Olinordered__idom(X5274) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_even__less__0__iff])])]) ).
fof(i_0_1682,plain,
! [X5269,X5270] :
( ( ~ c_Orderings_Oord__class_Oless(X5270,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5270),X5269),X5269),c_Groups_Ozero__class_Ozero(X5270))
| c_Orderings_Oord__class_Oless(X5270,X5269,c_Groups_Ozero__class_Ozero(X5270))
| ~ class_Groups_Olinordered__ab__group__add(X5270) )
& ( ~ c_Orderings_Oord__class_Oless(X5270,X5269,c_Groups_Ozero__class_Ozero(X5270))
| c_Orderings_Oord__class_Oless(X5270,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5270),X5269),X5269),c_Groups_Ozero__class_Ozero(X5270))
| ~ class_Groups_Olinordered__ab__group__add(X5270) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_double__add__less__zero__iff__single__add__less__zero])])]) ).
fof(i_0_1683,plain,
! [X5604,X5605] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X5605)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X5605),X5604)) )
& ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X5604)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X5605),X5604)) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X5605)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X5604)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X5605),X5604)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__0__less__mult__iff])])]) ).
fof(i_0_1684,plain,
! [X3661,X3662,X3663,X3664] :
( ~ class_Rings_Ocomm__semiring__0(X3664)
| hAPP(hAPP(c_Polynomial_Osmult(X3664),X3663),c_Polynomial_Omonom(X3664,X3662,X3661)) = c_Polynomial_Omonom(X3664,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3664),X3663),X3662),X3661) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_smult__monom])]) ).
fof(i_0_1685,plain,
! [X5859,X5860] :
( ( ~ c_Polynomial_Opos__poly(X5860,X5859)
| c_Orderings_Oord__class_Oless(X5860,c_Groups_Ozero__class_Ozero(X5860),hAPP(c_Polynomial_Ocoeff(X5860,X5859),c_Polynomial_Odegree(X5860,X5859)))
| ~ class_Rings_Olinordered__idom(X5860) )
& ( ~ c_Orderings_Oord__class_Oless(X5860,c_Groups_Ozero__class_Ozero(X5860),hAPP(c_Polynomial_Ocoeff(X5860,X5859),c_Polynomial_Odegree(X5860,X5859)))
| c_Polynomial_Opos__poly(X5860,X5859)
| ~ class_Rings_Olinordered__idom(X5860) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pos__poly__def])])]) ).
fof(i_0_1686,plain,
! [X5831,X5832] :
( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X5832)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X5832,X5831)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X5831),X5832)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1191])]) ).
fof(i_0_1687,plain,
! [X5578,X5579] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X5579)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X5579,X5578)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X5578),X5579)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1192])]) ).
fof(i_0_1688,plain,
! [X5880,X5881,X5882,X5883] :
( ( c_Divides_Odiv__class_Odiv(X5883,X5881,X5882) != X5880
| X5881 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5883),X5880),X5882)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X5883),X5882),X5881))
| X5882 = c_Groups_Ozero__class_Ozero(X5883)
| ~ class_Divides_Osemiring__div(X5883) )
& ( X5881 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5883),X5880),X5882)
| c_Divides_Odiv__class_Odiv(X5883,X5881,X5882) = X5880
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X5883),X5882),X5881))
| X5882 = c_Groups_Ozero__class_Ozero(X5883)
| ~ class_Divides_Osemiring__div(X5883) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvd__div__eq__mult])])]) ).
fof(i_0_1689,plain,
! [X5612,X5613] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X5613)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X5612)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X5612),X5613),X5612) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__less])]) ).
fof(i_0_1690,plain,
! [X5551,X5552,X5553] :
( ~ class_Fields_Olinordered__field(X5553)
| ~ c_Orderings_Oord__class_Oless(X5553,X5552,X5551)
| ~ c_Orderings_Oord__class_Oless(X5553,c_Groups_Ozero__class_Ozero(X5553),X5552)
| c_Orderings_Oord__class_Oless(X5553,hAPP(c_Rings_Oinverse__class_Oinverse(X5553),X5551),hAPP(c_Rings_Oinverse__class_Oinverse(X5553),X5552)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__imp__inverse__less])]) ).
fof(i_0_1691,plain,
! [X5554,X5555,X5556] :
( ~ class_Fields_Olinordered__field(X5556)
| ~ c_Orderings_Oord__class_Oless(X5556,X5555,X5554)
| ~ c_Orderings_Oord__class_Oless(X5556,X5554,c_Groups_Ozero__class_Ozero(X5556))
| c_Orderings_Oord__class_Oless(X5556,hAPP(c_Rings_Oinverse__class_Oinverse(X5556),X5554),hAPP(c_Rings_Oinverse__class_Oinverse(X5556),X5555)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__imp__inverse__less__neg])]) ).
fof(i_0_1692,plain,
! [X3870,X3871,X3872] :
( ~ class_Rings_Oidom(X3872)
| X3871 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3872))
| X3870 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3872))
| c_Polynomial_Odegree(X3872,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X3872)),X3871),X3870)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Polynomial_Odegree(X3872,X3871)),c_Polynomial_Odegree(X3872,X3870)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_degree__mult__eq])]) ).
fof(i_0_1693,plain,
! [X5275,X5276,X5277] :
( ( ~ c_Orderings_Oord__class_Oless(X5277,X5276,X5275)
| c_Orderings_Oord__class_Oless(X5277,hAPP(hAPP(c_Groups_Ominus__class_Ominus(X5277),X5276),X5275),c_Groups_Ozero__class_Ozero(X5277))
| ~ class_Groups_Oordered__ab__group__add(X5277) )
& ( ~ c_Orderings_Oord__class_Oless(X5277,hAPP(hAPP(c_Groups_Ominus__class_Ominus(X5277),X5276),X5275),c_Groups_Ozero__class_Ozero(X5277))
| c_Orderings_Oord__class_Oless(X5277,X5276,X5275)
| ~ class_Groups_Oordered__ab__group__add(X5277) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__iff__diff__less__0])])]) ).
fof(i_0_1694,plain,
! [X4284,X4285,X4286] :
( ~ class_Rings_Ocomm__semiring__1(X4286)
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X4286),X4285),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4286),X4285),X4284))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvd__triv__left])]) ).
fof(i_0_1695,plain,
! [X4281,X4282,X4283] :
( ~ class_Rings_Ocomm__semiring__1(X4283)
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X4283),X4282),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4283),X4281),X4282))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvd__triv__right])]) ).
fof(i_0_1696,plain,
! [X5812,X5813,X5814] :
( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X5814,X5813)
| c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X5814),X5812),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X5813),X5812)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zadd__strict__right__mono])]) ).
fof(i_0_1697,plain,
! [X5374,X5375,X5376] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X5376,X5375)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X5376),X5374),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X5375),X5374)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__less__mono1])]) ).
fof(i_0_1698,plain,
! [X3219,X3220,X3221,X3222] :
( ~ class_Rings_Ocomm__semiring__1(X3222)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3222),X3221),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3222),X3220),X3219)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3222),X3220),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3222),X3221),X3219)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J])]) ).
fof(i_0_1699,plain,
! [X3243,X3244,X3245,X3246] :
( ~ class_Rings_Ocomm__semiring__1(X3246)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X3246),X3245),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X3246),X3244),X3243)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X3246),X3244),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X3246),X3245),X3243)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J])]) ).
fof(i_0_1700,plain,
! [X4040,X4041,X4042] :
( ~ class_Groups_Ogroup__add(X4042)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4042),X4041),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4042),hAPP(c_Groups_Ouminus__class_Ouminus(X4042),X4041)),X4040)) = X4040 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__minus__cancel])]) ).
fof(i_0_1701,plain,
! [X4176,X4177,X4178,X4179] :
( ~ class_Groups_Ozero(X4179)
| hAPP(c_Polynomial_Ocoeff(X4179,hAPP(hAPP(c_Polynomial_OpCons(X4179),X4178),X4177)),hAPP(c_Nat_OSuc,X4176)) = hAPP(c_Polynomial_Ocoeff(X4179,X4177),X4176) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_coeff__pCons__Suc])]) ).
fof(i_0_1702,plain,
! [X5321,X5322,X5323,X5324,X5325] :
( ( ~ c_Orderings_Oord__class_Oless(X5325,X5324,X5323)
| c_Orderings_Oord__class_Oless(X5325,X5322,X5321)
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(X5325),X5324),X5323) != hAPP(hAPP(c_Groups_Ominus__class_Ominus(X5325),X5322),X5321)
| ~ class_Groups_Oordered__ab__group__add(X5325) )
& ( ~ c_Orderings_Oord__class_Oless(X5325,X5322,X5321)
| c_Orderings_Oord__class_Oless(X5325,X5324,X5323)
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(X5325),X5324),X5323) != hAPP(hAPP(c_Groups_Ominus__class_Ominus(X5325),X5322),X5321)
| ~ class_Groups_Oordered__ab__group__add(X5325) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__eq__diff__less])])]) ).
fof(i_0_1703,plain,
! [X5732,X5733,X5734] :
( ~ class_Rings_Olinordered__semidom(X5734)
| ~ c_Orderings_Oord__class_Oless(X5734,c_Groups_Oone__class_Oone(X5734),X5733)
| c_Orderings_Oord__class_Oless(X5734,c_Groups_Oone__class_Oone(X5734),hAPP(hAPP(c_Power_Opower__class_Opower(X5734),X5733),hAPP(c_Nat_OSuc,X5732))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__gt1])]) ).
fof(i_0_1704,plain,
! [X4719,X4720] :
( ( hAPP(c_Nat_OSuc,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X4720,X4719)) != X4719
| c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,X4720),X4719) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( hAPP(c_Nat_OSuc,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X4720,X4719)) = X4719
| c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,X4720),X4719) = hAPP(c_Nat_OSuc,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X4720,X4719)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__Suc])]) ).
fof(i_0_1705,plain,
! [X4174,X4175] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X4175),hAPP(c_Nat_OSuc,X4174)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X4175),c_Groups_Oone__class_Oone(tc_Nat_Onat))),X4174),
inference(variable_rename,[status(thm)],[fact_diff__Suc__eq__diff__pred]) ).
fof(i_0_1706,plain,
! [X4349,X4350,X4351] :
( ~ class_Rings_Odivision__ring(X4351)
| X4350 = c_Groups_Ozero__class_Ozero(X4351)
| X4349 = c_Groups_Ozero__class_Ozero(X4351)
| hAPP(c_Rings_Oinverse__class_Oinverse(X4351),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4351),X4350),X4349)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4351),hAPP(c_Rings_Oinverse__class_Oinverse(X4351),X4349)),hAPP(c_Rings_Oinverse__class_Oinverse(X4351),X4350)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nonzero__inverse__mult__distrib])]) ).
fof(i_0_1707,plain,
! [X5838,X5839,X5841,X5842,X5843] :
( ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X5839,X5838)
| X5838 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X5839),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,hAPP(c_Nat_OSuc,esk17_2(X5838,X5839)))) )
& ( X5841 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X5842),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,hAPP(c_Nat_OSuc,X5843)))
| c_Orderings_Oord__class_Oless(tc_Int_Oint,X5842,X5841) ) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zless__iff__Suc__zadd])])])])]) ).
fof(i_0_1708,plain,
! [X5958,X5959] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X5959),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X5958,X5959)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X5958),c_Divides_Odiv__class_Omod(tc_Int_Oint,X5958,X5959)),
inference(variable_rename,[status(thm)],[fact_zmult__div__cancel]) ).
fof(i_0_1709,plain,
! [X5976,X5977] :
( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X5977),X5976))
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X5977),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X5976,X5977)) = X5976 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zdvd__mult__div__cancel])]) ).
fof(i_0_1710,plain,
! [X4527,X4528] :
( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X4528),X4527))
| X4528 != X4527 )
& ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X4527),X4528))
| X4528 != X4527 )
& ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X4528),X4527))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X4527),X4528))
| X4528 = X4527 ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvd_Oeq__iff])])]) ).
fof(i_0_1711,plain,
! [X4525,X4526] :
( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X4526),X4525))
| X4526 = X4525
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X4526),X4525)) )
& ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X4525),X4526))
| X4526 = X4525
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X4526),X4525)) )
& ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X4526),X4525))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X4525),X4526))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X4526),X4525)) )
& ( X4526 != X4525
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X4526),X4525)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1193])])]) ).
fof(i_0_1712,plain,
! [X4523,X4524] :
( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X4524),X4523))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X4524),X4523))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X4523),X4524)) )
& ( X4524 != X4523
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X4524),X4523))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X4523),X4524)) )
& ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X4524),X4523))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X4524),X4523))
| X4524 = X4523 )
& ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X4523),X4524))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X4524),X4523))
| X4524 = X4523 ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1194])])]) ).
fof(i_0_1713,plain,
! [X4521,X4522] :
( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X4522),X4521))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X4522),X4521))
| X4522 = X4521 )
& ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X4521),X4522))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X4522),X4521))
| X4522 = X4521 ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1195])])]) ).
fof(i_0_1714,plain,
! [X4517,X4518] :
( ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X4517),X4518))
| X4517 = X4518
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X4518),X4517)) )
& ( X4517 != X4518
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X4517),X4518))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X4518),X4517)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvd_Oantisym__conv])])]) ).
fof(i_0_1715,plain,
! [X4515,X4516] :
( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X4516),X4515))
| X4516 = X4515
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X4516),X4515)) )
& ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X4515),X4516))
| X4516 = X4515
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X4516),X4515)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1196])])]) ).
fof(i_0_1716,plain,
! [X4513,X4514] :
( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X4514),X4513))
| X4514 = X4513
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X4514),X4513)) )
& ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X4513),X4514))
| X4514 = X4513
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X4514),X4513)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1197])])]) ).
fof(i_0_1717,plain,
! [X4505,X4506] :
( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X4506),X4505))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X4505),X4506))
| X4506 = X4505 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvd__antisym])]) ).
fof(i_0_1718,plain,
! [X4503,X4504] :
( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X4504),X4503))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X4503),X4504))
| X4504 = X4503 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvd_Oantisym])]) ).
fof(i_0_1719,plain,
! [X5730,X5731] :
( ~ class_Fields_Olinordered__field(X5731)
| ~ c_Orderings_Oord__class_Oless(X5731,c_Groups_Ozero__class_Ozero(X5731),X5730)
| ~ c_Orderings_Oord__class_Oless(X5731,X5730,c_Groups_Oone__class_Oone(X5731))
| c_Orderings_Oord__class_Oless(X5731,c_Groups_Oone__class_Oone(X5731),hAPP(c_Rings_Oinverse__class_Oinverse(X5731),X5730)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_one__less__inverse])]) ).
fof(i_0_1720,plain,
! [X5728,X5729] :
( ( c_Orderings_Oord__class_Oless(X5729,c_Groups_Ozero__class_Ozero(X5729),X5728)
| ~ c_Orderings_Oord__class_Oless(X5729,c_Groups_Oone__class_Oone(X5729),hAPP(c_Rings_Oinverse__class_Oinverse(X5729),X5728))
| ~ class_Fields_Olinordered__field__inverse__zero(X5729) )
& ( c_Orderings_Oord__class_Oless(X5729,X5728,c_Groups_Oone__class_Oone(X5729))
| ~ c_Orderings_Oord__class_Oless(X5729,c_Groups_Oone__class_Oone(X5729),hAPP(c_Rings_Oinverse__class_Oinverse(X5729),X5728))
| ~ class_Fields_Olinordered__field__inverse__zero(X5729) )
& ( ~ c_Orderings_Oord__class_Oless(X5729,c_Groups_Ozero__class_Ozero(X5729),X5728)
| ~ c_Orderings_Oord__class_Oless(X5729,X5728,c_Groups_Oone__class_Oone(X5729))
| c_Orderings_Oord__class_Oless(X5729,c_Groups_Oone__class_Oone(X5729),hAPP(c_Rings_Oinverse__class_Oinverse(X5729),X5728))
| ~ class_Fields_Olinordered__field__inverse__zero(X5729) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_one__less__inverse__iff])])]) ).
fof(i_0_1721,plain,
! [X4217,X4218,X4219] :
( ~ class_Groups_Oab__group__add(X4219)
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(X4219),hAPP(c_Groups_Ouminus__class_Ouminus(X4219),X4218)),hAPP(c_Groups_Ouminus__class_Ouminus(X4219),X4217)) = hAPP(c_Groups_Ouminus__class_Ouminus(X4219),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X4219),X4218),X4217)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Limits_Ominus__diff__minus])]) ).
fof(i_0_1722,plain,
! [X4449,X4450,X4451] :
( ~ class_Fields_Ofield__inverse__zero(X4451)
| hAPP(c_Rings_Oinverse__class_Oinverse(X4451),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4451),X4450),X4449)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4451),hAPP(c_Rings_Oinverse__class_Oinverse(X4451),X4450)),hAPP(c_Rings_Oinverse__class_Oinverse(X4451),X4449)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inverse__mult__distrib])]) ).
fof(i_0_1723,plain,
! [X4034,X4035,X4036] :
( ~ class_Groups_Oab__group__add(X4036)
| hAPP(c_Groups_Ouminus__class_Ouminus(X4036),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4036),X4035),X4034)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4036),hAPP(c_Groups_Ouminus__class_Ouminus(X4036),X4035)),hAPP(c_Groups_Ouminus__class_Ouminus(X4036),X4034)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_minus__add__distrib])]) ).
fof(i_0_1724,plain,
! [X4037,X4038,X4039] :
( ~ class_Groups_Ogroup__add(X4039)
| hAPP(c_Groups_Ouminus__class_Ouminus(X4039),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4039),X4038),X4037)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4039),hAPP(c_Groups_Ouminus__class_Ouminus(X4039),X4037)),hAPP(c_Groups_Ouminus__class_Ouminus(X4039),X4038)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_minus__add])]) ).
fof(i_0_1725,plain,
! [X5576,X5577] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X5577)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X5576),X5577))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X5576) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvd__pos__nat])]) ).
fof(i_0_1726,plain,
! [X4571,X4572,X4573] :
( ~ class_RealVector_Oreal__normed__field(X4573)
| c_Deriv_Oderiv(X4573,hAPP(c_Groups_Otimes__class_Otimes(X4573),X4572),X4571,X4572) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_DERIV__cmult__Id])]) ).
fof(i_0_1727,plain,
! [X4074,X4075,X4076] :
( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,X4076)),X4075) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,X4076)),X4074)
| X4075 = X4074 )
& ( X4075 != X4074
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,X4076)),X4075) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,X4076)),X4074) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Suc__mult__cancel1])]) ).
fof(i_0_1728,plain,
! [X5823,X5824] :
( ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X5824,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X5823),c_Groups_Oone__class_Oone(tc_Int_Oint)))
| c_Orderings_Oord__class_Oless(tc_Int_Oint,X5824,X5823)
| X5824 = X5823 )
& ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X5824,X5823)
| c_Orderings_Oord__class_Oless(tc_Int_Oint,X5824,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X5823),c_Groups_Oone__class_Oone(tc_Int_Oint))) )
& ( X5824 != X5823
| c_Orderings_Oord__class_Oless(tc_Int_Oint,X5824,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X5823),c_Groups_Oone__class_Oone(tc_Int_Oint))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zless__add1__eq])])]) ).
fof(i_0_1729,plain,
! [X4728,X4729] :
( ( c_Divides_Odiv__class_Omod(tc_Int_Oint,X4729,X4728) != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X4729),X4728) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
& ( c_Divides_Odiv__class_Omod(tc_Int_Oint,X4729,X4728) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X4729),X4728) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X4728),c_Divides_Odiv__class_Omod(tc_Int_Oint,X4729,X4728)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zmod__zminus1__eq__if])]) ).
fof(i_0_1730,plain,
! [X5803,X5804] :
( ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X5804),X5803))
| X5803 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X5804) )
& ( X5803 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X5804),X5803)) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X5804)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X5804),X5803)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__less__power__nat__eq])])]) ).
fof(i_0_1731,plain,
! [X5635,X5636] :
( ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X5636),X5635))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X5636)
| X5635 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X5636)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X5636),X5635)) )
& ( X5635 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X5636),X5635)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__zero__less__power__iff])])]) ).
fof(i_0_1732,plain,
! [X4180,X4181] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X4181),hAPP(c_Nat_OSuc,X4180)) = hAPP(c_Nat_Onat_Onat__case(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_COMBI(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X4181),X4180)),
inference(variable_rename,[status(thm)],[fact_diff__Suc]) ).
fof(i_0_1733,plain,
! [X4953,X4954,X4955,X4956,X4957] :
( ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4957),X4954),X4956) != hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4957),X4953),X4955)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4957),X4954),X4955) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4957),X4953),X4956)
| X4955 = c_Groups_Ozero__class_Ozero(X4957)
| X4956 = c_Groups_Ozero__class_Ozero(X4957)
| ~ class_Fields_Ofield(X4957) )
& ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4957),X4954),X4955) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4957),X4953),X4956)
| hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4957),X4954),X4956) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4957),X4953),X4955)
| X4955 = c_Groups_Ozero__class_Ozero(X4957)
| X4956 = c_Groups_Ozero__class_Ozero(X4957)
| ~ class_Fields_Ofield(X4957) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_frac__eq__eq])])]) ).
fof(i_0_1734,plain,
! [X5825,X5826] :
( ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X5826,X5825)
| c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X5826),X5825),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X5826),X5825),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| c_Orderings_Oord__class_Oless(tc_Int_Oint,X5826,X5825) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__bin__lemma])]) ).
fof(i_0_1735,plain,
! [X5614,X5615] :
( ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X5615),X5614))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X5614,X5615) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X5614,X5615)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X5615),X5614)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__less__diff])]) ).
fof(i_0_1736,plain,
! [X5366,X5367,X5368,X5369] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X5369,X5368)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X5367),X5368) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X5369),X5366)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X5367,X5366) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__add__eq__less])]) ).
fof(i_0_1737,plain,
! [X4596,X4597,X4598] :
( ~ class_Fields_Ofield(X4598)
| c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(X4598),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X4598)),X4597),X4596) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X4598)),c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(X4598),X4597,X4596)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_poly__mod__minus__left])]) ).
fof(i_0_1738,plain,
! [X5363,X5364,X5365] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X5365),X5364),X5363)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X5365,X5363) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__lessD1])]) ).
fof(i_0_1739,plain,
! [X5741,X5742] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X5742)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X5742),hAPP(c_Nat_OSuc,X5741)),X5742) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__Suc__less])]) ).
fof(i_0_1740,plain,
! [X3985,X3986,X3987] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X3987),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X3986),X3985)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X3986),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X3987),X3985)),
inference(variable_rename,[status(thm)],[fact_zadd__left__commute]) ).
fof(i_0_1741,plain,
! [X3426,X3427,X3428] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3428),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3427),X3426)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3427),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3428),X3426)),
inference(variable_rename,[status(thm)],[fact_nat__add__left__commute]) ).
fof(i_0_1742,plain,
! [X3585,X3586,X3587] :
( ~ class_Rings_Ocomm__semiring__0(X3587)
| c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X3587,hAPP(hAPP(c_Polynomial_OpCons(X3587),X3586),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3587))),X3585) = hAPP(hAPP(c_Polynomial_OpCons(X3587),X3586),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3587))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_offset__poly__single])]) ).
fof(i_0_1743,plain,
! [X3992,X3993,X3994] :
( ~ class_Rings_Ocomm__ring(X3994)
| hAPP(hAPP(c_Polynomial_Osmult(X3994),hAPP(c_Groups_Ouminus__class_Ouminus(X3994),X3993)),X3992) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X3994)),hAPP(hAPP(c_Polynomial_Osmult(X3994),X3993),X3992)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_smult__minus__left])]) ).
fof(i_0_1744,plain,
! [X3995,X3996,X3997] :
( ~ class_Groups_Oab__group__add(X3997)
| hAPP(c_Polynomial_Ocoeff(X3997,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X3997)),X3996)),X3995) = hAPP(c_Groups_Ouminus__class_Ouminus(X3997),hAPP(c_Polynomial_Ocoeff(X3997,X3996),X3995)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_coeff__minus])]) ).
fof(i_0_1745,plain,
! [X3928,X3929,X3930] :
( ~ class_Rings_Ocomm__ring(X3930)
| hAPP(c_Polynomial_Opoly(X3930,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X3930)),X3929)),X3928) = hAPP(c_Groups_Ouminus__class_Ouminus(X3930),hAPP(c_Polynomial_Opoly(X3930,X3929),X3928)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_poly__minus])]) ).
fof(i_0_1746,plain,
! [X4679,X4680] : c_Divides_Odiv__class_Omod(tc_Int_Oint,X4680,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X4679)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X4680),X4679)),
inference(variable_rename,[status(thm)],[fact_zmod__zminus2]) ).
fof(i_0_1747,plain,
! [X5535,X5536,X5537,X5538] :
( ( hAPP(hAPP(c_Power_Opower__class_Opower(X5538),X5537),X5536) != hAPP(hAPP(c_Power_Opower__class_Opower(X5538),X5537),X5535)
| X5536 = X5535
| ~ c_Orderings_Oord__class_Oless(X5538,c_Groups_Oone__class_Oone(X5538),X5537)
| ~ class_Rings_Olinordered__semidom(X5538) )
& ( X5536 != X5535
| hAPP(hAPP(c_Power_Opower__class_Opower(X5538),X5537),X5536) = hAPP(hAPP(c_Power_Opower__class_Opower(X5538),X5537),X5535)
| ~ c_Orderings_Oord__class_Oless(X5538,c_Groups_Oone__class_Oone(X5538),X5537)
| ~ class_Rings_Olinordered__semidom(X5538) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__inject__exp])])]) ).
fof(i_0_1748,plain,
! [X5326,X5327,X5328] :
( ( ~ c_Orderings_Oord__class_Oless(X5328,hAPP(c_Groups_Ouminus__class_Ouminus(X5328),X5327),hAPP(c_Groups_Ouminus__class_Ouminus(X5328),X5326))
| c_Orderings_Oord__class_Oless(X5328,X5326,X5327)
| ~ class_Groups_Oordered__ab__group__add(X5328) )
& ( ~ c_Orderings_Oord__class_Oless(X5328,X5326,X5327)
| c_Orderings_Oord__class_Oless(X5328,hAPP(c_Groups_Ouminus__class_Ouminus(X5328),X5327),hAPP(c_Groups_Ouminus__class_Ouminus(X5328),X5326))
| ~ class_Groups_Oordered__ab__group__add(X5328) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_neg__less__iff__less])])]) ).
fof(i_0_1749,plain,
! [X3649,X3650,X3651,X3652] :
( ( X3651 != X3650
| hAPP(c_Polynomial_Ocoeff(X3652,c_Polynomial_Omonom(X3652,X3649,X3651)),X3650) = X3649
| ~ class_Groups_Ozero(X3652) )
& ( X3651 = X3650
| hAPP(c_Polynomial_Ocoeff(X3652,c_Polynomial_Omonom(X3652,X3649,X3651)),X3650) = c_Groups_Ozero__class_Ozero(X3652)
| ~ class_Groups_Ozero(X3652) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_coeff__monom])])]) ).
fof(i_0_1750,plain,
! [X4611,X4612] :
( ~ class_RealVector_Oreal__normed__field(X4612)
| c_Deriv_Oderiv(X4612,c_COMBI(X4612),X4611,c_Groups_Oone__class_Oone(X4612)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_DERIV__ident])]) ).
fof(i_0_1751,plain,
! [X5504,X5505,X5506] :
( ~ class_Rings_Olinordered__semidom(X5506)
| ~ c_Orderings_Oord__class_Oless(X5506,c_Groups_Ozero__class_Ozero(X5506),X5505)
| c_Orderings_Oord__class_Oless(X5506,c_Groups_Ozero__class_Ozero(X5506),hAPP(hAPP(c_Power_Opower__class_Opower(X5506),X5505),X5504)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__less__power])]) ).
fof(i_0_1752,plain,
! [X5861,X5862,X5863] :
( ( X5861 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X5863))
| c_Polynomial_Opos__poly(X5863,X5861)
| ~ c_Polynomial_Opos__poly(X5863,hAPP(hAPP(c_Polynomial_OpCons(X5863),X5862),X5861))
| ~ class_Rings_Olinordered__idom(X5863) )
& ( c_Orderings_Oord__class_Oless(X5863,c_Groups_Ozero__class_Ozero(X5863),X5862)
| c_Polynomial_Opos__poly(X5863,X5861)
| ~ c_Polynomial_Opos__poly(X5863,hAPP(hAPP(c_Polynomial_OpCons(X5863),X5862),X5861))
| ~ class_Rings_Olinordered__idom(X5863) )
& ( ~ c_Polynomial_Opos__poly(X5863,X5861)
| c_Polynomial_Opos__poly(X5863,hAPP(hAPP(c_Polynomial_OpCons(X5863),X5862),X5861))
| ~ class_Rings_Olinordered__idom(X5863) )
& ( X5861 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X5863))
| ~ c_Orderings_Oord__class_Oless(X5863,c_Groups_Ozero__class_Ozero(X5863),X5862)
| c_Polynomial_Opos__poly(X5863,hAPP(hAPP(c_Polynomial_OpCons(X5863),X5862),X5861))
| ~ class_Rings_Olinordered__idom(X5863) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pos__poly__pCons])])]) ).
fof(i_0_1753,plain,
! [X3791,X3792,X3793] :
( ~ class_Groups_Ogroup__add(X3793)
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(X3793),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X3793),X3792),X3791)),X3791) = X3792 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__diff__cancel])]) ).
fof(i_0_1754,plain,
! [X3794,X3795,X3796] :
( ~ class_Groups_Ogroup__add(X3796)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X3796),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X3796),X3795),X3794)),X3794) = X3795 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__add__cancel])]) ).
fof(i_0_1755,plain,
! [X5257,X5258] :
( ~ class_Rings_Olinordered__ring(X5258)
| ~ c_Orderings_Oord__class_Oless(X5258,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5258),X5257),X5257),c_Groups_Ozero__class_Ozero(X5258)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1198])]) ).
fof(i_0_1756,plain,
! [X4357,X4358,X4359] :
( ~ class_Rings_Odivision__ring(X4359)
| X4358 = c_Groups_Ozero__class_Ozero(X4359)
| hAPP(c_Rings_Oinverse__class_Oinverse(X4359),hAPP(hAPP(c_Power_Opower__class_Opower(X4359),X4358),X4357)) = hAPP(hAPP(c_Power_Opower__class_Opower(X4359),hAPP(c_Rings_Oinverse__class_Oinverse(X4359),X4358)),X4357) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nonzero__power__inverse])]) ).
fof(i_0_1757,plain,
! [X5146,X5147,X5148] :
( ~ class_Rings_Osemiring__1(X5148)
| c_Nat_Osemiring__1__class_Oof__nat__aux(X5148,X5147,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X5146) = X5146 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__nat__aux_Osimps_I1_J])]) ).
fof(i_0_1758,plain,
! [X4909,X4910,X4911] :
( ~ class_RealVector_Oreal__normed__field(X4911)
| hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4911),hAPP(c_Groups_Ouminus__class_Ouminus(X4911),X4910)),X4909) = hAPP(c_Groups_Ouminus__class_Ouminus(X4911),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4911),X4910),X4909)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divide_Ominus])]) ).
fof(i_0_1759,plain,
! [X4022,X4023,X4024] :
( ~ class_RealVector_Oreal__normed__algebra(X4024)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4024),hAPP(c_Groups_Ouminus__class_Ouminus(X4024),X4023)),X4022) = hAPP(c_Groups_Ouminus__class_Ouminus(X4024),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4024),X4023),X4022)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__left_Ominus])]) ).
fof(i_0_1760,plain,
! [X4019,X4020,X4021] :
( ~ class_RealVector_Oreal__normed__algebra(X4021)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4021),hAPP(c_Groups_Ouminus__class_Ouminus(X4021),X4020)),X4019) = hAPP(c_Groups_Ouminus__class_Ouminus(X4021),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4021),X4020),X4019)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult_Ominus__left])]) ).
fof(i_0_1761,plain,
! [X4322,X4323,X4324] :
( ~ class_Rings_Odivision__ring__inverse__zero(X4324)
| hAPP(c_Rings_Oinverse__class_Oinverse(X4324),hAPP(hAPP(c_Power_Opower__class_Opower(X4324),X4323),X4322)) = hAPP(hAPP(c_Power_Opower__class_Opower(X4324),hAPP(c_Rings_Oinverse__class_Oinverse(X4324),X4323)),X4322) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__inverse])]) ).
fof(i_0_1762,plain,
! [X4912,X4913,X4914] :
( ~ class_Rings_Odivision__ring(X4914)
| hAPP(c_Groups_Ouminus__class_Ouminus(X4914),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4914),X4913),X4912)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4914),hAPP(c_Groups_Ouminus__class_Ouminus(X4914),X4913)),X4912) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_minus__divide__left])]) ).
fof(i_0_1763,plain,
! [X4010,X4011,X4012] :
( ~ class_Rings_Oring(X4012)
| hAPP(c_Groups_Ouminus__class_Ouminus(X4012),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4012),X4011),X4010)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4012),hAPP(c_Groups_Ouminus__class_Ouminus(X4012),X4011)),X4010) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_minus__mult__left])]) ).
fof(i_0_1764,plain,
! [X3378,X3379,X3380,X3381] : hAPP(hAPP(c_Power_Opower_Opower(X3381,X3380,X3379),X3378),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X3380,
inference(variable_rename,[status(thm)],[fact_power_Opower_Opower__0]) ).
fof(i_0_1765,plain,
! [X4089,X4090,X4091] :
( ~ class_Rings_Ocomm__ring(X4091)
| hAPP(hAPP(c_Polynomial_Osmult(X4091),X4090),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X4091)),X4089)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X4091)),hAPP(hAPP(c_Polynomial_Osmult(X4091),X4090),X4089)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_smult__minus__right])]) ).
fof(i_0_1766,plain,
! [X4444] :
( ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X4444),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))
| X4444 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
& ( X4444 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X4444),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvd__1__iff__1])]) ).
fof(i_0_1767,plain,
! [X5590,X5591] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,X5591,hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X5591),X5590))),
inference(variable_rename,[status(thm)],[fact_less__add__Suc1]) ).
fof(i_0_1768,plain,
! [X5588,X5589] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,X5589,hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X5588),X5589))),
inference(variable_rename,[status(thm)],[fact_less__add__Suc2]) ).
fof(i_0_1769,plain,
! [X4200,X4201,X4202] :
( ~ class_Groups_Ozero(X4202)
| c_Polynomial_Omonom(X4202,X4201,hAPP(c_Nat_OSuc,X4200)) = hAPP(hAPP(c_Polynomial_OpCons(X4202),c_Groups_Ozero__class_Ozero(X4202)),c_Polynomial_Omonom(X4202,X4201,X4200)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_monom__Suc])]) ).
fof(i_0_1770,plain,
! [X3638,X3639,X3640] :
( ~ class_Groups_Ozero(X3640)
| hAPP(c_Polynomial_Ocoeff(X3640,hAPP(hAPP(c_Polynomial_OpCons(X3640),X3639),X3638)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X3639 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_coeff__pCons__0])]) ).
fof(i_0_1771,plain,
! [X5743] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X5743)
| hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X5743),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = X5743 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Suc__pred])]) ).
fof(i_0_1772,plain,
! [X5630,X5631] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X5631,X5630)
| c_Divides_Odiv__class_Omod(tc_Nat_Onat,X5631,X5630) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X5631),X5630),X5630) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1199])]) ).
fof(i_0_1773,plain,
! [X5628,X5629] :
( ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X5629,X5628)
| c_Divides_Odiv__class_Omod(tc_Nat_Onat,X5629,X5628) = X5629 )
& ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X5629,X5628)
| c_Divides_Odiv__class_Omod(tc_Nat_Onat,X5629,X5628) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X5629),X5628),X5628) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1200])]) ).
fof(i_0_1774,plain,
! [X3979,X3980] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X3980),X3979)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X3980)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X3979)),
inference(variable_rename,[status(thm)],[fact_zminus__zadd__distrib]) ).
fof(i_0_1775,plain,
! [X4621,X4622,X4623] :
( ~ class_Fields_Ofield(X4623)
| X4622 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4623))
| c_Polynomial_Opoly__gcd(X4623,X4621,X4622) = c_Polynomial_Opoly__gcd(X4623,X4622,c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(X4623),X4621,X4622)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_poly__gcd_Osimps_I2_J])]) ).
fof(i_0_1776,plain,
! [X5329,X5330,X5331] :
( ( ~ c_Orderings_Oord__class_Oless(X5331,hAPP(c_Groups_Ouminus__class_Ouminus(X5331),X5330),X5329)
| c_Orderings_Oord__class_Oless(X5331,hAPP(c_Groups_Ouminus__class_Ouminus(X5331),X5329),X5330)
| ~ class_Groups_Oordered__ab__group__add(X5331) )
& ( ~ c_Orderings_Oord__class_Oless(X5331,hAPP(c_Groups_Ouminus__class_Ouminus(X5331),X5329),X5330)
| c_Orderings_Oord__class_Oless(X5331,hAPP(c_Groups_Ouminus__class_Ouminus(X5331),X5330),X5329)
| ~ class_Groups_Oordered__ab__group__add(X5331) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_minus__less__iff])])]) ).
fof(i_0_1777,plain,
! [X5332,X5333,X5334] :
( ( ~ c_Orderings_Oord__class_Oless(X5334,X5333,hAPP(c_Groups_Ouminus__class_Ouminus(X5334),X5332))
| c_Orderings_Oord__class_Oless(X5334,X5332,hAPP(c_Groups_Ouminus__class_Ouminus(X5334),X5333))
| ~ class_Groups_Oordered__ab__group__add(X5334) )
& ( ~ c_Orderings_Oord__class_Oless(X5334,X5332,hAPP(c_Groups_Ouminus__class_Ouminus(X5334),X5333))
| c_Orderings_Oord__class_Oless(X5334,X5333,hAPP(c_Groups_Ouminus__class_Ouminus(X5334),X5332))
| ~ class_Groups_Oordered__ab__group__add(X5334) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__minus__iff])])]) ).
fof(i_0_1778,plain,
! [X5827,X5828] :
( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X5828)
| c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Divides_Odiv__class_Omod(tc_Int_Oint,X5827,X5828),X5828) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pos__mod__bound])]) ).
fof(i_0_1779,plain,
! [X5626,X5627] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X5627)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X5626,X5627),X5627) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__less__divisor])]) ).
fof(i_0_1780,plain,
! [X5829,X5830] :
( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X5830,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| c_Orderings_Oord__class_Oless(tc_Int_Oint,X5830,c_Divides_Odiv__class_Omod(tc_Int_Oint,X5829,X5830)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_neg__mod__bound])]) ).
fof(i_0_1781,plain,
! [X5810,X5811] : c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,hAPP(c_Nat_OSuc,X5811))),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,X5810)),
inference(variable_rename,[status(thm)],[fact_negative__zless]) ).
fof(i_0_1782,plain,
! [X5396,X5397,X5398] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X5398,X5397)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X5397,X5396)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(c_Nat_OSuc,X5398),X5396) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__trans__Suc])]) ).
fof(i_0_1783,plain,
! [X6046,X6047,X6048] :
( ~ class_Fields_Ofield(X6048)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(X6048,X6047),c_Polynomial_Odegree(X6048,X6046))
| c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(X6048),X6047,X6046) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X6048)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_div__poly__less])]) ).
fof(i_0_1784,plain,
! [X5833,X5834] : ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,X5834),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,X5833))),
inference(variable_rename,[status(thm)],[i_0_1201]) ).
fof(i_0_1785,plain,
! [X4984,X4985,X4986] :
( ~ class_Rings_Osemiring__1(X4986)
| c_Nat_Osemiring__1__class_Oof__nat(X4986,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4985),X4984)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4986),c_Nat_Osemiring__1__class_Oof__nat(X4986,X4985)),c_Nat_Osemiring__1__class_Oof__nat(X4986,X4984)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__nat__mult])]) ).
fof(i_0_1786,plain,
! [X4981,X4982,X4983] :
( ~ class_Rings_Osemiring__1(X4983)
| c_Nat_Osemiring__1__class_Oof__nat(X4983,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X4982),X4981)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4983),c_Nat_Osemiring__1__class_Oof__nat(X4983,X4982)),c_Nat_Osemiring__1__class_Oof__nat(X4983,X4981)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__nat__add])]) ).
fof(i_0_1787,plain,
! [X5582,X5583,X5585,X5586,X5587] :
( ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X5583,X5582)
| X5582 = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X5583),esk12_2(X5582,X5583))) )
& ( X5585 != hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X5586),X5587))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X5586,X5585) ) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__iff__Suc__add])])])])]) ).
fof(i_0_1788,plain,
! [X4043,X4044,X4045] :
( ~ class_Groups_Ogroup__add(X4045)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4045),hAPP(c_Groups_Ouminus__class_Ouminus(X4045),X4044)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4045),X4044),X4043)) = X4043 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_minus__add__cancel])]) ).
fof(i_0_1789,plain,
! [X3919,X3920,X3921] :
( ~ class_Groups_Oab__group__add(X3921)
| hAPP(c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X3921)),c_Polynomial_Omonom(X3921,X3920,X3919)) = c_Polynomial_Omonom(X3921,hAPP(c_Groups_Ouminus__class_Ouminus(X3921),X3920),X3919) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_minus__monom])]) ).
fof(i_0_1790,plain,
! [X4677,X4678] : c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X4678),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X4677)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,X4678,X4677)),
inference(variable_rename,[status(thm)],[fact_zmod__zminus__zminus]) ).
fof(i_0_1791,plain,
! [X4155,X4156,X4157] :
( ~ class_Rings_Ocomm__semiring__1(X4157)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4157),X4156),hAPP(hAPP(c_Power_Opower__class_Opower(X4157),X4156),X4155)) = hAPP(hAPP(c_Power_Opower__class_Opower(X4157),X4156),hAPP(c_Nat_OSuc,X4155)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I27_J])]) ).
fof(i_0_1792,plain,
! [X4149,X4150,X4151] :
( ~ class_Rings_Ocomm__semiring__1(X4151)
| hAPP(hAPP(c_Power_Opower__class_Opower(X4151),X4150),hAPP(c_Nat_OSuc,X4149)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4151),X4150),hAPP(hAPP(c_Power_Opower__class_Opower(X4151),X4150),X4149)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I35_J])]) ).
fof(i_0_1793,plain,
! [X4146,X4147,X4148] :
( ~ class_Power_Opower(X4148)
| hAPP(hAPP(c_Power_Opower__class_Opower(X4148),X4147),hAPP(c_Nat_OSuc,X4146)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4148),X4147),hAPP(hAPP(c_Power_Opower__class_Opower(X4148),X4147),X4146)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__Suc])]) ).
fof(i_0_1794,plain,
! [X5609,X5610,X5611] :
( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X5611),X5610) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X5611),X5609)
| X5610 = X5609
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X5611) )
& ( X5610 != X5609
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X5611),X5610) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X5611),X5609)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X5611) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__mult__eq__cancel1])])]) ).
fof(i_0_1795,plain,
! [X4617,X4618,X4619,X4620] :
( ~ class_Fields_Ofield(X4620)
| X4619 = c_Groups_Ozero__class_Ozero(X4620)
| c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(X4620),X4618,hAPP(hAPP(c_Polynomial_Osmult(X4620),X4619),X4617)) = c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(X4620),X4618,X4617) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__smult__right])]) ).
fof(i_0_1796,plain,
! [X5474,X5475,X5476,X5477] :
( ~ class_Orderings_Opreorder(X5477)
| ~ c_Orderings_Oord__class_Oless(X5477,X5476,X5475)
| ~ c_Orderings_Oord__class_Oless(X5477,X5475,X5474)
| c_Orderings_Oord__class_Oless(X5477,X5476,X5474) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__less__trans])]) ).
fof(i_0_1797,plain,
! [X5478,X5479,X5480,X5481] :
( ~ class_Orderings_Oorder(X5481)
| ~ c_Orderings_Oord__class_Oless(X5481,X5480,X5479)
| ~ c_Orderings_Oord__class_Oless(X5481,X5478,X5480)
| c_Orderings_Oord__class_Oless(X5481,X5478,X5479) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_xt1_I10_J])]) ).
fof(i_0_1798,plain,
! [X5650,X5651,X5652] :
( ~ class_Fields_Ofield(X5652)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(X5652,X5651),c_Polynomial_Odegree(X5652,X5650))
| c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(X5652),X5651,X5650) = X5651 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__poly__less])]) ).
fof(i_0_1799,plain,
! [X4652,X4653,X4654] :
( ~ class_Divides_Osemiring__div(X4654)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X4654),X4653),X4652))
| c_Divides_Odiv__class_Omod(X4654,X4652,X4653) = c_Groups_Ozero__class_Ozero(X4654) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvd__imp__mod__0])]) ).
fof(i_0_1800,plain,
! [X4649,X4650,X4651] :
( ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X4651),X4650),X4649))
| c_Divides_Odiv__class_Omod(X4651,X4649,X4650) = c_Groups_Ozero__class_Ozero(X4651)
| ~ class_Divides_Osemiring__div(X4651) )
& ( c_Divides_Odiv__class_Omod(X4651,X4649,X4650) != c_Groups_Ozero__class_Ozero(X4651)
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X4651),X4650),X4649))
| ~ class_Divides_Osemiring__div(X4651) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvd__eq__mod__eq__0])])]) ).
fof(i_0_1801,plain,
! [X3827,X3828,X3829] :
( ~ class_Groups_Ozero(X3829)
| hAPP(hAPP(c_Polynomial_OpCons(X3829),X3828),X3827) = c_Polynomial_OAbs__poly(X3829,c_Nat_Onat_Onat__case(X3829,X3828,c_Polynomial_Ocoeff(X3829,X3827))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pCons__def])]) ).
fof(i_0_1802,plain,
! [X5805] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X5805,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))
| X5805 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X5805 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__lt__two__imp__zero__or__one])]) ).
fof(i_0_1803,plain,
! [X4987,X4988,X4989] :
( ~ class_Rings_Odivision__ring(X4989)
| X4988 = c_Groups_Ozero__class_Ozero(X4989)
| hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4989),hAPP(c_Groups_Ouminus__class_Ouminus(X4989),X4987)),hAPP(c_Groups_Ouminus__class_Ouminus(X4989),X4988)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4989),X4987),X4988) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nonzero__minus__divide__divide])]) ).
fof(i_0_1804,plain,
! [X5547,X5548] :
( ~ class_Fields_Olinordered__field(X5548)
| ~ c_Orderings_Oord__class_Oless(X5548,c_Groups_Ozero__class_Ozero(X5548),hAPP(c_Rings_Oinverse__class_Oinverse(X5548),X5547))
| X5547 = c_Groups_Ozero__class_Ozero(X5548)
| c_Orderings_Oord__class_Oless(X5548,c_Groups_Ozero__class_Ozero(X5548),X5547) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inverse__positive__imp__positive])]) ).
fof(i_0_1805,plain,
! [X5557,X5558] :
( ~ class_Fields_Olinordered__field(X5558)
| ~ c_Orderings_Oord__class_Oless(X5558,hAPP(c_Rings_Oinverse__class_Oinverse(X5558),X5557),c_Groups_Ozero__class_Ozero(X5558))
| X5557 = c_Groups_Ozero__class_Ozero(X5558)
| c_Orderings_Oord__class_Oless(X5558,X5557,c_Groups_Ozero__class_Ozero(X5558)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inverse__negative__imp__negative])]) ).
fof(i_0_1806,plain,
! [X3749,X3750,X3751] :
( ~ class_Rings_Ocomm__semiring__0(X3751)
| c_Polynomial_Odegree(X3751,c_Polynomial_Osynthetic__div(X3751,X3750,X3749)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),c_Polynomial_Odegree(X3751,X3750)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_degree__synthetic__div])]) ).
fof(i_0_1807,plain,
! [X5197,X5198,X5199] :
( ~ class_Rings_Olinordered__semidom(X5199)
| ~ c_Orderings_Oord__class_Oless(X5199,c_Nat_Osemiring__1__class_Oof__nat(X5199,X5198),c_Nat_Osemiring__1__class_Oof__nat(X5199,X5197))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X5198,X5197) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__nat__less__imp__less])]) ).
fof(i_0_1808,plain,
! [X5191,X5192,X5193] :
( ( ~ c_Orderings_Oord__class_Oless(X5193,c_Nat_Osemiring__1__class_Oof__nat(X5193,X5192),c_Nat_Osemiring__1__class_Oof__nat(X5193,X5191))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X5192,X5191)
| ~ class_Rings_Olinordered__semidom(X5193) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X5192,X5191)
| c_Orderings_Oord__class_Oless(X5193,c_Nat_Osemiring__1__class_Oof__nat(X5193,X5192),c_Nat_Osemiring__1__class_Oof__nat(X5193,X5191))
| ~ class_Rings_Olinordered__semidom(X5193) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__nat__less__iff])])]) ).
fof(i_0_1809,plain,
! [X4167,X4168] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,X4168)),X4167) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X4167),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4168),X4167)),
inference(variable_rename,[status(thm)],[fact_mult__Suc]) ).
fof(i_0_1810,plain,
! [X5360,X5361,X5362] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X5362,X5361)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X5362),X5360),X5361) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__imp__diff__less])]) ).
fof(i_0_1811,plain,
! [X5856,X5857,X5858] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X5858,X5857)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X5858,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X5857),X5856)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_termination__basic__simps_I1_J])]) ).
fof(i_0_1812,plain,
! [X5380,X5381,X5382] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X5382,X5381)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X5382,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X5381),X5380)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_trans__less__add1])]) ).
fof(i_0_1813,plain,
! [X5851,X5852,X5853] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X5853,X5852)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X5853,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X5851),X5852)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_termination__basic__simps_I2_J])]) ).
fof(i_0_1814,plain,
! [X5377,X5378,X5379] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X5379,X5378)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X5379,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X5377),X5378)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_trans__less__add2])]) ).
fof(i_0_1815,plain,
! [X3811,X3812] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3812),X3811)),X3812) = X3811,
inference(variable_rename,[status(thm)],[fact_diff__add__inverse]) ).
fof(i_0_1816,plain,
! [X3813,X3814] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3814),X3813)),X3813) = X3814,
inference(variable_rename,[status(thm)],[fact_diff__add__inverse2]) ).
fof(i_0_1817,plain,
! [X4933,X4934,X4935] :
( ~ class_Fields_Ofield__inverse__zero(X4935)
| hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4935),hAPP(c_Groups_Ouminus__class_Ouminus(X4935),X4934)),hAPP(c_Groups_Ouminus__class_Ouminus(X4935),X4933)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4935),X4934),X4933) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_minus__divide__divide])]) ).
fof(i_0_1818,plain,
! [X4028,X4029,X4030] :
( ~ class_Rings_Oring(X4030)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4030),hAPP(c_Groups_Ouminus__class_Ouminus(X4030),X4029)),hAPP(c_Groups_Ouminus__class_Ouminus(X4030),X4028)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4030),X4029),X4028) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_minus__mult__minus])]) ).
fof(i_0_1819,plain,
! [X4025,X4026,X4027] :
( ~ class_Rings_Oring(X4027)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4027),hAPP(c_Groups_Ouminus__class_Ouminus(X4027),X4026)),X4025) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4027),X4026),hAPP(c_Groups_Ouminus__class_Ouminus(X4027),X4025)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_minus__mult__commute])]) ).
fof(i_0_1820,plain,
! [X5848] : c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,hAPP(c_Nat_OSuc,X5848))),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),
inference(variable_rename,[status(thm)],[fact_negative__zless__0]) ).
fof(i_0_1821,plain,
! [X5388,X5389] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X5389),X5388),X5389),
inference(variable_rename,[status(thm)],[i_0_1202]) ).
fof(i_0_1822,plain,
! [X5386,X5387] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X5387),X5386),X5386),
inference(variable_rename,[status(thm)],[i_0_1203]) ).
fof(i_0_1823,plain,
! [X4990,X4991,X4992] :
( ~ class_Rings_Odivision__ring(X4992)
| X4991 = c_Groups_Ozero__class_Ozero(X4992)
| hAPP(c_Groups_Ouminus__class_Ouminus(X4992),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4992),X4990),X4991)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4992),X4990),hAPP(c_Groups_Ouminus__class_Ouminus(X4992),X4991)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nonzero__minus__divide__right])]) ).
fof(i_0_1824,plain,
! [X5497,X5498] :
( ( ~ c_Orderings_Oord__class_Oless(X5498,hAPP(c_Groups_Ouminus__class_Ouminus(X5498),X5497),c_Groups_Ozero__class_Ozero(X5498))
| c_Orderings_Oord__class_Oless(X5498,c_Groups_Ozero__class_Ozero(X5498),X5497)
| ~ class_Groups_Oordered__ab__group__add(X5498) )
& ( ~ c_Orderings_Oord__class_Oless(X5498,c_Groups_Ozero__class_Ozero(X5498),X5497)
| c_Orderings_Oord__class_Oless(X5498,hAPP(c_Groups_Ouminus__class_Ouminus(X5498),X5497),c_Groups_Ozero__class_Ozero(X5498))
| ~ class_Groups_Oordered__ab__group__add(X5498) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_neg__less__0__iff__less])])]) ).
fof(i_0_1825,plain,
! [X5541,X5542] :
( ( ~ c_Orderings_Oord__class_Oless(X5542,c_Groups_Ozero__class_Ozero(X5542),hAPP(c_Rings_Oinverse__class_Oinverse(X5542),X5541))
| c_Orderings_Oord__class_Oless(X5542,c_Groups_Ozero__class_Ozero(X5542),X5541)
| ~ class_Fields_Olinordered__field__inverse__zero(X5542) )
& ( ~ c_Orderings_Oord__class_Oless(X5542,c_Groups_Ozero__class_Ozero(X5542),X5541)
| c_Orderings_Oord__class_Oless(X5542,c_Groups_Ozero__class_Ozero(X5542),hAPP(c_Rings_Oinverse__class_Oinverse(X5542),X5541))
| ~ class_Fields_Olinordered__field__inverse__zero(X5542) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inverse__positive__iff__positive])])]) ).
fof(i_0_1826,plain,
! [X5543,X5544] :
( ( ~ c_Orderings_Oord__class_Oless(X5544,hAPP(c_Rings_Oinverse__class_Oinverse(X5544),X5543),c_Groups_Ozero__class_Ozero(X5544))
| c_Orderings_Oord__class_Oless(X5544,X5543,c_Groups_Ozero__class_Ozero(X5544))
| ~ class_Fields_Olinordered__field__inverse__zero(X5544) )
& ( ~ c_Orderings_Oord__class_Oless(X5544,X5543,c_Groups_Ozero__class_Ozero(X5544))
| c_Orderings_Oord__class_Oless(X5544,hAPP(c_Rings_Oinverse__class_Oinverse(X5544),X5543),c_Groups_Ozero__class_Ozero(X5544))
| ~ class_Fields_Olinordered__field__inverse__zero(X5544) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inverse__negative__iff__negative])])]) ).
fof(i_0_1827,plain,
! [X5499,X5500] :
( ( ~ c_Orderings_Oord__class_Oless(X5500,c_Groups_Ozero__class_Ozero(X5500),hAPP(c_Groups_Ouminus__class_Ouminus(X5500),X5499))
| c_Orderings_Oord__class_Oless(X5500,X5499,c_Groups_Ozero__class_Ozero(X5500))
| ~ class_Groups_Oordered__ab__group__add(X5500) )
& ( ~ c_Orderings_Oord__class_Oless(X5500,X5499,c_Groups_Ozero__class_Ozero(X5500))
| c_Orderings_Oord__class_Oless(X5500,c_Groups_Ozero__class_Ozero(X5500),hAPP(c_Groups_Ouminus__class_Ouminus(X5500),X5499))
| ~ class_Groups_Oordered__ab__group__add(X5500) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_neg__0__less__iff__less])])]) ).
fof(i_0_1828,plain,
! [X4732,X4733,X4734] :
( ~ class_Divides_Osemiring__div(X4734)
| c_Divides_Odiv__class_Omod(X4734,c_Divides_Odiv__class_Omod(X4734,X4733,X4732),X4732) = c_Divides_Odiv__class_Omod(X4734,X4733,X4732) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__mod__trivial])]) ).
fof(i_0_1829,plain,
! [X4016,X4017,X4018] :
( ~ class_RealVector_Oreal__normed__algebra(X4018)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4018),X4017),hAPP(c_Groups_Ouminus__class_Ouminus(X4018),X4016)) = hAPP(c_Groups_Ouminus__class_Ouminus(X4018),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4018),X4017),X4016)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__right_Ominus])]) ).
fof(i_0_1830,plain,
! [X4013,X4014,X4015] :
( ~ class_RealVector_Oreal__normed__algebra(X4015)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4015),X4014),hAPP(c_Groups_Ouminus__class_Ouminus(X4015),X4013)) = hAPP(c_Groups_Ouminus__class_Ouminus(X4015),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4015),X4014),X4013)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult_Ominus__right])]) ).
fof(i_0_1831,plain,
! [X4930,X4931,X4932] :
( ~ class_Fields_Ofield__inverse__zero(X4932)
| hAPP(c_Groups_Ouminus__class_Ouminus(X4932),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4932),X4931),X4930)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4932),X4931),hAPP(c_Groups_Ouminus__class_Ouminus(X4932),X4930)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_minus__divide__right])]) ).
fof(i_0_1832,plain,
! [X4007,X4008,X4009] :
( ~ class_Rings_Oring(X4009)
| hAPP(c_Groups_Ouminus__class_Ouminus(X4009),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4009),X4008),X4007)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4009),X4008),hAPP(c_Groups_Ouminus__class_Ouminus(X4009),X4007)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_minus__mult__right])]) ).
fof(i_0_1833,plain,
! [X4254,X4255] :
( ~ class_Rings_Ocomm__semiring__1(X4255)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X4255),c_Groups_Ozero__class_Ozero(X4255)),X4254))
| X4254 = c_Groups_Ozero__class_Ozero(X4255) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvd__0__left])]) ).
fof(i_0_1834,plain,
! [X4797,X4798,X4799] :
( ~ class_Divides_Osemiring__div(X4799)
| c_Divides_Odiv__class_Omod(X4799,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4799),X4798),X4797),X4798) = c_Divides_Odiv__class_Omod(X4799,X4797,X4798) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__add__self1])]) ).
fof(i_0_1835,plain,
! [X4800,X4801,X4802] :
( ~ class_Divides_Osemiring__div(X4802)
| c_Divides_Odiv__class_Omod(X4802,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4802),X4801),X4800),X4800) = c_Divides_Odiv__class_Omod(X4802,X4801,X4800) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__add__self2])]) ).
fof(i_0_1836,plain,
! [X5868,X5869,X5870] :
( ~ class_Rings_Olinordered__idom(X5870)
| ~ c_Polynomial_Opos__poly(X5870,X5869)
| ~ c_Polynomial_Opos__poly(X5870,X5868)
| c_Polynomial_Opos__poly(X5870,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X5870)),X5869),X5868)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pos__poly__mult])]) ).
fof(i_0_1837,plain,
! [X5871,X5872,X5873] :
( ~ class_Rings_Olinordered__idom(X5873)
| ~ c_Polynomial_Opos__poly(X5873,X5872)
| ~ c_Polynomial_Opos__poly(X5873,X5871)
| c_Polynomial_Opos__poly(X5873,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X5873)),X5872),X5871)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pos__poly__add])]) ).
fof(i_0_1838,plain,
! [X5169,X5170] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,X5170)),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,X5169)) = c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X5170),X5169)),
inference(variable_rename,[status(thm)],[fact_Nat__Transfer_Otransfer__int__nat__functions_I2_J]) ).
fof(i_0_1839,plain,
! [X5019,X5020] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,X5020)),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,X5019)) = c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X5020),X5019)),
inference(variable_rename,[status(thm)],[fact_zmult__int]) ).
fof(i_0_1840,plain,
! [X5167,X5168] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,X5168)),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,X5167)) = c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X5168),X5167)),
inference(variable_rename,[status(thm)],[fact_Nat__Transfer_Otransfer__int__nat__functions_I1_J]) ).
fof(i_0_1841,plain,
! [X5012,X5013] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,X5013)),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,X5012)) = c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X5013),X5012)),
inference(variable_rename,[status(thm)],[fact_zadd__int]) ).
fof(i_0_1842,plain,
! [X4070,X4071] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X4071)),X4070) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X4071),X4070)),
inference(variable_rename,[status(thm)],[fact_zmult__zminus]) ).
fof(i_0_1843,plain,
! [X5021,X5022] : c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X5022),X5021)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,X5022)),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,X5021)),
inference(variable_rename,[status(thm)],[fact_int__mult]) ).
fof(i_0_1844,plain,
! [X5023,X5024,X5025] :
( ~ class_Rings_Osemiring__1(X5025)
| c_Nat_Osemiring__1__class_Oof__nat(X5025,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X5024),X5023)) = hAPP(hAPP(c_Power_Opower__class_Opower(X5025),c_Nat_Osemiring__1__class_Oof__nat(X5025,X5024)),X5023) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__nat__power])]) ).
fof(i_0_1845,plain,
! [X4872,X4873] : c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,X4873),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,X4872)) = c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X4873,X4872)),
inference(variable_rename,[status(thm)],[fact_Divides_Otransfer__int__nat__functions_I2_J]) ).
fof(i_0_1846,plain,
! [X4874,X4875] : c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X4875,X4874)) = c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,X4875),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,X4874)),
inference(variable_rename,[status(thm)],[fact_zmod__int]) ).
fof(i_0_1847,plain,
! [X5495,X5496] :
( ( ~ c_Orderings_Oord__class_Oless(X5496,hAPP(c_Groups_Ouminus__class_Ouminus(X5496),X5495),X5495)
| c_Orderings_Oord__class_Oless(X5496,c_Groups_Ozero__class_Ozero(X5496),X5495)
| ~ class_Groups_Olinordered__ab__group__add(X5496) )
& ( ~ c_Orderings_Oord__class_Oless(X5496,c_Groups_Ozero__class_Ozero(X5496),X5495)
| c_Orderings_Oord__class_Oless(X5496,hAPP(c_Groups_Ouminus__class_Ouminus(X5496),X5495),X5495)
| ~ class_Groups_Olinordered__ab__group__add(X5496) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_neg__less__nonneg])])]) ).
fof(i_0_1848,plain,
! [X5493,X5494] :
( ( ~ c_Orderings_Oord__class_Oless(X5494,X5493,hAPP(c_Groups_Ouminus__class_Ouminus(X5494),X5493))
| c_Orderings_Oord__class_Oless(X5494,X5493,c_Groups_Ozero__class_Ozero(X5494))
| ~ class_Rings_Olinordered__idom(X5494) )
& ( ~ c_Orderings_Oord__class_Oless(X5494,X5493,c_Groups_Ozero__class_Ozero(X5494))
| c_Orderings_Oord__class_Oless(X5494,X5493,hAPP(c_Groups_Ouminus__class_Ouminus(X5494),X5493))
| ~ class_Rings_Olinordered__idom(X5494) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__minus__self__iff])])]) ).
fof(i_0_1849,plain,
! [X4189,X4190,X4191] :
( ~ class_Lattices_Oab__semigroup__idem__mult(X4191)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4191),X4190),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4191),X4190),X4189)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4191),X4190),X4189) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__left__idem])]) ).
fof(i_0_1850,plain,
! [X4416] : hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X4416)),
inference(variable_rename,[status(thm)],[fact_dvd__1__left]) ).
fof(i_0_1851,plain,
! [X3959,X3960,X3961,X3962] :
( ~ class_Groups_Ouminus(X3962)
| hAPP(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X3961,X3962)),X3960),X3959) = hAPP(c_Groups_Ouminus__class_Ouminus(X3962),hAPP(X3960,X3959)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fun__Compl__def])]) ).
fof(i_0_1852,plain,
! [X3951,X3952,X3953,X3954] :
( ~ class_Groups_Ouminus(X3954)
| hAPP(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X3953,X3954)),X3952),X3951) = hAPP(c_Groups_Ouminus__class_Ouminus(X3954),hAPP(X3952,X3951)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_uminus__apply])]) ).
fof(i_0_1853,plain,
! [X5821,X5822] :
( ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,X5822),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,X5821))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X5822,X5821) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X5822,X5821)
| c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,X5822),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,X5821)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Nat__Transfer_Otransfer__int__nat__relations_I2_J])]) ).
fof(i_0_1854,plain,
! [X5819,X5820] :
( ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,X5820),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,X5819))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X5820,X5819) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X5820,X5819)
| c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,X5820),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,X5819)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zless__int])]) ).
fof(i_0_1855,plain,
! [X5407,X5408] :
( ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(c_Nat_OSuc,X5408),hAPP(c_Nat_OSuc,X5407))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X5408,X5407) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X5408,X5407)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(c_Nat_OSuc,X5408),hAPP(c_Nat_OSuc,X5407)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Suc__less__eq])]) ).
fof(i_0_1856,plain,
! [X5390,X5391] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(c_Nat_OSuc,X5391),hAPP(c_Nat_OSuc,X5390))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X5391,X5390) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Suc__less__SucD])]) ).
fof(i_0_1857,plain,
! [X5663] :
( ~ class_Rings_Olinordered__semidom(X5663)
| c_Orderings_Oord__class_Oless(X5663,c_Groups_Ozero__class_Ozero(X5663),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5663),c_Groups_Oone__class_Oone(X5663)),c_Groups_Oone__class_Oone(X5663))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__less__two])]) ).
fof(i_0_1858,plain,
! [X4169,X4170] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4170),hAPP(c_Nat_OSuc,X4169)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X4170),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4170),X4169)),
inference(variable_rename,[status(thm)],[fact_mult__Suc__right]) ).
fof(i_0_1859,plain,
! [X3712,X3713,X3714] :
( ~ class_Groups_Ozero(X3714)
| c_Polynomial_Ocoeff(X3714,hAPP(hAPP(c_Polynomial_OpCons(X3714),X3713),X3712)) = c_Nat_Onat_Onat__case(X3714,X3713,c_Polynomial_Ocoeff(X3714,X3712)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_coeff__pCons])]) ).
fof(i_0_1860,plain,
! [X5411,X5412] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X5412,X5411)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X5411,hAPP(c_Nat_OSuc,X5412)) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X5411,hAPP(c_Nat_OSuc,X5412))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X5412,X5411) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1204])]) ).
fof(i_0_1861,plain,
! [X5565,X5566,X5568,X5569,X5570] :
( ( X5566 = hAPP(c_Nat_OSuc,esk10_2(X5565,X5566))
| X5566 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X5566,hAPP(c_Nat_OSuc,X5565)) )
& ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,esk10_2(X5565,X5566),X5565)
| X5566 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X5566,hAPP(c_Nat_OSuc,X5565)) )
& ( X5569 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X5569,hAPP(c_Nat_OSuc,X5568)) )
& ( X5569 != hAPP(c_Nat_OSuc,X5570)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X5570,X5568)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X5569,hAPP(c_Nat_OSuc,X5568)) ) ),
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)],[fact_less__Suc__eq__0__disj])])])])])]) ).
fof(i_0_1862,plain,
! [X5549,X5550] :
( ~ class_Fields_Olinordered__field(X5550)
| ~ c_Orderings_Oord__class_Oless(X5550,X5549,c_Groups_Ozero__class_Ozero(X5550))
| c_Orderings_Oord__class_Oless(X5550,hAPP(c_Rings_Oinverse__class_Oinverse(X5550),X5549),c_Groups_Ozero__class_Ozero(X5550)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_negative__imp__inverse__negative])]) ).
fof(i_0_1863,plain,
! [X5545,X5546] :
( ~ class_Fields_Olinordered__field(X5546)
| ~ c_Orderings_Oord__class_Oless(X5546,c_Groups_Ozero__class_Ozero(X5546),X5545)
| c_Orderings_Oord__class_Oless(X5546,c_Groups_Ozero__class_Ozero(X5546),hAPP(c_Rings_Oinverse__class_Oinverse(X5546),X5545)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_positive__imp__inverse__positive])]) ).
fof(i_0_1864,plain,
! [X5189,X5190] :
( ( ~ c_Orderings_Oord__class_Oless(X5190,c_Groups_Ozero__class_Ozero(X5190),c_Nat_Osemiring__1__class_Oof__nat(X5190,X5189))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X5189)
| ~ class_Rings_Olinordered__semidom(X5190) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X5189)
| c_Orderings_Oord__class_Oless(X5190,c_Groups_Ozero__class_Ozero(X5190),c_Nat_Osemiring__1__class_Oof__nat(X5190,X5189))
| ~ class_Rings_Olinordered__semidom(X5190) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__nat__0__less__iff])])]) ).
fof(i_0_1865,plain,
! [X5878] :
( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X5878,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| X5878 = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,hAPP(c_Nat_OSuc,esk18_1(X5878)))) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_negD])])]) ).
fof(i_0_1866,plain,
! [X5781] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X5781)
| hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X5781),c_Groups_Oone__class_Oone(tc_Nat_Onat))) = X5781 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Suc__diff__1])]) ).
fof(i_0_1867,plain,
! [X5782] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X5782)
| X5782 = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X5782),c_Groups_Oone__class_Oone(tc_Nat_Onat))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Suc__pred_H])]) ).
fof(i_0_1868,plain,
! [X4264,X4265,X4266,X4267] :
( ~ class_Rings_Odvd(X4267)
| X4266 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4267),X4265),X4264)
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X4267),X4265),X4266)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvdI])]) ).
fof(i_0_1869,plain,
! [X5194,X5195,X5196] :
( ~ class_Rings_Olinordered__semidom(X5196)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X5195,X5194)
| c_Orderings_Oord__class_Oless(X5196,c_Nat_Osemiring__1__class_Oof__nat(X5196,X5195),c_Nat_Osemiring__1__class_Oof__nat(X5196,X5194)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__imp__of__nat__less])]) ).
fof(i_0_1870,plain,
! [X4031,X4032,X4033] :
( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4033),X4032),X4032) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4033),X4031),X4031)
| X4032 = X4031
| X4032 = hAPP(c_Groups_Ouminus__class_Ouminus(X4033),X4031)
| ~ class_Rings_Oidom(X4033) )
& ( X4032 != X4031
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4033),X4032),X4032) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4033),X4031),X4031)
| ~ class_Rings_Oidom(X4033) )
& ( X4032 != hAPP(c_Groups_Ouminus__class_Ouminus(X4033),X4031)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4033),X4032),X4032) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4033),X4031),X4031)
| ~ class_Rings_Oidom(X4033) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_square__eq__iff])])]) ).
fof(i_0_1871,plain,
! [X5096,X5097] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,X5097)),X5096) = c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X5097),X5096)),
inference(variable_rename,[status(thm)],[fact_Nat__Transfer_Otransfer__int__nat__functions_I4_J]) ).
fof(i_0_1872,plain,
! [X5030,X5031] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,X5031)),X5030) = c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X5031),X5030)),
inference(variable_rename,[status(thm)],[fact_zpower__int]) ).
fof(i_0_1873,plain,
! [X4066,X4067] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_OSuc,X4067)),X4066) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X4067),X4066)),
inference(variable_rename,[status(thm)],[fact_add__Suc]) ).
fof(i_0_1874,plain,
! [X5028,X5029] : c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X5029),X5028)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,X5029)),X5028),
inference(variable_rename,[status(thm)],[fact_int__power]) ).
fof(i_0_1875,plain,
! [X5354,X5355,X5356] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X5355,X5356)
| hBOOL(hAPP(hAPP(X5354,X5355),X5356))
| X5356 = X5355
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X5356,X5355) )
& ( ~ hBOOL(hAPP(hAPP(X5354,X5355),X5356))
| hBOOL(hAPP(hAPP(X5354,X5355),X5356))
| X5356 = X5355
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X5356,X5355) )
& ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X5355,X5356)
| hBOOL(hAPP(hAPP(X5354,X5355),X5356))
| ~ hBOOL(hAPP(hAPP(X5354,X5355),X5356))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X5356,X5355) )
& ( ~ hBOOL(hAPP(hAPP(X5354,X5355),X5356))
| hBOOL(hAPP(hAPP(X5354,X5355),X5356))
| ~ hBOOL(hAPP(hAPP(X5354,X5355),X5356))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X5356,X5355) )
& ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X5355,X5356)
| hBOOL(hAPP(hAPP(X5354,X5355),X5356))
| X5356 = X5355
| ~ hBOOL(hAPP(hAPP(X5354,X5355),X5356)) )
& ( ~ hBOOL(hAPP(hAPP(X5354,X5355),X5356))
| hBOOL(hAPP(hAPP(X5354,X5355),X5356))
| X5356 = X5355
| ~ hBOOL(hAPP(hAPP(X5354,X5355),X5356)) )
& ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X5355,X5356)
| hBOOL(hAPP(hAPP(X5354,X5355),X5356))
| ~ hBOOL(hAPP(hAPP(X5354,X5355),X5356))
| ~ hBOOL(hAPP(hAPP(X5354,X5355),X5356)) )
& ( ~ hBOOL(hAPP(hAPP(X5354,X5355),X5356))
| hBOOL(hAPP(hAPP(X5354,X5355),X5356))
| ~ hBOOL(hAPP(hAPP(X5354,X5355),X5356))
| ~ hBOOL(hAPP(hAPP(X5354,X5355),X5356)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__less__cases])])]) ).
fof(i_0_1876,plain,
! [X4593,X4594,X4595] :
( ~ class_Fields_Ofield(X4595)
| c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(X4595),X4594,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X4595)),X4593)) = c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(X4595),X4594,X4593) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_poly__mod__minus__right])]) ).
fof(i_0_1877,plain,
! [X5621,X5622] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X5622,X5621)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X5621),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X5622),X5621)) = X5622 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1205])]) ).
fof(i_0_1878,plain,
! [X5185,X5186] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X5186,X5185)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(c_Nat_OSuc,X5186),hAPP(c_Nat_OSuc,X5185)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Suc__mono])]) ).
fof(i_0_1879,plain,
! [X3645,X3646,X3647,X3648] :
( ~ class_Rings_Ocomm__semiring__0(X3648)
| hAPP(hAPP(c_Polynomial_Osmult(X3648),X3647),X3646) != hAPP(hAPP(c_Polynomial_OpCons(X3648),X3645),X3646)
| X3646 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3648)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_synthetic__div__unique__lemma])]) ).
fof(i_0_1880,plain,
! [X5488,X5489,X5490] :
( ~ class_Orderings_Owellorder(X5490)
| ~ c_Orderings_Oord__class_Oless(X5490,X5489,c_Orderings_Oord__class_OLeast(X5490,X5488))
| ~ hBOOL(hAPP(X5488,X5489)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1206])]) ).
fof(i_0_1881,plain,
! [X4927,X4928,X4929] :
( ~ class_Fields_Ofield__inverse__zero(X4929)
| hAPP(c_Rings_Oinverse__class_Oinverse(X4929),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4929),X4928),X4927)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4929),X4927),X4928) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inverse__divide])]) ).
fof(i_0_1882,plain,
! [X4046,X4047,X4048] :
( ~ class_Groups_Oab__group__add(X4048)
| hAPP(c_Groups_Ouminus__class_Ouminus(X4048),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X4048),X4047),X4046)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(X4048),X4046),X4047) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_minus__diff__eq])]) ).
fof(i_0_1883,plain,
! [X5844] :
( ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,X5844))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X5844) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X5844)
| c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,X5844)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__less__int__conv])]) ).
fof(i_0_1884,plain,
! [X3502,X3503,X3504,X3505] :
( ( c_Polynomial_Omonom(X3505,X3504,X3503) != c_Polynomial_Omonom(X3505,X3502,X3503)
| X3504 = X3502
| ~ class_Groups_Ozero(X3505) )
& ( X3504 != X3502
| c_Polynomial_Omonom(X3505,X3504,X3503) = c_Polynomial_Omonom(X3505,X3502,X3503)
| ~ class_Groups_Ozero(X3505) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_monom__eq__iff])])]) ).
fof(i_0_1885,plain,
! [X4128,X4129] :
( ~ class_Rings_Ocomm__ring__1(X4129)
| hAPP(c_Groups_Ouminus__class_Ouminus(X4129),X4128) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4129),hAPP(c_Groups_Ouminus__class_Ouminus(X4129),c_Groups_Oone__class_Oone(X4129))),X4128) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__ring__1__class_Onormalizing__ring__rules_I1_J])]) ).
fof(i_0_1886,plain,
! [X5455,X5456,X5457] :
( ~ class_Orderings_Oorder(X5457)
| ~ c_Orderings_Oord__class_Oless(X5457,X5456,X5455)
| ~ c_Orderings_Oord__class_Oless(X5457,X5455,X5456) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1207])]) ).
fof(i_0_1887,plain,
! [X5425,X5426,X5427] :
( ( c_Orderings_Oord__class_Oless(X5427,X5426,X5425)
| c_Orderings_Oord__class_Oless(X5427,X5425,X5426)
| X5426 = X5425
| ~ class_Orderings_Olinorder(X5427) )
& ( ~ c_Orderings_Oord__class_Oless(X5427,X5425,X5426)
| ~ c_Orderings_Oord__class_Oless(X5427,X5426,X5425)
| ~ class_Orderings_Olinorder(X5427) )
& ( X5426 != X5425
| ~ c_Orderings_Oord__class_Oless(X5427,X5426,X5425)
| ~ class_Orderings_Olinorder(X5427) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1208])])]) ).
fof(i_0_1888,plain,
! [X5482,X5483,X5484] :
( ~ class_Orderings_Opreorder(X5484)
| ~ c_Orderings_Oord__class_Oless(X5484,X5483,X5482)
| ~ c_Orderings_Oord__class_Oless(X5484,X5482,X5483) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1209])]) ).
fof(i_0_1889,plain,
! [X5452,X5453,X5454] :
( ~ class_Orderings_Opreorder(X5454)
| ~ c_Orderings_Oord__class_Oless(X5454,X5453,X5452)
| ~ c_Orderings_Oord__class_Oless(X5454,X5452,X5453) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1210])]) ).
fof(i_0_1890,plain,
! [X5443,X5444,X5445] :
( ~ class_Orderings_Opreorder(X5445)
| ~ c_Orderings_Oord__class_Oless(X5445,X5444,X5443)
| ~ c_Orderings_Oord__class_Oless(X5445,X5443,X5444) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1211])]) ).
fof(i_0_1891,plain,
! [X5440,X5441,X5442] :
( ~ class_Orderings_Opreorder(X5442)
| ~ c_Orderings_Oord__class_Oless(X5442,X5441,X5440)
| ~ c_Orderings_Oord__class_Oless(X5442,X5440,X5441) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1212])]) ).
fof(i_0_1892,plain,
! [X3941,X3942,X3943] :
( ~ class_Fields_Ofield(X3943)
| c_Polynomial_Opoly__gcd(X3943,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X3943)),X3942),X3941) = c_Polynomial_Opoly__gcd(X3943,X3942,X3941) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_poly__gcd__minus__left])]) ).
fof(i_0_1893,plain,
! [X3934,X3935,X3936] :
( ~ class_Fields_Ofield(X3936)
| c_Polynomial_Opoly__gcd(X3936,X3935,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X3936)),X3934)) = c_Polynomial_Opoly__gcd(X3936,X3935,X3934) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_poly__gcd__minus__right])]) ).
fof(i_0_1894,plain,
! [X3351,X3352,X3353] :
( ( hAPP(c_Polynomial_Opoly(X3353,X3352),X3351) != c_Groups_Ozero__class_Ozero(X3353)
| X3352 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3353))
| c_Polynomial_Oorder(X3353,X3351,X3352) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ class_Rings_Oidom(X3353) )
& ( X3352 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3353))
| hAPP(c_Polynomial_Opoly(X3353,X3352),X3351) = c_Groups_Ozero__class_Ozero(X3353)
| ~ class_Rings_Oidom(X3353) )
& ( c_Polynomial_Oorder(X3353,X3351,X3352) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(c_Polynomial_Opoly(X3353,X3352),X3351) = c_Groups_Ozero__class_Ozero(X3353)
| ~ class_Rings_Oidom(X3353) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__root])])]) ).
fof(i_0_1895,plain,
! [X3741,X3742,X3743,X3744,X3745] :
( ( X3744 != X3743
| X3742 = X3741
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(X3745),X3744),X3743) != hAPP(hAPP(c_Groups_Ominus__class_Ominus(X3745),X3742),X3741)
| ~ class_Groups_Oab__group__add(X3745) )
& ( X3742 != X3741
| X3744 = X3743
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(X3745),X3744),X3743) != hAPP(hAPP(c_Groups_Ominus__class_Ominus(X3745),X3742),X3741)
| ~ class_Groups_Oab__group__add(X3745) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__eq__diff__eq])])]) ).
fof(i_0_1896,plain,
! [X5507,X5508] :
( ~ class_Rings_Olinordered__semidom(X5508)
| c_Orderings_Oord__class_Oless(X5508,X5507,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5508),X5507),c_Groups_Oone__class_Oone(X5508))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__add__one])]) ).
fof(i_0_1897,plain,
! [X5766,X5767,X5768] :
( ~ class_Groups_Ozero(X5768)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(X5768,X5767),X5766)
| hAPP(c_Polynomial_Ocoeff(X5768,X5767),X5766) = c_Groups_Ozero__class_Ozero(X5768) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_coeff__eq__0])]) ).
fof(i_0_1898,plain,
! [X5409,X5410] :
( ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X5410,hAPP(c_Nat_OSuc,X5409))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X5410,X5409)
| X5410 = X5409 )
& ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X5410,X5409)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X5410,hAPP(c_Nat_OSuc,X5409)) )
& ( X5410 != X5409
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X5410,hAPP(c_Nat_OSuc,X5409)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__Suc__eq])])]) ).
fof(i_0_1899,plain,
! [X5405,X5406] :
( ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X5406,hAPP(c_Nat_OSuc,X5405))
| X5406 = X5405
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X5406,X5405) )
& ( X5406 != X5405
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X5406,hAPP(c_Nat_OSuc,X5405))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X5406,X5405) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1213])])]) ).
fof(i_0_1900,plain,
! [X5403,X5404] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X5404,X5403)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X5404,hAPP(c_Nat_OSuc,X5403))
| X5403 = X5404 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1214])]) ).
fof(i_0_1901,plain,
! [X5394,X5395] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X5395,hAPP(c_Nat_OSuc,X5394))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X5395,X5394)
| X5395 = X5394 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1215])]) ).
fof(i_0_1902,plain,
! [X4702,X4703] :
( c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X4703),X4702) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| c_Divides_Odiv__class_Omod(tc_Int_Oint,X4703,X4702) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zmod__zminus1__not__zero])]) ).
fof(i_0_1903,plain,
! [X4700,X4701] :
( c_Divides_Odiv__class_Omod(tc_Int_Oint,X4701,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X4700)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| c_Divides_Odiv__class_Omod(tc_Int_Oint,X4701,X4700) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zmod__zminus2__not__zero])]) ).
fof(i_0_1904,plain,
! [X5399,X5400] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X5400,X5399)
| hAPP(c_Nat_OSuc,X5400) = X5399
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(c_Nat_OSuc,X5400),X5399) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Suc__lessI])]) ).
fof(i_0_1905,plain,
! [X6033,X6034] :
( ( X6033 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X6034))
| c_Groups_Osgn__class_Osgn(tc_Polynomial_Opoly(X6034),X6033) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X6034))
| ~ class_Rings_Olinordered__idom(X6034) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(X6034),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X6034)),X6033)
| c_Groups_Osgn__class_Osgn(tc_Polynomial_Opoly(X6034),X6033) = c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(X6034))
| X6033 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X6034))
| ~ class_Rings_Olinordered__idom(X6034) )
& ( c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(X6034),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X6034)),X6033)
| c_Groups_Osgn__class_Osgn(tc_Polynomial_Opoly(X6034),X6033) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X6034)),c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(X6034)))
| X6033 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X6034))
| ~ class_Rings_Olinordered__idom(X6034) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1216])])]) ).
fof(i_0_1906,plain,
! [X3250,X3251,X3252,X3253,X3254] :
( ( X3253 = X3251
| hAPP(hAPP(c_Polynomial_OpCons(X3254),X3253),X3252) != hAPP(hAPP(c_Polynomial_OpCons(X3254),X3251),X3250)
| ~ class_Groups_Ozero(X3254) )
& ( X3252 = X3250
| hAPP(hAPP(c_Polynomial_OpCons(X3254),X3253),X3252) != hAPP(hAPP(c_Polynomial_OpCons(X3254),X3251),X3250)
| ~ class_Groups_Ozero(X3254) )
& ( X3253 != X3251
| X3252 != X3250
| hAPP(hAPP(c_Polynomial_OpCons(X3254),X3253),X3252) = hAPP(hAPP(c_Polynomial_OpCons(X3254),X3251),X3250)
| ~ class_Groups_Ozero(X3254) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pCons__eq__iff])])]) ).
fof(i_0_1907,plain,
! [X3408,X3409,X3410,X3411] :
( ~ class_Groups_Ocancel__semigroup__add(X3411)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X3411),X3410),X3409) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(X3411),X3408),X3409)
| X3410 = X3408 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__right__imp__eq])]) ).
fof(i_0_1908,plain,
! [X3396,X3397,X3398,X3399] :
( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X3399),X3398),X3397) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(X3399),X3396),X3397)
| X3398 = X3396
| ~ class_Groups_Ocancel__semigroup__add(X3399) )
& ( X3398 != X3396
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X3399),X3398),X3397) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X3399),X3396),X3397)
| ~ class_Groups_Ocancel__semigroup__add(X3399) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__right__cancel])])]) ).
fof(i_0_1909,plain,
! [X3404,X3405,X3406,X3407] :
( ~ class_Groups_Ocancel__ab__semigroup__add(X3407)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X3407),X3406),X3405) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(X3407),X3406),X3404)
| X3405 = X3404 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__imp__eq])]) ).
fof(i_0_1910,plain,
! [X3400,X3401,X3402,X3403] :
( ~ class_Groups_Ocancel__semigroup__add(X3403)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X3403),X3402),X3401) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(X3403),X3402),X3400)
| X3401 = X3400 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__left__imp__eq])]) ).
fof(i_0_1911,plain,
! [X3392,X3393,X3394,X3395] :
( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X3395),X3394),X3393) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(X3395),X3394),X3392)
| X3393 = X3392
| ~ class_Groups_Ocancel__semigroup__add(X3395) )
& ( X3393 != X3392
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X3395),X3394),X3393) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X3395),X3394),X3392)
| ~ class_Groups_Ocancel__semigroup__add(X3395) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__left__cancel])])]) ).
fof(i_0_1912,plain,
! [X4208,X4209,X4210] :
( ( X4209 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4210))
| c_Polynomial_Odegree(X4210,hAPP(hAPP(c_Polynomial_OpCons(X4210),X4208),X4209)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ class_Groups_Ozero(X4210) )
& ( X4209 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4210))
| c_Polynomial_Odegree(X4210,hAPP(hAPP(c_Polynomial_OpCons(X4210),X4208),X4209)) = hAPP(c_Nat_OSuc,c_Polynomial_Odegree(X4210,X4209))
| ~ class_Groups_Ozero(X4210) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_degree__pCons__eq__if])])]) ).
fof(i_0_1913,plain,
! [X4197,X4198,X4199] :
( ~ class_Groups_Ozero(X4199)
| X4198 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4199))
| c_Polynomial_Odegree(X4199,hAPP(hAPP(c_Polynomial_OpCons(X4199),X4197),X4198)) = hAPP(c_Nat_OSuc,c_Polynomial_Odegree(X4199,X4198)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_degree__pCons__eq])]) ).
fof(i_0_1914,plain,
! [X5392,X5393] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(c_Nat_OSuc,X5393),X5392)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X5393,X5392) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Suc__lessD])]) ).
fof(i_0_1915,plain,
! [X5932,X5933,X5934] :
( ~ class_Divides_Osemiring__div(X5934)
| c_Divides_Odiv__class_Odiv(X5934,c_Divides_Odiv__class_Omod(X5934,X5933,X5932),X5932) = c_Groups_Ozero__class_Ozero(X5934) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__div__trivial])]) ).
fof(i_0_1916,plain,
! [X4064,X4065] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X4065),hAPP(c_Nat_OSuc,X4064)) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X4065),X4064)),
inference(variable_rename,[status(thm)],[fact_add__Suc__right]) ).
fof(i_0_1917,plain,
! [X5896,X5897,X5898] :
( ~ class_Divides_Osemiring__div(X5898)
| X5897 = c_Groups_Ozero__class_Ozero(X5898)
| c_Divides_Odiv__class_Odiv(X5898,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5898),X5897),X5896),X5897) = X5896 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_div__mult__self1__is__id])]) ).
fof(i_0_1918,plain,
! [X5893,X5894,X5895] :
( ~ class_Divides_Osemiring__div(X5895)
| X5894 = c_Groups_Ozero__class_Ozero(X5895)
| c_Divides_Odiv__class_Odiv(X5895,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5895),X5893),X5894),X5894) = X5893 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_div__mult__self2__is__id])]) ).
fof(i_0_1919,plain,
! [X5970,X5971] : c_Divides_Odiv__class_Odiv(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X5971),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X5970)) = c_Divides_Odiv__class_Odiv(tc_Int_Oint,X5971,X5970),
inference(variable_rename,[status(thm)],[fact_zdiv__zminus__zminus]) ).
fof(i_0_1920,plain,
! [X5968,X5969] : c_Divides_Odiv__class_Odiv(tc_Int_Oint,X5969,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X5968)) = c_Divides_Odiv__class_Odiv(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X5969),X5968),
inference(variable_rename,[status(thm)],[fact_zdiv__zminus2]) ).
fof(i_0_1921,plain,
! [X5836,X5837] :
( ( X5837 = c_Groups_Oone__class_Oone(tc_Int_Oint)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X5837),X5836) != c_Groups_Oone__class_Oone(tc_Int_Oint)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X5837) )
& ( X5836 = c_Groups_Oone__class_Oone(tc_Int_Oint)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X5837),X5836) != c_Groups_Oone__class_Oone(tc_Int_Oint)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X5837) )
& ( X5837 != c_Groups_Oone__class_Oone(tc_Int_Oint)
| X5836 != c_Groups_Oone__class_Oone(tc_Int_Oint)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X5837),X5836) = c_Groups_Oone__class_Oone(tc_Int_Oint)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X5837) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pos__zmult__eq__1__iff])])]) ).
fof(i_0_1922,plain,
! [X4847,X4848,X4849] :
( ~ class_Divides_Osemiring__div(X4849)
| c_Divides_Odiv__class_Omod(X4849,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4849),X4848),X4847),X4848) = c_Groups_Ozero__class_Ozero(X4849) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__mult__self1__is__0])]) ).
fof(i_0_1923,plain,
! [X4844,X4845,X4846] :
( ~ class_Divides_Osemiring__div(X4846)
| c_Divides_Odiv__class_Omod(X4846,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4846),X4845),X4844),X4844) = c_Groups_Ozero__class_Ozero(X4846) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__mult__self2__is__0])]) ).
fof(i_0_1924,plain,
! [X5619,X5620] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X5620),X5619),hAPP(c_Nat_OSuc,X5620)),
inference(variable_rename,[status(thm)],[fact_diff__less__Suc]) ).
fof(i_0_1925,plain,
! [X3868,X3869] :
( ~ class_Groups_Ozero(X3869)
| c_Polynomial_Odegree(X3869,hAPP(hAPP(c_Polynomial_OpCons(X3869),X3868),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3869)))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_degree__pCons__0])]) ).
fof(i_0_1926,plain,
! [X4429] :
( ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X4429),c_Groups_Oone__class_Oone(tc_Nat_Onat)))
| X4429 = c_Groups_Oone__class_Oone(tc_Nat_Onat) )
& ( X4429 != c_Groups_Oone__class_Oone(tc_Nat_Onat)
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X4429),c_Groups_Oone__class_Oone(tc_Nat_Onat))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__dvd__1__iff__1])]) ).
fof(i_0_1927,plain,
! [X4078,X4079] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,X4079)),hAPP(c_Nat_OSuc,X4078)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X4079),X4078),
inference(variable_rename,[status(thm)],[fact_diff__Suc__Suc]) ).
fof(i_0_1928,plain,
! [X4068,X4069] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_OSuc,X4069)),X4068) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X4069),hAPP(c_Nat_OSuc,X4068)),
inference(variable_rename,[status(thm)],[fact_add__Suc__shift]) ).
fof(i_0_1929,plain,
! [X4707,X4708,X4710,X4711,X4712] :
( ( c_Divides_Odiv__class_Omod(tc_Int_Oint,X4708,X4707) != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| X4708 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X4707),esk8_2(X4707,X4708)) )
& ( X4711 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X4710),X4712)
| c_Divides_Odiv__class_Omod(tc_Int_Oint,X4711,X4710) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zmod__eq__0__iff])])])])]) ).
fof(i_0_1930,plain,
! [X4713,X4714,X4716,X4717,X4718] :
( ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,X4714,X4713) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X4714 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4713),esk9_2(X4713,X4714)) )
& ( X4717 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4716),X4718)
| c_Divides_Odiv__class_Omod(tc_Nat_Onat,X4717,X4716) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__eq__0__iff])])])])]) ).
fof(i_0_1931,plain,
( ~ class_Rings_Oidom(t_a)
| ~ c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(t_a,t_a,c_Polynomial_Opoly(t_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)))) ),
inference(fof_nnf,[status(thm)],[i_0_1217]) ).
fof(i_0_1932,plain,
! [X5401,X5402] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X5402,X5401)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X5402,hAPP(c_Nat_OSuc,X5401)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__SucI])]) ).
fof(i_0_1933,plain,
! [X5982,X5983] : c_Divides_Odiv__class_Odiv(tc_Int_Oint,c_Divides_Odiv__class_Omod(tc_Int_Oint,X5983,X5982),X5982) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
inference(variable_rename,[status(thm)],[fact_zmod__zdiv__trivial]) ).
fof(i_0_1934,plain,
! [X4097,X4098,X4099,X4100] : hAPP(c_Nat_Onat_Onat__case(X4100,X4099,X4098),hAPP(c_Nat_OSuc,X4097)) = hAPP(X4098,X4097),
inference(variable_rename,[status(thm)],[fact_nat__case__Suc]) ).
fof(i_0_1935,plain,
! [X3797,X3798] :
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X3798),X3797) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X3797),X3798) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X3798 = X3797 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diffs0__imp__equal])]) ).
fof(i_0_1936,plain,
! [X6044,X6045] : c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,X6045)),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,X6044)),
inference(variable_rename,[status(thm)],[fact_negative__zle]) ).
fof(i_0_1937,plain,
! [X4941,X4942,X4943,X4944] :
( ( X4942 = c_Groups_Ozero__class_Ozero(X4944)
| X4943 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4944),X4941),X4942)
| hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4944),X4943),X4942) != X4941
| ~ class_Fields_Ofield__inverse__zero(X4944) )
& ( X4942 != c_Groups_Ozero__class_Ozero(X4944)
| X4941 = c_Groups_Ozero__class_Ozero(X4944)
| hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4944),X4943),X4942) != X4941
| ~ class_Fields_Ofield__inverse__zero(X4944) )
& ( X4942 = c_Groups_Ozero__class_Ozero(X4944)
| X4942 != c_Groups_Ozero__class_Ozero(X4944)
| hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4944),X4943),X4942) = X4941
| ~ class_Fields_Ofield__inverse__zero(X4944) )
& ( X4941 != c_Groups_Ozero__class_Ozero(X4944)
| X4942 != c_Groups_Ozero__class_Ozero(X4944)
| hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4944),X4943),X4942) = X4941
| ~ class_Fields_Ofield__inverse__zero(X4944) )
& ( X4942 = c_Groups_Ozero__class_Ozero(X4944)
| X4943 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4944),X4941),X4942)
| hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4944),X4943),X4942) = X4941
| ~ class_Fields_Ofield__inverse__zero(X4944) )
& ( X4941 != c_Groups_Ozero__class_Ozero(X4944)
| X4943 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4944),X4941),X4942)
| hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4944),X4943),X4942) = X4941
| ~ class_Fields_Ofield__inverse__zero(X4944) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divide__eq__eq])])]) ).
fof(i_0_1938,plain,
! [X4937,X4938,X4939,X4940] :
( ( X4937 = c_Groups_Ozero__class_Ozero(X4940)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4940),X4939),X4937) = X4938
| X4939 != hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4940),X4938),X4937)
| ~ class_Fields_Ofield__inverse__zero(X4940) )
& ( X4937 != c_Groups_Ozero__class_Ozero(X4940)
| X4939 = c_Groups_Ozero__class_Ozero(X4940)
| X4939 != hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4940),X4938),X4937)
| ~ class_Fields_Ofield__inverse__zero(X4940) )
& ( X4937 = c_Groups_Ozero__class_Ozero(X4940)
| X4937 != c_Groups_Ozero__class_Ozero(X4940)
| X4939 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4940),X4938),X4937)
| ~ class_Fields_Ofield__inverse__zero(X4940) )
& ( X4939 != c_Groups_Ozero__class_Ozero(X4940)
| X4937 != c_Groups_Ozero__class_Ozero(X4940)
| X4939 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4940),X4938),X4937)
| ~ class_Fields_Ofield__inverse__zero(X4940) )
& ( X4937 = c_Groups_Ozero__class_Ozero(X4940)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4940),X4939),X4937) != X4938
| X4939 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4940),X4938),X4937)
| ~ class_Fields_Ofield__inverse__zero(X4940) )
& ( X4939 != c_Groups_Ozero__class_Ozero(X4940)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4940),X4939),X4937) != X4938
| X4939 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4940),X4938),X4937)
| ~ class_Fields_Ofield__inverse__zero(X4940) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_eq__divide__eq])])]) ).
fof(i_0_1939,plain,
! [X3914,X3915] :
( ~ class_Groups_Oab__group__add(X3915)
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X3915)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3915))),X3914) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X3915)),X3914) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__poly__code_I1_J])]) ).
fof(i_0_1940,plain,
! [X3421,X3422,X3423] :
( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3423),X3422) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3421),X3422)
| X3423 = X3421
| X3422 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( X3423 != X3421
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3423),X3422) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3421),X3422) )
& ( X3422 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3423),X3422) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3421),X3422) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__cancel2])])]) ).
fof(i_0_1941,plain,
! [X3470,X3471,X3472] :
( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3472),X3471) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3472),X3470)
| X3472 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X3471 = X3470 )
& ( X3472 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3472),X3471) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3472),X3470) )
& ( X3471 != X3470
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3472),X3471) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3472),X3470) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__mult__eq__cancel__disj])])]) ).
fof(i_0_1942,plain,
! [X3418,X3419,X3420] :
( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3420),X3419) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3420),X3418)
| X3419 = X3418
| X3420 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( X3419 != X3418
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3420),X3419) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3420),X3418) )
& ( X3420 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3420),X3419) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3420),X3418) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__cancel1])])]) ).
fof(i_0_1943,plain,
! [X4966,X4967,X4968,X4969] :
( ~ class_Rings_Odivision__ring(X4969)
| X4968 = c_Groups_Ozero__class_Ozero(X4969)
| X4967 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4969),X4966),X4968)
| hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4969),X4967),X4968) = X4966 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divide__eq__imp])]) ).
fof(i_0_1944,plain,
! [X4962,X4963,X4964,X4965] :
( ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4965),X4963),X4964) != X4962
| X4963 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4965),X4962),X4964)
| X4964 = c_Groups_Ozero__class_Ozero(X4965)
| ~ class_Rings_Odivision__ring(X4965) )
& ( X4963 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4965),X4962),X4964)
| hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4965),X4963),X4964) = X4962
| X4964 = c_Groups_Ozero__class_Ozero(X4965)
| ~ class_Rings_Odivision__ring(X4965) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nonzero__divide__eq__eq])])]) ).
fof(i_0_1945,plain,
! [X4958,X4959,X4960,X4961] :
( ( X4959 != hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4961),X4958),X4960)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4961),X4959),X4960) = X4958
| X4960 = c_Groups_Ozero__class_Ozero(X4961)
| ~ class_Rings_Odivision__ring(X4961) )
& ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4961),X4959),X4960) != X4958
| X4959 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4961),X4958),X4960)
| X4960 = c_Groups_Ozero__class_Ozero(X4961)
| ~ class_Rings_Odivision__ring(X4961) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nonzero__eq__divide__eq])])]) ).
fof(i_0_1946,plain,
! [X4970,X4971,X4972,X4973] :
( ~ class_Rings_Odivision__ring(X4973)
| X4972 = c_Groups_Ozero__class_Ozero(X4973)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4973),X4971),X4972) != X4970
| X4971 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4973),X4970),X4972) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_eq__divide__imp])]) ).
fof(i_0_1947,plain,
! [X4135,X4136,X4137] :
( ~ class_Groups_Ogroup__add(X4137)
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(X4137),X4136),hAPP(c_Groups_Ouminus__class_Ouminus(X4137),X4135)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4137),X4136),X4135) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__minus__eq__add])]) ).
fof(i_0_1948,plain,
! [X5005,X5006,X5007] :
( ~ class_Rings_Odivision__ring(X5007)
| hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X5007),X5006),X5005) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5007),X5006),hAPP(c_Rings_Oinverse__class_Oinverse(X5007),X5005)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divide__inverse])]) ).
fof(i_0_1949,plain,
! [X5002,X5003,X5004] :
( ~ class_Fields_Ofield(X5004)
| hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X5004),X5003),X5002) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5004),X5003),hAPP(c_Rings_Oinverse__class_Oinverse(X5004),X5002)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_field__divide__inverse])]) ).
fof(i_0_1950,plain,
! [X4141,X4142,X4143] :
( ~ class_Groups_Ogroup__add(X4143)
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(X4143),X4142),X4141) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4143),X4142),hAPP(c_Groups_Ouminus__class_Ouminus(X4143),X4141)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__def])]) ).
fof(i_0_1951,plain,
! [X4138,X4139,X4140] :
( ~ class_Groups_Oab__group__add(X4140)
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(X4140),X4139),X4138) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4140),X4139),hAPP(c_Groups_Ouminus__class_Ouminus(X4140),X4138)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ab__diff__minus])]) ).
fof(i_0_1952,plain,
! [X4132,X4133,X4134] :
( ~ class_Rings_Ocomm__ring__1(X4134)
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(X4134),X4133),X4132) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4134),X4133),hAPP(c_Groups_Ouminus__class_Ouminus(X4134),X4132)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__ring__1__class_Onormalizing__ring__rules_I2_J])]) ).
fof(i_0_1953,plain,
! [X3435,X3436,X3437] :
( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3437),X3436) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3435),X3436)
| X3437 = X3435 )
& ( X3437 != X3435
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3437),X3436) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3435),X3436) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__add__right__cancel])]) ).
fof(i_0_1954,plain,
! [X3432,X3433,X3434] :
( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3434),X3433) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3434),X3432)
| X3433 = X3432 )
& ( X3433 != X3432
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3434),X3433) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3434),X3432) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__add__left__cancel])]) ).
fof(i_0_1955,plain,
! [X4381,X4382] :
( ~ class_Rings_Odivision__ring(X4382)
| X4381 = c_Groups_Ozero__class_Ozero(X4382)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4382),hAPP(c_Rings_Oinverse__class_Oinverse(X4382),X4381)),X4381) = c_Groups_Oone__class_Oone(X4382) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_left__inverse])]) ).
fof(i_0_1956,plain,
! [X4392,X4393] :
( ~ class_Fields_Ofield(X4393)
| X4392 = c_Groups_Ozero__class_Ozero(X4393)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4393),hAPP(c_Rings_Oinverse__class_Oinverse(X4393),X4392)),X4392) = c_Groups_Oone__class_Oone(X4393) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_field__inverse])]) ).
fof(i_0_1957,plain,
! [X5539,X5540] :
( ~ class_Rings_Olinordered__semidom(X5540)
| ~ c_Orderings_Oord__class_Oless(X5540,c_Nat_Osemiring__1__class_Oof__nat(X5540,X5539),c_Groups_Ozero__class_Ozero(X5540)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1218])]) ).
fof(i_0_1958,plain,
! [X3861,X3862,X3863] :
( ( X3862 != c_Groups_Ozero__class_Ozero(X3863)
| c_Polynomial_Odegree(X3863,hAPP(hAPP(c_Polynomial_Osmult(X3863),X3862),X3861)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ class_Rings_Oidom(X3863) )
& ( X3862 = c_Groups_Ozero__class_Ozero(X3863)
| c_Polynomial_Odegree(X3863,hAPP(hAPP(c_Polynomial_Osmult(X3863),X3862),X3861)) = c_Polynomial_Odegree(X3863,X3861)
| ~ class_Rings_Oidom(X3863) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_degree__smult__eq])])]) ).
fof(i_0_1959,plain,
! [X3824,X3825,X3826] :
( ~ class_Rings_Ocomm__semiring__0(X3826)
| c_Polynomial_Odegree(X3826,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X3826,X3825,X3824)) = c_Polynomial_Odegree(X3826,X3825) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_degree__offset__poly])]) ).
fof(i_0_1960,plain,
! [X4119,X4120] :
( ~ class_Groups_Ogroup__add(X4120)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4120),hAPP(c_Groups_Ouminus__class_Ouminus(X4120),X4119)),X4119) = c_Groups_Ozero__class_Ozero(X4120) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_left__minus])]) ).
fof(i_0_1961,plain,
! [X4121,X4122] :
( ~ class_Groups_Oab__group__add(X4122)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4122),hAPP(c_Groups_Ouminus__class_Ouminus(X4122),X4121)),X4121) = c_Groups_Ozero__class_Ozero(X4122) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ab__left__minus])]) ).
fof(i_0_1962,plain,
! [X3853,X3854] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X3854),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3854),X3853)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(variable_rename,[status(thm)],[fact_diff__add__0]) ).
fof(i_0_1963,plain,
! [X4307,X4308] :
( ~ class_Rings_Ocomm__semiring__1(X4308)
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X4308),c_Groups_Oone__class_Oone(X4308)),X4307)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_one__dvd])]) ).
fof(i_0_1964,plain,
! [X5491,X5492] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X5492,X5491)
| c_Divides_Odiv__class_Omod(tc_Nat_Onat,X5492,X5491) = X5492 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__less])]) ).
fof(i_0_1965,plain,
! [X4646,X4647,X4648] :
( ~ class_Orderings_Owellorder(X4647)
| ~ hBOOL(hAPP(X4646,X4648))
| hBOOL(hAPP(X4646,c_Orderings_Oord__class_OLeast(X4647,X4646))) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_LeastI__ex])])]) ).
fof(i_0_1966,plain,
! [X4548,X4549,X4550] :
( ~ class_Orderings_Owellorder(X4550)
| ~ hBOOL(hAPP(X4549,X4548))
| hBOOL(hAPP(X4549,c_Orderings_Oord__class_OLeast(X4550,X4549))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_LeastI])]) ).
fof(i_0_1967,plain,
! [X3525,X3526] :
( ~ class_Groups_Ozero(X3526)
| c_Polynomial_Omonom(X3526,X3525,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(hAPP(c_Polynomial_OpCons(X3526),X3525),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3526))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_monom__0])]) ).
fof(i_0_1968,plain,
! [X3850,X3851,X3852] :
( ~ class_Groups_Ozero(X3852)
| X3851 = c_Groups_Ozero__class_Ozero(X3852)
| c_Polynomial_Odegree(X3852,c_Polynomial_Omonom(X3852,X3851,X3850)) = X3850 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_degree__monom__eq])]) ).
fof(i_0_1969,plain,
! [X5032,X5033] :
( ~ class_Rings_Osemiring__1(X5033)
| c_Nat_Osemiring__1__class_Oof__nat(X5033,hAPP(c_Nat_OSuc,X5032)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5033),c_Groups_Oone__class_Oone(X5033)),c_Nat_Osemiring__1__class_Oof__nat(X5033,X5032)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__nat__Suc])]) ).
fof(i_0_1970,plain,
! [X5571] :
( ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X5571,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| X5571 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( X5571 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X5571,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__Suc0])]) ).
fof(i_0_1971,plain,
! [X3180,X3181] :
( ~ class_Rings_Ocomm__semiring__0(X3181)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X3181)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3181))),X3180) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3181)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__poly__0__left])]) ).
fof(i_0_1972,plain,
! [X4163,X4164] :
( ( X4164 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X4164 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X4164),X4163) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
& ( X4163 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| X4164 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X4164),X4163) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
& ( X4164 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X4163 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X4164),X4163) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
& ( X4163 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| X4163 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X4164),X4163) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
& ( X4164 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| X4163 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X4164),X4163) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
& ( X4164 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X4163 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X4164),X4163) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__is__1])])]) ).
fof(i_0_1973,plain,
! [X4161,X4162] :
( ( X4162 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X4162 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X4162),X4161) )
& ( X4161 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| X4162 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X4162),X4161) )
& ( X4162 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X4161 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X4162),X4161) )
& ( X4161 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| X4161 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X4162),X4161) )
& ( X4162 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| X4161 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X4162),X4161) )
& ( X4162 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X4161 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X4162),X4161) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_one__is__add])])]) ).
fof(i_0_1974,plain,
! [X4352,X4353] :
( ~ class_Rings_Odivision__ring(X4353)
| X4352 = c_Groups_Ozero__class_Ozero(X4353)
| hAPP(c_Rings_Oinverse__class_Oinverse(X4353),hAPP(c_Groups_Ouminus__class_Ouminus(X4353),X4352)) = hAPP(c_Groups_Ouminus__class_Ouminus(X4353),hAPP(c_Rings_Oinverse__class_Oinverse(X4353),X4352)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nonzero__inverse__minus__eq])]) ).
fof(i_0_1975,plain,
! [X3866,X3867] :
( ( hAPP(c_Polynomial_Ocoeff(X3867,X3866),c_Polynomial_Odegree(X3867,X3866)) != c_Groups_Ozero__class_Ozero(X3867)
| X3866 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3867))
| ~ class_Groups_Ozero(X3867) )
& ( X3866 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3867))
| hAPP(c_Polynomial_Ocoeff(X3867,X3866),c_Polynomial_Odegree(X3867,X3866)) = c_Groups_Ozero__class_Ozero(X3867)
| ~ class_Groups_Ozero(X3867) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_leading__coeff__0__iff])])]) ).
fof(i_0_1976,plain,
! [X3864,X3865] :
( ~ class_Groups_Ozero(X3865)
| X3864 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3865))
| hAPP(c_Polynomial_Ocoeff(X3865,X3864),c_Polynomial_Odegree(X3865,X3864)) != c_Groups_Ozero__class_Ozero(X3865) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_leading__coeff__neq__0])]) ).
fof(i_0_1977,plain,
! [X4130,X4131] :
( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4131),X4130),X4130) != c_Groups_Oone__class_Oone(X4131)
| X4130 = c_Groups_Oone__class_Oone(X4131)
| X4130 = hAPP(c_Groups_Ouminus__class_Ouminus(X4131),c_Groups_Oone__class_Oone(X4131))
| ~ class_Rings_Oring__1__no__zero__divisors(X4131) )
& ( X4130 != c_Groups_Oone__class_Oone(X4131)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4131),X4130),X4130) = c_Groups_Oone__class_Oone(X4131)
| ~ class_Rings_Oring__1__no__zero__divisors(X4131) )
& ( X4130 != hAPP(c_Groups_Ouminus__class_Ouminus(X4131),c_Groups_Oone__class_Oone(X4131))
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4131),X4130),X4130) = c_Groups_Oone__class_Oone(X4131)
| ~ class_Rings_Oring__1__no__zero__divisors(X4131) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_square__eq__1__iff])])]) ).
fof(i_0_1978,plain,
! [X3131,X3132] :
( hAPP(X3132,esk1_2(X3131,X3132)) != hAPP(X3131,esk1_2(X3131,X3132))
| X3132 = X3131 ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ext])])]) ).
fof(i_0_1979,plain,
! [X4231,X4232] :
( ~ class_Rings_Ocomm__semiring__1(X4232)
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X4232),X4231),c_Groups_Ozero__class_Ozero(X4232))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvd__0__right])]) ).
fof(i_0_1980,plain,
! [X3821,X3822,X3823] :
( ( c_Polynomial_Osynthetic__div(X3823,X3822,X3821) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3823))
| c_Polynomial_Odegree(X3823,X3822) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ class_Rings_Ocomm__semiring__0(X3823) )
& ( c_Polynomial_Odegree(X3823,X3822) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Polynomial_Osynthetic__div(X3823,X3822,X3821) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3823))
| ~ class_Rings_Ocomm__semiring__0(X3823) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_synthetic__div__eq__0__iff])])]) ).
fof(i_0_1981,plain,
! [X3855,X3856,X3857] : hAPP(c_Nat_Onat_Onat__case(X3857,X3856,X3855),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X3856,
inference(variable_rename,[status(thm)],[fact_nat__case__0]) ).
fof(i_0_1982,plain,
! [X5818] : ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,X5818),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),
inference(variable_rename,[status(thm)],[i_0_1219]) ).
fof(i_0_1983,plain,
! [X6189,X6190] :
( ~ hBOOL(hAPP(hAPP(c_fconj,X6190),X6189))
| hBOOL(X6190) ),
inference(variable_rename,[status(thm)],[i_0_1220]) ).
fof(i_0_1984,plain,
! [X6191,X6192] :
( ~ hBOOL(hAPP(hAPP(c_fconj,X6192),X6191))
| hBOOL(X6191) ),
inference(variable_rename,[status(thm)],[i_0_1221]) ).
fof(i_0_1985,plain,
! [X3910,X3911] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X3911),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X3910)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X3911),X3910),
inference(variable_rename,[status(thm)],[fact_diff__int__def__symmetric]) ).
fof(i_0_1986,plain,
! [X3912,X3913] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X3913),X3912) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X3913),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X3912)),
inference(variable_rename,[status(thm)],[fact_diff__int__def]) ).
fof(i_0_1987,plain,
! [X4320,X4321] :
( ~ class_Rings_Odivision__ring__inverse__zero(X4321)
| hAPP(c_Rings_Oinverse__class_Oinverse(X4321),hAPP(c_Groups_Ouminus__class_Ouminus(X4321),X4320)) = hAPP(c_Groups_Ouminus__class_Ouminus(X4321),hAPP(c_Rings_Oinverse__class_Oinverse(X4321),X4320)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inverse__minus__eq])]) ).
fof(i_0_1988,plain,
! [X3161,X3162,X3163] :
( ( X3162 = c_Groups_Ozero__class_Ozero(X3163)
| hAPP(hAPP(c_Power_Opower__class_Opower(X3163),X3162),X3161) != c_Groups_Ozero__class_Ozero(X3163)
| ~ class_Power_Opower(X3163)
| ~ class_Rings_Omult__zero(X3163)
| ~ class_Rings_Ono__zero__divisors(X3163)
| ~ class_Rings_Ozero__neq__one(X3163) )
& ( X3161 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Power_Opower__class_Opower(X3163),X3162),X3161) != c_Groups_Ozero__class_Ozero(X3163)
| ~ class_Power_Opower(X3163)
| ~ class_Rings_Omult__zero(X3163)
| ~ class_Rings_Ono__zero__divisors(X3163)
| ~ class_Rings_Ozero__neq__one(X3163) )
& ( X3162 != c_Groups_Ozero__class_Ozero(X3163)
| X3161 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Power_Opower__class_Opower(X3163),X3162),X3161) = c_Groups_Ozero__class_Ozero(X3163)
| ~ class_Power_Opower(X3163)
| ~ class_Rings_Omult__zero(X3163)
| ~ class_Rings_Ono__zero__divisors(X3163)
| ~ class_Rings_Ozero__neq__one(X3163) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__eq__0__iff])])]) ).
fof(i_0_1989,plain,
! [X3631,X3632,X3633] :
( ( hAPP(hAPP(c_Polynomial_Osmult(X3633),X3632),X3631) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3633))
| X3632 = c_Groups_Ozero__class_Ozero(X3633)
| X3631 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3633))
| ~ class_Rings_Oidom(X3633) )
& ( X3632 != c_Groups_Ozero__class_Ozero(X3633)
| hAPP(hAPP(c_Polynomial_Osmult(X3633),X3632),X3631) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3633))
| ~ class_Rings_Oidom(X3633) )
& ( X3631 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3633))
| hAPP(hAPP(c_Polynomial_Osmult(X3633),X3632),X3631) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3633))
| ~ class_Rings_Oidom(X3633) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_smult__eq__0__iff])])]) ).
fof(i_0_1990,plain,
! [X3176,X3177] :
( ~ class_Groups_Ocomm__monoid__add(X3177)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X3177)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3177))),X3176) = X3176 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__poly__code_I1_J])]) ).
fof(i_0_1991,plain,
! [X4102,X4103,X4104] :
( ( X4103 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4104))
| c_Polynomial_Opoly__gcd(X4104,X4103,X4102) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4104))
| ~ class_Fields_Ofield(X4104) )
& ( X4102 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4104))
| c_Polynomial_Opoly__gcd(X4104,X4103,X4102) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4104))
| ~ class_Fields_Ofield(X4104) )
& ( X4103 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4104))
| X4102 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4104))
| c_Polynomial_Opoly__gcd(X4104,X4103,X4102) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4104))
| ~ class_Fields_Ofield(X4104) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_poly__gcd__zero__iff])])]) ).
fof(i_0_1992,plain,
! [X3667,X3668,X3669] :
( ( c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X3669,X3668,X3667) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3669))
| X3668 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3669))
| ~ class_Rings_Ocomm__semiring__0(X3669) )
& ( X3668 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3669))
| c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X3669,X3668,X3667) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3669))
| ~ class_Rings_Ocomm__semiring__0(X3669) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_offset__poly__eq__0__iff])])]) ).
fof(i_0_1993,plain,
! [X4057] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X4057) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(variable_rename,[status(thm)],[fact_power__Suc__0]) ).
fof(i_0_1994,plain,
! [X5422,X5423,X5424] :
( ( X5423 = X5422
| c_Orderings_Oord__class_Oless(X5424,X5423,X5422)
| c_Orderings_Oord__class_Oless(X5424,X5422,X5423)
| ~ class_Orderings_Olinorder(X5424) )
& ( ~ c_Orderings_Oord__class_Oless(X5424,X5423,X5422)
| X5423 != X5422
| ~ class_Orderings_Olinorder(X5424) )
& ( ~ c_Orderings_Oord__class_Oless(X5424,X5422,X5423)
| X5423 != X5422
| ~ class_Orderings_Olinorder(X5424) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_linorder__neq__iff])])]) ).
fof(i_0_1995,plain,
! [X5485,X5486,X5487] :
( ~ class_Orderings_Olinorder(X5487)
| c_Orderings_Oord__class_Oless(X5487,X5486,X5485)
| X5486 = X5485
| c_Orderings_Oord__class_Oless(X5487,X5485,X5486) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1222])]) ).
fof(i_0_1996,plain,
! [X5434,X5435,X5436] :
( ~ class_Orderings_Olinorder(X5436)
| X5435 = X5434
| c_Orderings_Oord__class_Oless(X5436,X5435,X5434)
| c_Orderings_Oord__class_Oless(X5436,X5434,X5435) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1223])]) ).
fof(i_0_1997,plain,
! [X5431,X5432,X5433] :
( ( c_Orderings_Oord__class_Oless(X5433,X5431,X5432)
| X5431 = X5432
| c_Orderings_Oord__class_Oless(X5433,X5432,X5431)
| ~ class_Orderings_Olinorder(X5433) )
& ( X5431 != X5432
| ~ c_Orderings_Oord__class_Oless(X5433,X5431,X5432)
| c_Orderings_Oord__class_Oless(X5433,X5432,X5431)
| ~ class_Orderings_Olinorder(X5433) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1224])])]) ).
fof(i_0_1998,plain,
! [X5428,X5429,X5430] :
( ~ class_Orderings_Olinorder(X5430)
| c_Orderings_Oord__class_Oless(X5430,X5429,X5428)
| X5429 = X5428
| c_Orderings_Oord__class_Oless(X5430,X5428,X5429) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_linorder__less__linear])]) ).
fof(i_0_1999,plain,
! [X5341,X5342,X5343] :
( ~ class_Rings_Olinordered__idom(X5343)
| X5342 = X5341
| c_Orderings_Oord__class_Oless(X5343,X5342,X5341)
| c_Orderings_Oord__class_Oless(X5343,X5341,X5342) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1225])]) ).
fof(i_0_2000,plain,
! [X3182,X3183,X3184,X3185,X3186,X3187,X3190,X3191] :
( ( ~ c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(X3184,X3183,X3182)
| hAPP(X3182,X3185) = hAPP(X3182,X3186) )
& ( hAPP(X3187,esk2_1(X3187)) != hAPP(X3187,esk3_1(X3187))
| c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(X3191,X3190,X3187) ) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_constant__def])])])])]) ).
fof(i_0_2001,plain,
! [X4055,X4056] :
( ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X4056),X4055) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| X4055 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X4056 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
& ( X4055 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X4056),X4055) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
& ( X4056 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X4056),X4055) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__power__eq__Suc__0__iff])])]) ).
fof(i_0_2002,plain,
( ~ class_Rings_Oidom(t_a)
| ~ c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(t_a,t_a,c_Polynomial_Opoly(t_a,v_p)) ),
inference(fof_nnf,[status(thm)],[i_0_1226]) ).
fof(i_0_2003,plain,
! [X4354,X4355,X4356] :
( ~ class_Rings_Odivision__ring(X4356)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4356),X4355),X4354) != c_Groups_Oone__class_Oone(X4356)
| hAPP(c_Rings_Oinverse__class_Oinverse(X4356),X4355) = X4354 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inverse__unique])]) ).
fof(i_0_2004,plain,
! [X4123,X4124,X4125] :
( ~ class_Groups_Ogroup__add(X4125)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4125),X4124),X4123) != c_Groups_Ozero__class_Ozero(X4125)
| hAPP(c_Groups_Ouminus__class_Ouminus(X4125),X4124) = X4123 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_minus__unique])]) ).
fof(i_0_2005,plain,
! [X4116,X4117,X4118] :
( ( X4117 != hAPP(c_Groups_Ouminus__class_Ouminus(X4118),X4116)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4118),X4117),X4116) = c_Groups_Ozero__class_Ozero(X4118)
| ~ class_Groups_Ogroup__add(X4118) )
& ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4118),X4117),X4116) != c_Groups_Ozero__class_Ozero(X4118)
| X4117 = hAPP(c_Groups_Ouminus__class_Ouminus(X4118),X4116)
| ~ class_Groups_Ogroup__add(X4118) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_eq__neg__iff__add__eq__0])])]) ).
fof(i_0_2006,plain,
! [X4092,X4093,X4094] :
( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4094),X4093),X4092) != c_Groups_Ozero__class_Ozero(X4094)
| X4092 = hAPP(c_Groups_Ouminus__class_Ouminus(X4094),X4093)
| ~ class_Groups_Ogroup__add(X4094) )
& ( X4092 != hAPP(c_Groups_Ouminus__class_Ouminus(X4094),X4093)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4094),X4093),X4092) = c_Groups_Ozero__class_Ozero(X4094)
| ~ class_Groups_Ogroup__add(X4094) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__eq__0__iff])])]) ).
fof(i_0_2007,plain,
! [X3146,X3147,X3148] :
( ( X3147 = c_Groups_Ozero__class_Ozero(X3148)
| hAPP(hAPP(c_Polynomial_OpCons(X3148),X3147),X3146) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3148))
| ~ class_Groups_Ozero(X3148) )
& ( X3146 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3148))
| hAPP(hAPP(c_Polynomial_OpCons(X3148),X3147),X3146) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3148))
| ~ class_Groups_Ozero(X3148) )
& ( X3147 != c_Groups_Ozero__class_Ozero(X3148)
| X3146 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3148))
| hAPP(hAPP(c_Polynomial_OpCons(X3148),X3147),X3146) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3148))
| ~ class_Groups_Ozero(X3148) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pCons__eq__0__iff])])]) ).
fof(i_0_2008,plain,
! [X3931,X3932,X3933] :
( ~ class_Fields_Ofield(X3933)
| c_Polynomial_Opoly__gcd(X3933,X3932,X3931) = c_Polynomial_Opoly__gcd(X3933,X3931,X3932) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_poly__gcd_Ocommute])]) ).
fof(i_0_2009,plain,
! [X3875] :
( ~ class_Groups_Ozero(X3875)
| c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3875)) = c_Polynomial_OAbs__poly(X3875,hAPP(c_COMBK(X3875,tc_Nat_Onat),c_Groups_Ozero__class_Ozero(X3875))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__poly__def])]) ).
fof(i_0_2010,plain,
! [X4165,X4166] :
( ( X4166 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4166),X4165) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
& ( X4165 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4166),X4165) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
& ( X4166 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| X4165 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4166),X4165) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__eq__1__iff])])]) ).
fof(i_0_2011,plain,
! [X3506,X3507,X3508] :
( ( c_Polynomial_Omonom(X3508,X3507,X3506) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3508))
| X3507 = c_Groups_Ozero__class_Ozero(X3508)
| ~ class_Groups_Ozero(X3508) )
& ( X3507 != c_Groups_Ozero__class_Ozero(X3508)
| c_Polynomial_Omonom(X3508,X3507,X3506) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3508))
| ~ class_Groups_Ozero(X3508) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_monom__eq__0__iff])])]) ).
fof(i_0_2012,plain,
! [X4252,X4253] :
( ~ class_Rings_Ocomm__semiring__1(X4253)
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X4253),X4252),X4252)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvd__refl])]) ).
fof(i_0_2013,plain,
! [X3988] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X3988)),X3988) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
inference(variable_rename,[status(thm)],[fact_zadd__zminus__inverse2]) ).
fof(i_0_2014,plain,
! [X5279] :
( ~ class_Rings_Olinordered__semidom(X5279)
| ~ c_Orderings_Oord__class_Oless(X5279,c_Groups_Oone__class_Oone(X5279),c_Groups_Ozero__class_Ozero(X5279)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1227])]) ).
fof(i_0_2015,plain,
! [X3178,X3179] :
( ~ class_Rings_Ocomm__semiring__0(X3179)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X3179)),X3178),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3179))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3179)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__poly__0__right])]) ).
fof(i_0_2016,plain,
! [X3223,X3224,X3225] :
( ~ class_Rings_Ocomm__semiring__1(X3225)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3225),X3224),X3223) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3225),X3223),X3224) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J])]) ).
fof(i_0_2017,plain,
! [X3247,X3248,X3249] :
( ~ class_Rings_Ocomm__semiring__1(X3249)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X3249),X3248),X3247) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X3249),X3247),X3248) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J])]) ).
fof(i_0_2018,plain,
! [X5076] : c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,hAPP(c_Nat_OSuc,X5076)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,X5076)),
inference(variable_rename,[status(thm)],[fact_int__Suc]) ).
fof(i_0_2019,plain,
! [X5874,X5875] :
( ~ class_Rings_Olinordered__idom(X5875)
| X5874 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X5875))
| c_Polynomial_Opos__poly(X5875,X5874)
| c_Polynomial_Opos__poly(X5875,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X5875)),X5874)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pos__poly__total])]) ).
fof(i_0_2020,plain,
! [X5854,X5855] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X5855,X5854)
| X5855 = X5854
| c_Orderings_Oord__class_Oless(tc_Int_Oint,X5854,X5855) ),
inference(variable_rename,[status(thm)],[fact_zless__linear]) ).
fof(i_0_2021,plain,
! [X5347,X5348] :
( X5348 = X5347
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X5348,X5347)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X5347,X5348) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1228])]) ).
fof(i_0_2022,plain,
! [X5345,X5346] :
( ( X5346 = X5345
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X5346,X5345)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X5345,X5346) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X5346,X5345)
| X5346 != X5345 )
& ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X5345,X5346)
| X5346 != X5345 ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__neq__iff])])]) ).
fof(i_0_2023,plain,
! [X4101] :
( ~ class_Fields_Ofield(X4101)
| c_Polynomial_Opoly__gcd(X4101,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4101)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4101))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4101)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_poly__gcd__0__0])]) ).
fof(i_0_2024,plain,
! [X5572,X5574,X5575] :
( ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X5572)
| X5572 = hAPP(c_Nat_OSuc,esk11_1(X5572)) )
& ( X5574 != hAPP(c_Nat_OSuc,X5575)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X5574) ) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_gr0__conv__Suc])])])])]) ).
fof(i_0_2025,plain,
! [X4383,X4384] :
( ~ class_Rings_Odivision__ring(X4384)
| X4383 = c_Groups_Ozero__class_Ozero(X4384)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4384),X4383),hAPP(c_Rings_Oinverse__class_Oinverse(X4384),X4383)) = c_Groups_Oone__class_Oone(X4384) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_right__inverse])]) ).
fof(i_0_2026,plain,
! [X4530] : hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X4530)),
inference(variable_rename,[status(thm)],[fact_gcd__lcm__complete__lattice__nat_Obot__least]) ).
fof(i_0_2027,plain,
! [X3538,X3539,X3540] :
( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3540),X3539),X3538) != c_Groups_Ozero__class_Ozero(X3540)
| X3539 = c_Groups_Ozero__class_Ozero(X3540)
| X3538 = c_Groups_Ozero__class_Ozero(X3540)
| ~ class_Rings_Oring__no__zero__divisors(X3540) )
& ( X3539 != c_Groups_Ozero__class_Ozero(X3540)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3540),X3539),X3538) = c_Groups_Ozero__class_Ozero(X3540)
| ~ class_Rings_Oring__no__zero__divisors(X3540) )
& ( X3538 != c_Groups_Ozero__class_Ozero(X3540)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3540),X3539),X3538) = c_Groups_Ozero__class_Ozero(X3540)
| ~ class_Rings_Oring__no__zero__divisors(X3540) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__eq__0__iff])])]) ).
fof(i_0_2028,plain,
! [X3535,X3536,X3537] :
( ~ class_Rings_Ono__zero__divisors(X3537)
| X3536 = c_Groups_Ozero__class_Ozero(X3537)
| X3535 = c_Groups_Ozero__class_Ozero(X3537)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3537),X3536),X3535) != c_Groups_Ozero__class_Ozero(X3537) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_no__zero__divisors])]) ).
fof(i_0_2029,plain,
! [X3532,X3533,X3534] :
( ~ class_Rings_Ono__zero__divisors(X3534)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3534),X3533),X3532) != c_Groups_Ozero__class_Ozero(X3534)
| X3533 = c_Groups_Ozero__class_Ozero(X3534)
| X3532 = c_Groups_Ozero__class_Ozero(X3534) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divisors__zero])]) ).
fof(i_0_2030,plain,
! [X4144,X4145] :
( ~ class_Power_Opower(X4145)
| ~ class_Rings_Osemiring__0(X4145)
| hAPP(hAPP(c_Power_Opower__class_Opower(X4145),c_Groups_Ozero__class_Ozero(X4145)),hAPP(c_Nat_OSuc,X4144)) = c_Groups_Ozero__class_Ozero(X4145) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__0__Suc])]) ).
fof(i_0_2031,plain,
! [X4978,X4979,X4980] :
( ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4980),X4978),X4979) != c_Groups_Oone__class_Oone(X4980)
| X4978 = X4979
| X4979 = c_Groups_Ozero__class_Ozero(X4980)
| ~ class_Rings_Odivision__ring(X4980) )
& ( X4978 != X4979
| hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4980),X4978),X4979) = c_Groups_Oone__class_Oone(X4980)
| X4979 = c_Groups_Ozero__class_Ozero(X4980)
| ~ class_Rings_Odivision__ring(X4980) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_right__inverse__eq])])]) ).
fof(i_0_2032,plain,
! [X4072,X4073] :
( ~ class_Groups_Oab__group__add(X4073)
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X4073)),X4072),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4073))) = X4072 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__poly__code_I2_J])]) ).
fof(i_0_2033,plain,
! [X3174,X3175] :
( ~ class_Groups_Ocomm__monoid__add(X3175)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X3175)),X3174),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3175))) = X3174 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__poly__code_I2_J])]) ).
fof(i_0_2034,plain,
! [X4114,X4115] :
( ~ class_Groups_Ogroup__add(X4115)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4115),X4114),hAPP(c_Groups_Ouminus__class_Ouminus(X4115),X4114)) = c_Groups_Ozero__class_Ozero(X4115) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_right__minus])]) ).
fof(i_0_2035,plain,
! [X3295,X3296,X3297] :
( ~ class_Rings_Oring__1__no__zero__divisors(X3297)
| X3296 = c_Groups_Ozero__class_Ozero(X3297)
| hAPP(hAPP(c_Power_Opower__class_Opower(X3297),X3296),X3295) != c_Groups_Ozero__class_Ozero(X3297) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_field__power__not__zero])]) ).
fof(i_0_2036,plain,
! [X3558,X3559] :
( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X3559),X3558),X3558) != c_Groups_Ozero__class_Ozero(X3559)
| X3558 = c_Groups_Ozero__class_Ozero(X3559)
| ~ class_Groups_Olinordered__ab__group__add(X3559) )
& ( X3558 != c_Groups_Ozero__class_Ozero(X3559)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X3559),X3558),X3558) = c_Groups_Ozero__class_Ozero(X3559)
| ~ class_Groups_Olinordered__ab__group__add(X3559) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_double__eq__0__iff])])]) ).
fof(i_0_2037,plain,
! [X3454,X3455] :
( ( c_Groups_Ozero__class_Ozero(X3455) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(X3455),X3454),X3454)
| X3454 = c_Groups_Ozero__class_Ozero(X3455)
| ~ class_Groups_Olinordered__ab__group__add(X3455) )
& ( X3454 != c_Groups_Ozero__class_Ozero(X3455)
| c_Groups_Ozero__class_Ozero(X3455) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X3455),X3454),X3454)
| ~ class_Groups_Olinordered__ab__group__add(X3455) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_double__zero__sym])])]) ).
fof(i_0_2038,plain,
! [X4529] : hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X4529),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(variable_rename,[status(thm)],[fact_gcd__lcm__complete__lattice__nat_Otop__greatest]) ).
fof(i_0_2039,plain,
! [X3145] :
( ~ class_Groups_Ozero(X3145)
| hAPP(hAPP(c_Polynomial_OpCons(X3145),c_Groups_Ozero__class_Ozero(X3145)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3145))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3145)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pCons__0__0])]) ).
fof(i_0_2040,plain,
! [X3144] :
( ~ class_Rings_Ocomm__semiring__1(X3144)
| c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(X3144)) = hAPP(hAPP(c_Polynomial_OpCons(X3144),c_Groups_Oone__class_Oone(X3144)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3144))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_one__poly__def])]) ).
fof(i_0_2041,plain,
! [X3334,X3335] :
( ( c_Polynomial_Opoly(X3335,X3334) != c_Polynomial_Opoly(X3335,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3335)))
| X3334 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3335))
| ~ class_Int_Oring__char__0(X3335)
| ~ class_Rings_Oidom(X3335) )
& ( X3334 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3335))
| c_Polynomial_Opoly(X3335,X3334) = c_Polynomial_Opoly(X3335,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3335)))
| ~ class_Int_Oring__char__0(X3335)
| ~ class_Rings_Oidom(X3335) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_poly__zero])])]) ).
fof(i_0_2042,plain,
! [X3765,X3766,X3767] :
( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(X3767),X3766),X3765) != c_Groups_Ozero__class_Ozero(X3767)
| X3766 = X3765
| ~ class_Groups_Ogroup__add(X3767) )
& ( X3766 != X3765
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(X3767),X3766),X3765) = c_Groups_Ozero__class_Ozero(X3767)
| ~ class_Groups_Ogroup__add(X3767) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_right__minus__eq])])]) ).
fof(i_0_2043,plain,
! [X3768,X3769,X3770] :
( ( X3769 != X3768
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(X3770),X3769),X3768) = c_Groups_Ozero__class_Ozero(X3770)
| ~ class_Groups_Oab__group__add(X3770) )
& ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(X3770),X3769),X3768) != c_Groups_Ozero__class_Ozero(X3770)
| X3769 = X3768
| ~ class_Groups_Oab__group__add(X3770) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_eq__iff__diff__eq__0])])]) ).
fof(i_0_2044,plain,
! [X4519,X4520] :
( X4520 != X4519
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X4520),X4519)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvd_Oeq__refl])]) ).
fof(i_0_2045,plain,
! [X4083,X4084] :
( ~ class_Groups_Oab__group__add(X4084)
| c_Polynomial_Odegree(X4084,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X4084)),X4083)) = c_Polynomial_Odegree(X4084,X4083) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_degree__minus])]) ).
fof(i_0_2046,plain,
! [X5074,X5075] :
( ~ class_Rings_Odivision__ring(X5075)
| X5074 = c_Groups_Ozero__class_Ozero(X5075)
| hAPP(c_Rings_Oinverse__class_Oinverse(X5075),X5074) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X5075),c_Groups_Oone__class_Oone(X5075)),X5074) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nonzero__inverse__eq__divide])]) ).
fof(i_0_2047,plain,
! [X5449,X5450,X5451] :
( ~ class_Orderings_Oorder(X5451)
| ~ c_Orderings_Oord__class_Oless(X5451,X5450,X5449)
| X5449 != X5450 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__less__imp__not__eq2])]) ).
fof(i_0_2048,plain,
! [X5446,X5447,X5448] :
( ~ class_Orderings_Oorder(X5448)
| ~ c_Orderings_Oord__class_Oless(X5448,X5447,X5446)
| X5447 != X5446 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__less__imp__not__eq])]) ).
fof(i_0_2049,plain,
! [X5437,X5438,X5439] :
( ~ class_Orderings_Oorder(X5439)
| ~ c_Orderings_Oord__class_Oless(X5439,X5438,X5437)
| X5438 != X5437 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__imp__neq])]) ).
fof(i_0_2050,plain,
! [X3262,X3263,X3264] :
( ( X3263 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(X3264),X3263),X3262)
| X3262 = c_Groups_Ozero__class_Ozero(X3264)
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X3264) )
& ( X3262 != c_Groups_Ozero__class_Ozero(X3264)
| X3263 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X3264),X3263),X3262)
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X3264) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__0__iff])])]) ).
fof(i_0_2051,plain,
! [X4173] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,X4173)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X4173,
inference(variable_rename,[status(thm)],[fact_diff__Suc__1]) ).
fof(i_0_2052,plain,
! [X5339] :
( ( X5339 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X5339) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X5339)
| X5339 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_neq0__conv])]) ).
fof(i_0_2053,plain,
! [X4468] : hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X4468),X4468)),
inference(variable_rename,[status(thm)],[fact_dvd_Oorder__refl]) ).
fof(i_0_2054,plain,
! [X3583,X3584] :
( ( X3583 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(c_Polynomial_Ocoeff(X3584,c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(X3584))),X3583) = c_Groups_Oone__class_Oone(X3584)
| ~ class_Rings_Ocomm__semiring__1(X3584) )
& ( X3583 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(c_Polynomial_Ocoeff(X3584,c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(X3584))),X3583) = c_Groups_Ozero__class_Ozero(X3584)
| ~ class_Rings_Ocomm__semiring__1(X3584) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_coeff__1])])]) ).
fof(i_0_2055,plain,
! [X5420,X5421] :
( ~ class_Orderings_Opreorder(X5421)
| ~ c_Orderings_Oord__class_Oless(X5421,X5420,X5420) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1229])]) ).
fof(i_0_2056,plain,
! [X6159,X6160,X6161,X6162] : hAPP(hAPP(c_COMBK(X6162,X6161),X6160),X6159) = X6160,
inference(variable_rename,[status(thm)],[help_c__COMBK__1]) ).
fof(i_0_2057,plain,
! [X3734,X3735] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X3735),X3734) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X3734),X3735),
inference(variable_rename,[status(thm)],[fact_zmult__commute]) ).
fof(i_0_2058,plain,
! [X3369,X3370] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3370),X3369) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3369),X3370),
inference(variable_rename,[status(thm)],[fact_nat__mult__commute]) ).
fof(i_0_2059,plain,
! [X3983,X3984] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X3984),X3983) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X3983),X3984),
inference(variable_rename,[status(thm)],[fact_zadd__commute]) ).
fof(i_0_2060,plain,
! [X3424,X3425] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3425),X3424) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3424),X3425),
inference(variable_rename,[status(thm)],[fact_nat__add__commute]) ).
fof(i_0_2061,plain,
! [X4126,X4127] :
( ~ class_Groups_Ogroup__add(X4127)
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(X4127),c_Groups_Ozero__class_Ozero(X4127)),X4126) = hAPP(c_Groups_Ouminus__class_Ouminus(X4127),X4126) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__0])]) ).
fof(i_0_2062,plain,
! [X5010,X5011] :
( ~ class_Rings_Odivision__ring(X5011)
| hAPP(c_Rings_Oinverse__class_Oinverse(X5011),X5010) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X5011),c_Groups_Oone__class_Oone(X5011)),X5010) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inverse__eq__divide])]) ).
fof(i_0_2063,plain,
! [X5008,X5009] :
( ~ class_Fields_Ofield(X5009)
| hAPP(c_Rings_Oinverse__class_Oinverse(X5009),X5008) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X5009),c_Groups_Oone__class_Oone(X5009)),X5008) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_field__class_Onormalizing__field__rules_I2_J])]) ).
fof(i_0_2064,plain,
! [X6187,X6188] :
( ~ hBOOL(X6188)
| ~ hBOOL(X6187)
| hBOOL(hAPP(hAPP(c_fconj,X6188),X6187)) ),
inference(variable_rename,[status(thm)],[i_0_1230]) ).
fof(i_0_2065,plain,
! [X4112,X4113] :
( ~ class_Fields_Ofield(X4113)
| c_Polynomial_Opoly__gcd(X4113,c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(X4113)),X4112) = c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(X4113)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_poly__gcd__1__left])]) ).
fof(i_0_2066,plain,
! [X3859,X3860] :
( ~ class_Rings_Ocomm__semiring__0(X3860)
| c_Polynomial_Osynthetic__div(X3860,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3860)),X3859) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3860)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_synthetic__div__0])]) ).
fof(i_0_2067,plain,
! [X3665,X3666] :
( ~ class_Rings_Ocomm__semiring__0(X3666)
| c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X3666,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3666)),X3665) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3666)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_offset__poly__0])]) ).
fof(i_0_2068,plain,
! [X3511,X3512] :
( ~ class_Rings_Ocomm__semiring__0(X3512)
| c_Polynomial_Opcompose(X3512,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3512)),X3511) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3512)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pcompose__0])]) ).
fof(i_0_2069,plain,
! [X4110,X4111] :
( ~ class_Fields_Ofield(X4111)
| c_Polynomial_Opoly__gcd(X4111,X4110,c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(X4111))) = c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(X4111)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_poly__gcd__1__right])]) ).
fof(i_0_2070,plain,
! [X5336,X5337] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X5337,X5336)
| X5336 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_gr__implies__not0])]) ).
fof(i_0_2071,plain,
! [X3140,X3141] :
( ( X3140 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Power_Opower__class_Opower(X3141),c_Groups_Ozero__class_Ozero(X3141)),X3140) = c_Groups_Oone__class_Oone(X3141)
| ~ class_Power_Opower(X3141)
| ~ class_Rings_Osemiring__0(X3141) )
& ( X3140 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Power_Opower__class_Opower(X3141),c_Groups_Ozero__class_Ozero(X3141)),X3140) = c_Groups_Ozero__class_Ozero(X3141)
| ~ class_Power_Opower(X3141)
| ~ class_Rings_Osemiring__0(X3141) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__0__left])])]) ).
fof(i_0_2072,plain,
! [X5340] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X5340,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(variable_rename,[status(thm)],[i_0_1231]) ).
fof(i_0_2073,plain,
! [X5338] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X5338,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(variable_rename,[status(thm)],[i_0_1232]) ).
fof(i_0_2074,plain,
! [X5184] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X5184,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(variable_rename,[status(thm)],[i_0_1233]) ).
fof(i_0_2075,plain,
! [X3606,X3607] :
( ~ class_Rings_Ocomm__semiring__0(X3607)
| hAPP(hAPP(c_Polynomial_Osmult(X3607),X3606),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3607))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3607)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_smult__0__right])]) ).
fof(i_0_2076,plain,
! [X3627,X3628] :
( ~ class_Groups_Ozero(X3628)
| hAPP(c_Polynomial_Ocoeff(X3628,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3628))),X3627) = c_Groups_Ozero__class_Ozero(X3628) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_coeff__0])]) ).
fof(i_0_2077,plain,
! [X3328,X3329] :
( ~ class_Rings_Ocomm__semiring__1(X3329)
| hAPP(c_Polynomial_Opoly(X3329,c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(X3329))),X3328) = c_Groups_Oone__class_Oone(X3329) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_poly__1])]) ).
fof(i_0_2078,plain,
! [X3142,X3143] :
( ~ class_Rings_Ocomm__semiring__0(X3143)
| hAPP(c_Polynomial_Opoly(X3143,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3143))),X3142) = c_Groups_Ozero__class_Ozero(X3143) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_poly__0])]) ).
fof(i_0_2079,plain,
! [X5352,X5353] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X5353,X5352)
| X5353 != X5352 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__not__refl3])]) ).
fof(i_0_2080,plain,
! [X5350,X5351] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X5351,X5350)
| X5350 != X5351 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__not__refl2])]) ).
fof(i_0_2081,plain,
! [X5017,X5018] :
( ( X5018 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,X5018)) != c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,X5017) )
& ( X5017 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,X5018)) != c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,X5017) )
& ( X5018 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X5017 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,X5018)) = c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,X5017) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_negative__eq__positive])])]) ).
fof(i_0_2082,plain,
! [X4721] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,X4721,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(variable_rename,[status(thm)],[fact_mod__1]) ).
fof(i_0_2083,plain,
! [X3416,X3417] :
( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3417),X3416) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X3417 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X3416 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( X3417 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3417),X3416) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( X3416 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3417),X3416) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__is__0])])]) ).
fof(i_0_2084,plain,
! [X5349] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X5349,X5349),
inference(variable_rename,[status(thm)],[i_0_1234]) ).
fof(i_0_2085,plain,
! [X5344] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X5344,X5344),
inference(variable_rename,[status(thm)],[i_0_1235]) ).
fof(i_0_2086,plain,
! [X4291,X4292,X4293] :
( ~ class_Rings_Odivision__ring(X4293)
| hAPP(c_Rings_Oinverse__class_Oinverse(X4293),X4292) != hAPP(c_Rings_Oinverse__class_Oinverse(X4293),X4291)
| X4292 = c_Groups_Ozero__class_Ozero(X4293)
| X4291 = c_Groups_Ozero__class_Ozero(X4293)
| X4292 = X4291 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nonzero__inverse__eq__imp__eq])]) ).
fof(i_0_2087,plain,
! [X3355,X3356] :
( X3356 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3356),X3355)
| X3355 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| X3356 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__eq__self__implies__10])]) ).
fof(i_0_2088,plain,
! [X3629,X3630] :
( ~ class_Rings_Ocomm__semiring__0(X3630)
| hAPP(hAPP(c_Polynomial_Osmult(X3630),c_Groups_Ozero__class_Ozero(X3630)),X3629) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3630)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_smult__0__left])]) ).
fof(i_0_2089,plain,
! [X3448,X3449] :
( ( X3449 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3449),X3448) != c_Groups_Oone__class_Oone(tc_Nat_Onat) )
& ( X3448 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3449),X3448) != c_Groups_Oone__class_Oone(tc_Nat_Onat) )
& ( X3449 != c_Groups_Oone__class_Oone(tc_Nat_Onat)
| X3448 != c_Groups_Oone__class_Oone(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3449),X3448) = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__mult__eq__1__iff])])]) ).
fof(i_0_2090,plain,
! [X3359,X3360] :
( ( X3360 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3360),X3359) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( X3359 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3360),X3359) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( X3360 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X3359 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3360),X3359) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__is__0])])]) ).
fof(i_0_2091,plain,
! [X3445,X3446] :
( ( X3446 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| c_Groups_Oone__class_Oone(tc_Nat_Onat) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3446),X3445) )
& ( X3445 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| c_Groups_Oone__class_Oone(tc_Nat_Onat) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3446),X3445) )
& ( X3446 != c_Groups_Oone__class_Oone(tc_Nat_Onat)
| X3445 != c_Groups_Oone__class_Oone(tc_Nat_Onat)
| c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3446),X3445) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__1__eq__mult__iff])])]) ).
fof(i_0_2092,plain,
! [X5188] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Nat_OSuc,X5188)),
inference(variable_rename,[status(thm)],[fact_zero__less__Suc]) ).
fof(i_0_2093,plain,
! [X3509,X3510] :
( ~ class_Groups_Ozero(X3510)
| c_Polynomial_Omonom(X3510,c_Groups_Ozero__class_Ozero(X3510),X3509) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3510)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_monom__eq__0])]) ).
fof(i_0_2094,plain,
! [X3354] :
( ~ class_Power_Opower(X3354)
| c_Power_Opower__class_Opower(X3354) = c_Power_Opower_Opower(X3354,c_Groups_Oone__class_Oone(X3354),c_Groups_Otimes__class_Otimes(X3354)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__power__power])]) ).
fof(i_0_2095,plain,
! [X3357,X3358] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3358),X3357) != X3358
| X3357 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__eq__self__zero])]) ).
fof(i_0_2096,plain,
! [X5187] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,X5187,hAPP(c_Nat_OSuc,X5187)),
inference(variable_rename,[status(thm)],[fact_lessI]) ).
fof(i_0_2097,plain,
! [X4883,X4884] :
( ~ class_RealVector_Oreal__normed__field(X4884)
| hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4884),c_Groups_Ozero__class_Ozero(X4884)),X4883) = c_Groups_Ozero__class_Ozero(X4884) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divide_Ozero])]) ).
fof(i_0_2098,plain,
! [X4885,X4886] :
( ~ class_Rings_Odivision__ring(X4886)
| hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4886),c_Groups_Ozero__class_Ozero(X4886)),X4885) = c_Groups_Ozero__class_Ozero(X4886) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divide__zero__left])]) ).
fof(i_0_2099,plain,
! [X3309,X3310] :
( ~ class_Groups_Omonoid__mult(X3310)
| hAPP(hAPP(c_Power_Opower__class_Opower(X3310),c_Groups_Oone__class_Oone(X3310)),X3309) = c_Groups_Oone__class_Oone(X3310) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__one])]) ).
fof(i_0_2100,plain,
! [X3549,X3550] :
( ~ class_RealVector_Oreal__normed__algebra(X3550)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3550),c_Groups_Ozero__class_Ozero(X3550)),X3549) = c_Groups_Ozero__class_Ozero(X3550) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult_Ozero__left])]) ).
fof(i_0_2101,plain,
! [X3547,X3548] :
( ~ class_RealVector_Oreal__normed__algebra(X3548)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3548),c_Groups_Ozero__class_Ozero(X3548)),X3547) = c_Groups_Ozero__class_Ozero(X3548) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__left_Ozero])]) ).
fof(i_0_2102,plain,
! [X3551,X3552] :
( ~ class_Rings_Omult__zero(X3552)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3552),c_Groups_Ozero__class_Ozero(X3552)),X3551) = c_Groups_Ozero__class_Ozero(X3552) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__zero__left])]) ).
fof(i_0_2103,plain,
! [X3260,X3261] :
( ~ class_Rings_Ocomm__semiring__1(X3261)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3261),c_Groups_Ozero__class_Ozero(X3261)),X3260) = c_Groups_Ozero__class_Ozero(X3261) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I9_J])]) ).
fof(i_0_2104,plain,
! [X5278] :
( ~ class_Rings_Olinordered__semidom(X5278)
| c_Orderings_Oord__class_Oless(X5278,c_Groups_Ozero__class_Ozero(X5278),c_Groups_Oone__class_Oone(X5278)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__less__one])]) ).
fof(i_0_2105,plain,
! [X4247,X4248,X4249] :
( ( hAPP(c_Rings_Oinverse__class_Oinverse(X4249),X4248) != hAPP(c_Rings_Oinverse__class_Oinverse(X4249),X4247)
| X4248 = X4247
| ~ class_Rings_Odivision__ring__inverse__zero(X4249) )
& ( X4248 != X4247
| hAPP(c_Rings_Oinverse__class_Oinverse(X4249),X4248) = hAPP(c_Rings_Oinverse__class_Oinverse(X4249),X4247)
| ~ class_Rings_Odivision__ring__inverse__zero(X4249) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inverse__eq__iff__eq])])]) ).
fof(i_0_2106,plain,
! [X4240,X4241,X4242] :
( ~ class_Rings_Odivision__ring__inverse__zero(X4242)
| hAPP(c_Rings_Oinverse__class_Oinverse(X4242),X4241) != hAPP(c_Rings_Oinverse__class_Oinverse(X4242),X4240)
| X4241 = X4240 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inverse__eq__imp__eq])]) ).
fof(i_0_2107,plain,
! [X3948,X3949,X3950] :
( ( hAPP(c_Groups_Ouminus__class_Ouminus(X3950),X3949) != hAPP(c_Groups_Ouminus__class_Ouminus(X3950),X3948)
| X3949 = X3948
| ~ class_Lattices_Oboolean__algebra(X3950) )
& ( X3949 != X3948
| hAPP(c_Groups_Ouminus__class_Ouminus(X3950),X3949) = hAPP(c_Groups_Ouminus__class_Ouminus(X3950),X3948)
| ~ class_Lattices_Oboolean__algebra(X3950) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_compl__eq__compl__iff])])]) ).
fof(i_0_2108,plain,
! [X3973,X3974,X3975] :
( ( hAPP(c_Groups_Ouminus__class_Ouminus(X3975),X3974) != hAPP(c_Groups_Ouminus__class_Ouminus(X3975),X3973)
| X3974 = X3973
| ~ class_Groups_Ogroup__add(X3975) )
& ( X3974 != X3973
| hAPP(c_Groups_Ouminus__class_Ouminus(X3975),X3974) = hAPP(c_Groups_Ouminus__class_Ouminus(X3975),X3973)
| ~ class_Groups_Ogroup__add(X3975) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_neg__equal__iff__equal])])]) ).
fof(i_0_2109,plain,
! [X3604,X3605] :
( ~ class_Rings_Ocomm__semiring__1(X3605)
| hAPP(hAPP(c_Polynomial_Osmult(X3605),c_Groups_Oone__class_Oone(X3605)),X3604) = X3604 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_smult__1__left])]) ).
fof(i_0_2110,plain,
! [X3367,X3368] :
( ~ class_Groups_Ocomm__monoid__mult(X3368)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3368),c_Groups_Oone__class_Oone(X3368)),X3367) = X3367 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__1])]) ).
fof(i_0_2111,plain,
! [X3460,X3461] :
( ~ class_Groups_Omonoid__mult(X3461)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3461),c_Groups_Oone__class_Oone(X3461)),X3460) = X3460 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__1__left])]) ).
fof(i_0_2112,plain,
! [X3293,X3294] :
( ~ class_Rings_Ocomm__semiring__1(X3294)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3294),c_Groups_Oone__class_Oone(X3294)),X3293) = X3293 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J])]) ).
fof(i_0_2113,plain,
! [X3450,X3451] :
( ~ class_Groups_Omonoid__add(X3451)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X3451),c_Groups_Ozero__class_Ozero(X3451)),X3450) = X3450 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__0__left])]) ).
fof(i_0_2114,plain,
! [X3452,X3453] :
( ~ class_Groups_Ocomm__monoid__add(X3453)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X3453),c_Groups_Ozero__class_Ozero(X3453)),X3452) = X3452 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__0])]) ).
fof(i_0_2115,plain,
! [X3267,X3268] :
( ~ class_Rings_Ocomm__semiring__1(X3268)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X3268),c_Groups_Ozero__class_Ozero(X3268)),X3267) = X3267 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J])]) ).
fof(i_0_2116,plain,
! [X4974,X4975] :
( ( X4974 != c_Groups_Ozero__class_Ozero(X4975)
| hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4975),X4974),X4974) = c_Groups_Ozero__class_Ozero(X4975)
| ~ class_Rings_Odivision__ring__inverse__zero(X4975) )
& ( X4974 = c_Groups_Ozero__class_Ozero(X4975)
| hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4975),X4974),X4974) = c_Groups_Oone__class_Oone(X4975)
| ~ class_Rings_Odivision__ring__inverse__zero(X4975) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divide__self__if])])]) ).
fof(i_0_2117,plain,
! [X4296,X4297] :
( ~ class_Rings_Odivision__ring(X4297)
| X4296 = c_Groups_Ozero__class_Ozero(X4297)
| hAPP(c_Rings_Oinverse__class_Oinverse(X4297),hAPP(c_Rings_Oinverse__class_Oinverse(X4297),X4296)) = X4296 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nonzero__inverse__inverse__eq])]) ).
fof(i_0_2118,plain,
! [X5965,X5966] :
( ~ class_Divides_Osemiring__div(X5966)
| c_Divides_Odiv__class_Odiv(X5966,c_Groups_Ozero__class_Ozero(X5966),X5965) = c_Groups_Ozero__class_Ozero(X5966) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_div__0])]) ).
fof(i_0_2119,plain,
! [X4739,X4740] :
( ~ class_Divides_Osemiring__div(X4740)
| c_Divides_Odiv__class_Omod(X4740,c_Groups_Ozero__class_Ozero(X4740),X4739) = c_Groups_Ozero__class_Ozero(X4740) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__0])]) ).
fof(i_0_2120,plain,
! [X5963,X5964] :
( ~ class_Divides_Osemiring__div(X5964)
| c_Divides_Odiv__class_Odiv(X5964,X5963,c_Groups_Ozero__class_Ozero(X5964)) = c_Groups_Ozero__class_Ozero(X5964) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_div__by__0])]) ).
fof(i_0_2121,plain,
! [X4850,X4851] :
( ~ class_Divides_Osemiring__div(X4851)
| c_Divides_Odiv__class_Omod(X4851,X4850,c_Groups_Oone__class_Oone(X4851)) = c_Groups_Ozero__class_Ozero(X4851) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__by__1])]) ).
fof(i_0_2122,plain,
! [X3903,X3904] :
( ( X3903 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3904))
| c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(X3904,X3903) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ class_Groups_Ozero(X3904) )
& ( X3903 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3904))
| c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(X3904,X3903) = hAPP(c_Nat_OSuc,c_Polynomial_Odegree(X3904,X3903))
| ~ class_Groups_Ozero(X3904) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_psize__def])])]) ).
fof(i_0_2123,plain,
! [X5907,X5908] :
( ~ class_Divides_Osemiring__div(X5908)
| X5907 = c_Groups_Ozero__class_Ozero(X5908)
| c_Divides_Odiv__class_Odiv(X5908,X5907,X5907) = c_Groups_Oone__class_Oone(X5908) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_div__self])]) ).
fof(i_0_2124,plain,
! [X4881,X4882] :
( ~ class_Rings_Odivision__ring__inverse__zero(X4882)
| hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4882),X4881),c_Groups_Ozero__class_Ozero(X4882)) = c_Groups_Ozero__class_Ozero(X4882) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divide__zero])]) ).
fof(i_0_2125,plain,
! [X3543,X3544] :
( ~ class_RealVector_Oreal__normed__algebra(X3544)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3544),X3543),c_Groups_Ozero__class_Ozero(X3544)) = c_Groups_Ozero__class_Ozero(X3544) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult_Ozero__right])]) ).
fof(i_0_2126,plain,
! [X3541,X3542] :
( ~ class_RealVector_Oreal__normed__algebra(X3542)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3542),X3541),c_Groups_Ozero__class_Ozero(X3542)) = c_Groups_Ozero__class_Ozero(X3542) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__right_Ozero])]) ).
fof(i_0_2127,plain,
! [X3545,X3546] :
( ~ class_Rings_Omult__zero(X3546)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3546),X3545),c_Groups_Ozero__class_Ozero(X3546)) = c_Groups_Ozero__class_Ozero(X3546) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__zero__right])]) ).
fof(i_0_2128,plain,
! [X3258,X3259] :
( ~ class_Rings_Ocomm__semiring__1(X3259)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3259),X3258),c_Groups_Ozero__class_Ozero(X3259)) = c_Groups_Ozero__class_Ozero(X3259) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J])]) ).
fof(i_0_2129,plain,
! [X6181,X6182] :
( ~ hBOOL(hAPP(c_fequal(X6182),X6181))
| X6182 = X6181 ),
inference(variable_rename,[status(thm)],[i_0_1236]) ).
fof(i_0_2130,plain,
! [X4976,X4977] :
( ~ class_Rings_Odivision__ring(X4977)
| X4976 = c_Groups_Ozero__class_Ozero(X4977)
| hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4977),X4976),X4976) = c_Groups_Oone__class_Oone(X4977) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divide__self])]) ).
fof(i_0_2131,plain,
! [X5961,X5962] :
( ~ class_Divides_Osemiring__div(X5962)
| c_Divides_Odiv__class_Odiv(X5962,X5961,c_Groups_Oone__class_Oone(X5962)) = X5961 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_div__by__1])]) ).
fof(i_0_2132,plain,
! [X4737,X4738] :
( ~ class_Divides_Osemiring__div(X4738)
| c_Divides_Odiv__class_Omod(X4738,X4737,c_Groups_Ozero__class_Ozero(X4738)) = X4737 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__by__0])]) ).
fof(i_0_2133,plain,
! [X4077] :
( ~ class_Groups_Oab__group__add(X4077)
| hAPP(c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X4077)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4077))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4077)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_minus__poly__code_I1_J])]) ).
fof(i_0_2134,plain,
! [X3159,X3160] :
( ~ class_Rings_Ocomm__semiring__1(X3160)
| hAPP(hAPP(c_Power_Opower__class_Opower(X3160),X3159),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(X3160) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I32_J])]) ).
fof(i_0_2135,plain,
! [X3157,X3158] :
( ~ class_Power_Opower(X3158)
| hAPP(hAPP(c_Power_Opower__class_Opower(X3158),X3157),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(X3158) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__0])]) ).
fof(i_0_2136,plain,
! [X4907,X4908] :
( ~ class_Rings_Odivision__ring(X4908)
| hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4908),X4907),c_Groups_Oone__class_Oone(X4908)) = X4907 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divide__1])]) ).
fof(i_0_2137,plain,
! [X3773,X3774] :
( ~ class_Groups_Ogroup__add(X3774)
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(X3774),X3773),c_Groups_Ozero__class_Ozero(X3774)) = X3773 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__0__right])]) ).
fof(i_0_2138,plain,
! [X3363,X3364] :
( ~ class_Groups_Ocomm__monoid__mult(X3364)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3364),X3363),c_Groups_Oone__class_Oone(X3364)) = X3363 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult_Ocomm__neutral])]) ).
fof(i_0_2139,plain,
! [X3365,X3366] :
( ~ class_Groups_Omonoid__mult(X3366)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3366),X3365),c_Groups_Oone__class_Oone(X3366)) = X3365 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__1__right])]) ).
fof(i_0_2140,plain,
! [X3291,X3292] :
( ~ class_Rings_Ocomm__semiring__1(X3292)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3292),X3291),c_Groups_Oone__class_Oone(X3292)) = X3291 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J])]) ).
fof(i_0_2141,plain,
! [X3456,X3457] :
( ~ class_Groups_Omonoid__add(X3457)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X3457),X3456),c_Groups_Ozero__class_Ozero(X3457)) = X3456 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__0__right])]) ).
fof(i_0_2142,plain,
! [X3458,X3459] :
( ~ class_Groups_Ocomm__monoid__add(X3459)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X3459),X3458),c_Groups_Ozero__class_Ozero(X3459)) = X3458 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add_Ocomm__neutral])]) ).
fof(i_0_2143,plain,
! [X3265,X3266] :
( ~ class_Rings_Ocomm__semiring__1(X3266)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X3266),X3265),c_Groups_Ozero__class_Ozero(X3266)) = X3265 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J])]) ).
fof(i_0_2144,plain,
! [X4250,X4251] :
( ~ class_Rings_Odivision__ring__inverse__zero(X4251)
| hAPP(c_Rings_Oinverse__class_Oinverse(X4251),hAPP(c_Rings_Oinverse__class_Oinverse(X4251),X4250)) = X4250 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inverse__inverse__eq])]) ).
fof(i_0_2145,plain,
! [X3955,X3956] :
( ~ class_Lattices_Oboolean__algebra(X3956)
| hAPP(c_Groups_Ouminus__class_Ouminus(X3956),hAPP(c_Groups_Ouminus__class_Ouminus(X3956),X3955)) = X3955 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_double__compl])]) ).
fof(i_0_2146,plain,
! [X3963,X3964] :
( ~ class_Groups_Ogroup__add(X3964)
| hAPP(c_Groups_Ouminus__class_Ouminus(X3964),hAPP(c_Groups_Ouminus__class_Ouminus(X3964),X3963)) = X3963 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_minus__minus])]) ).
fof(i_0_2147,plain,
! [X4735,X4736] :
( ~ class_Divides_Osemiring__div(X4736)
| c_Divides_Odiv__class_Omod(X4736,X4735,X4735) = c_Groups_Ozero__class_Ozero(X4736) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__self])]) ).
fof(i_0_2148,plain,
! [X4171] : hAPP(c_Nat_OSuc,X4171) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X4171),
inference(variable_rename,[status(thm)],[fact_Suc__eq__plus1__left]) ).
fof(i_0_2149,plain,
! [X3313,X3314] :
( ~ class_Groups_Omonoid__mult(X3314)
| hAPP(hAPP(c_Power_Opower__class_Opower(X3314),X3313),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X3313 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__one__right])]) ).
fof(i_0_2150,plain,
! [X3311,X3312] :
( ~ class_Rings_Ocomm__semiring__1(X3312)
| hAPP(hAPP(c_Power_Opower__class_Opower(X3312),X3311),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X3311 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J])]) ).
fof(i_0_2151,plain,
! [X3771,X3772] :
( ~ class_Groups_Ogroup__add(X3772)
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(X3772),X3771),X3771) = c_Groups_Ozero__class_Ozero(X3772) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__self])]) ).
fof(i_0_2152,plain,
! [X3968,X3969,X3970] :
( ( hAPP(c_Groups_Ouminus__class_Ouminus(X3970),X3969) != X3968
| hAPP(c_Groups_Ouminus__class_Ouminus(X3970),X3968) = X3969
| ~ class_Groups_Ogroup__add(X3970) )
& ( hAPP(c_Groups_Ouminus__class_Ouminus(X3970),X3968) != X3969
| hAPP(c_Groups_Ouminus__class_Ouminus(X3970),X3969) = X3968
| ~ class_Groups_Ogroup__add(X3970) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_minus__equation__iff])])]) ).
fof(i_0_2153,plain,
! [X3965,X3966,X3967] :
( ( X3966 != hAPP(c_Groups_Ouminus__class_Ouminus(X3967),X3965)
| X3965 = hAPP(c_Groups_Ouminus__class_Ouminus(X3967),X3966)
| ~ class_Groups_Ogroup__add(X3967) )
& ( X3965 != hAPP(c_Groups_Ouminus__class_Ouminus(X3967),X3966)
| X3966 = hAPP(c_Groups_Ouminus__class_Ouminus(X3967),X3965)
| ~ class_Groups_Ogroup__add(X3967) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_equation__minus__iff])])]) ).
fof(i_0_2154,plain,
! [X6042,X6043] :
( ~ class_Orderings_Opreorder(X6043)
| c_Orderings_Oord__class_Oless__eq(X6043,X6042,X6042) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__refl])]) ).
fof(i_0_2155,plain,
! [X4172] : hAPP(c_Nat_OSuc,X4172) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X4172),c_Groups_Oone__class_Oone(tc_Nat_Onat)),
inference(variable_rename,[status(thm)],[fact_Suc__eq__plus1]) ).
fof(i_0_2156,plain,
! [X3255,X3256,X3257] :
( ( c_Polynomial_Opoly(X3257,X3256) != c_Polynomial_Opoly(X3257,X3255)
| X3256 = X3255
| ~ class_Int_Oring__char__0(X3257)
| ~ class_Rings_Oidom(X3257) )
& ( X3256 != X3255
| c_Polynomial_Opoly(X3257,X3256) = c_Polynomial_Opoly(X3257,X3255)
| ~ class_Int_Oring__char__0(X3257)
| ~ class_Rings_Oidom(X3257) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_poly__eq__iff])])]) ).
fof(i_0_2157,plain,
! [X4187,X4188] :
( ~ class_Lattices_Oab__semigroup__idem__mult(X4188)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4188),X4187),X4187) = X4187 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__idem])]) ).
fof(i_0_2158,plain,
! [X4185,X4186] :
( ~ class_Lattices_Oab__semigroup__idem__mult(X4186)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4186),X4185),X4185) = X4185 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_times_Oidem])]) ).
fof(i_0_2159,plain,
! [X5335] :
( X5335 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X5335) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_gr0I])]) ).
fof(i_0_2160,plain,
! [X5960] :
( X5960 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| c_Divides_Odiv__class_Odiv(tc_Int_Oint,X5960,X5960) = c_Groups_Oone__class_Oone(tc_Int_Oint) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zdiv__self])]) ).
fof(i_0_2161,plain,
! [X5867] :
( ~ class_Rings_Olinordered__idom(X5867)
| ~ c_Polynomial_Opos__poly(X5867,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X5867))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1237])]) ).
fof(i_0_2162,plain,
! [X5967] : c_Divides_Odiv__class_Odiv(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X5967) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
inference(variable_rename,[status(thm)],[fact_zdiv__zero]) ).
fof(i_0_2163,plain,
! [X4682] : c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X4682) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
inference(variable_rename,[status(thm)],[fact_zmod__zero]) ).
fof(i_0_2164,plain,
! [X5981] :
( c_Divides_Odiv__class_Odiv(tc_Int_Oint,X5981,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
& c_Divides_Odiv__class_Omod(tc_Int_Oint,X5981,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = X5981 ),
inference(variable_rename,[status(thm)],[fact_DIVISION__BY__ZERO]) ).
fof(i_0_2165,plain,
! [X4681] : c_Divides_Odiv__class_Omod(tc_Int_Oint,X4681,X4681) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
inference(variable_rename,[status(thm)],[fact_zmod__self]) ).
fof(i_0_2166,plain,
! [X3801] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X3801) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(variable_rename,[status(thm)],[fact_diff__0__eq__0]) ).
fof(i_0_2167,plain,
! [X3414] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X3414) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(variable_rename,[status(thm)],[fact_mult__0]) ).
fof(i_0_2168,plain,
! [X4919,X4920,X4921] :
( ( c_Nat_Osemiring__1__class_Oof__nat(X4921,X4920) != c_Nat_Osemiring__1__class_Oof__nat(X4921,X4919)
| X4920 = X4919
| ~ class_Nat_Osemiring__char__0(X4921) )
& ( X4920 != X4919
| c_Nat_Osemiring__1__class_Oof__nat(X4921,X4920) = c_Nat_Osemiring__1__class_Oof__nat(X4921,X4919)
| ~ class_Nat_Osemiring__char__0(X4921) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__nat__eq__iff])])]) ).
fof(i_0_2169,plain,
! [X3593,X3594,X3595] :
( ( c_Polynomial_Ocoeff(X3595,X3594) != c_Polynomial_Ocoeff(X3595,X3593)
| X3594 = X3593
| ~ class_Groups_Ozero(X3595) )
& ( X3594 != X3593
| c_Polynomial_Ocoeff(X3595,X3594) = c_Polynomial_Ocoeff(X3595,X3593)
| ~ class_Groups_Ozero(X3595) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_coeff__inject])])]) ).
fof(i_0_2170,plain,
! [X3740] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X3740) = X3740,
inference(variable_rename,[status(thm)],[fact_zmult__1]) ).
fof(i_0_2171,plain,
! [X3444] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X3444) = X3444,
inference(variable_rename,[status(thm)],[fact_nat__mult__1]) ).
fof(i_0_2172,plain,
! [X3981] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3981) = X3981,
inference(variable_rename,[status(thm)],[fact_zadd__0]) ).
fof(i_0_2173,plain,
! [X3362] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X3362) = X3362,
inference(variable_rename,[status(thm)],[fact_plus__nat_Oadd__0]) ).
fof(i_0_2174,plain,
! [X3415] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3415),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(variable_rename,[status(thm)],[fact_mult__0__right]) ).
fof(i_0_2175,plain,
! [X3999,X4000] :
( ( c_Groups_Ozero__class_Ozero(X4000) != hAPP(c_Groups_Ouminus__class_Ouminus(X4000),X3999)
| c_Groups_Ozero__class_Ozero(X4000) = X3999
| ~ class_Groups_Ogroup__add(X4000) )
& ( c_Groups_Ozero__class_Ozero(X4000) != X3999
| c_Groups_Ozero__class_Ozero(X4000) = hAPP(c_Groups_Ouminus__class_Ouminus(X4000),X3999)
| ~ class_Groups_Ogroup__add(X4000) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_neg__0__equal__iff__equal])])]) ).
fof(i_0_2176,plain,
! [X4452,X4453] :
( ( hAPP(c_Rings_Oinverse__class_Oinverse(X4453),X4452) != c_Groups_Oone__class_Oone(X4453)
| X4452 = c_Groups_Oone__class_Oone(X4453)
| ~ class_Fields_Ofield__inverse__zero(X4453) )
& ( X4452 != c_Groups_Oone__class_Oone(X4453)
| hAPP(c_Rings_Oinverse__class_Oinverse(X4453),X4452) = c_Groups_Oone__class_Oone(X4453)
| ~ class_Fields_Ofield__inverse__zero(X4453) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inverse__eq__1__iff])])]) ).
fof(i_0_2177,plain,
! [X4298,X4299] :
( ~ class_Rings_Odivision__ring(X4299)
| X4298 = c_Groups_Ozero__class_Ozero(X4299)
| hAPP(c_Rings_Oinverse__class_Oinverse(X4299),X4298) != c_Groups_Ozero__class_Ozero(X4299) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nonzero__imp__inverse__nonzero])]) ).
fof(i_0_2178,plain,
! [X4294,X4295] :
( ~ class_Rings_Odivision__ring(X4295)
| hAPP(c_Rings_Oinverse__class_Oinverse(X4295),X4294) != c_Groups_Ozero__class_Ozero(X4295)
| X4294 = c_Groups_Ozero__class_Ozero(X4295) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inverse__zero__imp__zero])]) ).
fof(i_0_2179,plain,
! [X4300,X4301] :
( ( hAPP(c_Rings_Oinverse__class_Oinverse(X4301),X4300) != c_Groups_Ozero__class_Ozero(X4301)
| X4300 = c_Groups_Ozero__class_Ozero(X4301)
| ~ class_Rings_Odivision__ring__inverse__zero(X4301) )
& ( X4300 != c_Groups_Ozero__class_Ozero(X4301)
| hAPP(c_Rings_Oinverse__class_Oinverse(X4301),X4300) = c_Groups_Ozero__class_Ozero(X4301)
| ~ class_Rings_Odivision__ring__inverse__zero(X4301) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inverse__nonzero__iff__nonzero])])]) ).
fof(i_0_2180,plain,
! [X4003,X4004] :
( ( hAPP(c_Groups_Ouminus__class_Ouminus(X4004),X4003) != c_Groups_Ozero__class_Ozero(X4004)
| X4003 = c_Groups_Ozero__class_Ozero(X4004)
| ~ class_Groups_Ogroup__add(X4004) )
& ( X4003 != c_Groups_Ozero__class_Ozero(X4004)
| hAPP(c_Groups_Ouminus__class_Ouminus(X4004),X4003) = c_Groups_Ozero__class_Ozero(X4004)
| ~ class_Groups_Ogroup__add(X4004) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_neg__equal__0__iff__equal])])]) ).
fof(i_0_2181,plain,
! [X6185] :
( ~ hBOOL(hAPP(c_fNot,X6185))
| ~ hBOOL(X6185) ),
inference(variable_rename,[status(thm)],[i_0_1238]) ).
fof(i_0_2182,plain,
! [X3800] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X3800),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X3800,
inference(variable_rename,[status(thm)],[fact_minus__nat_Odiff__0]) ).
fof(i_0_2183,plain,
! [X3739] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X3739),c_Groups_Oone__class_Oone(tc_Int_Oint)) = X3739,
inference(variable_rename,[status(thm)],[fact_zmult__1__right]) ).
fof(i_0_2184,plain,
! [X3447] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3447),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X3447,
inference(variable_rename,[status(thm)],[fact_nat__mult__1__right]) ).
fof(i_0_2185,plain,
! [X3982] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X3982),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = X3982,
inference(variable_rename,[status(thm)],[fact_zadd__0__right]) ).
fof(i_0_2186,plain,
! [X3361] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3361),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X3361,
inference(variable_rename,[status(thm)],[fact_Nat_Oadd__0__right]) ).
fof(i_0_2187,plain,
! [X4239] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X4239)) = X4239,
inference(variable_rename,[status(thm)],[fact_zminus__zminus]) ).
fof(i_0_2188,plain,
! [X3799] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X3799),X3799) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(variable_rename,[status(thm)],[fact_diff__self__eq__0]) ).
fof(i_0_2189,plain,
! [X3830,X3831] :
( ~ class_Groups_Ozero(X3831)
| c_Polynomial_OAbs__poly(X3831,c_Polynomial_Ocoeff(X3831,X3830)) = X3830 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_coeff__inverse])]) ).
fof(i_0_2190,plain,
! [X6183,X6184] :
( X6184 != X6183
| hBOOL(hAPP(c_fequal(X6184),X6183)) ),
inference(variable_rename,[status(thm)],[help_c__fequal__2]) ).
fof(i_0_2191,plain,
! [X4005,X4006] :
( ( hAPP(c_Groups_Ouminus__class_Ouminus(X4006),X4005) != X4005
| X4005 = c_Groups_Ozero__class_Ozero(X4006)
| ~ class_Groups_Olinordered__ab__group__add(X4006) )
& ( X4005 != c_Groups_Ozero__class_Ozero(X4006)
| hAPP(c_Groups_Ouminus__class_Ouminus(X4006),X4005) = X4005
| ~ class_Groups_Olinordered__ab__group__add(X4006) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_neg__equal__zero])])]) ).
fof(i_0_2192,plain,
! [X4001,X4002] :
( ( X4001 != hAPP(c_Groups_Ouminus__class_Ouminus(X4002),X4001)
| X4001 = c_Groups_Ozero__class_Ozero(X4002)
| ~ class_Groups_Olinordered__ab__group__add(X4002) )
& ( X4001 != c_Groups_Ozero__class_Ozero(X4002)
| X4001 = hAPP(c_Groups_Ouminus__class_Ouminus(X4002),X4001)
| ~ class_Groups_Olinordered__ab__group__add(X4002) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_equal__neg__zero])])]) ).
fof(i_0_2193,plain,
! [X3134,X3135] :
( ( c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(X3135,X3134) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X3134 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3135))
| ~ class_Groups_Ozero(X3135) )
& ( X3134 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3135))
| c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(X3135,X3134) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ class_Groups_Ozero(X3135) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_psize__eq__0__iff])])]) ).
fof(i_0_2194,plain,
! [X3858] :
( ~ class_Rings_Ocomm__semiring__1(X3858)
| c_Polynomial_Odegree(X3858,c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(X3858))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_degree__1])]) ).
fof(i_0_2195,plain,
! [X3832] :
( ~ class_Groups_Ozero(X3832)
| c_Polynomial_Odegree(X3832,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3832))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_degree__0])]) ).
fof(i_0_2196,plain,
! [X5100,X5101] :
( ( c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,X5101) != c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,X5100)
| X5101 = X5100 )
& ( X5101 != X5100
| c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,X5101) = c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,X5100) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_int__int__eq])]) ).
fof(i_0_2197,plain,
! [X5098,X5099] :
( ( c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,X5099) != c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,X5098)
| X5099 = X5098 )
& ( X5099 != X5098
| c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,X5099) = c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,X5098) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Nat__Transfer_Otransfer__int__nat__relations_I1_J])]) ).
fof(i_0_2198,plain,
! [X3976,X3977] :
( hAPP(c_Nat_OSuc,X3977) != hAPP(c_Nat_OSuc,X3976)
| X3977 = X3976 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Suc__inject])]) ).
fof(i_0_2199,plain,
! [X3971,X3972] :
( ( hAPP(c_Nat_OSuc,X3972) != hAPP(c_Nat_OSuc,X3971)
| X3972 = X3971 )
& ( X3972 != X3971
| hAPP(c_Nat_OSuc,X3972) = hAPP(c_Nat_OSuc,X3971) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat_Oinject])]) ).
fof(i_0_2200,plain,
! [X4319] :
( ~ class_Rings_Odivision__ring(X4319)
| hAPP(c_Rings_Oinverse__class_Oinverse(X4319),c_Groups_Oone__class_Oone(X4319)) = c_Groups_Oone__class_Oone(X4319) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inverse__1])]) ).
fof(i_0_2201,plain,
! [X4448] :
( ~ class_Fields_Ofield__inverse__zero(X4448)
| hAPP(c_Rings_Oinverse__class_Oinverse(X4448),c_Groups_Ozero__class_Ozero(X4448)) = c_Groups_Ozero__class_Ozero(X4448) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_field__inverse__zero])]) ).
fof(i_0_2202,plain,
! [X4302] :
( ~ class_Rings_Odivision__ring__inverse__zero(X4302)
| hAPP(c_Rings_Oinverse__class_Oinverse(X4302),c_Groups_Ozero__class_Ozero(X4302)) = c_Groups_Ozero__class_Ozero(X4302) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inverse__zero])]) ).
fof(i_0_2203,plain,
! [X3998] :
( ~ class_Groups_Ogroup__add(X3998)
| hAPP(c_Groups_Ouminus__class_Ouminus(X3998),c_Groups_Ozero__class_Ozero(X3998)) = c_Groups_Ozero__class_Ozero(X3998) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_minus__zero])]) ).
fof(i_0_2204,plain,
! [X6098,X6099] :
( ~ class_Orderings_Oord(X6099)
| class_Orderings_Oord(tc_fun(X6098,X6099)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_fun__Orderings_Oord])]) ).
fof(i_0_2205,plain,
! [X6096,X6097] :
( ~ class_Orderings_Oorder(X6097)
| class_Orderings_Oorder(tc_fun(X6096,X6097)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_fun__Orderings_Oorder])]) ).
fof(i_0_2206,plain,
! [X6094,X6095] :
( ~ class_Orderings_Opreorder(X6095)
| class_Orderings_Opreorder(tc_fun(X6094,X6095)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_fun__Orderings_Opreorder])]) ).
fof(i_0_2207,plain,
! [X6100,X6101] :
( ~ class_Groups_Ouminus(X6101)
| class_Groups_Ouminus(tc_fun(X6100,X6101)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_fun__Groups_Ouminus])]) ).
fof(i_0_2208,plain,
! [X6092,X6093] :
( ~ class_Lattices_Oboolean__algebra(X6093)
| class_Lattices_Oboolean__algebra(tc_fun(X6092,X6093)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_fun__Lattices_Oboolean__algebra])]) ).
fof(i_0_2209,plain,
! [X6102,X6103] :
( ~ class_Groups_Ominus(X6103)
| class_Groups_Ominus(tc_fun(X6102,X6103)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_fun__Groups_Ominus])]) ).
fof(i_0_2210,plain,
! [X6186] :
( hBOOL(X6186)
| hBOOL(hAPP(c_fNot,X6186)) ),
inference(variable_rename,[status(thm)],[i_0_1239]) ).
fof(i_0_2211,plain,
! [X4997] :
( ~ class_Rings_Osemiring__1(X4997)
| c_Nat_Osemiring__1__class_Oof__nat(X4997,c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(X4997) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__nat__1])]) ).
fof(i_0_2212,plain,
! [X4936] :
( ~ class_Rings_Osemiring__1(X4936)
| c_Nat_Osemiring__1__class_Oof__nat(X4936,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(X4936) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__nat__0])]) ).
fof(i_0_2213,plain,
! [X5001] :
( ( c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,X5001) != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| X5001 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( X5001 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,X5001) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_int__eq__0__conv])]) ).
fof(i_0_2214,plain,
! [X4054] : hAPP(c_Nat_OSuc,X4054) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(variable_rename,[status(thm)],[fact_Suc__neq__Zero]) ).
fof(i_0_2215,plain,
! [X4052] : hAPP(c_Nat_OSuc,X4052) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(variable_rename,[status(thm)],[fact_nat_Osimps_I3_J]) ).
fof(i_0_2216,plain,
! [X4051] : hAPP(c_Nat_OSuc,X4051) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(variable_rename,[status(thm)],[fact_Suc__not__Zero]) ).
fof(i_0_2217,plain,
! [X4053] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,X4053),
inference(variable_rename,[status(thm)],[fact_Zero__neq__Suc]) ).
fof(i_0_2218,plain,
! [X4050] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,X4050),
inference(variable_rename,[status(thm)],[fact_nat_Osimps_I2_J]) ).
fof(i_0_2219,plain,
! [X4049] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,X4049),
inference(variable_rename,[status(thm)],[fact_Zero__not__Suc]) ).
fof(i_0_2220,plain,
! [X3958] : hAPP(c_Nat_OSuc,X3958) != X3958,
inference(variable_rename,[status(thm)],[fact_Suc__n__not__n]) ).
fof(i_0_2221,plain,
! [X3957] : X3957 != hAPP(c_Nat_OSuc,X3957),
inference(variable_rename,[status(thm)],[fact_n__not__Suc__n]) ).
fof(i_0_2222,plain,
! [X6157,X6158] : hAPP(c_COMBI(X6158),X6157) = X6157,
inference(variable_rename,[status(thm)],[help_c__COMBI__1]) ).
fof(i_0_2223,plain,
! [X3554] :
( ~ class_Rings_Ozero__neq__one(X3554)
| c_Groups_Oone__class_Oone(X3554) != c_Groups_Ozero__class_Ozero(X3554) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_one__neq__zero])]) ).
fof(i_0_2224,plain,
! [X3553] :
( ~ class_Rings_Ozero__neq__one(X3553)
| c_Groups_Ozero__class_Ozero(X3553) != c_Groups_Oone__class_Oone(X3553) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__neq__one])]) ).
fof(i_0_2225,plain,
! [X6091] :
( ~ class_Groups_Ocancel__comm__monoid__add(X6091)
| class_Groups_Ocancel__comm__monoid__add(tc_Polynomial_Opoly(X6091)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Groups_Ocancel__comm__monoid__add])]) ).
fof(i_0_2226,plain,
! [X6132] :
( ~ class_Rings_Olinordered__idom(X6132)
| class_Rings_Oordered__ring(tc_Polynomial_Opoly(X6132)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Rings_Oordered__ring])]) ).
fof(i_0_2227,plain,
! [X6147] :
( ~ class_Rings_Olinordered__idom(X6147)
| class_Orderings_Oord(tc_Polynomial_Opoly(X6147)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Orderings_Oord])]) ).
fof(i_0_2228,plain,
! [X6144] :
( ~ class_Rings_Olinordered__idom(X6144)
| class_Orderings_Oorder(tc_Polynomial_Opoly(X6144)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Orderings_Oorder])]) ).
fof(i_0_2229,plain,
! [X6134] :
( ~ class_Rings_Olinordered__idom(X6134)
| class_Orderings_Olinorder(tc_Polynomial_Opoly(X6134)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Orderings_Olinorder])]) ).
fof(i_0_2230,plain,
! [X6133] :
( ~ class_Rings_Olinordered__idom(X6133)
| class_Orderings_Opreorder(tc_Polynomial_Opoly(X6133)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Orderings_Opreorder])]) ).
fof(i_0_2231,plain,
! [X6105] :
( ~ class_Rings_Olinordered__idom(X6105)
| class_Groups_Oordered__cancel__ab__semigroup__add(tc_Polynomial_Opoly(X6105)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Groups_Oordered__cancel__ab__semigroup__add])]) ).
fof(i_0_2232,plain,
! [X6106] :
( ~ class_Rings_Olinordered__idom(X6106)
| class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Polynomial_Opoly(X6106)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Groups_Oordered__ab__semigroup__add__imp__le])]) ).
fof(i_0_2233,plain,
! [X6115] :
( ~ class_Rings_Olinordered__idom(X6115)
| class_Groups_Oordered__ab__group__add(tc_Polynomial_Opoly(X6115)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Groups_Oordered__ab__group__add])]) ).
fof(i_0_2234,plain,
! [X6124] :
( ~ class_Rings_Olinordered__idom(X6124)
| class_Rings_Olinordered__idom(tc_Polynomial_Opoly(X6124)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Rings_Olinordered__idom])]) ).
fof(i_0_2235,plain,
! [X6109] :
( ~ class_Rings_Olinordered__idom(X6109)
| class_Groups_Oordered__comm__monoid__add(tc_Polynomial_Opoly(X6109)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Groups_Oordered__comm__monoid__add])]) ).
fof(i_0_2236,plain,
! [X6123] :
( ~ class_Rings_Olinordered__idom(X6123)
| class_Rings_Olinordered__ring(tc_Polynomial_Opoly(X6123)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Rings_Olinordered__ring])]) ).
fof(i_0_2237,plain,
! [X6108] :
( ~ class_Rings_Olinordered__idom(X6108)
| class_Rings_Olinordered__semiring__strict(tc_Polynomial_Opoly(X6108)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Rings_Olinordered__semiring__strict])]) ).
fof(i_0_2238,plain,
! [X6107] :
( ~ class_Rings_Olinordered__idom(X6107)
| class_Rings_Olinordered__comm__semiring__strict(tc_Polynomial_Opoly(X6107)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Rings_Olinordered__comm__semiring__strict])]) ).
fof(i_0_2239,plain,
! [X6117] :
( ~ class_Rings_Olinordered__idom(X6117)
| class_Rings_Olinordered__semidom(tc_Polynomial_Opoly(X6117)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Rings_Olinordered__semidom])]) ).
fof(i_0_2240,plain,
! [X6138] :
( ~ class_Rings_Ocomm__semiring__1(X6138)
| class_Rings_Osemiring__1(tc_Polynomial_Opoly(X6138)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Rings_Osemiring__1])]) ).
fof(i_0_2241,plain,
! [X6129] :
( ~ class_Rings_Olinordered__idom(X6129)
| class_Nat_Osemiring__char__0(tc_Polynomial_Opoly(X6129)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Nat_Osemiring__char__0])]) ).
fof(i_0_2242,plain,
! [X6141] :
( ~ class_Fields_Ofield(X6141)
| class_Divides_Oring__div(tc_Polynomial_Opoly(X6141)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Divides_Oring__div])]) ).
fof(i_0_2243,plain,
! [X6127] :
( ~ class_Fields_Ofield(X6127)
| class_Divides_Osemiring__div(tc_Polynomial_Opoly(X6127)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Divides_Osemiring__div])]) ).
fof(i_0_2244,plain,
! [X6156] :
( ~ class_Rings_Ocomm__semiring__1(X6156)
| class_Rings_Odvd(tc_Polynomial_Opoly(X6156)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Rings_Odvd])]) ).
fof(i_0_2245,plain,
! [X6148] :
( ~ class_Groups_Oab__group__add(X6148)
| class_Groups_Ouminus(tc_Polynomial_Opoly(X6148)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Groups_Ouminus])]) ).
fof(i_0_2246,plain,
! [X6150] :
( ~ class_Groups_Oab__group__add(X6150)
| class_Groups_Ominus(tc_Polynomial_Opoly(X6150)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Groups_Ominus])]) ).
fof(i_0_2247,plain,
! [X6149] :
( ~ class_Rings_Ocomm__ring__1(X6149)
| class_Rings_Oring__1(tc_Polynomial_Opoly(X6149)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Rings_Oring__1])]) ).
fof(i_0_2248,plain,
! [X6153] :
( ~ class_Rings_Ocomm__ring(X6153)
| class_Rings_Oring(tc_Polynomial_Opoly(X6153)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Rings_Oring])]) ).
fof(i_0_2249,plain,
! [X6140] :
( ~ class_Groups_Oab__group__add(X6140)
| class_Groups_Ogroup__add(tc_Polynomial_Opoly(X6140)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Groups_Ogroup__add])]) ).
fof(i_0_2250,plain,
! [X6143] :
( ~ class_Rings_Ocomm__ring(X6143)
| class_Rings_Ocomm__ring(tc_Polynomial_Opoly(X6143)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Rings_Ocomm__ring])]) ).
fof(i_0_2251,plain,
! [X6130] :
( ~ class_Groups_Oab__group__add(X6130)
| class_Groups_Oab__group__add(tc_Polynomial_Opoly(X6130)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Groups_Oab__group__add])]) ).
fof(i_0_2252,plain,
! [X6114] :
( ~ class_Rings_Oidom(X6114)
| class_Rings_Oring__no__zero__divisors(tc_Polynomial_Opoly(X6114)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Rings_Oring__no__zero__divisors])]) ).
fof(i_0_2253,plain,
! [X6136] :
( ~ class_Rings_Ocomm__ring__1(X6136)
| class_Rings_Ocomm__ring__1(tc_Polynomial_Opoly(X6136)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Rings_Ocomm__ring__1])]) ).
fof(i_0_2254,plain,
! [X6146] :
( ~ class_Rings_Ocomm__semiring__0(X6146)
| class_Rings_Osemiring(tc_Polynomial_Opoly(X6146)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Rings_Osemiring])]) ).
fof(i_0_2255,plain,
! [X6128] :
( ~ class_Rings_Ocomm__semiring__0(X6128)
| class_Rings_Ocomm__semiring(tc_Polynomial_Opoly(X6128)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Rings_Ocomm__semiring])]) ).
fof(i_0_2256,plain,
! [X6110] :
( ~ class_Rings_Olinordered__idom(X6110)
| class_Groups_Olinordered__ab__group__add(tc_Polynomial_Opoly(X6110)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Groups_Olinordered__ab__group__add])]) ).
fof(i_0_2257,plain,
! [X6137] :
( ~ class_Groups_Ocomm__monoid__add(X6137)
| class_Groups_Omonoid__add(tc_Polynomial_Opoly(X6137)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Groups_Omonoid__add])]) ).
fof(i_0_2258,plain,
! [X6155] :
( ~ class_Rings_Ocomm__semiring__1(X6155)
| class_Groups_Oone(tc_Polynomial_Opoly(X6155)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Groups_Oone])]) ).
fof(i_0_2259,plain,
! [X6111] :
( ~ class_Groups_Ocancel__comm__monoid__add(X6111)
| class_Groups_Ocancel__ab__semigroup__add(tc_Polynomial_Opoly(X6111)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Groups_Ocancel__ab__semigroup__add])]) ).
fof(i_0_2260,plain,
! [X6116] :
( ~ class_Groups_Ocancel__comm__monoid__add(X6116)
| class_Groups_Ocancel__semigroup__add(tc_Polynomial_Opoly(X6116)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Groups_Ocancel__semigroup__add])]) ).
fof(i_0_2261,plain,
! [X6120] :
( ~ class_Groups_Ocomm__monoid__add(X6120)
| class_Groups_Oab__semigroup__add(tc_Polynomial_Opoly(X6120)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Groups_Oab__semigroup__add])]) ).
fof(i_0_2262,plain,
! [X6118] :
( ~ class_Rings_Ocomm__semiring__0(X6118)
| class_Groups_Oab__semigroup__mult(tc_Polynomial_Opoly(X6118)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Groups_Oab__semigroup__mult])]) ).
fof(i_0_2263,plain,
! [X6113] :
( ~ class_Rings_Olinordered__idom(X6113)
| class_Rings_Olinordered__ring__strict(tc_Polynomial_Opoly(X6113)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Rings_Olinordered__ring__strict])]) ).
fof(i_0_2264,plain,
! [X6119] :
( ~ class_Rings_Ocomm__semiring__1(X6119)
| class_Groups_Ocomm__monoid__mult(tc_Polynomial_Opoly(X6119)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Groups_Ocomm__monoid__mult])]) ).
fof(i_0_2265,plain,
! [X6112] :
( ~ class_Rings_Oidom(X6112)
| class_Rings_Oring__1__no__zero__divisors(tc_Polynomial_Opoly(X6112)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Rings_Oring__1__no__zero__divisors])]) ).
fof(i_0_2266,plain,
! [X6104] :
( ~ class_Rings_Oidom(X6104)
| class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Polynomial_Opoly(X6104)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct])]) ).
fof(i_0_2267,plain,
! [X6145] :
( ~ class_Rings_Olinordered__idom(X6145)
| class_Int_Oring__char__0(tc_Polynomial_Opoly(X6145)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Int_Oring__char__0])]) ).
fof(i_0_2268,plain,
! [X6122] :
( ~ class_Groups_Ocomm__monoid__add(X6122)
| class_Groups_Ocomm__monoid__add(tc_Polynomial_Opoly(X6122)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Groups_Ocomm__monoid__add])]) ).
fof(i_0_2269,plain,
! [X6131] :
( ~ class_Rings_Ocomm__semiring__1(X6131)
| class_Rings_Ozero__neq__one(tc_Polynomial_Opoly(X6131)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Rings_Ozero__neq__one])]) ).
fof(i_0_2270,plain,
! [X6121] :
( ~ class_Rings_Oidom(X6121)
| class_Rings_Ono__zero__divisors(tc_Polynomial_Opoly(X6121)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Rings_Ono__zero__divisors])]) ).
fof(i_0_2271,plain,
! [X6142] :
( ~ class_Rings_Ocomm__semiring__0(X6142)
| class_Rings_Omult__zero(tc_Polynomial_Opoly(X6142)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Rings_Omult__zero])]) ).
fof(i_0_2272,plain,
! [X6135] :
( ~ class_Rings_Ocomm__semiring__1(X6135)
| class_Groups_Omonoid__mult(tc_Polynomial_Opoly(X6135)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Groups_Omonoid__mult])]) ).
fof(i_0_2273,plain,
! [X6125] :
( ~ class_Rings_Ocomm__semiring__1(X6125)
| class_Rings_Ocomm__semiring__1(tc_Polynomial_Opoly(X6125)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Rings_Ocomm__semiring__1])]) ).
fof(i_0_2274,plain,
! [X6139] :
( ~ class_Rings_Ocomm__semiring__0(X6139)
| class_Rings_Osemiring__0(tc_Polynomial_Opoly(X6139)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Rings_Osemiring__0])]) ).
fof(i_0_2275,plain,
! [X6151] :
( ~ class_Rings_Ocomm__semiring__1(X6151)
| class_Power_Opower(tc_Polynomial_Opoly(X6151)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Power_Opower])]) ).
fof(i_0_2276,plain,
! [X6126] :
( ~ class_Rings_Ocomm__semiring__0(X6126)
| class_Rings_Ocomm__semiring__0(tc_Polynomial_Opoly(X6126)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Rings_Ocomm__semiring__0])]) ).
fof(i_0_2277,plain,
! [X6152] :
( ~ class_Groups_Ozero(X6152)
| class_Groups_Ozero(tc_Polynomial_Opoly(X6152)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Groups_Ozero])]) ).
fof(i_0_2278,plain,
! [X6154] :
( ~ class_Rings_Oidom(X6154)
| class_Rings_Oidom(tc_Polynomial_Opoly(X6154)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Rings_Oidom])]) ).
fof(i_0_2279,plain,
! [X6090] :
( ~ class_Rings_Oidom(X6090)
| class_Groups_Ocancel__comm__monoid__add(X6090) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[clrel_Rings_Oidom__Groups_Ocancel__comm__monoid__add])]) ).
fof(i_0_2280,plain,
! [X6076] :
( ~ class_Rings_Oidom(X6076)
| class_Rings_Osemiring__1(X6076) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[clrel_Rings_Oidom__Rings_Osemiring__1])]) ).
fof(i_0_2281,plain,
! [X6089] :
( ~ class_Rings_Oidom(X6089)
| class_Rings_Odvd(X6089) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[clrel_Rings_Oidom__Rings_Odvd])]) ).
fof(i_0_2282,plain,
! [X6082] :
( ~ class_Rings_Oidom(X6082)
| class_Groups_Ouminus(X6082) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[clrel_Rings_Oidom__Groups_Ouminus])]) ).
fof(i_0_2283,plain,
! [X6084] :
( ~ class_Rings_Oidom(X6084)
| class_Groups_Ominus(X6084) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[clrel_Rings_Oidom__Groups_Ominus])]) ).
fof(i_0_2284,plain,
! [X6083] :
( ~ class_Rings_Oidom(X6083)
| class_Rings_Oring__1(X6083) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[clrel_Rings_Oidom__Rings_Oring__1])]) ).
fof(i_0_2285,plain,
! [X6087] :
( ~ class_Rings_Oidom(X6087)
| class_Rings_Oring(X6087) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[clrel_Rings_Oidom__Rings_Oring])]) ).
fof(i_0_2286,plain,
! [X6078] :
( ~ class_Rings_Oidom(X6078)
| class_Groups_Ogroup__add(X6078) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[clrel_Rings_Oidom__Groups_Ogroup__add])]) ).
fof(i_0_2287,plain,
! [X6080] :
( ~ class_Rings_Oidom(X6080)
| class_Rings_Ocomm__ring(X6080) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[clrel_Rings_Oidom__Rings_Ocomm__ring])]) ).
fof(i_0_2288,plain,
! [X6071] :
( ~ class_Rings_Oidom(X6071)
| class_Groups_Oab__group__add(X6071) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[clrel_Rings_Oidom__Groups_Oab__group__add])]) ).
fof(i_0_2289,plain,
! [X6061] :
( ~ class_Rings_Oidom(X6061)
| class_Rings_Oring__no__zero__divisors(X6061) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[clrel_Rings_Oidom__Rings_Oring__no__zero__divisors])]) ).
fof(i_0_2290,plain,
! [X6074] :
( ~ class_Rings_Oidom(X6074)
| class_Rings_Ocomm__ring__1(X6074) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[clrel_Rings_Oidom__Rings_Ocomm__ring__1])]) ).
fof(i_0_2291,plain,
! [X6081] :
( ~ class_Rings_Oidom(X6081)
| class_Rings_Osemiring(X6081) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[clrel_Rings_Oidom__Rings_Osemiring])]) ).
fof(i_0_2292,plain,
! [X6070] :
( ~ class_Rings_Oidom(X6070)
| class_Rings_Ocomm__semiring(X6070) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[clrel_Rings_Oidom__Rings_Ocomm__semiring])]) ).
fof(i_0_2293,plain,
! [X6075] :
( ~ class_Rings_Oidom(X6075)
| class_Groups_Omonoid__add(X6075) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[clrel_Rings_Oidom__Groups_Omonoid__add])]) ).
fof(i_0_2294,plain,
! [X6088] :
( ~ class_Rings_Oidom(X6088)
| class_Groups_Oone(X6088) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[clrel_Rings_Oidom__Groups_Oone])]) ).
fof(i_0_2295,plain,
! [X6059] :
( ~ class_Rings_Oidom(X6059)
| class_Groups_Ocancel__ab__semigroup__add(X6059) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[clrel_Rings_Oidom__Groups_Ocancel__ab__semigroup__add])]) ).
fof(i_0_2296,plain,
! [X6062] :
( ~ class_Rings_Oidom(X6062)
| class_Groups_Ocancel__semigroup__add(X6062) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[clrel_Rings_Oidom__Groups_Ocancel__semigroup__add])]) ).
fof(i_0_2297,plain,
! [X6065] :
( ~ class_Rings_Oidom(X6065)
| class_Groups_Oab__semigroup__add(X6065) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[clrel_Rings_Oidom__Groups_Oab__semigroup__add])]) ).
fof(i_0_2298,plain,
! [X6063] :
( ~ class_Rings_Oidom(X6063)
| class_Groups_Oab__semigroup__mult(X6063) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[clrel_Rings_Oidom__Groups_Oab__semigroup__mult])]) ).
fof(i_0_2299,plain,
! [X6064] :
( ~ class_Rings_Oidom(X6064)
| class_Groups_Ocomm__monoid__mult(X6064) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[clrel_Rings_Oidom__Groups_Ocomm__monoid__mult])]) ).
fof(i_0_2300,plain,
! [X6060] :
( ~ class_Rings_Oidom(X6060)
| class_Rings_Oring__1__no__zero__divisors(X6060) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[clrel_Rings_Oidom__Rings_Oring__1__no__zero__divisors])]) ).
fof(i_0_2301,plain,
! [X6058] :
( ~ class_Rings_Oidom(X6058)
| class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X6058) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[clrel_Rings_Oidom__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct])]) ).
fof(i_0_2302,plain,
! [X6067] :
( ~ class_Rings_Oidom(X6067)
| class_Groups_Ocomm__monoid__add(X6067) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[clrel_Rings_Oidom__Groups_Ocomm__monoid__add])]) ).
fof(i_0_2303,plain,
! [X6072] :
( ~ class_Rings_Oidom(X6072)
| class_Rings_Ozero__neq__one(X6072) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[clrel_Rings_Oidom__Rings_Ozero__neq__one])]) ).
fof(i_0_2304,plain,
! [X6066] :
( ~ class_Rings_Oidom(X6066)
| class_Rings_Ono__zero__divisors(X6066) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[clrel_Rings_Oidom__Rings_Ono__zero__divisors])]) ).
fof(i_0_2305,plain,
! [X6079] :
( ~ class_Rings_Oidom(X6079)
| class_Rings_Omult__zero(X6079) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[clrel_Rings_Oidom__Rings_Omult__zero])]) ).
fof(i_0_2306,plain,
! [X6073] :
( ~ class_Rings_Oidom(X6073)
| class_Groups_Omonoid__mult(X6073) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[clrel_Rings_Oidom__Groups_Omonoid__mult])]) ).
fof(i_0_2307,plain,
! [X6068] :
( ~ class_Rings_Oidom(X6068)
| class_Rings_Ocomm__semiring__1(X6068) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[clrel_Rings_Oidom__Rings_Ocomm__semiring__1])]) ).
fof(i_0_2308,plain,
! [X6077] :
( ~ class_Rings_Oidom(X6077)
| class_Rings_Osemiring__0(X6077) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[clrel_Rings_Oidom__Rings_Osemiring__0])]) ).
fof(i_0_2309,plain,
! [X6085] :
( ~ class_Rings_Oidom(X6085)
| class_Power_Opower(X6085) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[clrel_Rings_Oidom__Power_Opower])]) ).
fof(i_0_2310,plain,
! [X6069] :
( ~ class_Rings_Oidom(X6069)
| class_Rings_Ocomm__semiring__0(X6069) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[clrel_Rings_Oidom__Rings_Ocomm__semiring__0])]) ).
fof(i_0_2311,plain,
! [X6086] :
( ~ class_Rings_Oidom(X6086)
| class_Groups_Ozero(X6086) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[clrel_Rings_Oidom__Groups_Ozero])]) ).
cnf(i_0_2312,plain,
( c_Polynomial_Oorder(X1,X2,X3) = c_Orderings_Oord__class_OLeast(tc_Nat_Onat,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot),hAPP(c_COMBC(tc_Nat_Onat,tc_Polynomial_Opoly(X1),tc_HOL_Obool,hAPP(hAPP(c_COMBB(tc_Polynomial_Opoly(X1),tc_fun(tc_Polynomial_Opoly(X1),tc_HOL_Obool),tc_Nat_Onat),c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X1))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Polynomial_Opoly(X1),tc_Nat_Onat),hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(X1)),hAPP(hAPP(c_Polynomial_OpCons(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)),hAPP(hAPP(c_Polynomial_OpCons(X1),c_Groups_Oone__class_Oone(X1)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)))))),c_Nat_OSuc))),X3)))
| ~ class_Rings_Oidom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1240]),
[final] ).
cnf(i_0_2313,plain,
( c_Polynomial_Opcompose(X1,X2,X3) = c_Polynomial_Opoly__rec(tc_Polynomial_Opoly(X1),X1,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),hAPP(hAPP(c_COMBB(tc_fun(tc_Polynomial_Opoly(X1),tc_Polynomial_Opoly(X1)),tc_fun(tc_Polynomial_Opoly(X1),tc_fun(tc_Polynomial_Opoly(X1),tc_Polynomial_Opoly(X1))),X1),c_COMBK(tc_fun(tc_Polynomial_Opoly(X1),tc_Polynomial_Opoly(X1)),tc_Polynomial_Opoly(X1))),hAPP(c_COMBC(X1,tc_fun(tc_Polynomial_Opoly(X1),tc_Polynomial_Opoly(X1)),tc_fun(tc_Polynomial_Opoly(X1),tc_Polynomial_Opoly(X1)),hAPP(hAPP(c_COMBB(tc_fun(tc_Polynomial_Opoly(X1),tc_Polynomial_Opoly(X1)),tc_fun(tc_fun(tc_Polynomial_Opoly(X1),tc_Polynomial_Opoly(X1)),tc_fun(tc_Polynomial_Opoly(X1),tc_Polynomial_Opoly(X1))),X1),c_COMBB(tc_Polynomial_Opoly(X1),tc_Polynomial_Opoly(X1),tc_Polynomial_Opoly(X1))),hAPP(hAPP(c_COMBB(tc_Polynomial_Opoly(X1),tc_fun(tc_Polynomial_Opoly(X1),tc_Polynomial_Opoly(X1)),X1),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X1))),hAPP(c_COMBC(X1,tc_Polynomial_Opoly(X1),tc_Polynomial_Opoly(X1),c_Polynomial_OpCons(X1)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)))))),hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X1)),X3))),X2)
| ~ class_Rings_Ocomm__semiring__0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1241]),
[final] ).
cnf(i_0_2314,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X1)),X2),X3) = c_Polynomial_Opoly__rec(tc_Polynomial_Opoly(X1),X1,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),hAPP(hAPP(c_COMBB(tc_fun(tc_Polynomial_Opoly(X1),tc_Polynomial_Opoly(X1)),tc_fun(tc_Polynomial_Opoly(X1),tc_fun(tc_Polynomial_Opoly(X1),tc_Polynomial_Opoly(X1))),X1),c_COMBK(tc_fun(tc_Polynomial_Opoly(X1),tc_Polynomial_Opoly(X1)),tc_Polynomial_Opoly(X1))),hAPP(c_COMBC(X1,tc_fun(tc_Polynomial_Opoly(X1),tc_Polynomial_Opoly(X1)),tc_fun(tc_Polynomial_Opoly(X1),tc_Polynomial_Opoly(X1)),hAPP(hAPP(c_COMBB(tc_fun(tc_Polynomial_Opoly(X1),tc_Polynomial_Opoly(X1)),tc_fun(tc_fun(tc_Polynomial_Opoly(X1),tc_Polynomial_Opoly(X1)),tc_fun(tc_Polynomial_Opoly(X1),tc_Polynomial_Opoly(X1))),X1),c_COMBB(tc_Polynomial_Opoly(X1),tc_Polynomial_Opoly(X1),tc_Polynomial_Opoly(X1))),hAPP(hAPP(c_COMBB(tc_Polynomial_Opoly(X1),tc_fun(tc_Polynomial_Opoly(X1),tc_Polynomial_Opoly(X1)),X1),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X1))),hAPP(c_COMBC(X1,tc_Polynomial_Opoly(X1),tc_Polynomial_Opoly(X1),c_Polynomial_Osmult(X1)),X3)))),hAPP(c_Polynomial_OpCons(X1),c_Groups_Ozero__class_Ozero(X1)))),X2)
| ~ class_Rings_Ocomm__semiring__0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1242]),
[final] ).
cnf(i_0_2315,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X4),X3))
| c_Orderings_Oord__class_Oless(X1,hAPP(X2,X3),hAPP(X2,X4))
| ~ class_Orderings_Oorder(X1)
| ~ c_Orderings_Oorder_Ostrict__mono(tc_Nat_Onat,X1,hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool,c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),X2)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X3),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_1243]),
[final] ).
cnf(i_0_2316,plain,
( c_Orderings_Oorder_Omono(tc_Nat_Onat,X1,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X2)
| ~ class_Orderings_Oorder(X1)
| ~ c_Orderings_Oorder_Ostrict__mono(tc_Nat_Onat,X1,hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool,c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),X2) ),
inference(split_conjunct,[status(thm)],[i_0_1244]),
[final] ).
cnf(i_0_2317,plain,
( c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X1,X2,X3) = c_Polynomial_Opoly__rec(tc_Polynomial_Opoly(X1),X1,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),hAPP(hAPP(c_COMBB(tc_fun(tc_Polynomial_Opoly(X1),tc_Polynomial_Opoly(X1)),tc_fun(tc_Polynomial_Opoly(X1),tc_fun(tc_Polynomial_Opoly(X1),tc_Polynomial_Opoly(X1))),X1),c_COMBK(tc_fun(tc_Polynomial_Opoly(X1),tc_Polynomial_Opoly(X1)),tc_Polynomial_Opoly(X1))),hAPP(hAPP(c_COMBB(tc_fun(tc_Polynomial_Opoly(X1),tc_Polynomial_Opoly(X1)),tc_fun(tc_Polynomial_Opoly(X1),tc_Polynomial_Opoly(X1)),X1),hAPP(c_COMBS(tc_Polynomial_Opoly(X1),tc_Polynomial_Opoly(X1),tc_Polynomial_Opoly(X1)),hAPP(hAPP(c_COMBB(tc_Polynomial_Opoly(X1),tc_fun(tc_Polynomial_Opoly(X1),tc_Polynomial_Opoly(X1)),tc_Polynomial_Opoly(X1)),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X1))),hAPP(c_Polynomial_Osmult(X1),X3)))),c_Polynomial_OpCons(X1))),X2)
| ~ class_Rings_Ocomm__semiring__0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1245]),
[final] ).
cnf(i_0_2318,plain,
( X2 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))
| c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(X1),hAPP(hAPP(c_Polynomial_OpCons(X1),X3),X4),X2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X1)),hAPP(hAPP(c_Polynomial_OpCons(X1),X3),c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(X1),X4,X2))),hAPP(hAPP(c_Polynomial_Osmult(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),hAPP(c_Polynomial_Ocoeff(X1,hAPP(hAPP(c_Polynomial_OpCons(X1),X3),c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(X1),X4,X2))),c_Polynomial_Odegree(X1,X2))),hAPP(c_Polynomial_Ocoeff(X1,X2),c_Polynomial_Odegree(X1,X2)))),X2))
| ~ class_Fields_Ofield(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1246]),
[final] ).
cnf(i_0_2319,plain,
( c_Polynomial_Omonom(X1,X2,X3) = c_Polynomial_OAbs__poly(X1,hAPP(c_COMBC(tc_Nat_Onat,X1,X1,hAPP(c_COMBC(tc_Nat_Onat,X1,tc_fun(X1,X1),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X1,tc_fun(X1,X1)),tc_Nat_Onat),c_If(X1)),c_fequal(X3))),X2)),c_Groups_Ozero__class_Ozero(X1)))
| ~ class_Groups_Ozero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1247]),
[final] ).
cnf(i_0_2320,plain,
( X2 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Oidom(X1)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X1)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(X1)),hAPP(hAPP(c_Polynomial_OpCons(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X3)),hAPP(hAPP(c_Polynomial_OpCons(X1),c_Groups_Oone__class_Oone(X1)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))))),hAPP(c_Nat_OSuc,c_Polynomial_Oorder(X1,X3,X2)))),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1248]),
[final] ).
cnf(i_0_2321,plain,
( X3 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X1)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(X1)),hAPP(hAPP(c_Polynomial_OpCons(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)),hAPP(hAPP(c_Polynomial_OpCons(X1),c_Groups_Oone__class_Oone(X1)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))))),hAPP(c_Nat_OSuc,c_Polynomial_Oorder(X1,X2,X3)))),X3))
| ~ class_Rings_Oidom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1249]),
[final] ).
cnf(i_0_2322,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X1)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(X1)),hAPP(hAPP(c_Polynomial_OpCons(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)),hAPP(hAPP(c_Polynomial_OpCons(X1),c_Groups_Oone__class_Oone(X1)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))))),c_Polynomial_Oorder(X1,X2,X3))),X3))
| X3 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Oidom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1249]),
[final] ).
cnf(i_0_2323,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X1)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(X1)),hAPP(hAPP(c_Polynomial_OpCons(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)),hAPP(hAPP(c_Polynomial_OpCons(X1),c_Groups_Oone__class_Oone(X1)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))))),c_Polynomial_Oorder(X1,X2,X3))),X3))
| ~ class_Rings_Oidom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1250]),
[final] ).
cnf(i_0_2324,plain,
( hAPP(X5,X3) = c_Groups_Ozero__class_Ozero(X1)
| c_Deriv_Oderiv(X1,hAPP(hAPP(c_COMBS(X1,X1,X1),hAPP(hAPP(c_COMBB(X1,tc_fun(X1,X1),X1),c_Rings_Oinverse__class_Odivide(X1)),X2)),X5),X3,hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),hAPP(X5,X3))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(X2,X3)),X6))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(X5,X3)),hAPP(X5,X3))))
| ~ class_RealVector_Oreal__normed__field(X1)
| ~ c_Deriv_Oderiv(X1,X2,X3,X4)
| ~ c_Deriv_Oderiv(X1,X5,X3,X6) ),
inference(split_conjunct,[status(thm)],[i_0_1251]),
[final] ).
cnf(i_0_2325,plain,
( hAPP(X5,X3) = c_Groups_Ozero__class_Ozero(X1)
| c_Deriv_Oderiv(X1,hAPP(hAPP(c_COMBS(X1,X1,X1),hAPP(hAPP(c_COMBB(X1,tc_fun(X1,X1),X1),c_Rings_Oinverse__class_Odivide(X1)),X2)),X5),X3,hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),hAPP(X5,X3))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X6),hAPP(X2,X3)))),hAPP(hAPP(c_Power_Opower__class_Opower(X1),hAPP(X5,X3)),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))))
| ~ class_RealVector_Oreal__normed__field(X1)
| ~ c_Deriv_Oderiv(X1,X2,X3,X4)
| ~ c_Deriv_Oderiv(X1,X5,X3,X6) ),
inference(split_conjunct,[status(thm)],[i_0_1252]),
[final] ).
cnf(i_0_2326,plain,
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X5)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X2),X4)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X3),X5))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X2),X4)),X5))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X3),X5)))
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1253]),
[final] ).
cnf(i_0_2327,plain,
( c_Polynomial_Opoly__rec(X2,X1,X3,X4,hAPP(hAPP(c_Polynomial_OpCons(X1),X5),X6)) = hAPP(hAPP(hAPP(X4,X5),X6),hAPP(hAPP(hAPP(c_If(X2),hAPP(c_fequal(X6),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)))),X3),c_Polynomial_Opoly__rec(X2,X1,X3,X4,X6)))
| ~ class_Groups_Ozero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1254]),
[final] ).
cnf(i_0_2328,plain,
( c_Deriv_Oderiv(X1,hAPP(c_COMBC(X1,tc_Nat_Onat,X1,hAPP(hAPP(c_COMBB(X1,tc_fun(tc_Nat_Onat,X1),X1),c_Power_Opower__class_Opower(X1)),X2)),X5),X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Nat_Osemiring__1__class_Oof__nat(X1,X5)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),hAPP(hAPP(c_Power_Opower__class_Opower(X1),hAPP(X2,X3)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X5),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))))
| ~ class_RealVector_Oreal__normed__field(X1)
| ~ c_Deriv_Oderiv(X1,X2,X3,X4) ),
inference(split_conjunct,[status(thm)],[i_0_1255]),
[final] ).
cnf(i_0_2329,negated_conjecture,
( X1 = c_Groups_Ozero__class_Ozero(t_a)
| X2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(t_a,X3)),X2)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) != c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(t_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)))
| hAPP(c_Polynomial_Opoly(t_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),esk21_3(X2,X1,X3)) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(t_a),hAPP(c_Polynomial_Opoly(t_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),c_Groups_Ozero__class_Ozero(t_a))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),hAPP(hAPP(c_Power_Opower__class_Opower(t_a),esk21_3(X2,X1,X3)),X2)),hAPP(c_Polynomial_Opoly(t_a,hAPP(hAPP(c_Polynomial_OpCons(t_a),X1),X3)),esk21_3(X2,X1,X3)))) ),
inference(split_conjunct,[status(thm)],[i_0_1256]),
[final] ).
cnf(i_0_2330,plain,
( c_Deriv_Oderiv(X1,hAPP(c_COMBC(X1,tc_Nat_Onat,X1,hAPP(hAPP(c_COMBB(X1,tc_fun(tc_Nat_Onat,X1),X1),c_Power_Opower__class_Opower(X1)),X2)),hAPP(c_Nat_OSuc,X5)),X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),c_Groups_Oone__class_Oone(X1)),c_Nat_Osemiring__1__class_Oof__nat(X1,X5))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),hAPP(hAPP(c_Power_Opower__class_Opower(X1),hAPP(X2,X3)),X5))))
| ~ class_RealVector_Oreal__normed__field(X1)
| ~ c_Deriv_Oderiv(X1,X2,X3,X4) ),
inference(split_conjunct,[status(thm)],[i_0_1257]),
[final] ).
cnf(i_0_2331,plain,
( X3 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))
| c_Polynomial_Opdivmod__rel(X1,hAPP(hAPP(c_Polynomial_OpCons(X1),X7),X2),X3,hAPP(hAPP(c_Polynomial_OpCons(X1),X6),X4),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X1)),hAPP(hAPP(c_Polynomial_OpCons(X1),X7),X5)),hAPP(hAPP(c_Polynomial_Osmult(X1),X6),X3)))
| ~ class_Fields_Ofield(X1)
| ~ c_Polynomial_Opdivmod__rel(X1,X2,X3,X4,X5)
| X6 != hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),hAPP(c_Polynomial_Ocoeff(X1,hAPP(hAPP(c_Polynomial_OpCons(X1),X7),X5)),c_Polynomial_Odegree(X1,X3))),hAPP(c_Polynomial_Ocoeff(X1,X3),c_Polynomial_Odegree(X1,X3))) ),
inference(split_conjunct,[status(thm)],[i_0_1258]),
[final] ).
cnf(i_0_2332,plain,
( X2 = c_Groups_Ozero__class_Ozero(X1)
| X3 = c_Groups_Ozero__class_Ozero(X1)
| hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),hAPP(c_Rings_Oinverse__class_Oinverse(X1),X2)),hAPP(c_Rings_Oinverse__class_Oinverse(X1),X3))),X4) = hAPP(c_Groups_Ouminus__class_Ouminus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(c_Rings_Oinverse__class_Oinverse(X1),X2)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X2),X3)),X4))),hAPP(c_Rings_Oinverse__class_Oinverse(X1),X3)))
| ~ class_RealVector_Oreal__normed__field(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1259]),
[final] ).
cnf(i_0_2333,plain,
( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X5))),X6) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X3),X5)),X6))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X2),X4)),X6)),X5))
| ~ class_RealVector_Oreal__field(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1260]),
[final] ).
cnf(i_0_2334,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X1)),hAPP(hAPP(c_Polynomial_OpCons(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)),hAPP(hAPP(c_Polynomial_OpCons(X1),c_Groups_Oone__class_Oone(X1)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))))),c_Polynomial_Osynthetic__div(X1,X3,X2))),hAPP(hAPP(c_Polynomial_OpCons(X1),hAPP(c_Polynomial_Opoly(X1,X3),X2)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)))) = X3
| ~ class_Rings_Ocomm__ring__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1261]),
[final] ).
cnf(i_0_2335,plain,
( c_Polynomial_Opdivmod__rel(X1,X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X1)),X3),X6),X7,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X1)),X3),X8)),X5))
| ~ class_Fields_Ofield(X1)
| ~ c_Polynomial_Opdivmod__rel(X1,X2,X3,X4,X5)
| ~ c_Polynomial_Opdivmod__rel(X1,X4,X6,X7,X8) ),
inference(split_conjunct,[status(thm)],[i_0_1262]),
[final] ).
cnf(i_0_2336,plain,
( c_Deriv_Oderiv(X1,hAPP(hAPP(c_COMBS(X1,X1,X1),hAPP(hAPP(c_COMBB(X1,tc_fun(X1,X1),X1),c_Groups_Oplus__class_Oplus(X1)),X2)),hAPP(hAPP(c_COMBB(X1,X1,X1),c_Groups_Ouminus__class_Ouminus(X1)),X5)),X3,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X4),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X6)))
| ~ class_RealVector_Oreal__normed__field(X1)
| ~ c_Deriv_Oderiv(X1,X2,X3,X4)
| ~ c_Deriv_Oderiv(X1,X5,X3,X6) ),
inference(split_conjunct,[status(thm)],[i_0_1263]),
[final] ).
cnf(i_0_2337,plain,
( c_Deriv_Oderiv(X1,hAPP(hAPP(c_COMBS(X1,X1,X1),hAPP(hAPP(c_COMBB(X1,tc_fun(X1,X1),X1),c_Groups_Otimes__class_Otimes(X1)),X2)),X5),X3,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(X2,X3)),X6)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),hAPP(X5,X3))))
| ~ class_RealVector_Oreal__normed__field(X1)
| ~ c_Deriv_Oderiv(X1,X2,X3,X4)
| ~ c_Deriv_Oderiv(X1,X5,X3,X6) ),
inference(split_conjunct,[status(thm)],[i_0_1264]),
[final] ).
cnf(i_0_2338,plain,
( c_Deriv_Oderiv(X1,hAPP(hAPP(c_COMBS(X1,X1,X1),hAPP(hAPP(c_COMBB(X1,tc_fun(X1,X1),X1),c_Groups_Otimes__class_Otimes(X1)),X2)),X5),X3,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),hAPP(X5,X3))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X6),hAPP(X2,X3))))
| ~ class_RealVector_Oreal__normed__field(X1)
| ~ c_Deriv_Oderiv(X1,X2,X3,X4)
| ~ c_Deriv_Oderiv(X1,X5,X3,X6) ),
inference(split_conjunct,[status(thm)],[i_0_1265]),
[final] ).
cnf(i_0_2339,plain,
( hAPP(X2,X3) = c_Groups_Ozero__class_Ozero(X1)
| c_Deriv_Oderiv(X1,hAPP(hAPP(c_COMBB(X1,X1,X1),c_Rings_Oinverse__class_Oinverse(X1)),X2),X3,hAPP(c_Groups_Ouminus__class_Ouminus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(c_Rings_Oinverse__class_Oinverse(X1),hAPP(X2,X3))),X4)),hAPP(c_Rings_Oinverse__class_Oinverse(X1),hAPP(X2,X3)))))
| ~ class_RealVector_Oreal__normed__field(X1)
| ~ c_Deriv_Oderiv(X1,X2,X3,X4) ),
inference(split_conjunct,[status(thm)],[i_0_1266]),
[final] ).
cnf(i_0_2340,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Divides_Odiv__class_Odiv(X1,X2,X3)),X3)),c_Divides_Odiv__class_Omod(X1,X2,X3))),X4) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X4)
| ~ class_Divides_Osemiring__div(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1267]),
[final] ).
cnf(i_0_2341,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X3),X6)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X5))),X6)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X2),X5))
| ~ class_Rings_Ocomm__ring(X1)
| ~ class_Rings_Odvd(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1268]),
[final] ).
cnf(i_0_2342,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X3),X6)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X5))),X6)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X2),X5))
| ~ class_Rings_Ocomm__ring(X1)
| ~ class_Rings_Odvd(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1269]),
[final] ).
cnf(i_0_2343,plain,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X2)),X2)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2))),X3) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X3),
inference(split_conjunct,[status(thm)],[i_0_1270]),
[final] ).
cnf(i_0_2344,plain,
( c_Deriv_Oderiv(X1,hAPP(c_COMBC(X1,X1,X1,hAPP(hAPP(c_COMBB(X1,tc_fun(X1,X1),X1),c_Rings_Oinverse__class_Odivide(X1)),X2)),X5),X3,hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X4),X5))
| ~ class_RealVector_Oreal__normed__field(X1)
| ~ c_Deriv_Oderiv(X1,X2,X3,X4) ),
inference(split_conjunct,[status(thm)],[i_0_1271]),
[final] ).
cnf(i_0_2345,plain,
( c_Deriv_Oderiv(X1,hAPP(hAPP(c_COMBS(X1,X1,X1),hAPP(hAPP(c_COMBB(X1,tc_fun(X1,X1),X1),c_Groups_Ominus__class_Ominus(X1)),X2)),X5),X3,hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X4),X6))
| ~ class_RealVector_Oreal__normed__field(X1)
| ~ c_Deriv_Oderiv(X1,X2,X3,X4)
| ~ c_Deriv_Oderiv(X1,X5,X3,X6) ),
inference(split_conjunct,[status(thm)],[i_0_1272]),
[final] ).
cnf(i_0_2346,plain,
( c_Deriv_Oderiv(X1,hAPP(hAPP(c_COMBS(X1,X1,X1),hAPP(hAPP(c_COMBB(X1,tc_fun(X1,X1),X1),c_Groups_Oplus__class_Oplus(X1)),X2)),X5),X3,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X4),X6))
| ~ class_RealVector_Oreal__normed__field(X1)
| ~ c_Deriv_Oderiv(X1,X2,X3,X4)
| ~ c_Deriv_Oderiv(X1,X5,X3,X6) ),
inference(split_conjunct,[status(thm)],[i_0_1273]),
[final] ).
cnf(i_0_2347,plain,
( c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4)),X5),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4)),X6))
| ~ c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X2),X3)),X4)),X5),X6)
| ~ class_Rings_Oordered__ring(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1274]),
[final] ).
cnf(i_0_2348,plain,
( c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X5)),X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X5)),X6))
| ~ c_Orderings_Oord__class_Oless(X1,X2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X3),X4)),X5)),X6))
| ~ class_Rings_Oordered__ring(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1275]),
[final] ).
cnf(i_0_2349,plain,
( hAPP(X2,X3) = c_Groups_Ozero__class_Ozero(X1)
| c_Deriv_Oderiv(X1,hAPP(hAPP(c_COMBB(X1,X1,X1),c_Rings_Oinverse__class_Oinverse(X1)),X2),X3,hAPP(c_Groups_Ouminus__class_Ouminus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),hAPP(c_Rings_Oinverse__class_Oinverse(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),hAPP(X2,X3)),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))))))
| ~ class_RealVector_Oreal__normed__field(X1)
| ~ c_Deriv_Oderiv(X1,X2,X3,X4) ),
inference(split_conjunct,[status(thm)],[i_0_1276]),
[final] ).
cnf(i_0_2350,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X5)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X3),X4))),X5)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X1),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_1277]),
[final] ).
cnf(i_0_2351,plain,
( c_Polynomial_Opoly__gcd(X1,X3,X4) = X2
| hAPP(c_Polynomial_Ocoeff(X1,X2),c_Polynomial_Odegree(X1,X2)) != c_Groups_Oone__class_Oone(X1)
| hAPP(c_Polynomial_Ocoeff(X1,X2),c_Polynomial_Odegree(X1,X2)) != c_Groups_Ozero__class_Ozero(X1)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X1)),esk7_4(X4,X3,X2,X1)),X2))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X1)),X2),X4))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X1)),X2),X3))
| ~ class_Fields_Ofield(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1278]),
[final] ).
cnf(i_0_2352,plain,
( c_Polynomial_Opoly__rec(X4,X1,X3,X2,hAPP(hAPP(c_Polynomial_OpCons(X1),X5),X6)) = hAPP(hAPP(hAPP(X2,X5),X6),c_Polynomial_Opoly__rec(X4,X1,X3,X2,X6))
| ~ class_Groups_Ozero(X1)
| hAPP(hAPP(hAPP(X2,c_Groups_Ozero__class_Ozero(X1)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))),X3) != X3 ),
inference(split_conjunct,[status(thm)],[i_0_1279]),
[final] ).
cnf(i_0_2353,plain,
( c_Polynomial_Opoly__gcd(X2,X1,X3) = X4
| X1 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| X3 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| hAPP(c_Polynomial_Ocoeff(X2,X4),c_Polynomial_Odegree(X2,X4)) != c_Groups_Ozero__class_Ozero(X2)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X2)),esk7_4(X3,X1,X4,X2)),X4))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X2)),X4),X3))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X2)),X4),X1))
| ~ class_Fields_Ofield(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1278]),
[final] ).
cnf(i_0_2354,plain,
( X3 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))
| c_Polynomial_Opoly__gcd(X1,X3,X4) = X2
| hAPP(c_Polynomial_Ocoeff(X1,X2),c_Polynomial_Odegree(X1,X2)) != c_Groups_Oone__class_Oone(X1)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X1)),esk7_4(X4,X3,X2,X1)),X2))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X1)),X2),X4))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X1)),X2),X3))
| ~ class_Fields_Ofield(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1278]),
[final] ).
cnf(i_0_2355,plain,
( X3 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))
| c_Polynomial_Opoly__gcd(X1,X4,X3) = X2
| hAPP(c_Polynomial_Ocoeff(X1,X2),c_Polynomial_Odegree(X1,X2)) != c_Groups_Oone__class_Oone(X1)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X1)),esk7_4(X3,X4,X2,X1)),X2))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X1)),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X1)),X2),X4))
| ~ class_Fields_Ofield(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1278]),
[final] ).
cnf(i_0_2356,plain,
( hAPP(c_Polynomial_Opoly(X1,X3),X2) = c_Groups_Ozero__class_Ozero(X1)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X1)),hAPP(hAPP(c_Polynomial_OpCons(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)),hAPP(hAPP(c_Polynomial_OpCons(X1),c_Groups_Oone__class_Oone(X1)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))))),X3))
| ~ class_Rings_Oidom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1280]),
[final] ).
cnf(i_0_2357,plain,
( c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X2),X5)),X3)),X4),X6)
| ~ c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),X4),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X5),X3)),X6))
| ~ class_Rings_Oordered__ring(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1274]),
[final] ).
cnf(i_0_2358,plain,
( c_Orderings_Oord__class_Oless(X1,X4,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X5),X2)),X3)),X6))
| ~ c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),X4),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X5),X3)),X6))
| ~ class_Rings_Oordered__ring(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1275]),
[final] ).
cnf(i_0_2359,plain,
( X1 = X2
| ~ c_Polynomial_Opdivmod__rel(X3,X4,X5,X2,X6)
| ~ c_Polynomial_Opdivmod__rel(X3,X4,X5,X1,X7)
| ~ class_Fields_Ofield(X3) ),
inference(split_conjunct,[status(thm)],[i_0_1281]),
[final] ).
cnf(i_0_2360,plain,
( X1 = X2
| ~ c_Polynomial_Opdivmod__rel(X3,X4,X5,X6,X2)
| ~ c_Polynomial_Opdivmod__rel(X3,X4,X5,X7,X1)
| ~ class_Fields_Ofield(X3) ),
inference(split_conjunct,[status(thm)],[i_0_1281]),
[final] ).
cnf(i_0_2361,plain,
( X4 = X6
| ~ class_Fields_Ofield(X1)
| ~ c_Polynomial_Opdivmod__rel(X1,X2,X3,X4,X5)
| ~ c_Polynomial_Opdivmod__rel(X1,X2,X3,X6,X7) ),
inference(split_conjunct,[status(thm)],[i_0_1282]),
[final] ).
cnf(i_0_2362,plain,
( X5 = X7
| ~ class_Fields_Ofield(X1)
| ~ c_Polynomial_Opdivmod__rel(X1,X2,X3,X4,X5)
| ~ c_Polynomial_Opdivmod__rel(X1,X2,X3,X6,X7) ),
inference(split_conjunct,[status(thm)],[i_0_1283]),
[final] ).
cnf(i_0_2363,plain,
( hAPP(c_Polynomial_Ocoeff(X1,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(X1)),hAPP(hAPP(c_Polynomial_OpCons(X1),X2),hAPP(hAPP(c_Polynomial_OpCons(X1),c_Groups_Oone__class_Oone(X1)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))))),X3)),X3) = c_Groups_Oone__class_Oone(X1)
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1284]),
[final] ).
cnf(i_0_2364,plain,
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X1)),X2),X3) = c_Polynomial_OAbs__poly(X1,hAPP(hAPP(c_COMBS(tc_Nat_Onat,X1,X1),hAPP(hAPP(c_COMBB(X1,tc_fun(X1,X1),tc_Nat_Onat),c_Groups_Ominus__class_Ominus(X1)),c_Polynomial_Ocoeff(X1,X2))),c_Polynomial_Ocoeff(X1,X3)))
| ~ class_Groups_Oab__group__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1285]),
[final] ).
cnf(i_0_2365,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X1)),X2),X3) = c_Polynomial_OAbs__poly(X1,hAPP(hAPP(c_COMBS(tc_Nat_Onat,X1,X1),hAPP(hAPP(c_COMBB(X1,tc_fun(X1,X1),tc_Nat_Onat),c_Groups_Oplus__class_Oplus(X1)),c_Polynomial_Ocoeff(X1,X2))),c_Polynomial_Ocoeff(X1,X3)))
| ~ class_Groups_Ocomm__monoid__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1286]),
[final] ).
cnf(i_0_2366,plain,
( X2 = c_Groups_Ozero__class_Ozero(X1)
| c_Polynomial_Opdivmod__rel(X1,X3,hAPP(hAPP(c_Polynomial_Osmult(X1),X2),X4),hAPP(hAPP(c_Polynomial_Osmult(X1),hAPP(c_Rings_Oinverse__class_Oinverse(X1),X2)),X5),X6)
| ~ class_Fields_Ofield(X1)
| ~ c_Polynomial_Opdivmod__rel(X1,X3,X4,X5,X6) ),
inference(split_conjunct,[status(thm)],[i_0_1287]),
[final] ).
cnf(i_0_2367,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X5),X6))),X4)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X3),X4)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X2),X6))
| ~ class_Rings_Ocomm__ring(X1)
| ~ class_Rings_Odvd(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1268]),
[final] ).
cnf(i_0_2368,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X5),X6))),X4)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X3),X4)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X2),X6))
| ~ class_Rings_Ocomm__ring(X1)
| ~ class_Rings_Odvd(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1269]),
[final] ).
cnf(i_0_2369,plain,
( c_Polynomial_Opdivmod__rel(X1,hAPP(hAPP(c_Polynomial_Osmult(X1),X6),X2),X3,hAPP(hAPP(c_Polynomial_Osmult(X1),X6),X4),hAPP(hAPP(c_Polynomial_Osmult(X1),X6),X5))
| ~ class_Fields_Ofield(X1)
| ~ c_Polynomial_Opdivmod__rel(X1,X2,X3,X4,X5) ),
inference(split_conjunct,[status(thm)],[i_0_1288]),
[final] ).
cnf(i_0_2370,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),c_Divides_Odiv__class_Odiv(X1,X3,X2))),c_Divides_Odiv__class_Omod(X1,X3,X2))),X4) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X3),X4)
| ~ class_Divides_Osemiring__div(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1289]),
[final] ).
cnf(i_0_2371,plain,
c_Divides_Odiv__class_Odiv(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X2),X3) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X3)),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X2,X3))),c_Divides_Odiv__class_Odiv(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X3)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X3)),X3)),
inference(split_conjunct,[status(thm)],[i_0_1290]),
[final] ).
cnf(i_0_2372,plain,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X2,X1))),c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X1))),X3) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X3),
inference(split_conjunct,[status(thm)],[i_0_1291]),
[final] ).
cnf(i_0_2373,plain,
( hAPP(c_Polynomial_Opoly(X1,X3),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)) = c_Groups_Ozero__class_Ozero(X1)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X1)),hAPP(hAPP(c_Polynomial_OpCons(X1),X2),hAPP(hAPP(c_Polynomial_OpCons(X1),c_Groups_Oone__class_Oone(X1)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))))),X3))
| ~ class_Rings_Oidom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1292]),
[final] ).
cnf(i_0_2374,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X4),X5))),X3)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X3)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X1),X5)) ),
inference(split_conjunct,[status(thm)],[i_0_1277]),
[final] ).
cnf(i_0_2375,plain,
( c_Polynomial_Opoly__gcd(X1,X3,X4) = X2
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X1)),esk7_4(X4,X3,X2,X1)),X3))
| hAPP(c_Polynomial_Ocoeff(X1,X2),c_Polynomial_Odegree(X1,X2)) != c_Groups_Oone__class_Oone(X1)
| hAPP(c_Polynomial_Ocoeff(X1,X2),c_Polynomial_Odegree(X1,X2)) != c_Groups_Ozero__class_Ozero(X1)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X1)),X2),X4))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X1)),X2),X3))
| ~ class_Fields_Ofield(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1278]),
[final] ).
cnf(i_0_2376,plain,
( c_Polynomial_Opoly__gcd(X1,X3,X4) = X2
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X1)),esk7_4(X4,X3,X2,X1)),X4))
| hAPP(c_Polynomial_Ocoeff(X1,X2),c_Polynomial_Odegree(X1,X2)) != c_Groups_Oone__class_Oone(X1)
| hAPP(c_Polynomial_Ocoeff(X1,X2),c_Polynomial_Odegree(X1,X2)) != c_Groups_Ozero__class_Ozero(X1)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X1)),X2),X4))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X1)),X2),X3))
| ~ class_Fields_Ofield(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1278]),
[final] ).
cnf(i_0_2377,plain,
( c_Polynomial_Opoly__gcd(X2,X1,X3) = X4
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X2)),esk7_4(X3,X1,X4,X2)),X1))
| X1 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| X3 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| hAPP(c_Polynomial_Ocoeff(X2,X4),c_Polynomial_Odegree(X2,X4)) != c_Groups_Ozero__class_Ozero(X2)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X2)),X4),X3))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X2)),X4),X1))
| ~ class_Fields_Ofield(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1278]),
[final] ).
cnf(i_0_2378,plain,
( c_Polynomial_Opoly__gcd(X2,X1,X3) = X4
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X2)),esk7_4(X3,X1,X4,X2)),X3))
| X1 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| X3 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| hAPP(c_Polynomial_Ocoeff(X2,X4),c_Polynomial_Odegree(X2,X4)) != c_Groups_Ozero__class_Ozero(X2)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X2)),X4),X3))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X2)),X4),X1))
| ~ class_Fields_Ofield(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1278]),
[final] ).
cnf(i_0_2379,plain,
( X3 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))
| c_Polynomial_Opoly__gcd(X1,X3,X4) = X2
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X1)),esk7_4(X4,X3,X2,X1)),X3))
| hAPP(c_Polynomial_Ocoeff(X1,X2),c_Polynomial_Odegree(X1,X2)) != c_Groups_Oone__class_Oone(X1)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X1)),X2),X4))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X1)),X2),X3))
| ~ class_Fields_Ofield(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1278]),
[final] ).
cnf(i_0_2380,plain,
( X3 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))
| c_Polynomial_Opoly__gcd(X1,X3,X4) = X2
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X1)),esk7_4(X4,X3,X2,X1)),X4))
| hAPP(c_Polynomial_Ocoeff(X1,X2),c_Polynomial_Odegree(X1,X2)) != c_Groups_Oone__class_Oone(X1)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X1)),X2),X4))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X1)),X2),X3))
| ~ class_Fields_Ofield(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1278]),
[final] ).
cnf(i_0_2381,plain,
( X3 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))
| c_Polynomial_Opoly__gcd(X1,X4,X3) = X2
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X1)),esk7_4(X3,X4,X2,X1)),X3))
| hAPP(c_Polynomial_Ocoeff(X1,X2),c_Polynomial_Odegree(X1,X2)) != c_Groups_Oone__class_Oone(X1)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X1)),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X1)),X2),X4))
| ~ class_Fields_Ofield(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1278]),
[final] ).
cnf(i_0_2382,plain,
( X3 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))
| c_Polynomial_Opoly__gcd(X1,X4,X3) = X2
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X1)),esk7_4(X3,X4,X2,X1)),X4))
| hAPP(c_Polynomial_Ocoeff(X1,X2),c_Polynomial_Odegree(X1,X2)) != c_Groups_Oone__class_Oone(X1)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X1)),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X1)),X2),X4))
| ~ class_Fields_Ofield(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1278]),
[final] ).
cnf(i_0_2383,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X1)),hAPP(hAPP(c_Polynomial_OpCons(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X3)),hAPP(hAPP(c_Polynomial_OpCons(X1),c_Groups_Oone__class_Oone(X1)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))))),X2))
| hAPP(c_Polynomial_Opoly(X1,X2),X3) != c_Groups_Ozero__class_Ozero(X1)
| ~ class_Rings_Oidom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1280]),
[final] ).
cnf(i_0_2384,plain,
( X1 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X2)),X3),X4)),X5)
| ~ c_Polynomial_Opdivmod__rel(X2,X1,X4,X3,X5)
| ~ class_Fields_Ofield(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1293]),
[final] ).
cnf(i_0_2385,plain,
( X2 = c_Groups_Ozero__class_Ozero(X1)
| X3 = c_Groups_Ozero__class_Ozero(X1)
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),hAPP(c_Rings_Oinverse__class_Oinverse(X1),X2)),hAPP(c_Rings_Oinverse__class_Oinverse(X1),X3)) = hAPP(c_Groups_Ouminus__class_Ouminus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(c_Rings_Oinverse__class_Oinverse(X1),X2)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X2),X3))),hAPP(c_Rings_Oinverse__class_Oinverse(X1),X3)))
| ~ class_Rings_Odivision__ring(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1294]),
[final] ).
cnf(i_0_2386,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4)),X5) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4)),X6)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X2),X3)),X4)),X5) != X6
| ~ class_Rings_Oring(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1295]),
[final] ).
cnf(i_0_2387,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X4),X5)),X1) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X3),X5)),X6)
| X1 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X2),X3),X4)),X5)),X6)
| ~ class_Rings_Oring(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1296]),
[final] ).
cnf(i_0_2388,plain,
( X1 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| X3 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(X2,X3),c_Polynomial_Odegree(X2,X1))
| ~ c_Polynomial_Opdivmod__rel(X2,X4,X1,X5,X3)
| ~ class_Fields_Ofield(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1293]),
[final] ).
cnf(i_0_2389,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X1)),hAPP(hAPP(c_Polynomial_OpCons(X1),X3),hAPP(hAPP(c_Polynomial_OpCons(X1),c_Groups_Oone__class_Oone(X1)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))))),X2))
| hAPP(c_Polynomial_Opoly(X1,X2),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X3)) != c_Groups_Ozero__class_Ozero(X1)
| ~ class_Rings_Oidom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1292]),
[final] ).
cnf(i_0_2390,plain,
( c_Polynomial_Opdivmod__rel(X1,X5,X3,X4,X2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(X1,X2),c_Polynomial_Odegree(X1,X3))
| X4 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))
| X5 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X1)),X4),X3)),X2)
| ~ class_Fields_Ofield(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1293]),
[final] ).
cnf(i_0_2391,plain,
( X3 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))
| c_Polynomial_Opdivmod__rel(X1,X4,X3,X5,X2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(X1,X2),c_Polynomial_Odegree(X1,X3))
| X4 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X1)),X5),X3)),X2)
| ~ class_Fields_Ofield(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1293]),
[final] ).
cnf(i_0_2392,plain,
( X2 = c_Groups_Ozero__class_Ozero(X1)
| X3 = c_Groups_Ozero__class_Ozero(X1)
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X4),X2)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X5),X3)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X5),X2))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3))
| ~ class_Fields_Ofield(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1297]),
[final] ).
cnf(i_0_2393,plain,
( X2 = c_Groups_Ozero__class_Ozero(X1)
| X3 = c_Groups_Ozero__class_Ozero(X1)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X4),X2)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X5),X3)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X5),X2))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3))
| ~ class_Fields_Ofield(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1298]),
[final] ).
cnf(i_0_2394,plain,
( c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(X1),X2,X3) = X5
| ~ class_Fields_Ofield(X1)
| ~ c_Polynomial_Opdivmod__rel(X1,X2,X3,X4,X5) ),
inference(split_conjunct,[status(thm)],[i_0_1299]),
[final] ).
cnf(i_0_2395,plain,
( X1 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| ~ c_Polynomial_Opdivmod__rel(X2,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)),X3,X1,X4)
| ~ class_Fields_Ofield(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1300]),
[final] ).
cnf(i_0_2396,plain,
( X1 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| ~ c_Polynomial_Opdivmod__rel(X2,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)),X3,X4,X1)
| ~ class_Fields_Ofield(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1300]),
[final] ).
cnf(i_0_2397,plain,
( X1 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| ~ c_Polynomial_Opdivmod__rel(X2,X3,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)),X1,X4)
| ~ class_Fields_Ofield(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1301]),
[final] ).
cnf(i_0_2398,plain,
( hBOOL(hAPP(hAPP(X1,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X2,X3)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X3)))
| ~ hBOOL(hAPP(hAPP(X1,esk19_3(X2,X1,X3)),esk20_3(X2,X1,X3)))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X3) ),
inference(split_conjunct,[status(thm)],[i_0_1302]),
[final] ).
cnf(i_0_2399,plain,
( X1 = X2
| ~ c_Polynomial_Opdivmod__rel(X3,X2,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)),X4,X1)
| ~ class_Fields_Ofield(X3) ),
inference(split_conjunct,[status(thm)],[i_0_1301]),
[final] ).
cnf(i_0_2400,plain,
( X3 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| X1 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| ~ c_Polynomial_Opdivmod__rel(X2,X4,X1,X3,X5)
| ~ class_Fields_Ofield(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1293]),
[final] ).
cnf(i_0_2401,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X2),X5)),X3)),X4) = X6
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),X4) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X5),X3)),X6)
| ~ class_Rings_Oring(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1295]),
[final] ).
cnf(i_0_2402,plain,
( X4 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X5),X2)),X3)),X6)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),X4) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X5),X3)),X6)
| ~ class_Rings_Oring(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1296]),
[final] ).
cnf(i_0_2403,plain,
( c_Polynomial_Odegree(X1,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(X1)),hAPP(hAPP(c_Polynomial_OpCons(X1),X2),hAPP(hAPP(c_Polynomial_OpCons(X1),c_Groups_Oone__class_Oone(X1)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))))),X3)) = X3
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1303]),
[final] ).
cnf(i_0_2404,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3)),X5)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X4)),X3)),X5)
| ~ class_Rings_Osemiring(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1304]),
[final] ).
cnf(i_0_2405,plain,
( c_Polynomial_Opdivmod__rel(X2,X4,X1,X3,X5)
| X1 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| X3 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| X4 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X2)),X3),X1)),X5)
| ~ class_Fields_Ofield(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1293]),
[final] ).
cnf(i_0_2406,plain,
( c_Polynomial_Opdivmod__rel(X2,X4,X5,X3,X1)
| X1 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| X3 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| X4 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X2)),X3),X5)),X1)
| ~ class_Fields_Ofield(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1293]),
[final] ).
cnf(i_0_2407,plain,
( X3 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| c_Polynomial_Opdivmod__rel(X2,X4,X3,X5,X1)
| X1 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| X4 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X2)),X5),X3)),X1)
| ~ class_Fields_Ofield(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1293]),
[final] ).
cnf(i_0_2408,plain,
( hBOOL(hAPP(hAPP(X1,X5),X4))
| ~ hBOOL(hAPP(hAPP(X1,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X2,X3)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X3)))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X4)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X4,X3)
| X2 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X3),X5)),X4)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X3) ),
inference(split_conjunct,[status(thm)],[i_0_1302]),
[final] ).
cnf(i_0_2409,plain,
( c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X3),X1)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X3),c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X2,X3),X1))),c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X3))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1) ),
inference(split_conjunct,[status(thm)],[i_0_1305]),
[final] ).
cnf(i_0_2410,plain,
c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X3)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),c_Divides_Odiv__class_Omod(tc_Nat_Onat,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X1,X2),X3))),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,X2)),
inference(split_conjunct,[status(thm)],[i_0_1306]),
[final] ).
cnf(i_0_2411,plain,
( c_Deriv_Oderiv(X1,hAPP(hAPP(c_COMBB(X1,X1,X1),X2),X3),X4,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X5),X6))
| ~ class_RealVector_Oreal__normed__field(X1)
| ~ c_Deriv_Oderiv(X1,X2,hAPP(X3,X4),X5)
| ~ c_Deriv_Oderiv(X1,X3,X4,X6) ),
inference(split_conjunct,[status(thm)],[i_0_1307]),
[final] ).
cnf(i_0_2412,plain,
( c_Deriv_Oderiv(X1,hAPP(hAPP(c_COMBB(X1,X1,X1),X5),X2),X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X6),X4))
| ~ class_RealVector_Oreal__normed__field(X1)
| ~ c_Deriv_Oderiv(X1,X2,X3,X4)
| ~ c_Deriv_Oderiv(X1,X5,hAPP(X2,X3),X6) ),
inference(split_conjunct,[status(thm)],[i_0_1308]),
[final] ).
cnf(i_0_2413,plain,
( hAPP(c_Polynomial_Opoly(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X1)),c_Polynomial_Omonom(X1,c_Groups_Oone__class_Oone(X1),X2)),X3)),X4) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X4),X2)),hAPP(c_Polynomial_Opoly(X1,X3),X4))
| ~ class_Rings_Ocomm__ring__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1309]),
[final] ).
cnf(i_0_2414,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X2),X4))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),c_Divides_Odiv__class_Odiv(X1,X2,X3)),c_Divides_Odiv__class_Odiv(X1,X4,X3)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X3),X4))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X3),X2))
| ~ class_Divides_Osemiring__div(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1310]),
[final] ).
cnf(i_0_2415,plain,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X2)),X4)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X3)),X2)),X4),
inference(split_conjunct,[status(thm)],[i_0_1311]),
[final] ).
cnf(i_0_2416,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X4,X1))),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X1))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_1312]),
[final] ).
cnf(i_0_2417,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),esk5_3(X2,X3,X1)),c_Groups_Ozero__class_Ozero(X1))))
| ~ hBOOL(hAPP(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4)))
| ~ class_Rings_Odvd(X1)
| ~ class_Rings_Osemiring__0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1313]),
[final] ).
cnf(i_0_2418,plain,
( X1 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),esk19_3(X1,X3,X2))),esk20_3(X1,X3,X2))
| hBOOL(hAPP(hAPP(X3,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X2)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2)))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2) ),
inference(split_conjunct,[status(thm)],[i_0_1302]),
[final] ).
cnf(i_0_2419,plain,
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X5)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X3),X5))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X2),X4)),X5))
| ~ class_Rings_Oring(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1314]),
[final] ).
cnf(i_0_2420,plain,
c_Divides_Odiv__class_Odiv(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X2),X3) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X2,X3))),c_Divides_Odiv__class_Odiv(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X3)),X3)),
inference(split_conjunct,[status(thm)],[i_0_1315]),
[final] ).
cnf(i_0_2421,plain,
c_Divides_Odiv__class_Odiv(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2),X3) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X2,X3))),c_Divides_Odiv__class_Odiv(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X2,X3)),X3)),
inference(split_conjunct,[status(thm)],[i_0_1316]),
[final] ).
cnf(i_0_2422,plain,
( c_Polynomial_Opoly__rec(X4,X1,X3,X2,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))) = X3
| ~ class_Groups_Ozero(X1)
| hAPP(hAPP(hAPP(X2,c_Groups_Ozero__class_Ozero(X1)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))),X3) != X3 ),
inference(split_conjunct,[status(thm)],[i_0_1317]),
[final] ).
cnf(i_0_2423,plain,
( X2 = c_Groups_Ozero__class_Ozero(X1)
| X3 = c_Groups_Ozero__class_Ozero(X1)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(c_Rings_Oinverse__class_Oinverse(X1),X2)),hAPP(c_Rings_Oinverse__class_Oinverse(X1),X3)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)),hAPP(c_Rings_Oinverse__class_Oinverse(X1),X2))),hAPP(c_Rings_Oinverse__class_Oinverse(X1),X3))
| ~ class_Fields_Ofield(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1318]),
[final] ).
cnf(i_0_2424,plain,
( c_Polynomial_Opdivmod__rel(X1,X2,X3,c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(X1),X2,X3),c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(X1),X2,X3))
| ~ class_Fields_Ofield(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1319]),
[final] ).
cnf(i_0_2425,plain,
( c_Deriv_Oderiv(X1,hAPP(hAPP(c_COMBB(X1,X1,X1),hAPP(c_Groups_Otimes__class_Otimes(X1),X5)),X2),X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X5),X4))
| ~ class_RealVector_Oreal__normed__field(X1)
| ~ c_Deriv_Oderiv(X1,X2,X3,X4) ),
inference(split_conjunct,[status(thm)],[i_0_1320]),
[final] ).
cnf(i_0_2426,plain,
( c_Nat_Osemiring__1__class_Oof__nat(X1,X2) = c_Nat_Osemiring__1__class_Oof__nat__aux(X1,hAPP(c_COMBC(X1,X1,X1,c_Groups_Oplus__class_Oplus(X1)),c_Groups_Oone__class_Oone(X1)),X2,c_Groups_Ozero__class_Ozero(X1))
| ~ class_Rings_Osemiring__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1321]),
[final] ).
cnf(i_0_2427,plain,
( c_Polynomial_Opdivmod__rel(X1,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),X2,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)))
| ~ class_Fields_Ofield(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1322]),
[final] ).
cnf(i_0_2428,plain,
( c_Polynomial_Opdivmod__rel(X2,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)),X4,X1,X3)
| X1 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| X3 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| ~ class_Fields_Ofield(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1300]),
[final] ).
cnf(i_0_2429,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),c_Divides_Odiv__class_Odiv(X1,X2,X4)),c_Divides_Odiv__class_Odiv(X1,X3,X4)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X4),X3))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X4),X2))
| ~ class_Divides_Osemiring__div(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1310]),
[final] ).
cnf(i_0_2430,plain,
( hBOOL(hAPP(X4,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),esk6_3(X2,X4,X1))))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X3),c_Groups_Ozero__class_Ozero(X1))))
| ~ hBOOL(hAPP(X4,X3))
| ~ class_Rings_Odvd(X1)
| ~ class_Rings_Osemiring__0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1313]),
[final] ).
cnf(i_0_2431,plain,
( X2 = c_Groups_Ozero__class_Ozero(X1)
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X3),X4))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4)))
| ~ class_Rings_Oidom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1323]),
[final] ).
cnf(i_0_2432,plain,
( X3 = c_Groups_Ozero__class_Ozero(X1)
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X2),X4))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3)))
| ~ class_Rings_Oidom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1324]),
[final] ).
cnf(i_0_2433,plain,
( c_Polynomial_Opdivmod__rel(X2,X4,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)),X1,X3)
| X1 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| X3 != X4
| ~ class_Fields_Ofield(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1301]),
[final] ).
cnf(i_0_2434,plain,
( c_Polynomial_Opdivmod__rel(X1,X2,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),X2)
| ~ class_Fields_Ofield(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1325]),
[final] ).
cnf(i_0_2435,plain,
( ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X3)))
| X2 != c_Groups_Ozero__class_Ozero(X1)
| X3 != c_Groups_Ozero__class_Ozero(X1)
| ~ class_Rings_Olinordered__ring__strict(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1326]),
[final] ).
cnf(i_0_2436,plain,
( X2 = c_Groups_Ozero__class_Ozero(X1)
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X3),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X4),X2)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),X4)),X2)
| ~ class_Fields_Ofield(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1327]),
[final] ).
cnf(i_0_2437,plain,
( X2 = c_Groups_Ozero__class_Ozero(X1)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X3),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X4),X2)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),X4)),X2)
| ~ class_Fields_Ofield(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1328]),
[final] ).
cnf(i_0_2438,plain,
( ~ class_Rings_Olinordered__ring(X1)
| ~ c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X3)),c_Groups_Ozero__class_Ozero(X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1329]),
[final] ).
cnf(i_0_2439,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Divides_Odiv__class_Odiv(X1,X2,X3)),X3)),c_Divides_Odiv__class_Omod(X1,X2,X3)) = X2
| ~ class_Divides_Osemiring__div(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1330]),
[final] ).
cnf(i_0_2440,plain,
( c_Deriv_Oderiv(X1,hAPP(hAPP(c_COMBB(X1,X1,X1),c_Groups_Ouminus__class_Ouminus(X1)),X2),X3,hAPP(c_Groups_Ouminus__class_Ouminus(X1),X4))
| ~ class_RealVector_Oreal__normed__field(X1)
| ~ c_Deriv_Oderiv(X1,X2,X3,X4) ),
inference(split_conjunct,[status(thm)],[i_0_1331]),
[final] ).
cnf(i_0_2441,plain,
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X3),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X2),X3)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3))
| ~ class_Rings_Ocomm__ring__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1332]),
[final] ).
cnf(i_0_2442,plain,
( X2 = c_Groups_Ozero__class_Ozero(X1)
| X3 = c_Groups_Ozero__class_Ozero(X1)
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),hAPP(c_Rings_Oinverse__class_Oinverse(X1),X2)),hAPP(c_Rings_Oinverse__class_Oinverse(X1),X3)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(c_Rings_Oinverse__class_Oinverse(X1),X2)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X3),X2))),hAPP(c_Rings_Oinverse__class_Oinverse(X1),X3))
| ~ class_Rings_Odivision__ring(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1333]),
[final] ).
cnf(i_0_2443,plain,
( X2 = c_Groups_Ozero__class_Ozero(X1)
| X3 = c_Groups_Ozero__class_Ozero(X1)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(c_Rings_Oinverse__class_Oinverse(X1),X2)),hAPP(c_Rings_Oinverse__class_Oinverse(X1),X3)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(c_Rings_Oinverse__class_Oinverse(X1),X2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3))),hAPP(c_Rings_Oinverse__class_Oinverse(X1),X3))
| ~ class_Rings_Odivision__ring(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1334]),
[final] ).
cnf(i_0_2444,plain,
( c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X1,hAPP(hAPP(c_Polynomial_OpCons(X1),X2),X3),X4) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X1)),hAPP(hAPP(c_Polynomial_Osmult(X1),X4),c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X1,X3,X4))),hAPP(hAPP(c_Polynomial_OpCons(X1),X2),c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X1,X3,X4)))
| ~ class_Rings_Ocomm__semiring__0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1335]),
[final] ).
cnf(i_0_2445,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X3)))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1) ),
inference(split_conjunct,[status(thm)],[i_0_1336]),
[final] ).
cnf(i_0_2446,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X3)))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1) ),
inference(split_conjunct,[status(thm)],[i_0_1337]),
[final] ).
cnf(i_0_2447,plain,
( X1 = X2
| X3 = X4
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X1),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X2),X4)) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X1),X4)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X2),X3))
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X5) ),
inference(split_conjunct,[status(thm)],[i_0_1338]),
[final] ).
cnf(i_0_2448,plain,
( X2 = X4
| X3 = X5
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X5)) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X5)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3))
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1339]),
[final] ).
cnf(i_0_2449,plain,
( X2 = c_Groups_Ozero__class_Ozero(X1)
| c_Deriv_Oderiv(X1,c_Rings_Oinverse__class_Oinverse(X1),X2,hAPP(c_Groups_Ouminus__class_Ouminus(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),hAPP(c_Rings_Oinverse__class_Oinverse(X1),X2)),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))))
| ~ class_RealVector_Oreal__normed__field(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1340]),
[final] ).
cnf(i_0_2450,plain,
( X1 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X3))) ),
inference(split_conjunct,[status(thm)],[i_0_1341]),
[final] ).
cnf(i_0_2451,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X2),X3))
| X1 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X3))) ),
inference(split_conjunct,[status(thm)],[i_0_1342]),
[final] ).
cnf(i_0_2452,plain,
( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X3))) ),
inference(split_conjunct,[status(thm)],[i_0_1343]),
[final] ).
cnf(i_0_2453,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X1),X3))
| X2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X1),X2)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X3),X2))) ),
inference(split_conjunct,[status(thm)],[i_0_1344]),
[final] ).
cnf(i_0_2454,plain,
( X2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X1),X3))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X1),X2)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X3),X2))) ),
inference(split_conjunct,[status(thm)],[i_0_1345]),
[final] ).
cnf(i_0_2455,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),X3))
| X2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X1),X2)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X3),X2))) ),
inference(split_conjunct,[status(thm)],[i_0_1346]),
[final] ).
cnf(i_0_2456,plain,
( X2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),X3))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X1),X2)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X3),X2))) ),
inference(split_conjunct,[status(thm)],[i_0_1347]),
[final] ).
cnf(i_0_2457,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X1),X2))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X3)))) ),
inference(split_conjunct,[status(thm)],[i_0_1348]),
[final] ).
cnf(i_0_2458,plain,
hAPP(hAPP(c_COMBC(X1,X2,X3,X4),X5),X6) = hAPP(hAPP(X4,X6),X5),
inference(split_conjunct,[status(thm)],[i_0_1349]),
[final] ).
cnf(i_0_2459,plain,
( hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| c_Orderings_Oord__class_OLeast(tc_Nat_Onat,X1) = hAPP(c_Nat_OSuc,c_Orderings_Oord__class_OLeast(tc_Nat_Onat,hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_Nat_Onat),X1),c_Nat_OSuc)))
| ~ hBOOL(hAPP(X1,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1350]),
[final] ).
cnf(i_0_2460,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X5)))
| ~ class_Rings_Ocomm__semiring__1(X1)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X4),X5)) ),
inference(split_conjunct,[status(thm)],[i_0_1351]),
[final] ).
cnf(i_0_2461,plain,
( X1 = c_Groups_Ozero__class_Ozero(X2)
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X2)),X3),X4))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X2)),hAPP(hAPP(c_Polynomial_Osmult(X2),X1),X3)),X4))
| ~ class_Fields_Ofield(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1352]),
[final] ).
cnf(i_0_2462,plain,
c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2)),X3)),X2) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,X3),X2),
inference(split_conjunct,[status(thm)],[i_0_1353]),
[final] ).
cnf(i_0_2463,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X1)),X3),X4))
| ~ class_Rings_Ocomm__semiring__1(X1)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X1)),hAPP(hAPP(c_Polynomial_Osmult(X1),X2),X3)),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_1354]),
[final] ).
cnf(i_0_2464,plain,
( X1 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),esk15_3(X2,X1,X3))),esk16_3(X2,X1,X3))
| hBOOL(hAPP(X3,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,X2)))
| ~ hBOOL(hAPP(X3,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1355]),
[final] ).
cnf(i_0_2465,plain,
( hAPP(c_Polynomial_Ocoeff(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X1)),X2),X3)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Polynomial_Odegree(X1,X2)),c_Polynomial_Odegree(X1,X3))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(c_Polynomial_Ocoeff(X1,X2),c_Polynomial_Odegree(X1,X2))),hAPP(c_Polynomial_Ocoeff(X1,X3),c_Polynomial_Odegree(X1,X3)))
| ~ class_Rings_Ocomm__semiring__0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1356]),
[final] ).
cnf(i_0_2466,plain,
( X1 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),esk15_3(X2,X1,X3))),esk16_3(X2,X1,X3))
| X2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hBOOL(hAPP(X3,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,X2))) ),
inference(split_conjunct,[status(thm)],[i_0_1355]),
[final] ).
cnf(i_0_2467,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X1)),hAPP(hAPP(c_Polynomial_OpCons(X1),X2),X3)),X4) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X1)),hAPP(hAPP(c_Polynomial_Osmult(X1),X2),X4)),hAPP(hAPP(c_Polynomial_OpCons(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X1)),X3),X4)))
| ~ class_Rings_Ocomm__semiring__0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1357]),
[final] ).
cnf(i_0_2468,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Divides_Odiv__class_Odiv(X1,X3,X2)),c_Divides_Odiv__class_Odiv(X1,X5,X4)) = c_Divides_Odiv__class_Odiv(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4))
| ~ class_Divides_Osemiring__div(X1)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X4),X5)) ),
inference(split_conjunct,[status(thm)],[i_0_1358]),
[final] ).
cnf(i_0_2469,plain,
( c_Divides_Odiv__class_Omod(X1,hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X2),X3),X4) = c_Divides_Odiv__class_Omod(X1,hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),c_Divides_Odiv__class_Omod(X1,X2,X4)),c_Divides_Odiv__class_Omod(X1,X3,X4)),X4)
| ~ class_Divides_Oring__div(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1359]),
[final] ).
cnf(i_0_2470,plain,
( c_Divides_Odiv__class_Omod(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),X4) = c_Divides_Odiv__class_Omod(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Divides_Odiv__class_Omod(X1,X2,X4)),c_Divides_Odiv__class_Omod(X1,X3,X4)),X4)
| ~ class_Divides_Osemiring__div(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1360]),
[final] ).
cnf(i_0_2471,plain,
( c_Divides_Odiv__class_Omod(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3),X4) = c_Divides_Odiv__class_Omod(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),c_Divides_Odiv__class_Omod(X1,X2,X4)),c_Divides_Odiv__class_Omod(X1,X3,X4)),X4)
| ~ class_Divides_Osemiring__div(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1361]),
[final] ).
cnf(i_0_2472,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),esk20_3(X1,X2,X3))
| hBOOL(hAPP(hAPP(X2,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X3)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X3)))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X3) ),
inference(split_conjunct,[status(thm)],[i_0_1302]),
[final] ).
cnf(i_0_2473,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,esk20_3(X1,X2,X3),X3)
| hBOOL(hAPP(hAPP(X2,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X3)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X3)))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X3) ),
inference(split_conjunct,[status(thm)],[i_0_1302]),
[final] ).
cnf(i_0_2474,plain,
( c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),c_Groups_Oone__class_Oone(X1)),c_Groups_Oone__class_Oone(X1))),X3)
| ~ class_Fields_Olinordered__field(X1)
| ~ c_Orderings_Oord__class_Oless(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_1362]),
[final] ).
cnf(i_0_2475,plain,
( c_Orderings_Oord__class_Oless(X1,X2,hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),c_Groups_Oone__class_Oone(X1)),c_Groups_Oone__class_Oone(X1))))
| ~ class_Fields_Olinordered__field(X1)
| ~ c_Orderings_Oord__class_Oless(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_1363]),
[final] ).
cnf(i_0_2476,plain,
( X2 = c_Groups_Ozero__class_Ozero(X1)
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X3),X2)),X4) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4))),X2)
| ~ class_Fields_Ofield(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1364]),
[final] ).
cnf(i_0_2477,plain,
( X2 = c_Groups_Ozero__class_Ozero(X1)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X3),X2)),X4) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4))),X2)
| ~ class_Fields_Ofield(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1365]),
[final] ).
cnf(i_0_2478,plain,
( X2 = c_Groups_Ozero__class_Ozero(X1)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X3),X2)),X4) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X2))),X2)
| ~ class_Fields_Ofield__inverse__zero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1366]),
[final] ).
cnf(i_0_2479,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X5)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),X5))
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1367]),
[final] ).
cnf(i_0_2480,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1)),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
inference(split_conjunct,[status(thm)],[i_0_1368]),
[final] ).
cnf(i_0_2481,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X2),X4))
| ~ class_Rings_Ocomm__semiring__1(X1)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_1369]),
[final] ).
cnf(i_0_2482,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X3),X4))
| ~ class_Rings_Ocomm__semiring__1(X1)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_1370]),
[final] ).
cnf(i_0_2483,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X1)),X2),X3)),X4) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X1)),X2),X4)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X1)),X3),X4))
| ~ class_Rings_Ocomm__semiring__0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1371]),
[final] ).
cnf(i_0_2484,plain,
( X3 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| X1 != c_Groups_Ozero__class_Ozero(X2)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X2)),hAPP(hAPP(c_Polynomial_Osmult(X2),X1),X4)),X3))
| ~ class_Fields_Ofield(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1352]),
[final] ).
cnf(i_0_2485,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)),X3) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),c_Groups_Oone__class_Oone(X1))),X3)),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3))
| ~ class_Rings_Oring__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1372]),
[final] ).
cnf(i_0_2486,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X1)),X2),hAPP(hAPP(c_Polynomial_OpCons(X1),X3),X4)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X1)),hAPP(hAPP(c_Polynomial_Osmult(X1),X3),X2)),hAPP(hAPP(c_Polynomial_OpCons(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X1)),X2),X4)))
| ~ class_Rings_Ocomm__semiring__0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1373]),
[final] ).
cnf(i_0_2487,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X4)),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X3),X4)))
| ~ class_Rings_Ocomm__semiring__1(X1)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1374]),
[final] ).
cnf(i_0_2488,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X2),X3))
| ~ class_Rings_Oidom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1324]),
[final] ).
cnf(i_0_2489,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X2),X3))
| ~ class_Rings_Oidom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1323]),
[final] ).
cnf(i_0_2490,plain,
( c_Polynomial_Opcompose(X1,hAPP(hAPP(c_Polynomial_OpCons(X1),X2),X3),X4) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X1)),hAPP(hAPP(c_Polynomial_OpCons(X1),X2),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X1)),X4),c_Polynomial_Opcompose(X1,X3,X4)))
| ~ class_Rings_Ocomm__semiring__0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1375]),
[final] ).
cnf(i_0_2491,plain,
( c_Divides_Odiv__class_Odiv(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X3),X4),X2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),c_Divides_Odiv__class_Odiv(X1,X3,X2)),c_Divides_Odiv__class_Odiv(X1,X4,X2))
| ~ class_Divides_Osemiring__div(X1)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X2),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_1376]),
[final] ).
cnf(i_0_2492,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X2)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),X2))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3) ),
inference(split_conjunct,[status(thm)],[i_0_1337]),
[final] ).
cnf(i_0_2493,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X1)),X2),c_Polynomial_Opoly__gcd(X1,X3,X4)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X1)),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X1)),X2),X4))
| ~ class_Fields_Ofield(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1377]),
[final] ).
cnf(i_0_2494,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X1)),X2),c_Polynomial_Opoly__gcd(X1,X3,X4)))
| ~ class_Fields_Ofield(X1)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X1)),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X1)),X2),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_1378]),
[final] ).
cnf(i_0_2495,plain,
( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hBOOL(hAPP(X5,X2))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1)
| X3 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X4)),X2)
| ~ hBOOL(hAPP(X5,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X3,X1))) ),
inference(split_conjunct,[status(thm)],[i_0_1355]),
[final] ).
cnf(i_0_2496,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X1)),hAPP(hAPP(c_Polynomial_Osmult(X1),X4),X2)),X3))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X1)),X2),X3))
| X3 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))
| ~ class_Fields_Ofield(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1352]),
[final] ).
cnf(i_0_2497,plain,
( X2 = c_Groups_Ozero__class_Ozero(X1)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X3),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X4),X2)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X2))),X2)
| ~ class_Fields_Ofield__inverse__zero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1379]),
[final] ).
cnf(i_0_2498,plain,
( X4 = c_Groups_Ozero__class_Ozero(X1)
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X1)),hAPP(hAPP(c_Polynomial_Osmult(X1),X4),X2)),X3))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X1)),X2),X3))
| ~ class_Fields_Ofield(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1352]),
[final] ).
cnf(i_0_2499,plain,
( X4 = c_Groups_Ozero__class_Ozero(X1)
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X1)),hAPP(hAPP(c_Polynomial_Osmult(X1),X4),X2)),X3))
| ~ class_Fields_Ofield(X1)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X1)),X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1380]),
[final] ).
cnf(i_0_2500,plain,
hAPP(hAPP(c_Power_Opower_Opower(X1,X2,X3),X4),hAPP(c_Nat_OSuc,X5)) = hAPP(hAPP(X3,X4),hAPP(hAPP(c_Power_Opower_Opower(X1,X2,X3),X4),X5)),
inference(split_conjunct,[status(thm)],[i_0_1381]),
[final] ).
cnf(i_0_2501,plain,
( X1 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2)),X2))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2) ),
inference(split_conjunct,[status(thm)],[i_0_1382]),
[final] ).
cnf(i_0_2502,plain,
( X2 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2)),X1))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1) ),
inference(split_conjunct,[status(thm)],[i_0_1383]),
[final] ).
cnf(i_0_2503,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),c_Divides_Odiv__class_Omod(X1,X2,X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Divides_Odiv__class_Odiv(X1,X2,X3)),X3)) = X2
| ~ class_Divides_Osemiring__div(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1384]),
[final] ).
cnf(i_0_2504,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),c_Divides_Odiv__class_Odiv(X1,X3,X2))),c_Divides_Odiv__class_Omod(X1,X3,X2)) = X3
| ~ class_Divides_Osemiring__div(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1385]),
[final] ).
cnf(i_0_2505,plain,
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X1)),hAPP(hAPP(c_Polynomial_OpCons(X1),X2),X3)),hAPP(hAPP(c_Polynomial_OpCons(X1),X4),X5)) = hAPP(hAPP(c_Polynomial_OpCons(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X2),X4)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X1)),X3),X5))
| ~ class_Groups_Oab__group__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1386]),
[final] ).
cnf(i_0_2506,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X1)),hAPP(hAPP(c_Polynomial_OpCons(X1),X2),X3)),hAPP(hAPP(c_Polynomial_OpCons(X1),X4),X5)) = hAPP(hAPP(c_Polynomial_OpCons(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X4)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X1)),X3),X5))
| ~ class_Groups_Ocomm__monoid__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1387]),
[final] ).
cnf(i_0_2507,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X3),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X2),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),X3) = hAPP(hAPP(c_Power_Opower__class_Opower(X1),X3),X2)
| ~ class_Groups_Omonoid__mult(X1)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2) ),
inference(split_conjunct,[status(thm)],[i_0_1388]),
[final] ).
cnf(i_0_2508,plain,
( X1 = c_Groups_Ozero__class_Ozero(X2)
| c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X3),X3)))
| ~ class_Rings_Olinordered__ring__strict(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1326]),
[final] ).
cnf(i_0_2509,plain,
( X1 = c_Groups_Ozero__class_Ozero(X2)
| c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X3),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X1)))
| ~ class_Rings_Olinordered__ring__strict(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1326]),
[final] ).
cnf(i_0_2510,plain,
( X4 = X5
| ~ class_RealVector_Oreal__normed__field(X1)
| ~ c_Deriv_Oderiv(X1,X2,X3,X4)
| ~ c_Deriv_Oderiv(X1,X2,X3,X5) ),
inference(split_conjunct,[status(thm)],[i_0_1389]),
[final] ).
cnf(i_0_2511,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X3),X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X3),X2)))
| X3 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1342]),
[final] ).
cnf(i_0_2512,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X1),X3)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X2),X3)))
| X3 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1344]),
[final] ).
cnf(i_0_2513,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X1),X3)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X2),X3)))
| X3 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1346]),
[final] ).
cnf(i_0_2514,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X2),c_Divides_Odiv__class_Omod(X1,X3,X4)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X2),X4))
| ~ class_Divides_Osemiring__div(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1390]),
[final] ).
cnf(i_0_2515,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X2),X3))
| ~ class_Divides_Osemiring__div(X1)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X2),c_Divides_Odiv__class_Omod(X1,X3,X4)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X2),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_1391]),
[final] ).
cnf(i_0_2516,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X2)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1343]),
[final] ).
cnf(i_0_2517,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X3))))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1348]),
[final] ).
cnf(i_0_2518,plain,
( hAPP(hAPP(c_Polynomial_Osmult(X1),X2),X3) = c_Polynomial_OAbs__poly(X1,hAPP(hAPP(c_COMBB(X1,X1,tc_Nat_Onat),hAPP(c_Groups_Otimes__class_Otimes(X1),X2)),c_Polynomial_Ocoeff(X1,X3)))
| ~ class_Rings_Ocomm__semiring__0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1392]),
[final] ).
cnf(i_0_2519,plain,
( c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X4),X3),X2)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),X4)
| ~ c_Orderings_Oord__class_Oless(X1,X4,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3))
| ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1393]),
[final] ).
cnf(i_0_2520,plain,
( c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X4),X2),X3)
| ~ c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X2),X4)
| ~ c_Orderings_Oord__class_Oless(X1,X4,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X2))
| ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1393]),
[final] ).
cnf(i_0_2521,plain,
( c_Orderings_Oord__class_Oless(X1,X2,hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X3),X4))
| ~ c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless(X1,X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4))
| ~ c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4),X3)
| ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1394]),
[final] ).
cnf(i_0_2522,plain,
( c_Orderings_Oord__class_Oless(X1,X4,hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X3),X2))
| ~ c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless(X1,X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X2))
| ~ c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X2),X3)
| ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1394]),
[final] ).
cnf(i_0_2523,plain,
( c_Divides_Odiv__class_Omod(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Divides_Odiv__class_Omod(X1,X2,X3)),X4),X3) = c_Divides_Odiv__class_Omod(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4),X3)
| ~ class_Divides_Osemiring__div(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1395]),
[final] ).
cnf(i_0_2524,plain,
( c_Divides_Odiv__class_Omod(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),c_Divides_Odiv__class_Omod(X1,X2,X3)),X4),X3) = c_Divides_Odiv__class_Omod(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X4),X3)
| ~ class_Divides_Osemiring__div(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1396]),
[final] ).
cnf(i_0_2525,plain,
( c_Divides_Odiv__class_Omod(X1,hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X2),X3),X4) = c_Divides_Odiv__class_Omod(X1,hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),c_Divides_Odiv__class_Omod(X1,X2,X4)),X3),X4)
| ~ class_Divides_Oring__div(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1397]),
[final] ).
cnf(i_0_2526,plain,
( c_Divides_Odiv__class_Omod(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),X4) = c_Divides_Odiv__class_Omod(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Divides_Odiv__class_Omod(X1,X2,X4)),X3),X4)
| ~ class_Divides_Osemiring__div(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1398]),
[final] ).
cnf(i_0_2527,plain,
( c_Divides_Odiv__class_Omod(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3),X4) = c_Divides_Odiv__class_Omod(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),c_Divides_Odiv__class_Omod(X1,X2,X4)),X3),X4)
| ~ class_Divides_Osemiring__div(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1399]),
[final] ).
cnf(i_0_2528,plain,
X1 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X2))),c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2)),
inference(split_conjunct,[status(thm)],[i_0_1400]),
[final] ).
cnf(i_0_2529,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X1)),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X1)),X2),c_Polynomial_Opoly__gcd(X1,X3,X4)))
| ~ class_Fields_Ofield(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1377]),
[final] ).
cnf(i_0_2530,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X1)),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X1)),X2),c_Polynomial_Opoly__gcd(X1,X4,X3)))
| ~ class_Fields_Ofield(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1377]),
[final] ).
cnf(i_0_2531,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X4)))
| X1 != c_Groups_Ozero__class_Ozero(X2)
| ~ class_Rings_Oidom(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1323]),
[final] ).
cnf(i_0_2532,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X3),X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X4),X1)))
| X1 != c_Groups_Ozero__class_Ozero(X2)
| ~ class_Rings_Oidom(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1324]),
[final] ).
cnf(i_0_2533,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X1)),X2),X4))
| X3 = c_Groups_Ozero__class_Ozero(X1)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X1)),X2),hAPP(hAPP(c_Polynomial_Osmult(X1),X3),X4)))
| ~ class_Fields_Ofield(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1401]),
[final] ).
cnf(i_0_2534,plain,
( X3 = c_Groups_Ozero__class_Ozero(X1)
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X1)),X2),X4))
| ~ class_Fields_Ofield(X1)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X1)),X2),hAPP(hAPP(c_Polynomial_Osmult(X1),X3),X4))) ),
inference(split_conjunct,[status(thm)],[i_0_1402]),
[final] ).
cnf(i_0_2535,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X1),X4)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X5)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X1),X5)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X4))
| X1 != X2
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X3) ),
inference(split_conjunct,[status(thm)],[i_0_1338]),
[final] ).
cnf(i_0_2536,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X1),X4)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X5)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X1),X5)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X4))
| X1 != X2
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X3) ),
inference(split_conjunct,[status(thm)],[i_0_1339]),
[final] ).
cnf(i_0_2537,plain,
( c_Polynomial_Opoly__gcd(X1,X2,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))) = hAPP(hAPP(c_Polynomial_Osmult(X1),hAPP(c_Rings_Oinverse__class_Oinverse(X1),hAPP(c_Polynomial_Ocoeff(X1,X2),c_Polynomial_Odegree(X1,X2)))),X2)
| ~ class_Fields_Ofield(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1403]),
[final] ).
cnf(i_0_2538,plain,
( c_Polynomial_Opoly__gcd(X2,X3,X1) = hAPP(hAPP(c_Polynomial_Osmult(X2),hAPP(c_Rings_Oinverse__class_Oinverse(X2),hAPP(c_Polynomial_Ocoeff(X2,X3),c_Polynomial_Odegree(X2,X3)))),X3)
| X1 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| ~ class_Fields_Ofield(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1404]),
[final] ).
cnf(i_0_2539,plain,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,X2)),X3)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2))),X3),
inference(split_conjunct,[status(thm)],[i_0_1405]),
[final] ).
cnf(i_0_2540,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X3)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X4),X5)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X5))
| ~ class_Fields_Ofield__inverse__zero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1406]),
[final] ).
cnf(i_0_2541,plain,
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X4),X5)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X2),X4)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X3),X5))
| ~ class_Groups_Oab__group__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1407]),
[final] ).
cnf(i_0_2542,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X5)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X5))
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1408]),
[final] ).
cnf(i_0_2543,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X4),X5)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X4)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X3),X5))
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1409]),
[final] ).
cnf(i_0_2544,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X5)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X5)))
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1410]),
[final] ).
cnf(i_0_2545,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X1),X2))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X1),c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X3)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X1),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1411]),
[final] ).
cnf(i_0_2546,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X1)),X2),hAPP(hAPP(c_Polynomial_Osmult(X1),X3),c_Polynomial_Osynthetic__div(X1,X2,X3))) = hAPP(hAPP(c_Polynomial_OpCons(X1),hAPP(c_Polynomial_Opoly(X1,X2),X3)),c_Polynomial_Osynthetic__div(X1,X2,X3))
| ~ class_Rings_Ocomm__semiring__0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1412]),
[final] ).
cnf(i_0_2547,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X3)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1)),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1)),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1413]),
[final] ).
cnf(i_0_2548,plain,
( X2 = X3
| ~ class_Rings_Oidom(X1)
| hAPP(c_Polynomial_Ocoeff(X1,X2),c_Polynomial_Odegree(X1,X2)) != hAPP(c_Polynomial_Ocoeff(X1,X3),c_Polynomial_Odegree(X1,X3))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X1)),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X1)),X3),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1414]),
[final] ).
cnf(i_0_2549,plain,
( c_Transcendental_Odiffs(X1,hAPP(hAPP(c_COMBB(X1,X1,tc_Nat_Onat),c_Groups_Ouminus__class_Ouminus(X1)),X2),X3) = hAPP(c_Groups_Ouminus__class_Ouminus(X1),c_Transcendental_Odiffs(X1,X2,X3))
| ~ class_Rings_Oring__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1415]),
[final] ).
cnf(i_0_2550,plain,
( c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X4),X3),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X4),X2))
| ~ class_Fields_Olinordered__field(X1)
| ~ c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X4)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1416]),
[final] ).
cnf(i_0_2551,plain,
( c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X4),X2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X4),X3))
| ~ class_Fields_Olinordered__field(X1)
| ~ c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless(X1,X4,c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1417]),
[final] ).
cnf(i_0_2552,plain,
c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2)),X3),X2) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X1),X3),X2),
inference(split_conjunct,[status(thm)],[i_0_1418]),
[final] ).
cnf(i_0_2553,plain,
c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2)),X3),X2) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X1),X3),X2),
inference(split_conjunct,[status(thm)],[i_0_1419]),
[final] ).
cnf(i_0_2554,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(X1),c_Divides_Odiv__class_Odiv(X1,X3,X2)),X4) = c_Divides_Odiv__class_Odiv(X1,hAPP(hAPP(c_Power_Opower__class_Opower(X1),X3),X4),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X4))
| ~ class_Divides_Osemiring__div(X1)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1420]),
[final] ).
cnf(i_0_2555,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X1),X2))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X2),X3)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X1),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1421]),
[final] ).
cnf(i_0_2556,plain,
( c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| c_Divides_Odiv__class_Odiv(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X1),X2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X2))),c_Groups_Oone__class_Oone(tc_Int_Oint))
| X2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
inference(split_conjunct,[status(thm)],[i_0_1422]),
[final] ).
cnf(i_0_2557,plain,
( c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X2))),c_Groups_Oone__class_Oone(tc_Int_Oint))
| X2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
inference(split_conjunct,[status(thm)],[i_0_1423]),
[final] ).
cnf(i_0_2558,plain,
( hBOOL(hAPP(X1,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X3,X2)))
| ~ hBOOL(hAPP(X1,esk16_3(X2,X3,X1)))
| ~ hBOOL(hAPP(X1,X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1355]),
[final] ).
cnf(i_0_2559,plain,
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X2)),c_Groups_Oone__class_Oone(X1)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),c_Groups_Oone__class_Oone(X1))),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X2),c_Groups_Oone__class_Oone(X1)))
| ~ class_Rings_Oring__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1424]),
[final] ).
cnf(i_0_2560,plain,
( c_Divides_Odiv__class_Omod(X1,hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X2),X5),X3) = c_Divides_Odiv__class_Omod(X1,hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X4),X6),X3)
| ~ class_Divides_Oring__div(X1)
| c_Divides_Odiv__class_Omod(X1,X2,X3) != c_Divides_Odiv__class_Omod(X1,X4,X3)
| c_Divides_Odiv__class_Omod(X1,X5,X3) != c_Divides_Odiv__class_Omod(X1,X6,X3) ),
inference(split_conjunct,[status(thm)],[i_0_1425]),
[final] ).
cnf(i_0_2561,plain,
( c_Divides_Odiv__class_Omod(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X5),X3) = c_Divides_Odiv__class_Omod(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X6),X3)
| ~ class_Divides_Osemiring__div(X1)
| c_Divides_Odiv__class_Omod(X1,X2,X3) != c_Divides_Odiv__class_Omod(X1,X4,X3)
| c_Divides_Odiv__class_Omod(X1,X5,X3) != c_Divides_Odiv__class_Omod(X1,X6,X3) ),
inference(split_conjunct,[status(thm)],[i_0_1426]),
[final] ).
cnf(i_0_2562,plain,
( c_Divides_Odiv__class_Omod(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X5),X3) = c_Divides_Odiv__class_Omod(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X4),X6),X3)
| ~ class_Divides_Osemiring__div(X1)
| c_Divides_Odiv__class_Omod(X1,X2,X3) != c_Divides_Odiv__class_Omod(X1,X4,X3)
| c_Divides_Odiv__class_Omod(X1,X5,X3) != c_Divides_Odiv__class_Omod(X1,X6,X3) ),
inference(split_conjunct,[status(thm)],[i_0_1427]),
[final] ).
cnf(i_0_2563,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X2),c_Divides_Odiv__class_Omod(X1,X3,X4)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X2),X4))
| ~ class_Divides_Osemiring__div(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1390]),
[final] ).
cnf(i_0_2564,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X2),c_Divides_Odiv__class_Omod(X1,X3,X4)))
| ~ class_Divides_Osemiring__div(X1)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X2),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_1428]),
[final] ).
cnf(i_0_2565,plain,
( c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3)),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3))
| ~ class_Rings_Olinordered__semidom(X1)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Oone__class_Oone(X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1429]),
[final] ).
cnf(i_0_2566,plain,
hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1)),X2)),hAPP(c_Nat_OSuc,X3)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),X2)),X3),
inference(split_conjunct,[status(thm)],[i_0_1430]),
[final] ).
cnf(i_0_2567,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X3),X4)))
| ~ class_Rings_Ocomm__ring__1(X1)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X2),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_1431]),
[final] ).
cnf(i_0_2568,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X3),X4)))
| ~ class_Rings_Ocomm__semiring__1(X1)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X2),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_1432]),
[final] ).
cnf(i_0_2569,plain,
( hBOOL(hAPP(X1,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X3),X2)))
| ~ hBOOL(hAPP(X1,esk14_3(X2,X3,X1)))
| ~ hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ),
inference(split_conjunct,[status(thm)],[i_0_1433]),
[final] ).
cnf(i_0_2570,plain,
( hBOOL(hAPP(X1,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X3),X2)))
| ~ hBOOL(hAPP(X1,esk13_3(X2,X3,X1)))
| ~ hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ),
inference(split_conjunct,[status(thm)],[i_0_1434]),
[final] ).
cnf(i_0_2571,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X1)),c_Polynomial_Omonom(X1,X2,X3)),c_Polynomial_Omonom(X1,X4,X5)) = c_Polynomial_Omonom(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3),X5))
| ~ class_Rings_Ocomm__semiring__0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1435]),
[final] ).
cnf(i_0_2572,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3,X2)
| hBOOL(hAPP(X1,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X3),X2)))
| ~ hBOOL(hAPP(X1,esk14_3(X2,X3,X1))) ),
inference(split_conjunct,[status(thm)],[i_0_1433]),
[final] ).
cnf(i_0_2573,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3,X2)
| hBOOL(hAPP(X1,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X3),X2)))
| ~ hBOOL(hAPP(X1,esk13_3(X2,X3,X1))) ),
inference(split_conjunct,[status(thm)],[i_0_1434]),
[final] ).
cnf(i_0_2574,plain,
( hAPP(hAPP(c_Polynomial_Osmult(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X2),X3)),X4) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X1)),hAPP(hAPP(c_Polynomial_Osmult(X1),X2),X4)),hAPP(hAPP(c_Polynomial_Osmult(X1),X3),X4))
| ~ class_Rings_Ocomm__ring(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1436]),
[final] ).
cnf(i_0_2575,plain,
( hAPP(hAPP(c_Polynomial_Osmult(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)),X4) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X1)),hAPP(hAPP(c_Polynomial_Osmult(X1),X2),X4)),hAPP(hAPP(c_Polynomial_Osmult(X1),X3),X4))
| ~ class_Rings_Ocomm__semiring__0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1437]),
[final] ).
cnf(i_0_2576,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1)),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
inference(split_conjunct,[status(thm)],[i_0_1368]),
[final] ).
cnf(i_0_2577,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X3)))
| X1 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(split_conjunct,[status(thm)],[i_0_1343]),
[final] ).
cnf(i_0_2578,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(X1,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X1)),X2),X4)),X3)
| ~ class_Groups_Oab__group__add(X1)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(X1,X2),X3)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(X1,X4),X3) ),
inference(split_conjunct,[status(thm)],[i_0_1438]),
[final] ).
cnf(i_0_2579,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X1)),X2),X4)),X3)
| ~ class_Groups_Ocomm__monoid__add(X1)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(X1,X2),X3)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(X1,X4),X3) ),
inference(split_conjunct,[status(thm)],[i_0_1439]),
[final] ).
cnf(i_0_2580,plain,
( X3 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Ocomm__semiring__0(X1)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X1)),hAPP(hAPP(c_Polynomial_Osmult(X1),X2),X3)),hAPP(hAPP(c_Polynomial_OpCons(X1),X4),X3)) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1440]),
[final] ).
cnf(i_0_2581,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),X3))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X3),X2))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),X2))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X3),X1))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1441]),
[final] ).
cnf(i_0_2582,plain,
( hAPP(c_Polynomial_Ocoeff(X1,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X1)),X2),X3)),X4) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),hAPP(c_Polynomial_Ocoeff(X1,X2),X4)),hAPP(c_Polynomial_Ocoeff(X1,X3),X4))
| ~ class_Groups_Oab__group__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1442]),
[final] ).
cnf(i_0_2583,plain,
( hAPP(c_Polynomial_Ocoeff(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X1)),X2),X3)),X4) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(c_Polynomial_Ocoeff(X1,X2),X4)),hAPP(c_Polynomial_Ocoeff(X1,X3),X4))
| ~ class_Groups_Ocomm__monoid__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1443]),
[final] ).
cnf(i_0_2584,plain,
( hAPP(c_Polynomial_Opoly(X1,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X1)),X2),X3)),X4) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),hAPP(c_Polynomial_Opoly(X1,X2),X4)),hAPP(c_Polynomial_Opoly(X1,X3),X4))
| ~ class_Rings_Ocomm__ring(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1444]),
[final] ).
cnf(i_0_2585,plain,
( hAPP(c_Polynomial_Opoly(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X1)),X2),X3)),X4) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(c_Polynomial_Opoly(X1,X2),X4)),hAPP(c_Polynomial_Opoly(X1,X3),X4))
| ~ class_Rings_Ocomm__semiring__0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1445]),
[final] ).
cnf(i_0_2586,plain,
( hAPP(c_Polynomial_Opoly(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X1)),X2),X3)),X4) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(c_Polynomial_Opoly(X1,X2),X4)),hAPP(c_Polynomial_Opoly(X1,X3),X4))
| ~ class_Rings_Ocomm__semiring__0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1446]),
[final] ).
cnf(i_0_2587,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X5) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4)
| X5 = c_Groups_Ozero__class_Ozero(X1)
| X3 = c_Groups_Ozero__class_Ozero(X1)
| c_Divides_Odiv__class_Odiv(X1,X2,X3) != c_Divides_Odiv__class_Odiv(X1,X4,X5)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X5),X4))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X3),X2))
| ~ class_Divides_Osemiring__div(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1447]),
[final] ).
cnf(i_0_2588,plain,
( X2 = c_Groups_Ozero__class_Ozero(X1)
| hAPP(hAPP(c_Power_Opower__class_Opower(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X3),X2)),X4) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X3),X4)),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X4))
| ~ class_Fields_Ofield(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1448]),
[final] ).
cnf(i_0_2589,plain,
( hBOOL(hAPP(X1,esk5_3(X2,X1,X3)))
| ~ hBOOL(hAPP(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X4)))
| ~ class_Rings_Odvd(X3)
| ~ class_Rings_Osemiring__0(X3) ),
inference(split_conjunct,[status(thm)],[i_0_1313]),
[final] ).
cnf(i_0_2590,plain,
( c_Divides_Odiv__class_Odiv(X1,X2,X4) = c_Divides_Odiv__class_Odiv(X1,X5,X3)
| X3 = c_Groups_Ozero__class_Ozero(X1)
| X4 = c_Groups_Ozero__class_Ozero(X1)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X5)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X3),X5))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X4),X2))
| ~ class_Divides_Osemiring__div(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1447]),
[final] ).
cnf(i_0_2591,plain,
( X2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hBOOL(hAPP(X1,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X3,X2)))
| ~ hBOOL(hAPP(X1,esk16_3(X2,X3,X1))) ),
inference(split_conjunct,[status(thm)],[i_0_1355]),
[final] ).
cnf(i_0_2592,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X4)),X3)
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1449]),
[final] ).
cnf(i_0_2593,plain,
( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X2),X3)),X4) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X4)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X3),X4))
| ~ class_RealVector_Oreal__normed__field(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1450]),
[final] ).
cnf(i_0_2594,plain,
( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X2),X3)),X4) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X4)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X3),X4))
| ~ class_Rings_Odivision__ring(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1451]),
[final] ).
cnf(i_0_2595,plain,
( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)),X4) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X4)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X3),X4))
| ~ class_RealVector_Oreal__normed__field(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1452]),
[final] ).
cnf(i_0_2596,plain,
( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)),X4) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X4)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X3),X4))
| ~ class_Rings_Odivision__ring(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1453]),
[final] ).
cnf(i_0_2597,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X3)),X4) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X4)),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X3),X4))
| ~ class_Fields_Ofield__inverse__zero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1454]),
[final] ).
cnf(i_0_2598,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),X4) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X4)),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X3),X4))
| ~ class_Groups_Ocomm__monoid__mult(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1455]),
[final] ).
cnf(i_0_2599,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),X4) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X4)),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X3),X4))
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1456]),
[final] ).
cnf(i_0_2600,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X2),X3)),X4) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4))
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1457]),
[final] ).
cnf(i_0_2601,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X2),X3)),X4) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4))
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1458]),
[final] ).
cnf(i_0_2602,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)),X4) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4))
| ~ class_Rings_Ocomm__semiring(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1459]),
[final] ).
cnf(i_0_2603,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)),X4) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4))
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1460]),
[final] ).
cnf(i_0_2604,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)),X4) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4))
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1461]),
[final] ).
cnf(i_0_2605,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)),X4) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4))
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1462]),
[final] ).
cnf(i_0_2606,plain,
( hAPP(c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X1)),X2) = c_Polynomial_OAbs__poly(X1,hAPP(hAPP(c_COMBB(X1,X1,tc_Nat_Onat),c_Groups_Ouminus__class_Ouminus(X1)),c_Polynomial_Ocoeff(X1,X2)))
| ~ class_Groups_Oab__group__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1463]),
[final] ).
cnf(i_0_2607,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X1)),X2),hAPP(hAPP(c_Polynomial_Osmult(X1),X4),X3)))
| X4 = c_Groups_Ozero__class_Ozero(X1)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X1)),X2),X3))
| ~ class_Fields_Ofield(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1401]),
[final] ).
cnf(i_0_2608,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X1)),X2),hAPP(hAPP(c_Polynomial_Osmult(X1),X4),X3)))
| ~ class_Rings_Ocomm__semiring__1(X1)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X1)),X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1464]),
[final] ).
cnf(i_0_2609,plain,
c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X2)),X2)),
inference(split_conjunct,[status(thm)],[i_0_1465]),
[final] ).
cnf(i_0_2610,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X1),c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X3)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X1),X2))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X1),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1466]),
[final] ).
cnf(i_0_2611,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X2)),hAPP(hAPP(c_Polynomial_Osmult(X2),X1),X4)),X3))
| X1 != c_Groups_Ozero__class_Ozero(X2)
| X3 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| ~ class_Fields_Ofield(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1352]),
[final] ).
cnf(i_0_2612,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Divides_Odiv__class_Odiv(X1,X3,X2)),X4) = c_Divides_Odiv__class_Odiv(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4),X2)
| ~ class_Divides_Osemiring__div(X1)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1467]),
[final] ).
cnf(i_0_2613,plain,
( hAPP(hAPP(c_Polynomial_Osmult(X1),X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X1)),X3),X4)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X1)),hAPP(hAPP(c_Polynomial_Osmult(X1),X2),X3)),hAPP(hAPP(c_Polynomial_Osmult(X1),X2),X4))
| ~ class_Rings_Ocomm__ring(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1468]),
[final] ).
cnf(i_0_2614,plain,
( hAPP(hAPP(c_Polynomial_Osmult(X1),X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X1)),X3),X4)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X1)),hAPP(hAPP(c_Polynomial_Osmult(X1),X2),X3)),hAPP(hAPP(c_Polynomial_Osmult(X1),X2),X4))
| ~ class_Rings_Ocomm__semiring__0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1469]),
[final] ).
cnf(i_0_2615,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X1)),c_Polynomial_Opoly__gcd(X1,X2,X3)),X2))
| ~ class_Fields_Ofield(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1470]),
[final] ).
cnf(i_0_2616,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X1)),c_Polynomial_Opoly__gcd(X1,X2,X3)),X3))
| ~ class_Fields_Ofield(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1471]),
[final] ).
cnf(i_0_2617,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,X3)),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,X3)),X2))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3) ),
inference(split_conjunct,[status(thm)],[i_0_1472]),
[final] ).
cnf(i_0_2618,plain,
hAPP(hAPP(hAPP(c_COMBS(X1,X2,X3),X4),X5),X6) = hAPP(hAPP(X4,X6),hAPP(X5,X6)),
inference(split_conjunct,[status(thm)],[i_0_1473]),
[final] ).
cnf(i_0_2619,plain,
( X1 = c_Groups_Ozero__class_Ozero(X2)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X3),X3)) != c_Groups_Ozero__class_Ozero(X2)
| ~ class_Rings_Olinordered__ring__strict(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1474]),
[final] ).
cnf(i_0_2620,plain,
( X1 = c_Groups_Ozero__class_Ozero(X2)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X3),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X1)) != c_Groups_Ozero__class_Ozero(X2)
| ~ class_Rings_Olinordered__ring__strict(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1474]),
[final] ).
cnf(i_0_2621,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),X2))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X2),X3))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X3),X1))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X3),X2))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1441]),
[final] ).
cnf(i_0_2622,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X2),X3)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),X2))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1475]),
[final] ).
cnf(i_0_2623,plain,
( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),c_Groups_Oone__class_Oone(tc_Nat_Onat))),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1476]),
[final] ).
cnf(i_0_2624,plain,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X3)
| c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X4),X3),X2)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),X4)
| ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1393]),
[final] ).
cnf(i_0_2625,plain,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X4),X2),X3)
| ~ c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X2),X4)
| ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1393]),
[final] ).
cnf(i_0_2626,plain,
( c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X2),X4)
| c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X4),X2),X3)
| ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1393]),
[final] ).
cnf(i_0_2627,plain,
( c_Orderings_Oord__class_Oless(X1,X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X2))
| c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless(X1,X4,hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X3),X2))
| ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1394]),
[final] ).
cnf(i_0_2628,plain,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| c_Orderings_Oord__class_Oless(X1,X4,hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X3),X2))
| ~ c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless(X1,X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X2))
| ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1394]),
[final] ).
cnf(i_0_2629,plain,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X4)
| c_Orderings_Oord__class_Oless(X1,X2,hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X3),X4))
| ~ c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless(X1,X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4))
| ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1394]),
[final] ).
cnf(i_0_2630,plain,
( c_Orderings_Oord__class_Oless(X1,X3,c_Groups_Ozero__class_Ozero(X1))
| c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X4),X3),X2)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ c_Orderings_Oord__class_Oless(X1,X4,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3))
| ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1393]),
[final] ).
cnf(i_0_2631,plain,
( c_Orderings_Oord__class_Oless(X1,X3,c_Groups_Ozero__class_Ozero(X1))
| c_Orderings_Oord__class_Oless(X1,X2,hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X4),X3))
| ~ c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),X4)
| ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1394]),
[final] ).
cnf(i_0_2632,plain,
( c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3)))
| ~ class_Rings_Olinordered__semidom(X1)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),X2) ),
inference(split_conjunct,[status(thm)],[i_0_1477]),
[final] ).
cnf(i_0_2633,plain,
( c_Orderings_Oord__class_Oless(X1,X3,X4)
| ~ c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4))
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ class_Rings_Olinordered__ring__strict(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1478]),
[final] ).
cnf(i_0_2634,plain,
( c_Orderings_Oord__class_Oless(X1,X4,X3)
| ~ c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4))
| ~ c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| ~ class_Rings_Olinordered__ring__strict(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1479]),
[final] ).
cnf(i_0_2635,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3,X4)
| ~ c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X4))
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),X2)
| ~ class_Rings_Olinordered__semidom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1480]),
[final] ).
cnf(i_0_2636,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3,X4)
| ~ class_Rings_Olinordered__semidom(X1)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),X2)
| ~ c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_1481]),
[final] ).
cnf(i_0_2637,plain,
( hAPP(c_Polynomial_Opoly(X1,hAPP(hAPP(c_Polynomial_OpCons(X1),X2),X3)),X4) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),hAPP(c_Polynomial_Opoly(X1,X3),X4)))
| ~ class_Rings_Ocomm__semiring__0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1482]),
[final] ).
cnf(i_0_2638,plain,
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X1)),c_Polynomial_Omonom(X1,X2,X3)),c_Polynomial_Omonom(X1,X4,X3)) = c_Polynomial_Omonom(X1,hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X2),X4),X3)
| ~ class_Groups_Oab__group__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1483]),
[final] ).
cnf(i_0_2639,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X1)),c_Polynomial_Omonom(X1,X2,X3)),c_Polynomial_Omonom(X1,X4,X3)) = c_Polynomial_Omonom(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X4),X3)
| ~ class_Groups_Ocomm__monoid__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1484]),
[final] ).
cnf(i_0_2640,plain,
hAPP(hAPP(hAPP(c_COMBB(X1,X2,X3),X4),X5),X6) = hAPP(X4,hAPP(X5,X6)),
inference(split_conjunct,[status(thm)],[i_0_1485]),
[final] ).
cnf(i_0_2641,plain,
( hAPP(c_Polynomial_Opoly(X1,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(X1)),X2),X3)),X4) = hAPP(hAPP(c_Power_Opower__class_Opower(X1),hAPP(c_Polynomial_Opoly(X1,X2),X4)),X3)
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1486]),
[final] ).
cnf(i_0_2642,plain,
c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2)),X3),X2) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,X3,X2),
inference(split_conjunct,[status(thm)],[i_0_1487]),
[final] ).
cnf(i_0_2643,plain,
( c_Nat_Osemiring__1__class_Oof__nat__aux(X1,X2,hAPP(c_Nat_OSuc,X3),X4) = c_Nat_Osemiring__1__class_Oof__nat__aux(X1,X2,X3,hAPP(X2,X4))
| ~ class_Rings_Osemiring__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1488]),
[final] ).
cnf(i_0_2644,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2)),X2))
| X1 != c_Groups_Oone__class_Oone(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2) ),
inference(split_conjunct,[status(thm)],[i_0_1382]),
[final] ).
cnf(i_0_2645,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1)),X2))
| X1 != c_Groups_Oone__class_Oone(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2) ),
inference(split_conjunct,[status(thm)],[i_0_1383]),
[final] ).
cnf(i_0_2646,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),X3) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),c_Groups_Oone__class_Oone(X1))),X3)
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1489]),
[final] ).
cnf(i_0_2647,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X1),X2)),X3) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X3)),
inference(split_conjunct,[status(thm)],[i_0_1490]),
[final] ).
cnf(i_0_2648,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X2)),X3) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X3)),
inference(split_conjunct,[status(thm)],[i_0_1491]),
[final] ).
cnf(i_0_2649,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),X2)),X3) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X3)),
inference(split_conjunct,[status(thm)],[i_0_1492]),
[final] ).
cnf(i_0_2650,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)),X3) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X3)),
inference(split_conjunct,[status(thm)],[i_0_1493]),
[final] ).
cnf(i_0_2651,plain,
( c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Power_Opower__class_Opower(X1),X4),X3),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X4),X2))
| ~ class_Rings_Olinordered__semidom(X1)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X3)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X4)
| ~ c_Orderings_Oord__class_Oless(X1,X4,c_Groups_Oone__class_Oone(X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1494]),
[final] ).
cnf(i_0_2652,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),X3))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),X2))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X3),X1))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1495]),
[final] ).
cnf(i_0_2653,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X3),X2))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),X2))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X3),X1))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1496]),
[final] ).
cnf(i_0_2654,plain,
( hAPP(c_Polynomial_Ocoeff(X2,c_Polynomial_Opoly__gcd(X2,X1,X3)),c_Polynomial_Odegree(X2,c_Polynomial_Opoly__gcd(X2,X1,X3))) = c_Groups_Ozero__class_Ozero(X2)
| X1 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| X3 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| ~ class_Fields_Ofield(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1497]),
[final] ).
cnf(i_0_2655,plain,
( c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X1) = c_Divides_Odiv__class_Omod(tc_Int_Oint,X3,X1)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X2),X3))) ),
inference(split_conjunct,[status(thm)],[i_0_1498]),
[final] ).
cnf(i_0_2656,plain,
( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),c_Groups_Oone__class_Oone(tc_Nat_Onat))),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1499]),
[final] ).
cnf(i_0_2657,plain,
( c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4))
| ~ class_Rings_Olinordered__ring__strict(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1500]),
[final] ).
cnf(i_0_2658,plain,
( c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X2))
| ~ class_Rings_Olinordered__ring__strict(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1501]),
[final] ).
cnf(i_0_2659,plain,
( c_Divides_Odiv__class_Omod(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),c_Divides_Odiv__class_Omod(X1,X3,X4)),X4) = c_Divides_Odiv__class_Omod(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3),X4)
| ~ class_Divides_Osemiring__div(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1502]),
[final] ).
cnf(i_0_2660,plain,
( c_Divides_Odiv__class_Omod(X1,hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X2),X3),X4) = c_Divides_Odiv__class_Omod(X1,hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X2),c_Divides_Odiv__class_Omod(X1,X3,X4)),X4)
| ~ class_Divides_Oring__div(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1503]),
[final] ).
cnf(i_0_2661,plain,
( c_Divides_Odiv__class_Omod(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),X4) = c_Divides_Odiv__class_Omod(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),c_Divides_Odiv__class_Omod(X1,X3,X4)),X4)
| ~ class_Divides_Osemiring__div(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1504]),
[final] ).
cnf(i_0_2662,plain,
( c_Divides_Odiv__class_Omod(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3),X4) = c_Divides_Odiv__class_Omod(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),c_Divides_Odiv__class_Omod(X1,X3,X4)),X4)
| ~ class_Divides_Osemiring__div(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1505]),
[final] ).
cnf(i_0_2663,plain,
( X2 = c_Groups_Ozero__class_Ozero(X1)
| c_Divides_Odiv__class_Odiv(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4)),X2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X4),c_Divides_Odiv__class_Odiv(X1,X3,X2))
| ~ class_Divides_Osemiring__div(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1506]),
[final] ).
cnf(i_0_2664,plain,
( X2 = c_Groups_Ozero__class_Ozero(X1)
| c_Divides_Odiv__class_Odiv(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X2)),X2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X4),c_Divides_Odiv__class_Odiv(X1,X3,X2))
| ~ class_Divides_Osemiring__div(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1507]),
[final] ).
cnf(i_0_2665,plain,
( c_Divides_Odiv__class_Omod(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Divides_Odiv__class_Omod(X1,X2,X4)),X3)
| ~ class_Divides_Osemiring__div(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1508]),
[final] ).
cnf(i_0_2666,plain,
( c_Orderings_Oord__class_Oless(X1,X2,X3)
| c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X4)
| ~ c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4))
| ~ class_Rings_Olinordered__ring__strict(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1501]),
[final] ).
cnf(i_0_2667,plain,
( c_Orderings_Oord__class_Oless(X1,X2,X3)
| c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X4)
| ~ c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X2))
| ~ class_Rings_Olinordered__ring__strict(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1500]),
[final] ).
cnf(i_0_2668,plain,
( c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| c_Orderings_Oord__class_Oless(X1,X3,X4)
| ~ c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4))
| ~ class_Rings_Olinordered__ring__strict(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1500]),
[final] ).
cnf(i_0_2669,plain,
( c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| c_Orderings_Oord__class_Oless(X1,X3,X4)
| ~ c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X2))
| ~ class_Rings_Olinordered__ring__strict(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1501]),
[final] ).
cnf(i_0_2670,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),X2))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X1))) ),
inference(split_conjunct,[status(thm)],[i_0_1509]),
[final] ).
cnf(i_0_2671,plain,
( c_Orderings_Oord__class_Oless(X1,X2,X3)
| c_Orderings_Oord__class_Oless(X1,X3,X2)
| ~ c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4))
| ~ class_Rings_Olinordered__ring__strict(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1501]),
[final] ).
cnf(i_0_2672,plain,
( c_Orderings_Oord__class_Oless(X1,X2,X3)
| c_Orderings_Oord__class_Oless(X1,X3,X2)
| ~ c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X2))
| ~ class_Rings_Olinordered__ring__strict(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1500]),
[final] ).
cnf(i_0_2673,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)),X3))
| ~ class_Rings_Ocomm__ring__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1510]),
[final] ).
cnf(i_0_2674,plain,
( hAPP(hAPP(c_Polynomial_Osmult(X1),X2),hAPP(hAPP(c_Polynomial_OpCons(X1),X3),X4)) = hAPP(hAPP(c_Polynomial_OpCons(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_Polynomial_Osmult(X1),X2),X4))
| ~ class_Rings_Ocomm__semiring__0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1511]),
[final] ).
cnf(i_0_2675,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X3),X4)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4))
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1512]),
[final] ).
cnf(i_0_2676,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X3),X4)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4))
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1513]),
[final] ).
cnf(i_0_2677,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X3),X4)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4))
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1514]),
[final] ).
cnf(i_0_2678,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X3),X4)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4))
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1515]),
[final] ).
cnf(i_0_2679,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X3),X4)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4))
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1516]),
[final] ).
cnf(i_0_2680,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),X4) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4)),X3)
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1517]),
[final] ).
cnf(i_0_2681,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)),X4) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X4)),X3)
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1518]),
[final] ).
cnf(i_0_2682,plain,
( X1 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| hAPP(c_Polynomial_Ocoeff(X2,c_Polynomial_Opoly__gcd(X2,X1,X3)),c_Polynomial_Odegree(X2,c_Polynomial_Opoly__gcd(X2,X1,X3))) = c_Groups_Oone__class_Oone(X2)
| ~ class_Fields_Ofield(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1497]),
[final] ).
cnf(i_0_2683,plain,
( X1 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| hAPP(c_Polynomial_Ocoeff(X2,c_Polynomial_Opoly__gcd(X2,X3,X1)),c_Polynomial_Odegree(X2,c_Polynomial_Opoly__gcd(X2,X3,X1))) = c_Groups_Oone__class_Oone(X2)
| ~ class_Fields_Ofield(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1497]),
[final] ).
cnf(i_0_2684,plain,
( c_Divides_Odiv__class_Odiv(tc_Int_Oint,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X2),X1),X2) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2) ),
inference(split_conjunct,[status(thm)],[i_0_1519]),
[final] ).
cnf(i_0_2685,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X3)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X1),X2),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X1),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1520]),
[final] ).
cnf(i_0_2686,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X3)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X3))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1) ),
inference(split_conjunct,[status(thm)],[i_0_1521]),
[final] ).
cnf(i_0_2687,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3)),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X4)) = hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3),X4))
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1522]),
[final] ).
cnf(i_0_2688,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3),X4)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3)),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X4))
| ~ class_Groups_Omonoid__mult(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1523]),
[final] ).
cnf(i_0_2689,plain,
( c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X4),X3)
| ~ c_Orderings_Oord__class_Oless(X1,X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4))
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X4)
| ~ class_Fields_Olinordered__field(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1524]),
[final] ).
cnf(i_0_2690,plain,
( c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X3),X2),X4)
| ~ class_Fields_Olinordered__field(X1)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ c_Orderings_Oord__class_Oless(X1,X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1525]),
[final] ).
cnf(i_0_2691,plain,
( c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X3),X2),X4)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ c_Orderings_Oord__class_Oless(X1,X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X2))
| ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1393]),
[final] ).
cnf(i_0_2692,plain,
( c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4),X3)
| ~ c_Orderings_Oord__class_Oless(X1,X2,hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X3),X4))
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X4)
| ~ class_Fields_Olinordered__field(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1526]),
[final] ).
cnf(i_0_2693,plain,
( c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X2),X4)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ c_Orderings_Oord__class_Oless(X1,X3,hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X4),X2))
| ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1394]),
[final] ).
cnf(i_0_2694,plain,
( c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X4),X3),X2)
| ~ c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),X4)
| ~ c_Orderings_Oord__class_Oless(X1,X3,c_Groups_Ozero__class_Ozero(X1))
| ~ class_Fields_Olinordered__field(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1527]),
[final] ).
cnf(i_0_2695,plain,
( c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3),X2)
| ~ c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X3),X4)
| ~ c_Orderings_Oord__class_Oless(X1,X3,c_Groups_Ozero__class_Ozero(X1))
| ~ class_Fields_Olinordered__field(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1527]),
[final] ).
cnf(i_0_2696,plain,
( c_Orderings_Oord__class_Oless(X1,X2,hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X4),X3))
| ~ c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),X4)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X3)
| ~ class_Fields_Olinordered__field(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1526]),
[final] ).
cnf(i_0_2697,plain,
( c_Orderings_Oord__class_Oless(X1,X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3))
| ~ c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X3),X4)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X3)
| ~ class_Fields_Olinordered__field(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1524]),
[final] ).
cnf(i_0_2698,plain,
( c_Orderings_Oord__class_Oless(X1,X3,hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X4),X2))
| ~ class_Fields_Olinordered__field(X1)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X2),X4) ),
inference(split_conjunct,[status(thm)],[i_0_1528]),
[final] ).
cnf(i_0_2699,plain,
( c_Orderings_Oord__class_Oless(X1,X3,hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X4),X2))
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X2),X4)
| ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1394]),
[final] ).
cnf(i_0_2700,plain,
( c_Orderings_Oord__class_Oless(X1,X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X2))
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X3),X2),X4)
| ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1393]),
[final] ).
cnf(i_0_2701,plain,
( c_Orderings_Oord__class_Oless(X1,X3,hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X4))
| ~ c_Orderings_Oord__class_Oless(X1,X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4))
| ~ c_Orderings_Oord__class_Oless(X1,X4,c_Groups_Ozero__class_Ozero(X1))
| ~ class_Fields_Olinordered__field(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1529]),
[final] ).
cnf(i_0_2702,plain,
( c_Orderings_Oord__class_Oless(X1,X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4))
| ~ c_Orderings_Oord__class_Oless(X1,X2,hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X3),X4))
| ~ c_Orderings_Oord__class_Oless(X1,X4,c_Groups_Ozero__class_Ozero(X1))
| ~ class_Fields_Olinordered__field(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1529]),
[final] ).
cnf(i_0_2703,plain,
( X2 = c_Groups_Ozero__class_Ozero(X1)
| X5 = X6
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X1)
| X3 != X4
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X5)) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X6)) ),
inference(split_conjunct,[status(thm)],[i_0_1530]),
[final] ).
cnf(i_0_2704,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,X3)),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,X3)),X2))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_1413]),
[final] ).
cnf(i_0_2705,plain,
c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X1),c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X3)),X3) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X1),X2),X3),
inference(split_conjunct,[status(thm)],[i_0_1531]),
[final] ).
cnf(i_0_2706,plain,
c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X3)),X3) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X2),X3),
inference(split_conjunct,[status(thm)],[i_0_1532]),
[final] ).
cnf(i_0_2707,plain,
c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X2),X3) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X3)),X3),
inference(split_conjunct,[status(thm)],[i_0_1533]),
[final] ).
cnf(i_0_2708,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X1)),hAPP(hAPP(c_Polynomial_Osmult(X1),X2),X3)),X4) = hAPP(hAPP(c_Polynomial_Osmult(X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X1)),X3),X4))
| ~ class_Rings_Ocomm__semiring__0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1534]),
[final] ).
cnf(i_0_2709,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),c_Divides_Odiv__class_Odiv(X1,X3,X2)) = c_Divides_Odiv__class_Odiv(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3),X2)
| ~ class_Divides_Osemiring__div(X1)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1535]),
[final] ).
cnf(i_0_2710,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,X2)),X3) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X3)),
inference(split_conjunct,[status(thm)],[i_0_1536]),
[final] ).
cnf(i_0_2711,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),X2))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X3),X2))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1495]),
[final] ).
cnf(i_0_2712,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),X2))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X3),X1))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X3),X2))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1496]),
[final] ).
cnf(i_0_2713,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4)))
| ~ class_Rings_Ocomm__semiring__1(X1)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1537]),
[final] ).
cnf(i_0_2714,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3)))
| ~ class_Rings_Ocomm__semiring__1(X1)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1538]),
[final] ).
cnf(i_0_2715,plain,
( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),c_Groups_Oone__class_Oone(X1)),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3)) = hAPP(hAPP(c_Power_Opower__class_Opower(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),c_Groups_Oone__class_Oone(X1)),X2)),X3)
| ~ class_Fields_Ofield__inverse__zero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1539]),
[final] ).
cnf(i_0_2716,plain,
( c_Polynomial_Osynthetic__div(X1,hAPP(hAPP(c_Polynomial_OpCons(X1),X2),X3),X4) = hAPP(hAPP(c_Polynomial_OpCons(X1),hAPP(c_Polynomial_Opoly(X1,X3),X4)),c_Polynomial_Osynthetic__div(X1,X3,X4))
| ~ class_Rings_Ocomm__semiring__0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1540]),
[final] ).
cnf(i_0_2717,plain,
( X2 = X3
| hAPP(c_Polynomial_Ocoeff(X1,X2),esk4_3(X3,X2,X1)) != hAPP(c_Polynomial_Ocoeff(X1,X3),esk4_3(X3,X2,X1))
| ~ class_Groups_Ozero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1541]),
[final] ).
cnf(i_0_2718,plain,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3)))
| ~ class_Rings_Olinordered__semidom(X1)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),X2) ),
inference(split_conjunct,[status(thm)],[i_0_1542]),
[final] ).
cnf(i_0_2719,plain,
( c_Orderings_Oord__class_Oless(X1,X2,X4)
| ~ c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X4),X3))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1543]),
[final] ).
cnf(i_0_2720,plain,
( c_Orderings_Oord__class_Oless(X1,X2,X4)
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X1)
| ~ c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X4),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1544]),
[final] ).
cnf(i_0_2721,plain,
( c_Orderings_Oord__class_Oless(X1,X3,X4)
| ~ c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X4))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1545]),
[final] ).
cnf(i_0_2722,plain,
( c_Orderings_Oord__class_Oless(X1,X3,X4)
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X1)
| ~ c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_1546]),
[final] ).
cnf(i_0_2723,plain,
( hAPP(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X2,X1)),X3),X4),X5) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),hAPP(X3,X5)),hAPP(X4,X5))
| ~ class_Groups_Ominus(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1547]),
[final] ).
cnf(i_0_2724,plain,
( hAPP(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X2,X1)),X3),X4),X5) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),hAPP(X3,X5)),hAPP(X4,X5))
| ~ class_Groups_Ominus(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1548]),
[final] ).
cnf(i_0_2725,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),X2))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,X1)),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,X2))) ),
inference(split_conjunct,[status(thm)],[i_0_1549]),
[final] ).
cnf(i_0_2726,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),X2))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,X1)),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,X2))) ),
inference(split_conjunct,[status(thm)],[i_0_1550]),
[final] ).
cnf(i_0_2727,plain,
hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X3)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X1),X2)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X1),X3)),
inference(split_conjunct,[status(thm)],[i_0_1551]),
[final] ).
cnf(i_0_2728,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X2),X3)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X3)),
inference(split_conjunct,[status(thm)],[i_0_1552]),
[final] ).
cnf(i_0_2729,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X3)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X3)),
inference(split_conjunct,[status(thm)],[i_0_1553]),
[final] ).
cnf(i_0_2730,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X2),X3)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X3)),
inference(split_conjunct,[status(thm)],[i_0_1554]),
[final] ).
cnf(i_0_2731,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X3)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X3)),
inference(split_conjunct,[status(thm)],[i_0_1555]),
[final] ).
cnf(i_0_2732,plain,
hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),X2)),X3) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),X3)),X2),
inference(split_conjunct,[status(thm)],[i_0_1556]),
[final] ).
cnf(i_0_2733,plain,
( hBOOL(hAPP(X3,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| ~ hBOOL(hAPP(X3,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),X2))) ),
inference(split_conjunct,[status(thm)],[i_0_1433]),
[final] ).
cnf(i_0_2734,plain,
( hBOOL(hAPP(X3,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| ~ hBOOL(hAPP(X3,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),X2))) ),
inference(split_conjunct,[status(thm)],[i_0_1434]),
[final] ).
cnf(i_0_2735,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X2),X4))
| ~ class_Rings_Ocomm__semiring__1(X1)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X3),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_1557]),
[final] ).
cnf(i_0_2736,plain,
( X2 = X3
| X2 = hAPP(c_Groups_Ouminus__class_Ouminus(X1),X3)
| hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) != hAPP(hAPP(c_Power_Opower__class_Opower(X1),X3),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))
| ~ class_Rings_Oidom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1558]),
[final] ).
cnf(i_0_2737,plain,
( c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X4),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X3),X4))
| ~ class_Fields_Olinordered__field(X1)
| ~ c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X4) ),
inference(split_conjunct,[status(thm)],[i_0_1559]),
[final] ).
cnf(i_0_2738,plain,
( c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4))
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ c_Orderings_Oord__class_Oless(X1,X3,X4)
| ~ class_Rings_Olinordered__ring__strict(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1500]),
[final] ).
cnf(i_0_2739,plain,
( c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4))
| ~ class_Rings_Olinordered__semiring__strict(X1)
| ~ c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X4) ),
inference(split_conjunct,[status(thm)],[i_0_1560]),
[final] ).
cnf(i_0_2740,plain,
( c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X2))
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ c_Orderings_Oord__class_Oless(X1,X3,X4)
| ~ class_Rings_Olinordered__ring__strict(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1501]),
[final] ).
cnf(i_0_2741,plain,
( c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3))
| ~ class_Rings_Olinordered__semiring__strict(X1)
| ~ c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X4) ),
inference(split_conjunct,[status(thm)],[i_0_1561]),
[final] ).
cnf(i_0_2742,plain,
( c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3))
| ~ class_Rings_Olinordered__comm__semiring__strict(X1)
| ~ c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X4) ),
inference(split_conjunct,[status(thm)],[i_0_1562]),
[final] ).
cnf(i_0_2743,plain,
( c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3))
| ~ c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X4)
| ~ class_Rings_Olinordered__ring__strict(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1478]),
[final] ).
cnf(i_0_2744,plain,
( c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X3),X4),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X4))
| ~ class_Fields_Olinordered__field(X1)
| ~ c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless(X1,X4,c_Groups_Ozero__class_Ozero(X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1563]),
[final] ).
cnf(i_0_2745,plain,
( c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3))
| ~ c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless(X1,X3,X4)
| ~ class_Rings_Olinordered__ring__strict(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1500]),
[final] ).
cnf(i_0_2746,plain,
( c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4))
| ~ class_Rings_Olinordered__ring__strict(X1)
| ~ c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless(X1,X4,c_Groups_Ozero__class_Ozero(X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1564]),
[final] ).
cnf(i_0_2747,plain,
( c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X2))
| ~ c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless(X1,X3,X4)
| ~ class_Rings_Olinordered__ring__strict(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1501]),
[final] ).
cnf(i_0_2748,plain,
( c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X2))
| ~ c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless(X1,X4,c_Groups_Ozero__class_Ozero(X1))
| ~ class_Rings_Olinordered__ring__strict(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1479]),
[final] ).
cnf(i_0_2749,plain,
( c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X2))
| ~ class_Rings_Olinordered__ring__strict(X1)
| ~ c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless(X1,X4,c_Groups_Ozero__class_Ozero(X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1565]),
[final] ).
cnf(i_0_2750,plain,
( c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Power_Opower__class_Opower(X1),X4),X2),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X4),X3))
| ~ class_Rings_Olinordered__semidom(X1)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X3)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),X4) ),
inference(split_conjunct,[status(thm)],[i_0_1566]),
[final] ).
cnf(i_0_2751,plain,
( c_Orderings_Oord__class_Oless(X3,hAPP(hAPP(c_Power_Opower__class_Opower(X3),X4),X1),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X4),X2))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| ~ c_Orderings_Oord__class_Oless(X3,c_Groups_Oone__class_Oone(X3),X4)
| ~ class_Rings_Olinordered__semidom(X3) ),
inference(split_conjunct,[status(thm)],[i_0_1480]),
[final] ).
cnf(i_0_2752,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,esk16_3(X1,X2,X3),X1)
| hBOOL(hAPP(X3,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X2,X1)))
| ~ hBOOL(hAPP(X3,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1355]),
[final] ).
cnf(i_0_2753,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X1),X2))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X1)),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1567]),
[final] ).
cnf(i_0_2754,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X3),c_Groups_Oone__class_Oone(X1))),X2)
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1568]),
[final] ).
cnf(i_0_2755,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Divides_Odiv__class_Odiv(X1,X3,X2)),X2) = X3
| ~ class_Divides_Osemiring__div(X1)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1569]),
[final] ).
cnf(i_0_2756,plain,
( X2 = c_Groups_Ozero__class_Ozero(X1)
| c_Divides_Odiv__class_Odiv(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3),X2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),c_Divides_Odiv__class_Odiv(X1,X3,X2)),c_Groups_Oone__class_Oone(X1))
| ~ class_Divides_Osemiring__div(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1570]),
[final] ).
cnf(i_0_2757,plain,
( X2 = c_Groups_Ozero__class_Ozero(X1)
| c_Divides_Odiv__class_Odiv(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X3),X2),X2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),c_Divides_Odiv__class_Odiv(X1,X3,X2)),c_Groups_Oone__class_Oone(X1))
| ~ class_Divides_Osemiring__div(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1571]),
[final] ).
cnf(i_0_2758,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X1),X3)))
| c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2) != c_Divides_Odiv__class_Omod(tc_Int_Oint,X3,X2) ),
inference(split_conjunct,[status(thm)],[i_0_1498]),
[final] ).
cnf(i_0_2759,plain,
( c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X4),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X3),X5))
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(X1)
| ~ c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless(X1,X4,X5) ),
inference(split_conjunct,[status(thm)],[i_0_1572]),
[final] ).
cnf(i_0_2760,plain,
( c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X3)
| c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X4),X2),X3)
| ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1393]),
[final] ).
cnf(i_0_2761,plain,
( c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| c_Orderings_Oord__class_Oless(X1,X3,c_Groups_Ozero__class_Ozero(X1))
| c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ c_Orderings_Oord__class_Oless(X1,X3,hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X4),X2))
| ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1394]),
[final] ).
cnf(i_0_2762,plain,
( hBOOL(hAPP(X4,X3))
| X1 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X3)
| ~ hBOOL(hAPP(X4,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),X2))) ),
inference(split_conjunct,[status(thm)],[i_0_1433]),
[final] ).
cnf(i_0_2763,plain,
( hBOOL(hAPP(X4,X3))
| X1 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X3)
| ~ hBOOL(hAPP(X4,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),X2))) ),
inference(split_conjunct,[status(thm)],[i_0_1434]),
[final] ).
cnf(i_0_2764,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)),X3))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X2),X3))
| ~ class_Rings_Ocomm__ring__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1510]),
[final] ).
cnf(i_0_2765,plain,
( X2 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))
| c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(X1),X3,X2) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(X1,c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(X1),X3,X2)),c_Polynomial_Odegree(X1,X2))
| ~ class_Fields_Ofield(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1573]),
[final] ).
cnf(i_0_2766,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2) ),
inference(split_conjunct,[status(thm)],[i_0_1574]),
[final] ).
cnf(i_0_2767,plain,
( X1 = c_Polynomial_Osynthetic__div(X2,X3,X4)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X2)),X3),hAPP(hAPP(c_Polynomial_Osmult(X2),X4),X1)) != hAPP(hAPP(c_Polynomial_OpCons(X2),X5),X1)
| ~ class_Rings_Ocomm__semiring__0(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1575]),
[final] ).
cnf(i_0_2768,plain,
( c_Divides_Odiv__class_Omod(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),c_Divides_Odiv__class_Omod(X1,X3,X4))
| ~ class_Divides_Osemiring__div(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1576]),
[final] ).
cnf(i_0_2769,plain,
( X2 = c_Groups_Ozero__class_Ozero(X1)
| hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X3),X4)
| ~ class_Fields_Ofield__inverse__zero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1577]),
[final] ).
cnf(i_0_2770,plain,
( X2 = c_Groups_Ozero__class_Ozero(X1)
| hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X2)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X3),X4)
| ~ class_Fields_Ofield__inverse__zero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1578]),
[final] ).
cnf(i_0_2771,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X1)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1509]),
[final] ).
cnf(i_0_2772,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1579]),
[final] ).
cnf(i_0_2773,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1580]),
[final] ).
cnf(i_0_2774,plain,
( c_Divides_Odiv__class_Omod(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4)),X3) = c_Divides_Odiv__class_Omod(X1,X2,X3)
| ~ class_Divides_Osemiring__div(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1581]),
[final] ).
cnf(i_0_2775,plain,
( c_Divides_Odiv__class_Omod(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4)),X4) = c_Divides_Odiv__class_Omod(X1,X2,X4)
| ~ class_Divides_Osemiring__div(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1582]),
[final] ).
cnf(i_0_2776,plain,
( X1 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),esk14_3(X2,X1,X3))
| hBOOL(hAPP(X3,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),X2)))
| ~ hBOOL(hAPP(X3,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ),
inference(split_conjunct,[status(thm)],[i_0_1433]),
[final] ).
cnf(i_0_2777,plain,
( X1 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),esk13_3(X2,X1,X3))
| hBOOL(hAPP(X3,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),X2)))
| ~ hBOOL(hAPP(X3,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ),
inference(split_conjunct,[status(thm)],[i_0_1434]),
[final] ).
cnf(i_0_2778,plain,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ class_Rings_Olinordered__semiring__strict(X1)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3))
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X3) ),
inference(split_conjunct,[status(thm)],[i_0_1583]),
[final] ).
cnf(i_0_2779,plain,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X3)
| ~ class_Rings_Olinordered__semiring__strict(X1)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3))
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2) ),
inference(split_conjunct,[status(thm)],[i_0_1584]),
[final] ).
cnf(i_0_2780,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1580]),
[final] ).
cnf(i_0_2781,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1579]),
[final] ).
cnf(i_0_2782,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X3)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1585]),
[final] ).
cnf(i_0_2783,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3)),X2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3))
| ~ class_Groups_Omonoid__mult(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1586]),
[final] ).
cnf(i_0_2784,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),X4) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4))
| ~ class_Groups_Oab__semigroup__mult(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1587]),
[final] ).
cnf(i_0_2785,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),X4) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4))
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1588]),
[final] ).
cnf(i_0_2786,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)),X4) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X3),X4))
| ~ class_Groups_Oab__semigroup__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1589]),
[final] ).
cnf(i_0_2787,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)),X4) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X3),X4))
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1590]),
[final] ).
cnf(i_0_2788,plain,
( hAPP(hAPP(c_Polynomial_Osmult(X1),X2),hAPP(hAPP(c_Polynomial_Osmult(X1),X3),X4)) = hAPP(hAPP(c_Polynomial_Osmult(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),X4)
| ~ class_Rings_Ocomm__semiring__0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1591]),
[final] ).
cnf(i_0_2789,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X3),X4)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),X4)
| ~ class_Rings_Odivision__ring(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1592]),
[final] ).
cnf(i_0_2790,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),X4)
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1593]),
[final] ).
cnf(i_0_2791,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X3),X4)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)),X4)
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1594]),
[final] ).
cnf(i_0_2792,plain,
( X1 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),esk14_3(X2,X1,X3))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| hBOOL(hAPP(X3,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),X2))) ),
inference(split_conjunct,[status(thm)],[i_0_1433]),
[final] ).
cnf(i_0_2793,plain,
( X1 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),esk13_3(X2,X1,X3))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| hBOOL(hAPP(X3,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),X2))) ),
inference(split_conjunct,[status(thm)],[i_0_1434]),
[final] ).
cnf(i_0_2794,plain,
( hAPP(c_Polynomial_Opoly(X1,c_Polynomial_Omonom(X1,X2,X3)),X4) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X4),X3))
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1595]),
[final] ).
cnf(i_0_2795,plain,
( X1 = hAPP(c_Polynomial_Opoly(X2,X3),X4)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X2)),X3),hAPP(hAPP(c_Polynomial_Osmult(X2),X4),X5)) != hAPP(hAPP(c_Polynomial_OpCons(X2),X1),X5)
| ~ class_Rings_Ocomm__semiring__0(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1575]),
[final] ).
cnf(i_0_2796,plain,
( hBOOL(hAPP(X2,X3))
| X1 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(X2,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X3,X1))) ),
inference(split_conjunct,[status(thm)],[i_0_1355]),
[final] ).
cnf(i_0_2797,plain,
( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Power_Opower__class_Opower(X2),X3),X1) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X3),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X3),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),c_Groups_Oone__class_Oone(tc_Nat_Onat))))
| ~ class_Power_Opower(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1596]),
[final] ).
cnf(i_0_2798,plain,
( c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(c_Nat_OSuc,X3)),c_Groups_Oone__class_Oone(X1))
| ~ class_Rings_Olinordered__semidom(X1)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Oone__class_Oone(X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1597]),
[final] ).
cnf(i_0_2799,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X2),X3),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X3),X1)))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
| ~ class_Rings_Ocomm__semiring__1(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1598]),
[final] ).
cnf(i_0_2800,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X4)) = hAPP(hAPP(c_Power_Opower__class_Opower(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3)),X4)
| ~ class_Groups_Omonoid__mult(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1599]),
[final] ).
cnf(i_0_2801,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3)),X4) = hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X4))
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1600]),
[final] ).
cnf(i_0_2802,plain,
( c_Divides_Odiv__class_Omod(X1,hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2),X3) = c_Divides_Odiv__class_Omod(X1,hAPP(c_Groups_Ouminus__class_Ouminus(X1),c_Divides_Odiv__class_Omod(X1,X2,X3)),X3)
| ~ class_Divides_Oring__div(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1601]),
[final] ).
cnf(i_0_2803,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X3),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X3),X2))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X3) ),
inference(split_conjunct,[status(thm)],[i_0_1602]),
[final] ).
cnf(i_0_2804,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X3))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_1579]),
[final] ).
cnf(i_0_2805,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X3))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3) ),
inference(split_conjunct,[status(thm)],[i_0_1603]),
[final] ).
cnf(i_0_2806,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X1))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_1580]),
[final] ).
cnf(i_0_2807,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X2))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3) ),
inference(split_conjunct,[status(thm)],[i_0_1521]),
[final] ).
cnf(i_0_2808,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X2))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3) ),
inference(split_conjunct,[status(thm)],[i_0_1604]),
[final] ).
cnf(i_0_2809,plain,
( hAPP(c_Polynomial_Opoly(X1,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X1,X2,X3)),X4) = hAPP(c_Polynomial_Opoly(X1,X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X3),X4))
| ~ class_Rings_Ocomm__semiring__0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1605]),
[final] ).
cnf(i_0_2810,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2) ),
inference(split_conjunct,[status(thm)],[i_0_1606]),
[final] ).
cnf(i_0_2811,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2) ),
inference(split_conjunct,[status(thm)],[i_0_1607]),
[final] ).
cnf(i_0_2812,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,esk16_3(X1,X2,X3),X1)
| X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hBOOL(hAPP(X3,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X2,X1))) ),
inference(split_conjunct,[status(thm)],[i_0_1355]),
[final] ).
cnf(i_0_2813,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X2),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X3)))
| ~ class_Rings_Ocomm__ring__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1608]),
[final] ).
cnf(i_0_2814,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X3),X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X3),X1))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X3) ),
inference(split_conjunct,[status(thm)],[i_0_1609]),
[final] ).
cnf(i_0_2815,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X3),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X4))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3,X4) ),
inference(split_conjunct,[status(thm)],[i_0_1610]),
[final] ).
cnf(i_0_2816,plain,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1)),X1) != c_Groups_Ozero__class_Ozero(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[i_0_1611]),
[final] ).
cnf(i_0_2817,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
inference(split_conjunct,[status(thm)],[i_0_1612]),
[final] ).
cnf(i_0_2818,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2) ),
inference(split_conjunct,[status(thm)],[i_0_1613]),
[final] ).
cnf(i_0_2819,plain,
( c_Divides_Odiv__class_Odiv(X1,hAPP(c_Groups_Ouminus__class_Ouminus(X1),X3),X2) = hAPP(c_Groups_Ouminus__class_Ouminus(X1),c_Divides_Odiv__class_Odiv(X1,X3,X2))
| ~ class_Divides_Oring__div(X1)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1614]),
[final] ).
cnf(i_0_2820,plain,
( c_Divides_Odiv__class_Odiv(X1,X3,hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)) = hAPP(c_Groups_Ouminus__class_Ouminus(X1),c_Divides_Odiv__class_Odiv(X1,X3,X2))
| ~ class_Divides_Oring__div(X1)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1615]),
[final] ).
cnf(i_0_2821,plain,
( c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2)),X2) ),
inference(split_conjunct,[status(thm)],[i_0_1616]),
[final] ).
cnf(i_0_2822,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),X3))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),X2))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1617]),
[final] ).
cnf(i_0_2823,plain,
( c_Divides_Odiv__class_Omod(X1,c_Divides_Odiv__class_Omod(X1,X4,X3),X2) = c_Divides_Odiv__class_Omod(X1,X4,X2)
| ~ class_Divides_Osemiring__div(X1)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1618]),
[final] ).
cnf(i_0_2824,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X1)),X2),hAPP(hAPP(c_Polynomial_Osmult(X1),X3),X4)) = hAPP(hAPP(c_Polynomial_Osmult(X1),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X1)),X2),X4))
| ~ class_Rings_Ocomm__semiring__0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1619]),
[final] ).
cnf(i_0_2825,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),c_Groups_Oone__class_Oone(X1)),c_Groups_Oone__class_Oone(X1))),X2)
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1620]),
[final] ).
cnf(i_0_2826,plain,
( c_Divides_Odiv__class_Odiv(tc_Int_Oint,X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X3),X1)) = c_Divides_Odiv__class_Odiv(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X2,X3),X1)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1) ),
inference(split_conjunct,[status(thm)],[i_0_1621]),
[final] ).
cnf(i_0_2827,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X3),X3)) = c_Groups_Ozero__class_Ozero(X2)
| X1 != c_Groups_Ozero__class_Ozero(X2)
| X3 != c_Groups_Ozero__class_Ozero(X2)
| ~ class_Rings_Olinordered__ring__strict(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1474]),
[final] ).
cnf(i_0_2828,plain,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X3)
| ~ c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X3),X2),c_Groups_Ozero__class_Ozero(X1))
| ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1622]),
[final] ).
cnf(i_0_2829,plain,
( c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X3),c_Groups_Ozero__class_Ozero(X1))
| ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1622]),
[final] ).
cnf(i_0_2830,plain,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X3),X2),c_Groups_Ozero__class_Ozero(X1))
| ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1622]),
[final] ).
cnf(i_0_2831,plain,
( c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X3))
| ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1623]),
[final] ).
cnf(i_0_2832,plain,
( c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X3),X2))
| ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1623]),
[final] ).
cnf(i_0_2833,plain,
( c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X3)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X3))
| ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1623]),
[final] ).
cnf(i_0_2834,plain,
( c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X3)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X3),X2))
| ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1623]),
[final] ).
cnf(i_0_2835,plain,
( c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| c_Orderings_Oord__class_Oless(X1,X3,c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X3),c_Groups_Ozero__class_Ozero(X1))
| ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1622]),
[final] ).
cnf(i_0_2836,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X2,X3)) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X3)),
inference(split_conjunct,[status(thm)],[i_0_1624]),
[final] ).
cnf(i_0_2837,plain,
( c_Orderings_Oord__class_Oless(X1,X3,c_Groups_Ozero__class_Ozero(X1))
| c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X3)
| c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X4),X3),X2)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1393]),
[final] ).
cnf(i_0_2838,plain,
( c_Orderings_Oord__class_Oless(X1,X3,c_Groups_Ozero__class_Ozero(X1))
| c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X3)
| c_Orderings_Oord__class_Oless(X1,X2,hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X4),X3))
| ~ c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1394]),
[final] ).
cnf(i_0_2839,plain,
( hAPP(c_Polynomial_Ocoeff(X1,hAPP(hAPP(c_Polynomial_Osmult(X1),X2),X3)),X4) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),hAPP(c_Polynomial_Ocoeff(X1,X3),X4))
| ~ class_Rings_Ocomm__semiring__0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1625]),
[final] ).
cnf(i_0_2840,plain,
( hAPP(c_Polynomial_Opoly(X1,hAPP(hAPP(c_Polynomial_Osmult(X1),X2),X3)),X4) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),hAPP(c_Polynomial_Opoly(X1,X3),X4))
| ~ class_Rings_Ocomm__semiring__0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1626]),
[final] ).
cnf(i_0_2841,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,X1)),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,X2)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1549]),
[final] ).
cnf(i_0_2842,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,X1)),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,X2)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1550]),
[final] ).
cnf(i_0_2843,plain,
( hAPP(c_Polynomial_Opoly(X1,c_Polynomial_Opcompose(X1,X2,X3)),X4) = hAPP(c_Polynomial_Opoly(X1,X2),hAPP(c_Polynomial_Opoly(X1,X3),X4))
| ~ class_Rings_Ocomm__semiring__0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1627]),
[final] ).
cnf(i_0_2844,plain,
( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X2),X1) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),c_Groups_Oone__class_Oone(tc_Nat_Onat)))) ),
inference(split_conjunct,[status(thm)],[i_0_1628]),
[final] ).
cnf(i_0_2845,plain,
c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2)),X2) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X1),X2),
inference(split_conjunct,[status(thm)],[i_0_1629]),
[final] ).
cnf(i_0_2846,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X1)),X2))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1567]),
[final] ).
cnf(i_0_2847,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X3),X2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1630]),
[final] ).
cnf(i_0_2848,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X3),X2))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2),X3) ),
inference(split_conjunct,[status(thm)],[i_0_1630]),
[final] ).
cnf(i_0_2849,plain,
( c_Orderings_Oord__class_Oless(X1,X3,X2)
| ~ class_Fields_Olinordered__field(X1)
| ~ c_Orderings_Oord__class_Oless(X1,hAPP(c_Rings_Oinverse__class_Oinverse(X1),X2),hAPP(c_Rings_Oinverse__class_Oinverse(X1),X3))
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2) ),
inference(split_conjunct,[status(thm)],[i_0_1631]),
[final] ).
cnf(i_0_2850,plain,
( c_Orderings_Oord__class_Oless(X1,X3,X2)
| ~ class_Fields_Olinordered__field(X1)
| ~ c_Orderings_Oord__class_Oless(X1,hAPP(c_Rings_Oinverse__class_Oinverse(X1),X2),hAPP(c_Rings_Oinverse__class_Oinverse(X1),X3))
| ~ c_Orderings_Oord__class_Oless(X1,X3,c_Groups_Ozero__class_Ozero(X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1632]),
[final] ).
cnf(i_0_2851,plain,
( c_Divides_Odiv__class_Omod(X1,hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2),X3) = c_Divides_Odiv__class_Omod(X1,hAPP(c_Groups_Ouminus__class_Ouminus(X1),X4),X3)
| ~ class_Divides_Oring__div(X1)
| c_Divides_Odiv__class_Omod(X1,X2,X3) != c_Divides_Odiv__class_Omod(X1,X4,X3) ),
inference(split_conjunct,[status(thm)],[i_0_1633]),
[final] ).
cnf(i_0_2852,plain,
hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X3)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X2),X3),
inference(split_conjunct,[status(thm)],[i_0_1634]),
[final] ).
cnf(i_0_2853,plain,
hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3),X2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),X3),
inference(split_conjunct,[status(thm)],[i_0_1635]),
[final] ).
cnf(i_0_2854,plain,
hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),X2)),X3) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X3)),
inference(split_conjunct,[status(thm)],[i_0_1636]),
[final] ).
cnf(i_0_2855,plain,
hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X1),X2)),X3) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X3)),
inference(split_conjunct,[status(thm)],[i_0_1637]),
[final] ).
cnf(i_0_2856,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X2)),X3) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X3)),
inference(split_conjunct,[status(thm)],[i_0_1638]),
[final] ).
cnf(i_0_2857,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2)),X3) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X3)),
inference(split_conjunct,[status(thm)],[i_0_1639]),
[final] ).
cnf(i_0_2858,plain,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X2)),X3) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X3)),
inference(split_conjunct,[status(thm)],[i_0_1640]),
[final] ).
cnf(i_0_2859,plain,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)),X3) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X3)),
inference(split_conjunct,[status(thm)],[i_0_1641]),
[final] ).
cnf(i_0_2860,plain,
( c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X3),c_Groups_Ozero__class_Ozero(X1))
| ~ class_Fields_Olinordered__field(X1)
| ~ c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X3) ),
inference(split_conjunct,[status(thm)],[i_0_1642]),
[final] ).
cnf(i_0_2861,plain,
( c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X3),c_Groups_Ozero__class_Ozero(X1))
| ~ class_Fields_Olinordered__field(X1)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ c_Orderings_Oord__class_Oless(X1,X3,c_Groups_Ozero__class_Ozero(X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1643]),
[final] ).
cnf(i_0_2862,plain,
( c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X3),c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X3)
| ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1622]),
[final] ).
cnf(i_0_2863,plain,
( c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X3),c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ c_Orderings_Oord__class_Oless(X1,X3,c_Groups_Ozero__class_Ozero(X1))
| ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1622]),
[final] ).
cnf(i_0_2864,plain,
( c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),c_Groups_Ozero__class_Ozero(X1))
| ~ class_Rings_Olinordered__semiring__strict(X1)
| ~ c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X3) ),
inference(split_conjunct,[status(thm)],[i_0_1644]),
[final] ).
cnf(i_0_2865,plain,
( c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),c_Groups_Ozero__class_Ozero(X1))
| ~ class_Rings_Olinordered__semiring__strict(X1)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ c_Orderings_Oord__class_Oless(X1,X3,c_Groups_Ozero__class_Ozero(X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1645]),
[final] ).
cnf(i_0_2866,plain,
( c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X2),c_Groups_Ozero__class_Ozero(X1))
| ~ class_Rings_Olinordered__semiring__strict(X1)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ c_Orderings_Oord__class_Oless(X1,X3,c_Groups_Ozero__class_Ozero(X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1646]),
[final] ).
cnf(i_0_2867,plain,
( c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3),c_Groups_Ozero__class_Ozero(X1))
| ~ class_Groups_Oordered__comm__monoid__add(X1)
| ~ c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless(X1,X3,c_Groups_Ozero__class_Ozero(X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1647]),
[final] ).
cnf(i_0_2868,plain,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3))
| ~ class_Rings_Olinordered__semidom(X1)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),X2)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),X3) ),
inference(split_conjunct,[status(thm)],[i_0_1648]),
[final] ).
cnf(i_0_2869,plain,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X3))
| ~ class_Fields_Olinordered__field(X1)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X3) ),
inference(split_conjunct,[status(thm)],[i_0_1649]),
[final] ).
cnf(i_0_2870,plain,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X3))
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X3)
| ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1623]),
[final] ).
cnf(i_0_2871,plain,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3))
| ~ class_Rings_Olinordered__semiring__strict(X1)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X3) ),
inference(split_conjunct,[status(thm)],[i_0_1650]),
[final] ).
cnf(i_0_2872,plain,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3))
| ~ class_Groups_Oordered__comm__monoid__add(X1)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X3) ),
inference(split_conjunct,[status(thm)],[i_0_1651]),
[final] ).
cnf(i_0_2873,plain,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X3))
| ~ class_Fields_Olinordered__field(X1)
| ~ c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless(X1,X3,c_Groups_Ozero__class_Ozero(X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1652]),
[final] ).
cnf(i_0_2874,plain,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X3))
| ~ c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless(X1,X3,c_Groups_Ozero__class_Ozero(X1))
| ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1623]),
[final] ).
cnf(i_0_2875,plain,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3))
| ~ class_Rings_Olinordered__ring__strict(X1)
| ~ c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless(X1,X3,c_Groups_Ozero__class_Ozero(X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1653]),
[final] ).
cnf(i_0_2876,plain,
c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,X1),X2) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,X2)),X2),
inference(split_conjunct,[status(thm)],[i_0_1654]),
[final] ).
cnf(i_0_2877,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X2),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X3)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X2),X3))
| ~ class_Rings_Ocomm__ring__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1608]),
[final] ).
cnf(i_0_2878,plain,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3))
| ~ class_Rings_Olinordered__semidom(X1)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),X2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3) ),
inference(split_conjunct,[status(thm)],[i_0_1655]),
[final] ).
cnf(i_0_2879,plain,
( c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X4),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X3),X4))
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(X1)
| ~ c_Orderings_Oord__class_Oless(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_1656]),
[final] ).
cnf(i_0_2880,plain,
( c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X4),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X3),X4))
| ~ c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1543]),
[final] ).
cnf(i_0_2881,plain,
( c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X4),X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X4),X3))
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(X1)
| ~ c_Orderings_Oord__class_Oless(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_1657]),
[final] ).
cnf(i_0_2882,plain,
( c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X4),X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X4),X3))
| ~ c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1545]),
[final] ).
cnf(i_0_2883,plain,
( c_Polynomial_Odegree(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X1)),X2),X3)) = c_Polynomial_Odegree(X1,X3)
| ~ class_Groups_Ocomm__monoid__add(X1)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(X1,X2),c_Polynomial_Odegree(X1,X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1658]),
[final] ).
cnf(i_0_2884,plain,
( c_Polynomial_Odegree(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X1)),X3),X2)) = c_Polynomial_Odegree(X1,X3)
| ~ class_Groups_Ocomm__monoid__add(X1)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(X1,X2),c_Polynomial_Odegree(X1,X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1659]),
[final] ).
cnf(i_0_2885,plain,
( c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2)),X1) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X1) ),
inference(split_conjunct,[status(thm)],[i_0_1660]),
[final] ).
cnf(i_0_2886,plain,
( c_Orderings_Oord__class_Oless(X1,X3,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X4))
| ~ class_Rings_Olinordered__semidom(X1)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ c_Orderings_Oord__class_Oless(X1,X3,X4) ),
inference(split_conjunct,[status(thm)],[i_0_1661]),
[final] ).
cnf(i_0_2887,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X1),X2))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X1),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X2))) ),
inference(split_conjunct,[status(thm)],[i_0_1662]),
[final] ).
cnf(i_0_2888,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1663]),
[final] ).
cnf(i_0_2889,plain,
( c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(X1),hAPP(hAPP(c_Polynomial_Osmult(X1),X2),X3),X4) = hAPP(hAPP(c_Polynomial_Osmult(X1),X2),c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(X1),X3,X4))
| ~ class_Fields_Ofield(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1664]),
[final] ).
cnf(i_0_2890,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3)),X2) = hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(c_Nat_OSuc,X3))
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1665]),
[final] ).
cnf(i_0_2891,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(c_Nat_OSuc,X3)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3)),X2)
| ~ class_Groups_Omonoid__mult(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1666]),
[final] ).
cnf(i_0_2892,plain,
( c_Deriv_Oderiv(X1,hAPP(c_COMBK(X1,X1),X2),X3,c_Groups_Ozero__class_Ozero(X1))
| ~ class_RealVector_Oreal__normed__field(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1667]),
[final] ).
cnf(i_0_2893,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2) ),
inference(split_conjunct,[status(thm)],[i_0_1613]),
[final] ).
cnf(i_0_2894,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2) ),
inference(split_conjunct,[status(thm)],[i_0_1668]),
[final] ).
cnf(i_0_2895,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
inference(split_conjunct,[status(thm)],[i_0_1612]),
[final] ).
cnf(i_0_2896,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),c_Divides_Odiv__class_Odiv(X1,X3,X2)) = X3
| ~ class_Divides_Osemiring__div(X1)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1669]),
[final] ).
cnf(i_0_2897,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X2),X1)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X2) ),
inference(split_conjunct,[status(thm)],[i_0_1670]),
[final] ).
cnf(i_0_2898,plain,
( hAPP(c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X1)),hAPP(hAPP(c_Polynomial_OpCons(X1),X2),X3)) = hAPP(hAPP(c_Polynomial_OpCons(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X1)),X3))
| ~ class_Groups_Oab__group__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1671]),
[final] ).
cnf(i_0_2899,plain,
( hAPP(c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X1)),hAPP(hAPP(c_Polynomial_OpCons(X1),X2),X3)) = hAPP(hAPP(c_Polynomial_OpCons(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X1)),X3))
| ~ class_Groups_Oab__group__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1672]),
[final] ).
cnf(i_0_2900,plain,
( c_Polynomial_Opoly__gcd(X1,c_Polynomial_Opoly__gcd(X1,X2,X3),X4) = c_Polynomial_Opoly__gcd(X1,X2,c_Polynomial_Opoly__gcd(X1,X3,X4))
| ~ class_Fields_Ofield(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1673]),
[final] ).
cnf(i_0_2901,plain,
( c_Polynomial_Opoly__gcd(X1,X2,c_Polynomial_Opoly__gcd(X1,X3,X4)) = c_Polynomial_Opoly__gcd(X1,X3,c_Polynomial_Opoly__gcd(X1,X2,X4))
| ~ class_Fields_Ofield(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1674]),
[final] ).
cnf(i_0_2902,plain,
( c_Transcendental_Odiffs(X1,X2,X3) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Nat_Osemiring__1__class_Oof__nat(X1,hAPP(c_Nat_OSuc,X3))),hAPP(X2,hAPP(c_Nat_OSuc,X3)))
| ~ class_Rings_Oring__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1675]),
[final] ).
cnf(i_0_2903,plain,
( c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(X1),X3,X2)
| ~ c_Polynomial_Opos__poly(X1,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X1)),X2),X3))
| ~ class_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1676]),
[final] ).
cnf(i_0_2904,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X2),X1),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),X3)))
| X1 != c_Groups_Oone__class_Oone(X2)
| ~ class_Rings_Ocomm__semiring__1(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1598]),
[final] ).
cnf(i_0_2905,plain,
( X1 = c_Groups_Ozero__class_Ozero(X2)
| c_Divides_Odiv__class_Odiv(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X4)) = c_Divides_Odiv__class_Odiv(X2,X3,X4)
| ~ class_Divides_Osemiring__div(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1677]),
[final] ).
cnf(i_0_2906,plain,
( X2 = c_Groups_Ozero__class_Ozero(X1)
| c_Divides_Odiv__class_Odiv(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4)) = c_Divides_Odiv__class_Odiv(X1,X3,X4)
| ~ class_Divides_Osemiring__div(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1678]),
[final] ).
cnf(i_0_2907,plain,
( X2 = c_Groups_Ozero__class_Ozero(X1)
| c_Divides_Odiv__class_Odiv(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X2)) = c_Divides_Odiv__class_Odiv(X1,X3,X4)
| ~ class_Divides_Osemiring__div(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1679]),
[final] ).
cnf(i_0_2908,plain,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X2))
| ~ class_Groups_Olinordered__ab__group__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1680]),
[final] ).
cnf(i_0_2909,plain,
( c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X2),c_Groups_Ozero__class_Ozero(X1))
| ~ class_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1681]),
[final] ).
cnf(i_0_2910,plain,
( c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X2),c_Groups_Ozero__class_Ozero(X1))
| ~ class_Groups_Olinordered__ab__group__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1682]),
[final] ).
cnf(i_0_2911,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2) ),
inference(split_conjunct,[status(thm)],[i_0_1683]),
[final] ).
cnf(i_0_2912,plain,
( hAPP(hAPP(c_Polynomial_Osmult(X1),X2),c_Polynomial_Omonom(X1,X3,X4)) = c_Polynomial_Omonom(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),X4)
| ~ class_Rings_Ocomm__semiring__0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1684]),
[final] ).
cnf(i_0_2913,plain,
( c_Polynomial_Opos__poly(X1,X2)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),hAPP(c_Polynomial_Ocoeff(X1,X2),c_Polynomial_Odegree(X1,X2)))
| ~ class_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1685]),
[final] ).
cnf(i_0_2914,plain,
( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X2),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1686]),
[final] ).
cnf(i_0_2915,plain,
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X2),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1687]),
[final] ).
cnf(i_0_2916,plain,
( X2 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3)
| X3 = c_Groups_Ozero__class_Ozero(X1)
| c_Divides_Odiv__class_Odiv(X1,X2,X3) != X4
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X3),X2))
| ~ class_Divides_Osemiring__div(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1688]),
[final] ).
cnf(i_0_2917,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X2),X1),X2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2) ),
inference(split_conjunct,[status(thm)],[i_0_1689]),
[final] ).
cnf(i_0_2918,plain,
( c_Orderings_Oord__class_Oless(X1,hAPP(c_Rings_Oinverse__class_Oinverse(X1),X3),hAPP(c_Rings_Oinverse__class_Oinverse(X1),X2))
| ~ class_Fields_Olinordered__field(X1)
| ~ c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2) ),
inference(split_conjunct,[status(thm)],[i_0_1690]),
[final] ).
cnf(i_0_2919,plain,
( c_Orderings_Oord__class_Oless(X1,hAPP(c_Rings_Oinverse__class_Oinverse(X1),X3),hAPP(c_Rings_Oinverse__class_Oinverse(X1),X2))
| ~ class_Fields_Olinordered__field(X1)
| ~ c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless(X1,X3,c_Groups_Ozero__class_Ozero(X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1691]),
[final] ).
cnf(i_0_2920,plain,
( c_Divides_Odiv__class_Odiv(X2,X1,X4) = X3
| X4 = c_Groups_Ozero__class_Ozero(X2)
| X1 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X3),X4)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X2),X4),X1))
| ~ class_Divides_Osemiring__div(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1688]),
[final] ).
cnf(i_0_2921,plain,
( X2 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))
| X3 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))
| c_Polynomial_Odegree(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X1)),X2),X3)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Polynomial_Odegree(X1,X2)),c_Polynomial_Odegree(X1,X3))
| ~ class_Rings_Oidom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1692]),
[final] ).
cnf(i_0_2922,plain,
( c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X2),X3),c_Groups_Ozero__class_Ozero(X1))
| ~ class_Groups_Oordered__ab__group__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1693]),
[final] ).
cnf(i_0_2923,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)))
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1694]),
[final] ).
cnf(i_0_2924,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X2)))
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1695]),
[final] ).
cnf(i_0_2925,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X3),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X3))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_1696]),
[final] ).
cnf(i_0_2926,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X3),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X3))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_1697]),
[final] ).
cnf(i_0_2927,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3),X2))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_1585]),
[final] ).
cnf(i_0_2928,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4))
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1698]),
[final] ).
cnf(i_0_2929,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X3),X4)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X3),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X4))
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1699]),
[final] ).
cnf(i_0_2930,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)),X3)) = X3
| ~ class_Groups_Ogroup__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1700]),
[final] ).
cnf(i_0_2931,plain,
( hAPP(c_Polynomial_Ocoeff(X1,hAPP(hAPP(c_Polynomial_OpCons(X1),X2),X3)),hAPP(c_Nat_OSuc,X4)) = hAPP(c_Polynomial_Ocoeff(X1,X3),X4)
| ~ class_Groups_Ozero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1701]),
[final] ).
cnf(i_0_2932,plain,
( c_Orderings_Oord__class_Oless(X1,X4,X5)
| ~ c_Orderings_Oord__class_Oless(X1,X2,X3)
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X2),X3) != hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X4),X5)
| ~ class_Groups_Oordered__ab__group__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1702]),
[final] ).
cnf(i_0_2933,plain,
( c_Orderings_Oord__class_Oless(X1,X4,X5)
| ~ c_Orderings_Oord__class_Oless(X1,X2,X3)
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X4),X5) != hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X2),X3)
| ~ class_Groups_Oordered__ab__group__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1702]),
[final] ).
cnf(i_0_2934,plain,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(c_Nat_OSuc,X3)))
| ~ class_Rings_Olinordered__semidom(X1)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),X2) ),
inference(split_conjunct,[status(thm)],[i_0_1703]),
[final] ).
cnf(i_0_2935,plain,
( hAPP(c_Nat_OSuc,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,X2)) = X2
| c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,X1),X2) = hAPP(c_Nat_OSuc,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1704]),
[final] ).
cnf(i_0_2936,plain,
hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,X2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),c_Groups_Oone__class_Oone(tc_Nat_Onat))),X2),
inference(split_conjunct,[status(thm)],[i_0_1705]),
[final] ).
cnf(i_0_2937,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X1),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X2)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1662]),
[final] ).
cnf(i_0_2938,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = hAPP(hAPP(c_Power_Opower__class_Opower(X2),X3),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))
| X1 != hAPP(c_Groups_Ouminus__class_Ouminus(X2),X3)
| ~ class_Rings_Oidom(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1558]),
[final] ).
cnf(i_0_2939,plain,
( X2 = c_Groups_Ozero__class_Ozero(X1)
| X3 = c_Groups_Ozero__class_Ozero(X1)
| hAPP(c_Rings_Oinverse__class_Oinverse(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(c_Rings_Oinverse__class_Oinverse(X1),X3)),hAPP(c_Rings_Oinverse__class_Oinverse(X1),X2))
| ~ class_Rings_Odivision__ring(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1706]),
[final] ).
cnf(i_0_2940,plain,
( X2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,hAPP(c_Nat_OSuc,esk17_2(X2,X1))))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_1707]),
[final] ).
cnf(i_0_2941,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X2,X1)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X2),c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X1)),
inference(split_conjunct,[status(thm)],[i_0_1708]),
[final] ).
cnf(i_0_2942,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X2,X1)) = X2
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1709]),
[final] ).
cnf(i_0_2943,plain,
( X1 = X2
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),X2))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X2),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1710]),
[final] ).
cnf(i_0_2944,plain,
( X2 = X1
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),X2))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X2),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1711]),
[final] ).
cnf(i_0_2945,plain,
( X2 = X1
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),X2))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X2),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1712]),
[final] ).
cnf(i_0_2946,plain,
( X2 = X1
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),X2))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X2),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1713]),
[final] ).
cnf(i_0_2947,plain,
( X1 = X2
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),X2))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X2),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1714]),
[final] ).
cnf(i_0_2948,plain,
( X2 = X1
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),X2))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X2),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1715]),
[final] ).
cnf(i_0_2949,plain,
( X2 = X1
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),X2))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X2),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1716]),
[final] ).
cnf(i_0_2950,plain,
( X1 = X2
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),X2))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X2),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1717]),
[final] ).
cnf(i_0_2951,plain,
( X1 = X2
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),X2))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X2),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1718]),
[final] ).
cnf(i_0_2952,plain,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),hAPP(c_Rings_Oinverse__class_Oinverse(X1),X2))
| ~ class_Fields_Olinordered__field(X1)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Oone__class_Oone(X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1719]),
[final] ).
cnf(i_0_2953,plain,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),hAPP(c_Rings_Oinverse__class_Oinverse(X1),X2))
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Oone__class_Oone(X1))
| ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1720]),
[final] ).
cnf(i_0_2954,plain,
( c_Divides_Odiv__class_Odiv(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X1),X2) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X2))
| X2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
inference(split_conjunct,[status(thm)],[i_0_1422]),
[final] ).
cnf(i_0_2955,plain,
( c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X2)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X2))
| X2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
inference(split_conjunct,[status(thm)],[i_0_1423]),
[final] ).
cnf(i_0_2956,plain,
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X3)) = hAPP(c_Groups_Ouminus__class_Ouminus(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X2),X3))
| ~ class_Groups_Oab__group__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1721]),
[final] ).
cnf(i_0_2957,plain,
( hAPP(c_Rings_Oinverse__class_Oinverse(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(c_Rings_Oinverse__class_Oinverse(X1),X2)),hAPP(c_Rings_Oinverse__class_Oinverse(X1),X3))
| ~ class_Fields_Ofield__inverse__zero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1722]),
[final] ).
cnf(i_0_2958,plain,
( hAPP(c_Groups_Ouminus__class_Ouminus(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X3))
| ~ class_Groups_Oab__group__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1723]),
[final] ).
cnf(i_0_2959,plain,
( hAPP(c_Groups_Ouminus__class_Ouminus(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X3)),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2))
| ~ class_Groups_Ogroup__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1724]),
[final] ).
cnf(i_0_2960,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X2),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1725]),
[final] ).
cnf(i_0_2961,plain,
( c_Deriv_Oderiv(X1,hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3,X2)
| ~ class_RealVector_Oreal__normed__field(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1726]),
[final] ).
cnf(i_0_2962,plain,
( hBOOL(hAPP(X2,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X3,X1)))
| X1 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(X2,X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1355]),
[final] ).
cnf(i_0_2963,plain,
( X2 = X3
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1)),X2) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1)),X3) ),
inference(split_conjunct,[status(thm)],[i_0_1727]),
[final] ).
cnf(i_0_2964,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2)
| X1 = X2
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),c_Groups_Oone__class_Oone(tc_Int_Oint))) ),
inference(split_conjunct,[status(thm)],[i_0_1728]),
[final] ).
cnf(i_0_2965,plain,
( c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X1),X2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X2),c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1729]),
[final] ).
cnf(i_0_2966,plain,
( X2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1730]),
[final] ).
cnf(i_0_2967,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
| X2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1731]),
[final] ).
cnf(i_0_2968,plain,
hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,X2)) = hAPP(c_Nat_Onat_Onat__case(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_COMBI(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),X2)),
inference(split_conjunct,[status(thm)],[i_0_1732]),
[final] ).
cnf(i_0_2969,plain,
( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X5) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X4),X3)
| X3 = c_Groups_Ozero__class_Ozero(X1)
| X5 = c_Groups_Ozero__class_Ozero(X1)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X5)
| ~ class_Fields_Ofield(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1733]),
[final] ).
cnf(i_0_2970,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X5) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3)
| X5 = c_Groups_Ozero__class_Ozero(X1)
| X3 = c_Groups_Ozero__class_Ozero(X1)
| hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X3) != hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X4),X5)
| ~ class_Fields_Ofield(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1733]),
[final] ).
cnf(i_0_2971,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1683]),
[final] ).
cnf(i_0_2972,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1683]),
[final] ).
cnf(i_0_2973,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X1),X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
inference(split_conjunct,[status(thm)],[i_0_1734]),
[final] ).
cnf(i_0_2974,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1735]),
[final] ).
cnf(i_0_2975,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3,X4)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3),X2) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X4) ),
inference(split_conjunct,[status(thm)],[i_0_1736]),
[final] ).
cnf(i_0_2976,plain,
( c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(X1),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X1)),X2),X3) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X1)),c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(X1),X2,X3))
| ~ class_Fields_Ofield(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1737]),
[final] ).
cnf(i_0_2977,plain,
( c_Divides_Odiv__class_Odiv(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X4)) = c_Groups_Ozero__class_Ozero(X2)
| X1 != c_Groups_Ozero__class_Ozero(X2)
| ~ class_Divides_Osemiring__div(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1677]),
[final] ).
cnf(i_0_2978,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X3)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2),X3) ),
inference(split_conjunct,[status(thm)],[i_0_1738]),
[final] ).
cnf(i_0_2979,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,X2)),X1)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1) ),
inference(split_conjunct,[status(thm)],[i_0_1739]),
[final] ).
cnf(i_0_2980,plain,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X3)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X3)),
inference(split_conjunct,[status(thm)],[i_0_1740]),
[final] ).
cnf(i_0_2981,plain,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X3)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X3)),
inference(split_conjunct,[status(thm)],[i_0_1741]),
[final] ).
cnf(i_0_2982,plain,
( c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X1,hAPP(hAPP(c_Polynomial_OpCons(X1),X2),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))),X3) = hAPP(hAPP(c_Polynomial_OpCons(X1),X2),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)))
| ~ class_Rings_Ocomm__semiring__0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1742]),
[final] ).
cnf(i_0_2983,plain,
( hAPP(hAPP(c_Polynomial_Osmult(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)),X3) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X1)),hAPP(hAPP(c_Polynomial_Osmult(X1),X2),X3))
| ~ class_Rings_Ocomm__ring(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1743]),
[final] ).
cnf(i_0_2984,plain,
( hAPP(c_Polynomial_Ocoeff(X1,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X1)),X2)),X3) = hAPP(c_Groups_Ouminus__class_Ouminus(X1),hAPP(c_Polynomial_Ocoeff(X1,X2),X3))
| ~ class_Groups_Oab__group__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1744]),
[final] ).
cnf(i_0_2985,plain,
( hAPP(c_Polynomial_Opoly(X1,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X1)),X2)),X3) = hAPP(c_Groups_Ouminus__class_Ouminus(X1),hAPP(c_Polynomial_Opoly(X1,X2),X3))
| ~ class_Rings_Ocomm__ring(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1745]),
[final] ).
cnf(i_0_2986,plain,
c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X2)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X1),X2)),
inference(split_conjunct,[status(thm)],[i_0_1746]),
[final] ).
cnf(i_0_2987,plain,
( X3 = X4
| hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3) != hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X4)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),X2)
| ~ class_Rings_Olinordered__semidom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1747]),
[final] ).
cnf(i_0_2988,plain,
( c_Polynomial_Opos__poly(X1,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X1)),X3),X2))
| ~ c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(X1),X2,X3)
| ~ class_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1676]),
[final] ).
cnf(i_0_2989,plain,
( c_Orderings_Oord__class_Oless(X1,X3,X2)
| ~ c_Orderings_Oord__class_Oless(X1,hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X3))
| ~ class_Groups_Oordered__ab__group__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1748]),
[final] ).
cnf(i_0_2990,plain,
( X1 = X2
| hAPP(c_Polynomial_Ocoeff(X3,c_Polynomial_Omonom(X3,X4,X1)),X2) = c_Groups_Ozero__class_Ozero(X3)
| ~ class_Groups_Ozero(X3) ),
inference(split_conjunct,[status(thm)],[i_0_1749]),
[final] ).
cnf(i_0_2991,plain,
( c_Deriv_Oderiv(X1,c_COMBI(X1),X2,c_Groups_Oone__class_Oone(X1))
| ~ class_RealVector_Oreal__normed__field(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1750]),
[final] ).
cnf(i_0_2992,plain,
( c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X2),c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| ~ class_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1681]),
[final] ).
cnf(i_0_2993,plain,
( c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X2),c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| ~ class_Groups_Olinordered__ab__group__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1682]),
[final] ).
cnf(i_0_2994,plain,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3))
| ~ class_Rings_Olinordered__semidom(X1)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2) ),
inference(split_conjunct,[status(thm)],[i_0_1751]),
[final] ).
cnf(i_0_2995,plain,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X2))
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ class_Groups_Olinordered__ab__group__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1680]),
[final] ).
cnf(i_0_2996,plain,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| c_Polynomial_Opos__poly(X1,X3)
| ~ c_Polynomial_Opos__poly(X1,hAPP(hAPP(c_Polynomial_OpCons(X1),X2),X3))
| ~ class_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1752]),
[final] ).
cnf(i_0_2997,plain,
( hAPP(c_Polynomial_Ocoeff(X3,c_Polynomial_Omonom(X3,X4,X1)),X2) = X4
| X1 != X2
| ~ class_Groups_Ozero(X3) ),
inference(split_conjunct,[status(thm)],[i_0_1749]),
[final] ).
cnf(i_0_2998,plain,
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)),X3) = X2
| ~ class_Groups_Ogroup__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1753]),
[final] ).
cnf(i_0_2999,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X2),X3)),X3) = X2
| ~ class_Groups_Ogroup__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1754]),
[final] ).
cnf(i_0_3000,plain,
( ~ class_Rings_Olinordered__ring(X1)
| ~ c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X2),c_Groups_Ozero__class_Ozero(X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1755]),
[final] ).
cnf(i_0_3001,plain,
( X2 = c_Groups_Ozero__class_Ozero(X1)
| hAPP(c_Rings_Oinverse__class_Oinverse(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3)) = hAPP(hAPP(c_Power_Opower__class_Opower(X1),hAPP(c_Rings_Oinverse__class_Oinverse(X1),X2)),X3)
| ~ class_Rings_Odivision__ring(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1756]),
[final] ).
cnf(i_0_3002,plain,
( c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,X1),X2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(c_Nat_OSuc,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,X2)) != X2 ),
inference(split_conjunct,[status(thm)],[i_0_1704]),
[final] ).
cnf(i_0_3003,plain,
( c_Nat_Osemiring__1__class_Oof__nat__aux(X1,X2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3) = X3
| ~ class_Rings_Osemiring__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1757]),
[final] ).
cnf(i_0_3004,plain,
( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)),X3) = hAPP(c_Groups_Ouminus__class_Ouminus(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X3))
| ~ class_RealVector_Oreal__normed__field(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1758]),
[final] ).
cnf(i_0_3005,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)),X3) = hAPP(c_Groups_Ouminus__class_Ouminus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3))
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1759]),
[final] ).
cnf(i_0_3006,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)),X3) = hAPP(c_Groups_Ouminus__class_Ouminus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3))
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1760]),
[final] ).
cnf(i_0_3007,plain,
( hAPP(c_Rings_Oinverse__class_Oinverse(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3)) = hAPP(hAPP(c_Power_Opower__class_Opower(X1),hAPP(c_Rings_Oinverse__class_Oinverse(X1),X2)),X3)
| ~ class_Rings_Odivision__ring__inverse__zero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1761]),
[final] ).
cnf(i_0_3008,plain,
( hAPP(c_Groups_Ouminus__class_Ouminus(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X3)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)),X3)
| ~ class_Rings_Odivision__ring(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1762]),
[final] ).
cnf(i_0_3009,plain,
( hAPP(c_Groups_Ouminus__class_Ouminus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)),X3)
| ~ class_Rings_Oring(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1763]),
[final] ).
cnf(i_0_3010,plain,
hAPP(hAPP(c_Power_Opower_Opower(X1,X2,X3),X4),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X2,
inference(split_conjunct,[status(thm)],[i_0_1764]),
[final] ).
cnf(i_0_3011,plain,
( c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X2),X3),c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ class_Groups_Oordered__ab__group__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1693]),
[final] ).
cnf(i_0_3012,plain,
( hAPP(hAPP(c_Polynomial_Osmult(X1),X2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X1)),X3)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X1)),hAPP(hAPP(c_Polynomial_Osmult(X1),X2),X3))
| ~ class_Rings_Ocomm__ring(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1765]),
[final] ).
cnf(i_0_3013,plain,
( X1 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) ),
inference(split_conjunct,[status(thm)],[i_0_1766]),
[final] ).
cnf(i_0_3014,plain,
c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2))),
inference(split_conjunct,[status(thm)],[i_0_1767]),
[final] ).
cnf(i_0_3015,plain,
c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X1))),
inference(split_conjunct,[status(thm)],[i_0_1768]),
[final] ).
cnf(i_0_3016,plain,
( c_Polynomial_Omonom(X1,X2,hAPP(c_Nat_OSuc,X3)) = hAPP(hAPP(c_Polynomial_OpCons(X1),c_Groups_Ozero__class_Ozero(X1)),c_Polynomial_Omonom(X1,X2,X3))
| ~ class_Groups_Ozero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1769]),
[final] ).
cnf(i_0_3017,plain,
( hAPP(c_Polynomial_Ocoeff(X1,hAPP(hAPP(c_Polynomial_OpCons(X1),X2),X3)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X2
| ~ class_Groups_Ozero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1770]),
[final] ).
cnf(i_0_3018,plain,
( hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = X1
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1) ),
inference(split_conjunct,[status(thm)],[i_0_1771]),
[final] ).
cnf(i_0_3019,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,X2) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),X2),X2) ),
inference(split_conjunct,[status(thm)],[i_0_1772]),
[final] ).
cnf(i_0_3020,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,X2) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),X2),X2) ),
inference(split_conjunct,[status(thm)],[i_0_1773]),
[final] ).
cnf(i_0_3021,plain,
hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X1)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X2)),
inference(split_conjunct,[status(thm)],[i_0_1774]),
[final] ).
cnf(i_0_3022,plain,
( X1 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| c_Polynomial_Opoly__gcd(X2,X3,X1) = c_Polynomial_Opoly__gcd(X2,X1,c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(X2),X3,X1))
| ~ class_Fields_Ofield(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1404]),
[final] ).
cnf(i_0_3023,plain,
( X2 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))
| c_Polynomial_Opoly__gcd(X1,X3,X2) = c_Polynomial_Opoly__gcd(X1,X2,c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(X1),X3,X2))
| ~ class_Fields_Ofield(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1775]),
[final] ).
cnf(i_0_3024,plain,
( c_Orderings_Oord__class_Oless(X1,hAPP(c_Groups_Ouminus__class_Ouminus(X1),X3),X2)
| ~ c_Orderings_Oord__class_Oless(X1,hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2),X3)
| ~ class_Groups_Oordered__ab__group__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1776]),
[final] ).
cnf(i_0_3025,plain,
( c_Orderings_Oord__class_Oless(X1,hAPP(c_Groups_Ouminus__class_Ouminus(X1),X3),X2)
| ~ c_Orderings_Oord__class_Oless(X1,hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2),X3)
| ~ class_Groups_Oordered__ab__group__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1776]),
[final] ).
cnf(i_0_3026,plain,
( c_Orderings_Oord__class_Oless(X1,X3,hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2))
| ~ c_Orderings_Oord__class_Oless(X1,X2,hAPP(c_Groups_Ouminus__class_Ouminus(X1),X3))
| ~ class_Groups_Oordered__ab__group__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1777]),
[final] ).
cnf(i_0_3027,plain,
( c_Orderings_Oord__class_Oless(X1,X3,hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2))
| ~ c_Orderings_Oord__class_Oless(X1,X2,hAPP(c_Groups_Ouminus__class_Ouminus(X1),X3))
| ~ class_Groups_Oordered__ab__group__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1777]),
[final] ).
cnf(i_0_3028,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X1),X1)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1) ),
inference(split_conjunct,[status(thm)],[i_0_1778]),
[final] ).
cnf(i_0_3029,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X2,X1),X1)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1) ),
inference(split_conjunct,[status(thm)],[i_0_1779]),
[final] ).
cnf(i_0_3030,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X1))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
inference(split_conjunct,[status(thm)],[i_0_1780]),
[final] ).
cnf(i_0_3031,plain,
c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,hAPP(c_Nat_OSuc,X1))),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,X2)),
inference(split_conjunct,[status(thm)],[i_0_1781]),
[final] ).
cnf(i_0_3032,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(c_Nat_OSuc,X1),X3)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_1782]),
[final] ).
cnf(i_0_3033,plain,
( c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(X1),X2,X3) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))
| ~ class_Fields_Ofield(X1)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(X1,X2),c_Polynomial_Odegree(X1,X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1783]),
[final] ).
cnf(i_0_3034,plain,
~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,X1),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,X2))),
inference(split_conjunct,[status(thm)],[i_0_1784]),
[final] ).
cnf(i_0_3035,plain,
( c_Nat_Osemiring__1__class_Oof__nat(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X3)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Nat_Osemiring__1__class_Oof__nat(X1,X2)),c_Nat_Osemiring__1__class_Oof__nat(X1,X3))
| ~ class_Rings_Osemiring__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1785]),
[final] ).
cnf(i_0_3036,plain,
( c_Nat_Osemiring__1__class_Oof__nat(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X3)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),c_Nat_Osemiring__1__class_Oof__nat(X1,X2)),c_Nat_Osemiring__1__class_Oof__nat(X1,X3))
| ~ class_Rings_Osemiring__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1786]),
[final] ).
cnf(i_0_3037,plain,
( X2 = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),esk12_2(X2,X1)))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_1787]),
[final] ).
cnf(i_0_3038,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)) = X3
| ~ class_Groups_Ogroup__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1788]),
[final] ).
cnf(i_0_3039,plain,
( hAPP(c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X1)),c_Polynomial_Omonom(X1,X2,X3)) = c_Polynomial_Omonom(X1,hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2),X3)
| ~ class_Groups_Oab__group__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1789]),
[final] ).
cnf(i_0_3040,plain,
c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X1),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X2)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2)),
inference(split_conjunct,[status(thm)],[i_0_1790]),
[final] ).
cnf(i_0_3041,plain,
( c_Polynomial_Opos__poly(X2,hAPP(hAPP(c_Polynomial_OpCons(X2),X3),X1))
| X1 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| ~ c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),X3)
| ~ class_Rings_Olinordered__idom(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1752]),
[final] ).
cnf(i_0_3042,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3)) = hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(c_Nat_OSuc,X3))
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1791]),
[final] ).
cnf(i_0_3043,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(c_Nat_OSuc,X3)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3))
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1792]),
[final] ).
cnf(i_0_3044,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(c_Nat_OSuc,X3)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3))
| ~ class_Power_Opower(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1793]),
[final] ).
cnf(i_0_3045,plain,
( X2 = X3
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X3)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1) ),
inference(split_conjunct,[status(thm)],[i_0_1794]),
[final] ).
cnf(i_0_3046,plain,
( X2 = c_Groups_Ozero__class_Ozero(X1)
| c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(X1),X3,hAPP(hAPP(c_Polynomial_Osmult(X1),X2),X4)) = c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(X1),X3,X4)
| ~ class_Fields_Ofield(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1795]),
[final] ).
cnf(i_0_3047,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,X1)
| X1 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,hAPP(c_Nat_OSuc,X3))) ),
inference(split_conjunct,[status(thm)],[i_0_1707]),
[final] ).
cnf(i_0_3048,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X1),X2))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1) ),
inference(split_conjunct,[status(thm)],[i_0_1730]),
[final] ).
cnf(i_0_3049,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X1),X2))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1) ),
inference(split_conjunct,[status(thm)],[i_0_1731]),
[final] ).
cnf(i_0_3050,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1) ),
inference(split_conjunct,[status(thm)],[i_0_1663]),
[final] ).
cnf(i_0_3051,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X1))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1) ),
inference(split_conjunct,[status(thm)],[i_0_1663]),
[final] ).
cnf(i_0_3052,plain,
( c_Orderings_Oord__class_Oless(X1,X2,X4)
| ~ class_Orderings_Opreorder(X1)
| ~ c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless(X1,X3,X4) ),
inference(split_conjunct,[status(thm)],[i_0_1796]),
[final] ).
cnf(i_0_3053,plain,
( c_Orderings_Oord__class_Oless(X1,X4,X3)
| ~ class_Orderings_Oorder(X1)
| ~ c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless(X1,X4,X2) ),
inference(split_conjunct,[status(thm)],[i_0_1797]),
[final] ).
cnf(i_0_3054,plain,
( c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(X1),X2,X3) = X2
| ~ class_Fields_Ofield(X1)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(X1,X2),c_Polynomial_Odegree(X1,X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1798]),
[final] ).
cnf(i_0_3055,plain,
( c_Divides_Odiv__class_Omod(X1,X3,X2) = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Divides_Osemiring__div(X1)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1799]),
[final] ).
cnf(i_0_3056,plain,
( c_Divides_Odiv__class_Omod(X1,X3,X2) = c_Groups_Ozero__class_Ozero(X1)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X2),X3))
| ~ class_Divides_Osemiring__div(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1800]),
[final] ).
cnf(i_0_3057,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),c_Groups_Oone__class_Oone(tc_Int_Oint)))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_1728]),
[final] ).
cnf(i_0_3058,plain,
( hAPP(hAPP(c_Polynomial_OpCons(X1),X2),X3) = c_Polynomial_OAbs__poly(X1,c_Nat_Onat_Onat__case(X1,X2,c_Polynomial_Ocoeff(X1,X3)))
| ~ class_Groups_Ozero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1801]),
[final] ).
cnf(i_0_3059,plain,
( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X1 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) ),
inference(split_conjunct,[status(thm)],[i_0_1802]),
[final] ).
cnf(i_0_3060,plain,
( X2 = c_Groups_Ozero__class_Ozero(X1)
| hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X3)),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X3),X2)
| ~ class_Rings_Odivision__ring(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1803]),
[final] ).
cnf(i_0_3061,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X1),X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_1734]),
[final] ).
cnf(i_0_3062,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X2),X1))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_1735]),
[final] ).
cnf(i_0_3063,plain,
( X2 = c_Groups_Ozero__class_Ozero(X1)
| c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ class_Fields_Olinordered__field(X1)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),hAPP(c_Rings_Oinverse__class_Oinverse(X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1804]),
[final] ).
cnf(i_0_3064,plain,
( X2 = c_Groups_Ozero__class_Ozero(X1)
| c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| ~ class_Fields_Olinordered__field(X1)
| ~ c_Orderings_Oord__class_Oless(X1,hAPP(c_Rings_Oinverse__class_Oinverse(X1),X2),c_Groups_Ozero__class_Ozero(X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1805]),
[final] ).
cnf(i_0_3065,plain,
( c_Polynomial_Odegree(X1,c_Polynomial_Osynthetic__div(X1,X2,X3)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),c_Polynomial_Odegree(X1,X2)),c_Groups_Oone__class_Oone(tc_Nat_Onat))
| ~ class_Rings_Ocomm__semiring__0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1806]),
[final] ).
cnf(i_0_3066,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X3)
| ~ class_Rings_Olinordered__semidom(X1)
| ~ c_Orderings_Oord__class_Oless(X1,c_Nat_Osemiring__1__class_Oof__nat(X1,X2),c_Nat_Osemiring__1__class_Oof__nat(X1,X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1807]),
[final] ).
cnf(i_0_3067,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X3)
| ~ c_Orderings_Oord__class_Oless(X1,c_Nat_Osemiring__1__class_Oof__nat(X1,X2),c_Nat_Osemiring__1__class_Oof__nat(X1,X3))
| ~ class_Rings_Olinordered__semidom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1808]),
[final] ).
cnf(i_0_3068,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1)),X2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2)),
inference(split_conjunct,[status(thm)],[i_0_1809]),
[final] ).
cnf(i_0_3069,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),X3),X2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_1810]),
[final] ).
cnf(i_0_3070,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X3))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_1811]),
[final] ).
cnf(i_0_3071,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X3))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_1812]),
[final] ).
cnf(i_0_3072,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3),X2))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_1813]),
[final] ).
cnf(i_0_3073,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3),X2))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_1814]),
[final] ).
cnf(i_0_3074,plain,
hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)),X1) = X2,
inference(split_conjunct,[status(thm)],[i_0_1815]),
[final] ).
cnf(i_0_3075,plain,
hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)),X2) = X1,
inference(split_conjunct,[status(thm)],[i_0_1816]),
[final] ).
cnf(i_0_3076,plain,
( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X3)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X3)
| ~ class_Fields_Ofield__inverse__zero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1817]),
[final] ).
cnf(i_0_3077,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X3)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)
| ~ class_Rings_Oring(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1818]),
[final] ).
cnf(i_0_3078,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)),X3) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X3))
| ~ class_Rings_Oring(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1819]),
[final] ).
cnf(i_0_3079,plain,
c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,hAPP(c_Nat_OSuc,X1))),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),
inference(split_conjunct,[status(thm)],[i_0_1820]),
[final] ).
cnf(i_0_3080,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2),X1),
inference(split_conjunct,[status(thm)],[i_0_1821]),
[final] ).
cnf(i_0_3081,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2),X2),
inference(split_conjunct,[status(thm)],[i_0_1822]),
[final] ).
cnf(i_0_3082,plain,
( X2 = c_Groups_Ozero__class_Ozero(X1)
| hAPP(c_Groups_Ouminus__class_Ouminus(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X3),X2)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X3),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2))
| ~ class_Rings_Odivision__ring(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1823]),
[final] ).
cnf(i_0_3083,plain,
( c_Orderings_Oord__class_Oless(X1,hAPP(c_Groups_Ouminus__class_Ouminus(X1),X3),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2))
| ~ c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ class_Groups_Oordered__ab__group__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1748]),
[final] ).
cnf(i_0_3084,plain,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ c_Orderings_Oord__class_Oless(X1,hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2),c_Groups_Ozero__class_Ozero(X1))
| ~ class_Groups_Oordered__ab__group__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1824]),
[final] ).
cnf(i_0_3085,plain,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),hAPP(c_Rings_Oinverse__class_Oinverse(X1),X2))
| ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1720]),
[final] ).
cnf(i_0_3086,plain,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),hAPP(c_Rings_Oinverse__class_Oinverse(X1),X2))
| ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1825]),
[final] ).
cnf(i_0_3087,plain,
( c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless(X1,hAPP(c_Rings_Oinverse__class_Oinverse(X1),X2),c_Groups_Ozero__class_Ozero(X1))
| ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1826]),
[final] ).
cnf(i_0_3088,plain,
( c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Oone__class_Oone(X1))
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),hAPP(c_Rings_Oinverse__class_Oinverse(X1),X2))
| ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1720]),
[final] ).
cnf(i_0_3089,plain,
( c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2))
| ~ class_Groups_Oordered__ab__group__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1827]),
[final] ).
cnf(i_0_3090,plain,
( c_Divides_Odiv__class_Omod(X1,c_Divides_Odiv__class_Omod(X1,X2,X3),X3) = c_Divides_Odiv__class_Omod(X1,X2,X3)
| ~ class_Divides_Osemiring__div(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1828]),
[final] ).
cnf(i_0_3091,plain,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),hAPP(c_Polynomial_Ocoeff(X1,X2),c_Polynomial_Odegree(X1,X2)))
| ~ c_Polynomial_Opos__poly(X1,X2)
| ~ class_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1685]),
[final] ).
cnf(i_0_3092,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X3)) = hAPP(c_Groups_Ouminus__class_Ouminus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3))
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1829]),
[final] ).
cnf(i_0_3093,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X3)) = hAPP(c_Groups_Ouminus__class_Ouminus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3))
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1830]),
[final] ).
cnf(i_0_3094,plain,
( hAPP(c_Groups_Ouminus__class_Ouminus(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X3)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X3))
| ~ class_Fields_Ofield__inverse__zero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1831]),
[final] ).
cnf(i_0_3095,plain,
( hAPP(c_Groups_Ouminus__class_Ouminus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X3))
| ~ class_Rings_Oring(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1832]),
[final] ).
cnf(i_0_3096,plain,
( X2 = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Rings_Ocomm__semiring__1(X1)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),c_Groups_Ozero__class_Ozero(X1)),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1833]),
[final] ).
cnf(i_0_3097,plain,
( c_Divides_Odiv__class_Omod(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3),X2) = c_Divides_Odiv__class_Omod(X1,X3,X2)
| ~ class_Divides_Osemiring__div(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1834]),
[final] ).
cnf(i_0_3098,plain,
( c_Divides_Odiv__class_Omod(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3),X3) = c_Divides_Odiv__class_Omod(X1,X2,X3)
| ~ class_Divides_Osemiring__div(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1835]),
[final] ).
cnf(i_0_3099,plain,
( c_Polynomial_Opos__poly(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X1)),X2),X3))
| ~ class_Rings_Olinordered__idom(X1)
| ~ c_Polynomial_Opos__poly(X1,X2)
| ~ c_Polynomial_Opos__poly(X1,X3) ),
inference(split_conjunct,[status(thm)],[i_0_1836]),
[final] ).
cnf(i_0_3100,plain,
( c_Polynomial_Opos__poly(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X1)),X2),X3))
| ~ class_Rings_Olinordered__idom(X1)
| ~ c_Polynomial_Opos__poly(X1,X2)
| ~ c_Polynomial_Opos__poly(X1,X3) ),
inference(split_conjunct,[status(thm)],[i_0_1837]),
[final] ).
cnf(i_0_3101,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,X1)),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,X2)) = c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2)),
inference(split_conjunct,[status(thm)],[i_0_1838]),
[final] ).
cnf(i_0_3102,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,X1)),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,X2)) = c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2)),
inference(split_conjunct,[status(thm)],[i_0_1839]),
[final] ).
cnf(i_0_3103,plain,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,X1)),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,X2)) = c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)),
inference(split_conjunct,[status(thm)],[i_0_1840]),
[final] ).
cnf(i_0_3104,plain,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,X1)),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,X2)) = c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)),
inference(split_conjunct,[status(thm)],[i_0_1841]),
[final] ).
cnf(i_0_3105,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X1)),X2) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X2)),
inference(split_conjunct,[status(thm)],[i_0_1842]),
[final] ).
cnf(i_0_3106,plain,
c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,X1)),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,X2)),
inference(split_conjunct,[status(thm)],[i_0_1843]),
[final] ).
cnf(i_0_3107,plain,
( X1 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| c_Polynomial_Opos__poly(X2,X1)
| ~ c_Polynomial_Opos__poly(X2,hAPP(hAPP(c_Polynomial_OpCons(X2),X3),X1))
| ~ class_Rings_Olinordered__idom(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1752]),
[final] ).
cnf(i_0_3108,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1)
| X1 != hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1787]),
[final] ).
cnf(i_0_3109,plain,
( c_Nat_Osemiring__1__class_Oof__nat(X1,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X2),X3)) = hAPP(hAPP(c_Power_Opower__class_Opower(X1),c_Nat_Osemiring__1__class_Oof__nat(X1,X2)),X3)
| ~ class_Rings_Osemiring__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1844]),
[final] ).
cnf(i_0_3110,plain,
c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,X1),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,X2)) = c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,X2)),
inference(split_conjunct,[status(thm)],[i_0_1845]),
[final] ).
cnf(i_0_3111,plain,
c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,X2)) = c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,X1),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,X2)),
inference(split_conjunct,[status(thm)],[i_0_1846]),
[final] ).
cnf(i_0_3112,plain,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ c_Orderings_Oord__class_Oless(X1,hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2),X2)
| ~ class_Groups_Olinordered__ab__group__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1847]),
[final] ).
cnf(i_0_3113,plain,
( c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless(X1,X2,hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2))
| ~ class_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1848]),
[final] ).
cnf(i_0_3114,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)
| ~ class_Lattices_Oab__semigroup__idem__mult(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1849]),
[final] ).
cnf(i_0_3115,plain,
hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X1)),
inference(split_conjunct,[status(thm)],[i_0_1850]),
[final] ).
cnf(i_0_3116,plain,
( hAPP(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X2,X1)),X3),X4) = hAPP(c_Groups_Ouminus__class_Ouminus(X1),hAPP(X3,X4))
| ~ class_Groups_Ouminus(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1851]),
[final] ).
cnf(i_0_3117,plain,
( hAPP(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X2,X1)),X3),X4) = hAPP(c_Groups_Ouminus__class_Ouminus(X1),hAPP(X3,X4))
| ~ class_Groups_Ouminus(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1852]),
[final] ).
cnf(i_0_3118,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,X1),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1853]),
[final] ).
cnf(i_0_3119,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,X1),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1854]),
[final] ).
cnf(i_0_3120,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(c_Nat_OSuc,X1),hAPP(c_Nat_OSuc,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1855]),
[final] ).
cnf(i_0_3121,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(c_Nat_OSuc,X1),hAPP(c_Nat_OSuc,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1856]),
[final] ).
cnf(i_0_3122,plain,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),c_Groups_Oone__class_Oone(X1)),c_Groups_Oone__class_Oone(X1)))
| ~ class_Rings_Olinordered__semidom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1857]),
[final] ).
cnf(i_0_3123,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X3),X2))
| c_Divides_Odiv__class_Omod(X1,X2,X3) != c_Groups_Ozero__class_Ozero(X1)
| ~ class_Divides_Osemiring__div(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1800]),
[final] ).
cnf(i_0_3124,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,X2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2)),
inference(split_conjunct,[status(thm)],[i_0_1858]),
[final] ).
cnf(i_0_3125,plain,
( c_Polynomial_Ocoeff(X1,hAPP(hAPP(c_Polynomial_OpCons(X1),X2),X3)) = c_Nat_Onat_Onat__case(X1,X2,c_Polynomial_Ocoeff(X1,X3))
| ~ class_Groups_Ozero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1859]),
[final] ).
cnf(i_0_3126,plain,
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,hAPP(c_Nat_OSuc,X2))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_1860]),
[final] ).
cnf(i_0_3127,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,esk10_2(X1,X2),X1)
| X2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,hAPP(c_Nat_OSuc,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1861]),
[final] ).
cnf(i_0_3128,plain,
( c_Orderings_Oord__class_Oless(X1,hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2),c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ class_Groups_Oordered__ab__group__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1824]),
[final] ).
cnf(i_0_3129,plain,
( c_Orderings_Oord__class_Oless(X1,hAPP(c_Rings_Oinverse__class_Oinverse(X1),X2),c_Groups_Ozero__class_Ozero(X1))
| ~ class_Fields_Olinordered__field(X1)
| ~ c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1862]),
[final] ).
cnf(i_0_3130,plain,
( c_Orderings_Oord__class_Oless(X1,hAPP(c_Rings_Oinverse__class_Oinverse(X1),X2),c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1826]),
[final] ).
cnf(i_0_3131,plain,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),hAPP(c_Rings_Oinverse__class_Oinverse(X1),X2))
| ~ class_Fields_Olinordered__field(X1)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2) ),
inference(split_conjunct,[status(thm)],[i_0_1863]),
[final] ).
cnf(i_0_3132,plain,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),hAPP(c_Rings_Oinverse__class_Oinverse(X1),X2))
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1825]),
[final] ).
cnf(i_0_3133,plain,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2))
| ~ c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| ~ class_Groups_Oordered__ab__group__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1827]),
[final] ).
cnf(i_0_3134,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Nat_Osemiring__1__class_Oof__nat(X1,X2))
| ~ class_Rings_Olinordered__semidom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1864]),
[final] ).
cnf(i_0_3135,plain,
( X1 = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,hAPP(c_Nat_OSuc,esk18_1(X1))))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
inference(split_conjunct,[status(thm)],[i_0_1865]),
[final] ).
cnf(i_0_3136,plain,
( hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),c_Groups_Oone__class_Oone(tc_Nat_Onat))) = X1
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1) ),
inference(split_conjunct,[status(thm)],[i_0_1866]),
[final] ).
cnf(i_0_3137,plain,
( X1 = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),c_Groups_Oone__class_Oone(tc_Nat_Onat)))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1) ),
inference(split_conjunct,[status(thm)],[i_0_1867]),
[final] ).
cnf(i_0_3138,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X3),X2))
| ~ class_Rings_Odvd(X1)
| X2 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4) ),
inference(split_conjunct,[status(thm)],[i_0_1868]),
[final] ).
cnf(i_0_3139,plain,
( c_Orderings_Oord__class_Oless(X1,c_Nat_Osemiring__1__class_Oof__nat(X1,X2),c_Nat_Osemiring__1__class_Oof__nat(X1,X3))
| ~ class_Rings_Olinordered__semidom(X1)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_1869]),
[final] ).
cnf(i_0_3140,plain,
( c_Orderings_Oord__class_Oless(X3,c_Nat_Osemiring__1__class_Oof__nat(X3,X1),c_Nat_Osemiring__1__class_Oof__nat(X3,X2))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| ~ class_Rings_Olinordered__semidom(X3) ),
inference(split_conjunct,[status(thm)],[i_0_1808]),
[final] ).
cnf(i_0_3141,plain,
( c_Orderings_Oord__class_Oless(X1,hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2),X2)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ class_Groups_Olinordered__ab__group__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1847]),
[final] ).
cnf(i_0_3142,plain,
( c_Orderings_Oord__class_Oless(X1,X2,hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2))
| ~ c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| ~ class_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1848]),
[final] ).
cnf(i_0_3143,plain,
( X2 = X3
| X2 = hAPP(c_Groups_Ouminus__class_Ouminus(X1),X3)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X2) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X3)
| ~ class_Rings_Oidom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1870]),
[final] ).
cnf(i_0_3144,plain,
hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,X1)),X2) = c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X1),X2)),
inference(split_conjunct,[status(thm)],[i_0_1871]),
[final] ).
cnf(i_0_3145,plain,
hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,X1)),X2) = c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X1),X2)),
inference(split_conjunct,[status(thm)],[i_0_1872]),
[final] ).
cnf(i_0_3146,plain,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1)),X2) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)),
inference(split_conjunct,[status(thm)],[i_0_1873]),
[final] ).
cnf(i_0_3147,plain,
c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X1),X2)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,X1)),X2),
inference(split_conjunct,[status(thm)],[i_0_1874]),
[final] ).
cnf(i_0_3148,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| hBOOL(hAPP(hAPP(X3,X1),X2))
| X2 = X1
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_1875]),
[final] ).
cnf(i_0_3149,plain,
( c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(X1),X2,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X1)),X3)) = c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(X1),X2,X3)
| ~ class_Fields_Ofield(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1876]),
[final] ).
cnf(i_0_3150,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),X2)) = X1 ),
inference(split_conjunct,[status(thm)],[i_0_1877]),
[final] ).
cnf(i_0_3151,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,X1),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,X2))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_1853]),
[final] ).
cnf(i_0_3152,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,X1),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,X2))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_1854]),
[final] ).
cnf(i_0_3153,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(c_Nat_OSuc,X1),hAPP(c_Nat_OSuc,X2))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_1855]),
[final] ).
cnf(i_0_3154,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(c_Nat_OSuc,X1),hAPP(c_Nat_OSuc,X2))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_1878]),
[final] ).
cnf(i_0_3155,plain,
( X3 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Ocomm__semiring__0(X1)
| hAPP(hAPP(c_Polynomial_Osmult(X1),X2),X3) != hAPP(hAPP(c_Polynomial_OpCons(X1),X4),X3) ),
inference(split_conjunct,[status(thm)],[i_0_1879]),
[final] ).
cnf(i_0_3156,plain,
( c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),c_Nat_Osemiring__1__class_Oof__nat(X2,X1))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
| ~ class_Rings_Olinordered__semidom(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1864]),
[final] ).
cnf(i_0_3157,plain,
( ~ class_Orderings_Owellorder(X1)
| ~ c_Orderings_Oord__class_Oless(X1,X2,c_Orderings_Oord__class_OLeast(X1,X3))
| ~ hBOOL(hAPP(X3,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1880]),
[final] ).
cnf(i_0_3158,plain,
( hAPP(c_Rings_Oinverse__class_Oinverse(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X3)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X3),X2)
| ~ class_Fields_Ofield__inverse__zero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1881]),
[final] ).
cnf(i_0_3159,plain,
( hAPP(c_Groups_Ouminus__class_Ouminus(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X2),X3)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X3),X2)
| ~ class_Groups_Oab__group__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1882]),
[final] ).
cnf(i_0_3160,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,hAPP(c_Nat_OSuc,X3))
| X1 != hAPP(c_Nat_OSuc,X2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_1861]),
[final] ).
cnf(i_0_3161,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1883]),
[final] ).
cnf(i_0_3162,plain,
( X2 = X4
| c_Polynomial_Omonom(X1,X2,X3) != c_Polynomial_Omonom(X1,X4,X3)
| ~ class_Groups_Ozero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1884]),
[final] ).
cnf(i_0_3163,plain,
( hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),c_Groups_Oone__class_Oone(X1))),X2)
| ~ class_Rings_Ocomm__ring__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1885]),
[final] ).
cnf(i_0_3164,plain,
( ~ class_Orderings_Oorder(X1)
| ~ c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless(X1,X3,X2) ),
inference(split_conjunct,[status(thm)],[i_0_1886]),
[final] ).
cnf(i_0_3165,plain,
( ~ c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless(X1,X3,X2)
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1887]),
[final] ).
cnf(i_0_3166,plain,
( ~ class_Orderings_Opreorder(X1)
| ~ c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless(X1,X3,X2) ),
inference(split_conjunct,[status(thm)],[i_0_1888]),
[final] ).
cnf(i_0_3167,plain,
( ~ class_Orderings_Opreorder(X1)
| ~ c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless(X1,X3,X2) ),
inference(split_conjunct,[status(thm)],[i_0_1889]),
[final] ).
cnf(i_0_3168,plain,
( ~ class_Orderings_Opreorder(X1)
| ~ c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless(X1,X3,X2) ),
inference(split_conjunct,[status(thm)],[i_0_1890]),
[final] ).
cnf(i_0_3169,plain,
( ~ class_Orderings_Opreorder(X1)
| ~ c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless(X1,X3,X2) ),
inference(split_conjunct,[status(thm)],[i_0_1891]),
[final] ).
cnf(i_0_3170,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))
| X1 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
inference(split_conjunct,[status(thm)],[i_0_1766]),
[final] ).
cnf(i_0_3171,plain,
( c_Polynomial_Opoly__gcd(X1,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X1)),X2),X3) = c_Polynomial_Opoly__gcd(X1,X2,X3)
| ~ class_Fields_Ofield(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1892]),
[final] ).
cnf(i_0_3172,plain,
( c_Polynomial_Opoly__gcd(X1,X2,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X1)),X3)) = c_Polynomial_Opoly__gcd(X1,X2,X3)
| ~ class_Fields_Ofield(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1893]),
[final] ).
cnf(i_0_3173,plain,
( X2 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))
| hAPP(c_Polynomial_Opoly(X1,X2),X3) != c_Groups_Ozero__class_Ozero(X1)
| c_Polynomial_Oorder(X1,X3,X2) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ class_Rings_Oidom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1894]),
[final] ).
cnf(i_0_3174,plain,
( X3 = X4
| X1 != X2
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(X5),X1),X2) != hAPP(hAPP(c_Groups_Ominus__class_Ominus(X5),X3),X4)
| ~ class_Groups_Oab__group__add(X5) ),
inference(split_conjunct,[status(thm)],[i_0_1895]),
[final] ).
cnf(i_0_3175,plain,
( X3 = X4
| X1 != X2
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(X5),X3),X4) != hAPP(hAPP(c_Groups_Ominus__class_Ominus(X5),X1),X2)
| ~ class_Groups_Oab__group__add(X5) ),
inference(split_conjunct,[status(thm)],[i_0_1895]),
[final] ).
cnf(i_0_3176,plain,
( c_Orderings_Oord__class_Oless(X1,X2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),c_Groups_Oone__class_Oone(X1)))
| ~ class_Rings_Olinordered__semidom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1896]),
[final] ).
cnf(i_0_3177,plain,
( hAPP(c_Polynomial_Ocoeff(X1,X2),X3) = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Groups_Ozero(X1)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(X1,X2),X3) ),
inference(split_conjunct,[status(thm)],[i_0_1897]),
[final] ).
cnf(i_0_3178,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| X1 = X2
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,hAPP(c_Nat_OSuc,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1898]),
[final] ).
cnf(i_0_3179,plain,
( X1 = X2
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,hAPP(c_Nat_OSuc,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1899]),
[final] ).
cnf(i_0_3180,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| X2 = X1
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,hAPP(c_Nat_OSuc,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1900]),
[final] ).
cnf(i_0_3181,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| X1 = X2
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,hAPP(c_Nat_OSuc,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1901]),
[final] ).
cnf(i_0_3182,plain,
( c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X1),X2) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
inference(split_conjunct,[status(thm)],[i_0_1729]),
[final] ).
cnf(i_0_3183,plain,
( c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X1),X2) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
inference(split_conjunct,[status(thm)],[i_0_1902]),
[final] ).
cnf(i_0_3184,plain,
( c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X2)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
inference(split_conjunct,[status(thm)],[i_0_1616]),
[final] ).
cnf(i_0_3185,plain,
( c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X2)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
inference(split_conjunct,[status(thm)],[i_0_1903]),
[final] ).
cnf(i_0_3186,plain,
( hAPP(c_Nat_OSuc,X1) = X2
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(c_Nat_OSuc,X1),X2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_1904]),
[final] ).
cnf(i_0_3187,plain,
( c_Groups_Osgn__class_Osgn(tc_Polynomial_Opoly(X1),X2) = c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(X1))
| X2 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))
| ~ c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(X1),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),X2)
| ~ class_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1905]),
[final] ).
cnf(i_0_3188,plain,
( X1 = X2
| hAPP(hAPP(c_Polynomial_OpCons(X3),X1),X4) != hAPP(hAPP(c_Polynomial_OpCons(X3),X2),X5)
| ~ class_Groups_Ozero(X3) ),
inference(split_conjunct,[status(thm)],[i_0_1906]),
[final] ).
cnf(i_0_3189,plain,
( X1 = X2
| hAPP(hAPP(c_Polynomial_OpCons(X3),X4),X1) != hAPP(hAPP(c_Polynomial_OpCons(X3),X5),X2)
| ~ class_Groups_Ozero(X3) ),
inference(split_conjunct,[status(thm)],[i_0_1906]),
[final] ).
cnf(i_0_3190,plain,
( X2 = X4
| ~ class_Groups_Ocancel__semigroup__add(X1)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X4),X3) ),
inference(split_conjunct,[status(thm)],[i_0_1907]),
[final] ).
cnf(i_0_3191,plain,
( X2 = X4
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X4),X3)
| ~ class_Groups_Ocancel__semigroup__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1908]),
[final] ).
cnf(i_0_3192,plain,
( X3 = X4
| ~ class_Groups_Ocancel__ab__semigroup__add(X1)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X4) ),
inference(split_conjunct,[status(thm)],[i_0_1909]),
[final] ).
cnf(i_0_3193,plain,
( X3 = X4
| ~ class_Groups_Ocancel__semigroup__add(X1)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X4) ),
inference(split_conjunct,[status(thm)],[i_0_1910]),
[final] ).
cnf(i_0_3194,plain,
( X3 = X4
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X4)
| ~ class_Groups_Ocancel__semigroup__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1911]),
[final] ).
cnf(i_0_3195,plain,
( X1 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| c_Polynomial_Odegree(X2,hAPP(hAPP(c_Polynomial_OpCons(X2),X3),X1)) = hAPP(c_Nat_OSuc,c_Polynomial_Odegree(X2,X1))
| ~ class_Groups_Ozero(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1912]),
[final] ).
cnf(i_0_3196,plain,
( X2 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))
| c_Polynomial_Odegree(X1,hAPP(hAPP(c_Polynomial_OpCons(X1),X3),X2)) = hAPP(c_Nat_OSuc,c_Polynomial_Odegree(X1,X2))
| ~ class_Groups_Ozero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1913]),
[final] ).
cnf(i_0_3197,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(c_Nat_OSuc,X1),X2) ),
inference(split_conjunct,[status(thm)],[i_0_1914]),
[final] ).
cnf(i_0_3198,plain,
( c_Divides_Odiv__class_Odiv(X1,c_Divides_Odiv__class_Omod(X1,X2,X3),X3) = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Divides_Osemiring__div(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1915]),
[final] ).
cnf(i_0_3199,plain,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,X2)) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)),
inference(split_conjunct,[status(thm)],[i_0_1916]),
[final] ).
cnf(i_0_3200,plain,
( X2 = c_Groups_Ozero__class_Ozero(X1)
| c_Divides_Odiv__class_Odiv(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),X2) = X3
| ~ class_Divides_Osemiring__div(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1917]),
[final] ).
cnf(i_0_3201,plain,
( X2 = c_Groups_Ozero__class_Ozero(X1)
| c_Divides_Odiv__class_Odiv(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X2),X2) = X3
| ~ class_Divides_Osemiring__div(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1918]),
[final] ).
cnf(i_0_3202,plain,
c_Divides_Odiv__class_Odiv(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X1),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X2)) = c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X2),
inference(split_conjunct,[status(thm)],[i_0_1919]),
[final] ).
cnf(i_0_3203,plain,
c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X2)) = c_Divides_Odiv__class_Odiv(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X1),X2),
inference(split_conjunct,[status(thm)],[i_0_1920]),
[final] ).
cnf(i_0_3204,plain,
( X1 = c_Groups_Oone__class_Oone(tc_Int_Oint)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X2) != c_Groups_Oone__class_Oone(tc_Int_Oint)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1) ),
inference(split_conjunct,[status(thm)],[i_0_1921]),
[final] ).
cnf(i_0_3205,plain,
( X1 = c_Groups_Oone__class_Oone(tc_Int_Oint)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X1) != c_Groups_Oone__class_Oone(tc_Int_Oint)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2) ),
inference(split_conjunct,[status(thm)],[i_0_1921]),
[final] ).
cnf(i_0_3206,plain,
( c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(X1),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),X2)
| c_Groups_Osgn__class_Osgn(tc_Polynomial_Opoly(X1),X2) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X1)),c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(X1)))
| X2 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1905]),
[final] ).
cnf(i_0_3207,plain,
( c_Divides_Odiv__class_Omod(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),X2) = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Divides_Osemiring__div(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1922]),
[final] ).
cnf(i_0_3208,plain,
( c_Divides_Odiv__class_Omod(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),X3) = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Divides_Osemiring__div(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1923]),
[final] ).
cnf(i_0_3209,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,X1))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1) ),
inference(split_conjunct,[status(thm)],[i_0_1883]),
[final] ).
cnf(i_0_3210,plain,
c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),X2),hAPP(c_Nat_OSuc,X1)),
inference(split_conjunct,[status(thm)],[i_0_1924]),
[final] ).
cnf(i_0_3211,plain,
( X1 = hAPP(c_Nat_OSuc,esk10_2(X2,X1))
| X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,hAPP(c_Nat_OSuc,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1861]),
[final] ).
cnf(i_0_3212,plain,
( c_Polynomial_Odegree(X1,hAPP(hAPP(c_Polynomial_OpCons(X1),X2),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ class_Groups_Ozero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1925]),
[final] ).
cnf(i_0_3213,plain,
( X1 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),c_Groups_Oone__class_Oone(tc_Nat_Onat))) ),
inference(split_conjunct,[status(thm)],[i_0_1926]),
[final] ).
cnf(i_0_3214,plain,
hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1)),hAPP(c_Nat_OSuc,X2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),X2),
inference(split_conjunct,[status(thm)],[i_0_1927]),
[final] ).
cnf(i_0_3215,plain,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1)),X2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,X2)),
inference(split_conjunct,[status(thm)],[i_0_1928]),
[final] ).
cnf(i_0_3216,plain,
( X1 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),esk8_2(X2,X1))
| c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
inference(split_conjunct,[status(thm)],[i_0_1929]),
[final] ).
cnf(i_0_3217,plain,
( X1 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),esk9_2(X2,X1))
| c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,X2) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(split_conjunct,[status(thm)],[i_0_1930]),
[final] ).
cnf(i_0_3218,plain,
( ~ class_Rings_Oidom(t_a)
| ~ c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(t_a,t_a,c_Polynomial_Opoly(t_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)))) ),
inference(split_conjunct,[status(thm)],[i_0_1931]),
[final] ).
cnf(i_0_3219,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,hAPP(c_Nat_OSuc,X2))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_1898]),
[final] ).
cnf(i_0_3220,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,hAPP(c_Nat_OSuc,X2))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_1932]),
[final] ).
cnf(i_0_3221,plain,
c_Divides_Odiv__class_Odiv(tc_Int_Oint,c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2),X2) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[i_0_1933]),
[final] ).
cnf(i_0_3222,plain,
hAPP(c_Nat_Onat_Onat__case(X1,X2,X3),hAPP(c_Nat_OSuc,X4)) = hAPP(X3,X4),
inference(split_conjunct,[status(thm)],[i_0_1934]),
[final] ).
cnf(i_0_3223,plain,
( X1 = X2
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),X2) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X2),X1) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(split_conjunct,[status(thm)],[i_0_1935]),
[final] ).
cnf(i_0_3224,plain,
c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,X1)),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,X2)),
inference(split_conjunct,[status(thm)],[i_0_1936]),
[final] ).
cnf(i_0_3225,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),c_Groups_Oone__class_Oone(tc_Int_Oint)))
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_1728]),
[final] ).
cnf(i_0_3226,plain,
( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X2),X3),X4) = X1
| X1 != c_Groups_Ozero__class_Ozero(X2)
| X3 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X4)
| ~ class_Fields_Ofield__inverse__zero(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1937]),
[final] ).
cnf(i_0_3227,plain,
( X1 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X2),X4),X3)
| X1 != c_Groups_Ozero__class_Ozero(X2)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X3) != X4
| ~ class_Fields_Ofield__inverse__zero(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1938]),
[final] ).
cnf(i_0_3228,plain,
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X1)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))),X2) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X1)),X2)
| ~ class_Groups_Oab__group__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1939]),
[final] ).
cnf(i_0_3229,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X2),X1))
| X1 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(split_conjunct,[status(thm)],[i_0_1730]),
[final] ).
cnf(i_0_3230,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X2),X1))
| X1 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(split_conjunct,[status(thm)],[i_0_1731]),
[final] ).
cnf(i_0_3231,plain,
( X1 = X3
| X2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X2) ),
inference(split_conjunct,[status(thm)],[i_0_1940]),
[final] ).
cnf(i_0_3232,plain,
( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X2 = X3
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X3) ),
inference(split_conjunct,[status(thm)],[i_0_1941]),
[final] ).
cnf(i_0_3233,plain,
( X2 = X3
| X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X3) ),
inference(split_conjunct,[status(thm)],[i_0_1942]),
[final] ).
cnf(i_0_3234,plain,
( X1 = c_Groups_Ozero__class_Ozero(X2)
| hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X2),X3),X1) = X4
| X3 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X4),X1)
| ~ class_Fields_Ofield__inverse__zero(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1937]),
[final] ).
cnf(i_0_3235,plain,
( X1 = c_Groups_Ozero__class_Ozero(X2)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X3),X1) = X4
| X3 != hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X2),X4),X1)
| ~ class_Fields_Ofield__inverse__zero(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1938]),
[final] ).
cnf(i_0_3236,plain,
( X2 = c_Groups_Ozero__class_Ozero(X1)
| hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X3),X2) = X4
| ~ class_Rings_Odivision__ring(X1)
| X3 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X2) ),
inference(split_conjunct,[status(thm)],[i_0_1943]),
[final] ).
cnf(i_0_3237,plain,
( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X2),X1),X4) = X3
| X4 = c_Groups_Ozero__class_Ozero(X2)
| X1 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X3),X4)
| ~ class_Rings_Odivision__ring(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1944]),
[final] ).
cnf(i_0_3238,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X4) = X3
| X4 = c_Groups_Ozero__class_Ozero(X2)
| X1 != hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X2),X3),X4)
| ~ class_Rings_Odivision__ring(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1945]),
[final] ).
cnf(i_0_3239,plain,
( X1 = c_Groups_Ozero__class_Ozero(X2)
| X3 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X2),X4),X1)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X3),X1) != X4
| ~ class_Fields_Ofield__inverse__zero(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1938]),
[final] ).
cnf(i_0_3240,plain,
( X1 = c_Groups_Ozero__class_Ozero(X2)
| X3 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X4),X1)
| hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X2),X3),X1) != X4
| ~ class_Fields_Ofield__inverse__zero(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1937]),
[final] ).
cnf(i_0_3241,plain,
( X2 = c_Groups_Ozero__class_Ozero(X1)
| X3 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X4),X2)
| ~ class_Rings_Odivision__ring(X1)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X2) != X4 ),
inference(split_conjunct,[status(thm)],[i_0_1946]),
[final] ).
cnf(i_0_3242,plain,
( X2 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X4),X3)
| X3 = c_Groups_Ozero__class_Ozero(X1)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3) != X4
| ~ class_Rings_Odivision__ring(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1945]),
[final] ).
cnf(i_0_3243,plain,
( X2 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3)
| X3 = c_Groups_Ozero__class_Ozero(X1)
| hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X3) != X4
| ~ class_Rings_Odivision__ring(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1944]),
[final] ).
cnf(i_0_3244,plain,
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X2),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X3)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)
| ~ class_Groups_Ogroup__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1947]),
[final] ).
cnf(i_0_3245,plain,
( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X3) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),hAPP(c_Rings_Oinverse__class_Oinverse(X1),X3))
| ~ class_Rings_Odivision__ring(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1948]),
[final] ).
cnf(i_0_3246,plain,
( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X3) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),hAPP(c_Rings_Oinverse__class_Oinverse(X1),X3))
| ~ class_Fields_Ofield(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1949]),
[final] ).
cnf(i_0_3247,plain,
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X2),X3) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X3))
| ~ class_Groups_Ogroup__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1950]),
[final] ).
cnf(i_0_3248,plain,
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X2),X3) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X3))
| ~ class_Groups_Oab__group__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1951]),
[final] ).
cnf(i_0_3249,plain,
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X2),X3) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X3))
| ~ class_Rings_Ocomm__ring__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1952]),
[final] ).
cnf(i_0_3250,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X2) = c_Groups_Oone__class_Oone(tc_Int_Oint)
| X1 != c_Groups_Oone__class_Oone(tc_Int_Oint)
| X2 != c_Groups_Oone__class_Oone(tc_Int_Oint)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1) ),
inference(split_conjunct,[status(thm)],[i_0_1921]),
[final] ).
cnf(i_0_3251,plain,
( X1 = X3
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3),X2) ),
inference(split_conjunct,[status(thm)],[i_0_1953]),
[final] ).
cnf(i_0_3252,plain,
( X2 = X3
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X3) ),
inference(split_conjunct,[status(thm)],[i_0_1954]),
[final] ).
cnf(i_0_3253,plain,
( c_Polynomial_Opos__poly(X1,hAPP(hAPP(c_Polynomial_OpCons(X1),X3),X2))
| ~ c_Polynomial_Opos__poly(X1,X2)
| ~ class_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1752]),
[final] ).
cnf(i_0_3254,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X1) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X3),X3)
| X1 != hAPP(c_Groups_Ouminus__class_Ouminus(X2),X3)
| ~ class_Rings_Oidom(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1870]),
[final] ).
cnf(i_0_3255,plain,
( X2 = c_Groups_Ozero__class_Ozero(X1)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(c_Rings_Oinverse__class_Oinverse(X1),X2)),X2) = c_Groups_Oone__class_Oone(X1)
| ~ class_Rings_Odivision__ring(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1955]),
[final] ).
cnf(i_0_3256,plain,
( X2 = c_Groups_Ozero__class_Ozero(X1)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(c_Rings_Oinverse__class_Oinverse(X1),X2)),X2) = c_Groups_Oone__class_Oone(X1)
| ~ class_Fields_Ofield(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1956]),
[final] ).
cnf(i_0_3257,plain,
( c_Polynomial_Odegree(X2,hAPP(hAPP(c_Polynomial_OpCons(X2),X3),X1)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X1 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| ~ class_Groups_Ozero(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1912]),
[final] ).
cnf(i_0_3258,plain,
( ~ class_Rings_Olinordered__semidom(X1)
| ~ c_Orderings_Oord__class_Oless(X1,c_Nat_Osemiring__1__class_Oof__nat(X1,X2),c_Groups_Ozero__class_Ozero(X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1957]),
[final] ).
cnf(i_0_3259,plain,
( X1 = c_Groups_Ozero__class_Ozero(X2)
| c_Polynomial_Odegree(X2,hAPP(hAPP(c_Polynomial_Osmult(X2),X1),X3)) = c_Polynomial_Odegree(X2,X3)
| ~ class_Rings_Oidom(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1958]),
[final] ).
cnf(i_0_3260,plain,
( c_Polynomial_Odegree(X1,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X1,X2,X3)) = c_Polynomial_Odegree(X1,X2)
| ~ class_Rings_Ocomm__semiring__0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1959]),
[final] ).
cnf(i_0_3261,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)),X2) = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Groups_Ogroup__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1960]),
[final] ).
cnf(i_0_3262,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)),X2) = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Groups_Oab__group__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1961]),
[final] ).
cnf(i_0_3263,plain,
hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[i_0_1962]),
[final] ).
cnf(i_0_3264,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),c_Groups_Oone__class_Oone(X1)),X2))
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1963]),
[final] ).
cnf(i_0_3265,plain,
( c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,X2) = X1
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_1773]),
[final] ).
cnf(i_0_3266,plain,
( c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,X2) = X1
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_1964]),
[final] ).
cnf(i_0_3267,plain,
( hBOOL(hAPP(X2,c_Orderings_Oord__class_OLeast(X1,X2)))
| ~ class_Orderings_Owellorder(X1)
| ~ hBOOL(hAPP(X2,X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1965]),
[final] ).
cnf(i_0_3268,plain,
( hBOOL(hAPP(X2,c_Orderings_Oord__class_OLeast(X1,X2)))
| ~ class_Orderings_Owellorder(X1)
| ~ hBOOL(hAPP(X2,X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1966]),
[final] ).
cnf(i_0_3269,plain,
( c_Polynomial_Omonom(X1,X2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(hAPP(c_Polynomial_OpCons(X1),X2),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)))
| ~ class_Groups_Ozero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1967]),
[final] ).
cnf(i_0_3270,plain,
( c_Polynomial_Odegree(X2,hAPP(hAPP(c_Polynomial_Osmult(X2),X1),X3)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X1 != c_Groups_Ozero__class_Ozero(X2)
| ~ class_Rings_Oidom(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1958]),
[final] ).
cnf(i_0_3271,plain,
( X2 = c_Groups_Ozero__class_Ozero(X1)
| c_Polynomial_Odegree(X1,c_Polynomial_Omonom(X1,X2,X3)) = X3
| ~ class_Groups_Ozero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1968]),
[final] ).
cnf(i_0_3272,plain,
( c_Nat_Osemiring__1__class_Oof__nat(X1,hAPP(c_Nat_OSuc,X2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),c_Groups_Oone__class_Oone(X1)),c_Nat_Osemiring__1__class_Oof__nat(X1,X2))
| ~ class_Rings_Osemiring__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1969]),
[final] ).
cnf(i_0_3273,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,hAPP(c_Nat_OSuc,X2))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_1899]),
[final] ).
cnf(i_0_3274,plain,
( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ),
inference(split_conjunct,[status(thm)],[i_0_1970]),
[final] ).
cnf(i_0_3275,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X1)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))),X2) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Ocomm__semiring__0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1971]),
[final] ).
cnf(i_0_3276,plain,
( X1 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| X2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X1) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
inference(split_conjunct,[status(thm)],[i_0_1972]),
[final] ).
cnf(i_0_3277,plain,
( X1 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| X2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X1) ),
inference(split_conjunct,[status(thm)],[i_0_1973]),
[final] ).
cnf(i_0_3278,plain,
( c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| X1 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X3) ),
inference(split_conjunct,[status(thm)],[i_0_1929]),
[final] ).
cnf(i_0_3279,plain,
( c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,X2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X1 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X3) ),
inference(split_conjunct,[status(thm)],[i_0_1930]),
[final] ).
cnf(i_0_3280,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,hAPP(c_Nat_OSuc,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1860]),
[final] ).
cnf(i_0_3281,plain,
( X2 = c_Groups_Ozero__class_Ozero(X1)
| hAPP(c_Rings_Oinverse__class_Oinverse(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)) = hAPP(c_Groups_Ouminus__class_Ouminus(X1),hAPP(c_Rings_Oinverse__class_Oinverse(X1),X2))
| ~ class_Rings_Odivision__ring(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1974]),
[final] ).
cnf(i_0_3282,plain,
( X2 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))
| hAPP(c_Polynomial_Ocoeff(X1,X2),c_Polynomial_Odegree(X1,X2)) != c_Groups_Ozero__class_Ozero(X1)
| ~ class_Groups_Ozero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1975]),
[final] ).
cnf(i_0_3283,plain,
( X2 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))
| ~ class_Groups_Ozero(X1)
| hAPP(c_Polynomial_Ocoeff(X1,X2),c_Polynomial_Odegree(X1,X2)) != c_Groups_Ozero__class_Ozero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1976]),
[final] ).
cnf(i_0_3284,plain,
( X2 = c_Groups_Oone__class_Oone(X1)
| X2 = hAPP(c_Groups_Ouminus__class_Ouminus(X1),c_Groups_Oone__class_Oone(X1))
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X2) != c_Groups_Oone__class_Oone(X1)
| ~ class_Rings_Oring__1__no__zero__divisors(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1977]),
[final] ).
cnf(i_0_3285,plain,
( X1 = X2
| hAPP(X1,esk1_2(X2,X1)) != hAPP(X2,esk1_2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1978]),
[final] ).
cnf(i_0_3286,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X2),c_Groups_Ozero__class_Ozero(X1)))
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1979]),
[final] ).
cnf(i_0_3287,plain,
( c_Polynomial_Odegree(X1,X2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Polynomial_Osynthetic__div(X1,X2,X3) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Ocomm__semiring__0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1980]),
[final] ).
cnf(i_0_3288,plain,
hAPP(c_Nat_Onat_Onat__case(X1,X2,X3),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X2,
inference(split_conjunct,[status(thm)],[i_0_1981]),
[final] ).
cnf(i_0_3289,plain,
~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),
inference(split_conjunct,[status(thm)],[i_0_1982]),
[final] ).
cnf(i_0_3290,plain,
( hBOOL(X1)
| ~ hBOOL(hAPP(hAPP(c_fconj,X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1983]),
[final] ).
cnf(i_0_3291,plain,
( hBOOL(X2)
| ~ hBOOL(hAPP(hAPP(c_fconj,X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1984]),
[final] ).
cnf(i_0_3292,plain,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X1),X2),
inference(split_conjunct,[status(thm)],[i_0_1985]),
[final] ).
cnf(i_0_3293,plain,
hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X1),X2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X2)),
inference(split_conjunct,[status(thm)],[i_0_1986]),
[final] ).
cnf(i_0_3294,plain,
( hAPP(c_Rings_Oinverse__class_Oinverse(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)) = hAPP(c_Groups_Ouminus__class_Ouminus(X1),hAPP(c_Rings_Oinverse__class_Oinverse(X1),X2))
| ~ class_Rings_Odivision__ring__inverse__zero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1987]),
[final] ).
cnf(i_0_3295,plain,
( X1 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Power_Opower__class_Opower(X2),X3),X1) != c_Groups_Ozero__class_Ozero(X2)
| ~ class_Power_Opower(X2)
| ~ class_Rings_Omult__zero(X2)
| ~ class_Rings_Ono__zero__divisors(X2)
| ~ class_Rings_Ozero__neq__one(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1988]),
[final] ).
cnf(i_0_3296,plain,
( X1 = c_Groups_Ozero__class_Ozero(X2)
| hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),X3) != c_Groups_Ozero__class_Ozero(X2)
| ~ class_Power_Opower(X2)
| ~ class_Rings_Omult__zero(X2)
| ~ class_Rings_Ono__zero__divisors(X2)
| ~ class_Rings_Ozero__neq__one(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1988]),
[final] ).
cnf(i_0_3297,plain,
( X2 = c_Groups_Ozero__class_Ozero(X1)
| X3 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))
| hAPP(hAPP(c_Polynomial_Osmult(X1),X2),X3) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Oidom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1989]),
[final] ).
cnf(i_0_3298,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X1)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))),X2) = X2
| ~ class_Groups_Ocomm__monoid__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1990]),
[final] ).
cnf(i_0_3299,plain,
( X1 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| c_Polynomial_Opoly__gcd(X2,X1,X3) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| ~ class_Fields_Ofield(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1991]),
[final] ).
cnf(i_0_3300,plain,
( X1 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| c_Polynomial_Opoly__gcd(X2,X3,X1) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| ~ class_Fields_Ofield(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1991]),
[final] ).
cnf(i_0_3301,plain,
( X2 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))
| c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X1,X2,X3) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Ocomm__semiring__0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1992]),
[final] ).
cnf(i_0_3302,plain,
hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X1) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(split_conjunct,[status(thm)],[i_0_1993]),
[final] ).
cnf(i_0_3303,plain,
( X1 = X2
| c_Orderings_Oord__class_Oless(X3,X1,X2)
| c_Orderings_Oord__class_Oless(X3,X2,X1)
| ~ class_Orderings_Olinorder(X3) ),
inference(split_conjunct,[status(thm)],[i_0_1994]),
[final] ).
cnf(i_0_3304,plain,
( c_Orderings_Oord__class_Oless(X1,X2,X3)
| X2 = X3
| c_Orderings_Oord__class_Oless(X1,X3,X2)
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1995]),
[final] ).
cnf(i_0_3305,plain,
( X2 = X3
| c_Orderings_Oord__class_Oless(X1,X2,X3)
| c_Orderings_Oord__class_Oless(X1,X3,X2)
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1996]),
[final] ).
cnf(i_0_3306,plain,
( c_Orderings_Oord__class_Oless(X1,X2,X3)
| X2 = X3
| c_Orderings_Oord__class_Oless(X1,X3,X2)
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1997]),
[final] ).
cnf(i_0_3307,plain,
( c_Orderings_Oord__class_Oless(X1,X2,X3)
| X2 = X3
| c_Orderings_Oord__class_Oless(X1,X3,X2)
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1998]),
[final] ).
cnf(i_0_3308,plain,
( c_Orderings_Oord__class_Oless(X1,X2,X3)
| c_Orderings_Oord__class_Oless(X1,X3,X2)
| X2 = X3
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1887]),
[final] ).
cnf(i_0_3309,plain,
( X2 = X3
| c_Orderings_Oord__class_Oless(X1,X2,X3)
| c_Orderings_Oord__class_Oless(X1,X3,X2)
| ~ class_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1999]),
[final] ).
cnf(i_0_3310,plain,
( c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(X2,X3,X1)
| hAPP(X1,esk2_1(X1)) != hAPP(X1,esk3_1(X1)) ),
inference(split_conjunct,[status(thm)],[i_0_2000]),
[final] ).
cnf(i_0_3311,plain,
( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X1 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
inference(split_conjunct,[status(thm)],[i_0_1972]),
[final] ).
cnf(i_0_3312,plain,
( X1 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X1) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
inference(split_conjunct,[status(thm)],[i_0_1972]),
[final] ).
cnf(i_0_3313,plain,
( X2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X1 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X1),X2) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
inference(split_conjunct,[status(thm)],[i_0_2001]),
[final] ).
cnf(i_0_3314,plain,
( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X1 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2) ),
inference(split_conjunct,[status(thm)],[i_0_1973]),
[final] ).
cnf(i_0_3315,plain,
( X1 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X1) ),
inference(split_conjunct,[status(thm)],[i_0_1973]),
[final] ).
cnf(i_0_3316,plain,
( ~ class_Rings_Oidom(t_a)
| ~ c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(t_a,t_a,c_Polynomial_Opoly(t_a,v_p)) ),
inference(split_conjunct,[status(thm)],[i_0_2002]),
[final] ).
cnf(i_0_3317,plain,
( hAPP(c_Rings_Oinverse__class_Oinverse(X1),X2) = X3
| ~ class_Rings_Odivision__ring(X1)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3) != c_Groups_Oone__class_Oone(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2003]),
[final] ).
cnf(i_0_3318,plain,
( hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2) = X3
| ~ class_Groups_Ogroup__add(X1)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3) != c_Groups_Ozero__class_Ozero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2004]),
[final] ).
cnf(i_0_3319,plain,
( X2 = hAPP(c_Groups_Ouminus__class_Ouminus(X1),X3)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3) != c_Groups_Ozero__class_Ozero(X1)
| ~ class_Groups_Ogroup__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2005]),
[final] ).
cnf(i_0_3320,plain,
( X3 = hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3) != c_Groups_Ozero__class_Ozero(X1)
| ~ class_Groups_Ogroup__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2006]),
[final] ).
cnf(i_0_3321,plain,
( X1 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| hAPP(hAPP(c_Polynomial_OpCons(X2),X3),X1) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| ~ class_Groups_Ozero(X2) ),
inference(split_conjunct,[status(thm)],[i_0_2007]),
[final] ).
cnf(i_0_3322,plain,
( c_Polynomial_Opoly__gcd(X1,X2,X3) = c_Polynomial_Opoly__gcd(X1,X3,X2)
| ~ class_Fields_Ofield(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2008]),
[final] ).
cnf(i_0_3323,plain,
( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)) = c_Polynomial_OAbs__poly(X1,hAPP(c_COMBK(X1,tc_Nat_Onat),c_Groups_Ozero__class_Ozero(X1)))
| ~ class_Groups_Ozero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2009]),
[final] ).
cnf(i_0_3324,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| X1 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| X2 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
inference(split_conjunct,[status(thm)],[i_0_2010]),
[final] ).
cnf(i_0_3325,plain,
( hAPP(X3,X4) = hAPP(X3,X5)
| ~ c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_2000]),
[final] ).
cnf(i_0_3326,plain,
( X2 = c_Groups_Ozero__class_Ozero(X1)
| c_Polynomial_Omonom(X1,X2,X3) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))
| ~ class_Groups_Ozero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2011]),
[final] ).
cnf(i_0_3327,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X2),X2))
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2012]),
[final] ).
cnf(i_0_3328,plain,
( X1 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
inference(split_conjunct,[status(thm)],[i_0_2010]),
[final] ).
cnf(i_0_3329,plain,
( X1 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
inference(split_conjunct,[status(thm)],[i_0_2010]),
[final] ).
cnf(i_0_3330,plain,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X1)),X1) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[i_0_2013]),
[final] ).
cnf(i_0_3331,plain,
( ~ class_Rings_Olinordered__semidom(X1)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),c_Groups_Ozero__class_Ozero(X1)) ),
inference(split_conjunct,[status(thm)],[i_0_2014]),
[final] ).
cnf(i_0_3332,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X1)),X2),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Ocomm__semiring__0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2015]),
[final] ).
cnf(i_0_3333,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X2)
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2016]),
[final] ).
cnf(i_0_3334,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X3),X2)
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2017]),
[final] ).
cnf(i_0_3335,plain,
( X1 = c_Groups_Ozero__class_Ozero(X2)
| hAPP(hAPP(c_Polynomial_OpCons(X2),X1),X3) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| ~ class_Groups_Ozero(X2) ),
inference(split_conjunct,[status(thm)],[i_0_2007]),
[final] ).
cnf(i_0_3336,plain,
c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,hAPP(c_Nat_OSuc,X1)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,X1)),
inference(split_conjunct,[status(thm)],[i_0_2018]),
[final] ).
cnf(i_0_3337,plain,
( X2 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))
| c_Polynomial_Opos__poly(X1,X2)
| c_Polynomial_Opos__poly(X1,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X1)),X2))
| ~ class_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2019]),
[final] ).
cnf(i_0_3338,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2)
| X1 = X2
| c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_2020]),
[final] ).
cnf(i_0_3339,plain,
( X1 = X2
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_2021]),
[final] ).
cnf(i_0_3340,plain,
( X1 = X2
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_2022]),
[final] ).
cnf(i_0_3341,plain,
( c_Polynomial_Oorder(X1,X2,X3) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(c_Polynomial_Opoly(X1,X3),X2) = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Rings_Oidom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1894]),
[final] ).
cnf(i_0_3342,plain,
( c_Polynomial_Opoly__gcd(X1,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))
| ~ class_Fields_Ofield(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2023]),
[final] ).
cnf(i_0_3343,plain,
( X1 = hAPP(c_Nat_OSuc,esk11_1(X1))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1) ),
inference(split_conjunct,[status(thm)],[i_0_2024]),
[final] ).
cnf(i_0_3344,plain,
( c_Polynomial_Opoly__gcd(X2,X1,X3) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| X1 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| X3 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| ~ class_Fields_Ofield(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1991]),
[final] ).
cnf(i_0_3345,plain,
( X2 = c_Groups_Ozero__class_Ozero(X1)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),hAPP(c_Rings_Oinverse__class_Oinverse(X1),X2)) = c_Groups_Oone__class_Oone(X1)
| ~ class_Rings_Odivision__ring(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2025]),
[final] ).
cnf(i_0_3346,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X1) = c_Groups_Oone__class_Oone(X2)
| X1 != hAPP(c_Groups_Ouminus__class_Ouminus(X2),c_Groups_Oone__class_Oone(X2))
| ~ class_Rings_Oring__1__no__zero__divisors(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1977]),
[final] ).
cnf(i_0_3347,plain,
hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X1)),
inference(split_conjunct,[status(thm)],[i_0_2026]),
[final] ).
cnf(i_0_3348,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),c_Groups_Oone__class_Oone(tc_Nat_Onat)))
| X1 != c_Groups_Oone__class_Oone(tc_Nat_Onat) ),
inference(split_conjunct,[status(thm)],[i_0_1926]),
[final] ).
cnf(i_0_3349,plain,
( X2 = c_Groups_Ozero__class_Ozero(X1)
| X3 = c_Groups_Ozero__class_Ozero(X1)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3) != c_Groups_Ozero__class_Ozero(X1)
| ~ class_Rings_Oring__no__zero__divisors(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2027]),
[final] ).
cnf(i_0_3350,plain,
( X2 = c_Groups_Ozero__class_Ozero(X1)
| X3 = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Rings_Ono__zero__divisors(X1)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3) != c_Groups_Ozero__class_Ozero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2028]),
[final] ).
cnf(i_0_3351,plain,
( X2 = c_Groups_Ozero__class_Ozero(X1)
| X3 = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Rings_Ono__zero__divisors(X1)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3) != c_Groups_Ozero__class_Ozero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2029]),
[final] ).
cnf(i_0_3352,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(c_Nat_OSuc,X2)) = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Power_Opower(X1)
| ~ class_Rings_Osemiring__0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2030]),
[final] ).
cnf(i_0_3353,plain,
( X3 = c_Groups_Ozero__class_Ozero(X2)
| X1 != c_Groups_Ozero__class_Ozero(X2)
| hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X2),X4),X1) != X3
| ~ class_Fields_Ofield__inverse__zero(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1937]),
[final] ).
cnf(i_0_3354,plain,
( X3 = c_Groups_Ozero__class_Ozero(X2)
| X1 != c_Groups_Ozero__class_Ozero(X2)
| X3 != hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X2),X4),X1)
| ~ class_Fields_Ofield__inverse__zero(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1938]),
[final] ).
cnf(i_0_3355,plain,
( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
inference(split_conjunct,[status(thm)],[i_0_1972]),
[final] ).
cnf(i_0_3356,plain,
( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2) ),
inference(split_conjunct,[status(thm)],[i_0_1973]),
[final] ).
cnf(i_0_3357,plain,
( X2 = X3
| X3 = c_Groups_Ozero__class_Ozero(X1)
| hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X3) != c_Groups_Oone__class_Oone(X1)
| ~ class_Rings_Odivision__ring(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2031]),
[final] ).
cnf(i_0_3358,plain,
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X1)),X2),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))) = X2
| ~ class_Groups_Oab__group__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2032]),
[final] ).
cnf(i_0_3359,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X1)),X2),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))) = X2
| ~ class_Groups_Ocomm__monoid__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2033]),
[final] ).
cnf(i_0_3360,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)) = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Groups_Ogroup__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2034]),
[final] ).
cnf(i_0_3361,plain,
( X2 = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Rings_Oring__1__no__zero__divisors(X1)
| hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3) != c_Groups_Ozero__class_Ozero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2035]),
[final] ).
cnf(i_0_3362,plain,
( X2 = c_Groups_Ozero__class_Ozero(X1)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X2) != c_Groups_Ozero__class_Ozero(X1)
| ~ class_Groups_Olinordered__ab__group__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2036]),
[final] ).
cnf(i_0_3363,plain,
( X2 = c_Groups_Ozero__class_Ozero(X1)
| c_Groups_Ozero__class_Ozero(X1) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X2)
| ~ class_Groups_Olinordered__ab__group__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2037]),
[final] ).
cnf(i_0_3364,plain,
hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(split_conjunct,[status(thm)],[i_0_2038]),
[final] ).
cnf(i_0_3365,plain,
( hAPP(hAPP(c_Polynomial_OpCons(X1),c_Groups_Ozero__class_Ozero(X1)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))
| ~ class_Groups_Ozero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2039]),
[final] ).
cnf(i_0_3366,plain,
( c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(X1)) = hAPP(hAPP(c_Polynomial_OpCons(X1),c_Groups_Oone__class_Oone(X1)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)))
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2040]),
[final] ).
cnf(i_0_3367,plain,
( X2 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))
| c_Polynomial_Opoly(X1,X2) != c_Polynomial_Opoly(X1,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)))
| ~ class_Int_Oring__char__0(X1)
| ~ class_Rings_Oidom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2041]),
[final] ).
cnf(i_0_3368,plain,
( c_Polynomial_Osynthetic__div(X1,X2,X3) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))
| c_Polynomial_Odegree(X1,X2) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ class_Rings_Ocomm__semiring__0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1980]),
[final] ).
cnf(i_0_3369,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X3)
| X1 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(split_conjunct,[status(thm)],[i_0_1941]),
[final] ).
cnf(i_0_3370,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X3)
| X1 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(split_conjunct,[status(thm)],[i_0_1942]),
[final] ).
cnf(i_0_3371,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X1)
| X1 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(split_conjunct,[status(thm)],[i_0_1940]),
[final] ).
cnf(i_0_3372,plain,
( X2 = X3
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X2),X3) != c_Groups_Ozero__class_Ozero(X1)
| ~ class_Groups_Ogroup__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2042]),
[final] ).
cnf(i_0_3373,plain,
( X2 = X3
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X2),X3) != c_Groups_Ozero__class_Ozero(X1)
| ~ class_Groups_Oab__group__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2043]),
[final] ).
cnf(i_0_3374,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),X2))
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_1710]),
[final] ).
cnf(i_0_3375,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),X2))
| X2 != X1 ),
inference(split_conjunct,[status(thm)],[i_0_1710]),
[final] ).
cnf(i_0_3376,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),X2))
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_1711]),
[final] ).
cnf(i_0_3377,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),X2))
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_2044]),
[final] ).
cnf(i_0_3378,plain,
( c_Polynomial_Odegree(X1,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X1)),X2)) = c_Polynomial_Odegree(X1,X2)
| ~ class_Groups_Oab__group__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2045]),
[final] ).
cnf(i_0_3379,plain,
( X3 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),X3) = c_Groups_Ozero__class_Ozero(X2)
| X1 != c_Groups_Ozero__class_Ozero(X2)
| ~ class_Power_Opower(X2)
| ~ class_Rings_Omult__zero(X2)
| ~ class_Rings_Ono__zero__divisors(X2)
| ~ class_Rings_Ozero__neq__one(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1988]),
[final] ).
cnf(i_0_3380,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2),X1),X3) = c_Groups_Ozero__class_Ozero(X2)
| X1 != hAPP(c_Groups_Ouminus__class_Ouminus(X2),X3)
| ~ class_Groups_Ogroup__add(X2) ),
inference(split_conjunct,[status(thm)],[i_0_2005]),
[final] ).
cnf(i_0_3381,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2),X3),X1) = c_Groups_Ozero__class_Ozero(X2)
| X1 != hAPP(c_Groups_Ouminus__class_Ouminus(X2),X3)
| ~ class_Groups_Ogroup__add(X2) ),
inference(split_conjunct,[status(thm)],[i_0_2006]),
[final] ).
cnf(i_0_3382,plain,
( X2 = c_Groups_Ozero__class_Ozero(X1)
| hAPP(c_Rings_Oinverse__class_Oinverse(X1),X2) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),c_Groups_Oone__class_Oone(X1)),X2)
| ~ class_Rings_Odivision__ring(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2046]),
[final] ).
cnf(i_0_3383,plain,
( X1 != X2
| ~ c_Orderings_Oord__class_Oless(X3,X1,X2)
| ~ class_Orderings_Olinorder(X3) ),
inference(split_conjunct,[status(thm)],[i_0_1887]),
[final] ).
cnf(i_0_3384,plain,
( ~ class_Orderings_Oorder(X1)
| ~ c_Orderings_Oord__class_Oless(X1,X2,X3)
| X3 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_2047]),
[final] ).
cnf(i_0_3385,plain,
( ~ class_Orderings_Oorder(X1)
| ~ c_Orderings_Oord__class_Oless(X1,X2,X3)
| X2 != X3 ),
inference(split_conjunct,[status(thm)],[i_0_2048]),
[final] ).
cnf(i_0_3386,plain,
( ~ class_Orderings_Oorder(X1)
| ~ c_Orderings_Oord__class_Oless(X1,X2,X3)
| X2 != X3 ),
inference(split_conjunct,[status(thm)],[i_0_2049]),
[final] ).
cnf(i_0_3387,plain,
( ~ c_Orderings_Oord__class_Oless(X1,X2,X3)
| X2 != X3
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1994]),
[final] ).
cnf(i_0_3388,plain,
( ~ c_Orderings_Oord__class_Oless(X1,X2,X3)
| X3 != X2
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1994]),
[final] ).
cnf(i_0_3389,plain,
( X3 = c_Groups_Ozero__class_Ozero(X2)
| X1 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2),X1),X3)
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X2) ),
inference(split_conjunct,[status(thm)],[i_0_2050]),
[final] ).
cnf(i_0_3390,plain,
( hAPP(hAPP(c_Polynomial_OpCons(X2),X1),X3) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| X1 != c_Groups_Ozero__class_Ozero(X2)
| X3 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| ~ class_Groups_Ozero(X2) ),
inference(split_conjunct,[status(thm)],[i_0_2007]),
[final] ).
cnf(i_0_3391,plain,
hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X1,
inference(split_conjunct,[status(thm)],[i_0_2051]),
[final] ).
cnf(i_0_3392,plain,
( hAPP(c_Polynomial_Ocoeff(X2,X1),c_Polynomial_Odegree(X2,X1)) = c_Groups_Ozero__class_Ozero(X2)
| X1 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| ~ class_Groups_Ozero(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1975]),
[final] ).
cnf(i_0_3393,plain,
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
| X1 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(split_conjunct,[status(thm)],[i_0_2052]),
[final] ).
cnf(i_0_3394,plain,
hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),X1)),
inference(split_conjunct,[status(thm)],[i_0_2053]),
[final] ).
cnf(i_0_3395,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| X1 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X2 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
inference(split_conjunct,[status(thm)],[i_0_1972]),
[final] ).
cnf(i_0_3396,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| X1 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| X2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(split_conjunct,[status(thm)],[i_0_1972]),
[final] ).
cnf(i_0_3397,plain,
( hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)
| X1 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X2 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
inference(split_conjunct,[status(thm)],[i_0_1973]),
[final] ).
cnf(i_0_3398,plain,
( hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)
| X1 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| X2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(split_conjunct,[status(thm)],[i_0_1973]),
[final] ).
cnf(i_0_3399,plain,
( hAPP(c_Polynomial_Ocoeff(X2,c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(X2))),X1) = c_Groups_Oone__class_Oone(X2)
| X1 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ class_Rings_Ocomm__semiring__1(X2) ),
inference(split_conjunct,[status(thm)],[i_0_2054]),
[final] ).
cnf(i_0_3400,plain,
( ~ class_Orderings_Opreorder(X1)
| ~ c_Orderings_Oord__class_Oless(X1,X2,X2) ),
inference(split_conjunct,[status(thm)],[i_0_2055]),
[final] ).
cnf(i_0_3401,plain,
hAPP(hAPP(c_COMBK(X1,X2),X3),X4) = X3,
inference(split_conjunct,[status(thm)],[i_0_2056]),
[final] ).
cnf(i_0_3402,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X1),
inference(split_conjunct,[status(thm)],[i_0_2057]),
[final] ).
cnf(i_0_3403,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1),
inference(split_conjunct,[status(thm)],[i_0_2058]),
[final] ).
cnf(i_0_3404,plain,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X1),
inference(split_conjunct,[status(thm)],[i_0_2059]),
[final] ).
cnf(i_0_3405,plain,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X1),
inference(split_conjunct,[status(thm)],[i_0_2060]),
[final] ).
cnf(i_0_3406,plain,
( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(c_Polynomial_Ocoeff(X2,c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(X2))),X1) = c_Groups_Ozero__class_Ozero(X2)
| ~ class_Rings_Ocomm__semiring__1(X2) ),
inference(split_conjunct,[status(thm)],[i_0_2054]),
[final] ).
cnf(i_0_3407,plain,
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),c_Groups_Ozero__class_Ozero(X1)),X2) = hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)
| ~ class_Groups_Ogroup__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2061]),
[final] ).
cnf(i_0_3408,plain,
( hAPP(c_Rings_Oinverse__class_Oinverse(X1),X2) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),c_Groups_Oone__class_Oone(X1)),X2)
| ~ class_Rings_Odivision__ring(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2062]),
[final] ).
cnf(i_0_3409,plain,
( hAPP(c_Rings_Oinverse__class_Oinverse(X1),X2) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),c_Groups_Oone__class_Oone(X1)),X2)
| ~ class_Fields_Ofield(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2063]),
[final] ).
cnf(i_0_3410,plain,
( hBOOL(hAPP(hAPP(c_fconj,X1),X2))
| ~ hBOOL(X1)
| ~ hBOOL(X2) ),
inference(split_conjunct,[status(thm)],[i_0_2064]),
[final] ).
cnf(i_0_3411,plain,
( c_Polynomial_Opoly__gcd(X1,c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(X1)),X2) = c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(X1))
| ~ class_Fields_Ofield(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2065]),
[final] ).
cnf(i_0_3412,plain,
( c_Polynomial_Osynthetic__div(X1,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),X2) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Ocomm__semiring__0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2066]),
[final] ).
cnf(i_0_3413,plain,
( c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X1,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),X2) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Ocomm__semiring__0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2067]),
[final] ).
cnf(i_0_3414,plain,
( c_Polynomial_Opcompose(X1,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),X2) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Ocomm__semiring__0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2068]),
[final] ).
cnf(i_0_3415,plain,
( c_Polynomial_Opoly__gcd(X1,X2,c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(X1))) = c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(X1))
| ~ class_Fields_Ofield(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2069]),
[final] ).
cnf(i_0_3416,plain,
( c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X2,X1,X3) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| X1 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| ~ class_Rings_Ocomm__semiring__0(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1992]),
[final] ).
cnf(i_0_3417,plain,
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| X2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(split_conjunct,[status(thm)],[i_0_2070]),
[final] ).
cnf(i_0_3418,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(X2),c_Groups_Ozero__class_Ozero(X2)),X1) = c_Groups_Oone__class_Oone(X2)
| X1 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ class_Power_Opower(X2)
| ~ class_Rings_Osemiring__0(X2) ),
inference(split_conjunct,[status(thm)],[i_0_2071]),
[final] ).
cnf(i_0_3419,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(split_conjunct,[status(thm)],[i_0_2072]),
[final] ).
cnf(i_0_3420,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(split_conjunct,[status(thm)],[i_0_2073]),
[final] ).
cnf(i_0_3421,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(split_conjunct,[status(thm)],[i_0_2074]),
[final] ).
cnf(i_0_3422,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| X1 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(split_conjunct,[status(thm)],[i_0_1970]),
[final] ).
cnf(i_0_3423,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X1),X2) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| X1 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
inference(split_conjunct,[status(thm)],[i_0_2001]),
[final] ).
cnf(i_0_3424,plain,
( hAPP(hAPP(c_Polynomial_Osmult(X1),X2),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Ocomm__semiring__0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2075]),
[final] ).
cnf(i_0_3425,plain,
( hAPP(c_Polynomial_Ocoeff(X1,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))),X2) = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Groups_Ozero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2076]),
[final] ).
cnf(i_0_3426,plain,
( hAPP(c_Polynomial_Opoly(X1,c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(X1))),X2) = c_Groups_Oone__class_Oone(X1)
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2077]),
[final] ).
cnf(i_0_3427,plain,
( hAPP(c_Polynomial_Opoly(X1,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))),X2) = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Rings_Ocomm__semiring__0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2078]),
[final] ).
cnf(i_0_3428,plain,
( hAPP(hAPP(c_Polynomial_Osmult(X2),X3),X1) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| X1 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| ~ class_Rings_Oidom(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1989]),
[final] ).
cnf(i_0_3429,plain,
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_2079]),
[final] ).
cnf(i_0_3430,plain,
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| X2 != X1 ),
inference(split_conjunct,[status(thm)],[i_0_2080]),
[final] ).
cnf(i_0_3431,plain,
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_2022]),
[final] ).
cnf(i_0_3432,plain,
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| X2 != X1 ),
inference(split_conjunct,[status(thm)],[i_0_2022]),
[final] ).
cnf(i_0_3433,plain,
( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Power_Opower__class_Opower(X2),c_Groups_Ozero__class_Ozero(X2)),X1) = c_Groups_Ozero__class_Ozero(X2)
| ~ class_Power_Opower(X2)
| ~ class_Rings_Osemiring__0(X2) ),
inference(split_conjunct,[status(thm)],[i_0_2071]),
[final] ).
cnf(i_0_3434,plain,
( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,X1)) != c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,X2) ),
inference(split_conjunct,[status(thm)],[i_0_2081]),
[final] ).
cnf(i_0_3435,plain,
( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,X2)) != c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,X1) ),
inference(split_conjunct,[status(thm)],[i_0_2081]),
[final] ).
cnf(i_0_3436,plain,
c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[i_0_2082]),
[final] ).
cnf(i_0_3437,plain,
( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(split_conjunct,[status(thm)],[i_0_2083]),
[final] ).
cnf(i_0_3438,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X1),
inference(split_conjunct,[status(thm)],[i_0_2084]),
[final] ).
cnf(i_0_3439,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X1),
inference(split_conjunct,[status(thm)],[i_0_2085]),
[final] ).
cnf(i_0_3440,plain,
( X2 = c_Groups_Ozero__class_Ozero(X1)
| X3 = c_Groups_Ozero__class_Ozero(X1)
| X2 = X3
| ~ class_Rings_Odivision__ring(X1)
| hAPP(c_Rings_Oinverse__class_Oinverse(X1),X2) != hAPP(c_Rings_Oinverse__class_Oinverse(X1),X3) ),
inference(split_conjunct,[status(thm)],[i_0_2086]),
[final] ).
cnf(i_0_3441,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,hAPP(c_Nat_OSuc,X2))
| X1 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(split_conjunct,[status(thm)],[i_0_1861]),
[final] ).
cnf(i_0_3442,plain,
( X2 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X1 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2) ),
inference(split_conjunct,[status(thm)],[i_0_2087]),
[final] ).
cnf(i_0_3443,plain,
( hAPP(hAPP(c_Polynomial_Osmult(X1),c_Groups_Ozero__class_Ozero(X1)),X2) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Ocomm__semiring__0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2088]),
[final] ).
cnf(i_0_3444,plain,
( X1 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2) != c_Groups_Oone__class_Oone(tc_Nat_Onat) ),
inference(split_conjunct,[status(thm)],[i_0_2089]),
[final] ).
cnf(i_0_3445,plain,
( X1 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1) != c_Groups_Oone__class_Oone(tc_Nat_Onat) ),
inference(split_conjunct,[status(thm)],[i_0_2089]),
[final] ).
cnf(i_0_3446,plain,
( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(split_conjunct,[status(thm)],[i_0_2090]),
[final] ).
cnf(i_0_3447,plain,
( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X1) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(split_conjunct,[status(thm)],[i_0_2090]),
[final] ).
cnf(i_0_3448,plain,
( X1 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| c_Groups_Oone__class_Oone(tc_Nat_Onat) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2) ),
inference(split_conjunct,[status(thm)],[i_0_2091]),
[final] ).
cnf(i_0_3449,plain,
( X1 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| c_Groups_Oone__class_Oone(tc_Nat_Onat) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1) ),
inference(split_conjunct,[status(thm)],[i_0_2091]),
[final] ).
cnf(i_0_3450,plain,
( c_Polynomial_Omonom(X2,X1,X3) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| X1 != c_Groups_Ozero__class_Ozero(X2)
| ~ class_Groups_Ozero(X2) ),
inference(split_conjunct,[status(thm)],[i_0_2011]),
[final] ).
cnf(i_0_3451,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,hAPP(c_Nat_OSuc,X2))
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_1898]),
[final] ).
cnf(i_0_3452,plain,
c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1)),
inference(split_conjunct,[status(thm)],[i_0_2092]),
[final] ).
cnf(i_0_3453,plain,
( hAPP(hAPP(c_Polynomial_Osmult(X2),X1),X3) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| X1 != c_Groups_Ozero__class_Ozero(X2)
| ~ class_Rings_Oidom(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1989]),
[final] ).
cnf(i_0_3454,plain,
( c_Polynomial_Omonom(X1,c_Groups_Ozero__class_Ozero(X1),X2) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))
| ~ class_Groups_Ozero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2093]),
[final] ).
cnf(i_0_3455,plain,
( c_Power_Opower__class_Opower(X1) = c_Power_Opower_Opower(X1,c_Groups_Oone__class_Oone(X1),c_Groups_Otimes__class_Otimes(X1))
| ~ class_Power_Opower(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2094]),
[final] ).
cnf(i_0_3456,plain,
( X2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2) != X1 ),
inference(split_conjunct,[status(thm)],[i_0_2095]),
[final] ).
cnf(i_0_3457,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
| X1 != hAPP(c_Nat_OSuc,X2) ),
inference(split_conjunct,[status(thm)],[i_0_2024]),
[final] ).
cnf(i_0_3458,plain,
( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X2),X4),X3) = X1
| X1 != c_Groups_Ozero__class_Ozero(X2)
| X3 != c_Groups_Ozero__class_Ozero(X2)
| ~ class_Fields_Ofield__inverse__zero(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1937]),
[final] ).
cnf(i_0_3459,plain,
( X1 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X2),X4),X3)
| X1 != c_Groups_Ozero__class_Ozero(X2)
| X3 != c_Groups_Ozero__class_Ozero(X2)
| ~ class_Fields_Ofield__inverse__zero(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1938]),
[final] ).
cnf(i_0_3460,plain,
c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,hAPP(c_Nat_OSuc,X1)),
inference(split_conjunct,[status(thm)],[i_0_2096]),
[final] ).
cnf(i_0_3461,plain,
( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),c_Groups_Ozero__class_Ozero(X1)),X2) = c_Groups_Ozero__class_Ozero(X1)
| ~ class_RealVector_Oreal__normed__field(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2097]),
[final] ).
cnf(i_0_3462,plain,
( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),c_Groups_Ozero__class_Ozero(X1)),X2) = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Rings_Odivision__ring(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2098]),
[final] ).
cnf(i_0_3463,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(X1),c_Groups_Oone__class_Oone(X1)),X2) = c_Groups_Oone__class_Oone(X1)
| ~ class_Groups_Omonoid__mult(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2099]),
[final] ).
cnf(i_0_3464,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ozero__class_Ozero(X1)),X2) = c_Groups_Ozero__class_Ozero(X1)
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2100]),
[final] ).
cnf(i_0_3465,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ozero__class_Ozero(X1)),X2) = c_Groups_Ozero__class_Ozero(X1)
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2101]),
[final] ).
cnf(i_0_3466,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ozero__class_Ozero(X1)),X2) = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Rings_Omult__zero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2102]),
[final] ).
cnf(i_0_3467,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ozero__class_Ozero(X1)),X2) = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2103]),
[final] ).
cnf(i_0_3468,plain,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Oone__class_Oone(X1))
| ~ class_Rings_Olinordered__semidom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2104]),
[final] ).
cnf(i_0_3469,plain,
( X2 = X3
| hAPP(c_Rings_Oinverse__class_Oinverse(X1),X2) != hAPP(c_Rings_Oinverse__class_Oinverse(X1),X3)
| ~ class_Rings_Odivision__ring__inverse__zero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2105]),
[final] ).
cnf(i_0_3470,plain,
( X2 = X3
| ~ class_Rings_Odivision__ring__inverse__zero(X1)
| hAPP(c_Rings_Oinverse__class_Oinverse(X1),X2) != hAPP(c_Rings_Oinverse__class_Oinverse(X1),X3) ),
inference(split_conjunct,[status(thm)],[i_0_2106]),
[final] ).
cnf(i_0_3471,plain,
( X2 = X3
| hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2) != hAPP(c_Groups_Ouminus__class_Ouminus(X1),X3)
| ~ class_Lattices_Oboolean__algebra(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2107]),
[final] ).
cnf(i_0_3472,plain,
( X2 = X3
| hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2) != hAPP(c_Groups_Ouminus__class_Ouminus(X1),X3)
| ~ class_Groups_Ogroup__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2108]),
[final] ).
cnf(i_0_3473,plain,
( hAPP(hAPP(c_Polynomial_Osmult(X1),c_Groups_Oone__class_Oone(X1)),X2) = X2
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2109]),
[final] ).
cnf(i_0_3474,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Oone__class_Oone(X1)),X2) = X2
| ~ class_Groups_Ocomm__monoid__mult(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2110]),
[final] ).
cnf(i_0_3475,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Oone__class_Oone(X1)),X2) = X2
| ~ class_Groups_Omonoid__mult(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2111]),
[final] ).
cnf(i_0_3476,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Oone__class_Oone(X1)),X2) = X2
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2112]),
[final] ).
cnf(i_0_3477,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),c_Groups_Ozero__class_Ozero(X1)),X2) = X2
| ~ class_Groups_Omonoid__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2113]),
[final] ).
cnf(i_0_3478,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),c_Groups_Ozero__class_Ozero(X1)),X2) = X2
| ~ class_Groups_Ocomm__monoid__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2114]),
[final] ).
cnf(i_0_3479,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),c_Groups_Ozero__class_Ozero(X1)),X2) = X2
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2115]),
[final] ).
cnf(i_0_3480,plain,
( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X3),X1),X2) = c_Groups_Oone__class_Oone(X3)
| X2 = c_Groups_Ozero__class_Ozero(X3)
| X1 != X2
| ~ class_Rings_Odivision__ring(X3) ),
inference(split_conjunct,[status(thm)],[i_0_2031]),
[final] ).
cnf(i_0_3481,plain,
( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X2),X1),X1) = c_Groups_Ozero__class_Ozero(X2)
| X1 != c_Groups_Ozero__class_Ozero(X2)
| ~ class_Rings_Odivision__ring__inverse__zero(X2) ),
inference(split_conjunct,[status(thm)],[i_0_2116]),
[final] ).
cnf(i_0_3482,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X1) = c_Groups_Oone__class_Oone(X2)
| X1 != c_Groups_Oone__class_Oone(X2)
| ~ class_Rings_Oring__1__no__zero__divisors(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1977]),
[final] ).
cnf(i_0_3483,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X3) = c_Groups_Ozero__class_Ozero(X2)
| X1 != c_Groups_Ozero__class_Ozero(X2)
| ~ class_Rings_Oring__no__zero__divisors(X2) ),
inference(split_conjunct,[status(thm)],[i_0_2027]),
[final] ).
cnf(i_0_3484,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X3),X1) = c_Groups_Ozero__class_Ozero(X2)
| X1 != c_Groups_Ozero__class_Ozero(X2)
| ~ class_Rings_Oring__no__zero__divisors(X2) ),
inference(split_conjunct,[status(thm)],[i_0_2027]),
[final] ).
cnf(i_0_3485,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2),X1),X1) = c_Groups_Ozero__class_Ozero(X2)
| X1 != c_Groups_Ozero__class_Ozero(X2)
| ~ class_Groups_Olinordered__ab__group__add(X2) ),
inference(split_conjunct,[status(thm)],[i_0_2036]),
[final] ).
cnf(i_0_3486,plain,
( c_Groups_Ozero__class_Ozero(X2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2),X1),X1)
| X1 != c_Groups_Ozero__class_Ozero(X2)
| ~ class_Groups_Olinordered__ab__group__add(X2) ),
inference(split_conjunct,[status(thm)],[i_0_2037]),
[final] ).
cnf(i_0_3487,plain,
( X2 = c_Groups_Ozero__class_Ozero(X1)
| hAPP(c_Rings_Oinverse__class_Oinverse(X1),hAPP(c_Rings_Oinverse__class_Oinverse(X1),X2)) = X2
| ~ class_Rings_Odivision__ring(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2117]),
[final] ).
cnf(i_0_3488,plain,
( c_Divides_Odiv__class_Odiv(X1,c_Groups_Ozero__class_Ozero(X1),X2) = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Divides_Osemiring__div(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2118]),
[final] ).
cnf(i_0_3489,plain,
( c_Divides_Odiv__class_Omod(X1,c_Groups_Ozero__class_Ozero(X1),X2) = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Divides_Osemiring__div(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2119]),
[final] ).
cnf(i_0_3490,plain,
( c_Divides_Odiv__class_Odiv(X1,X2,c_Groups_Ozero__class_Ozero(X1)) = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Divides_Osemiring__div(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2120]),
[final] ).
cnf(i_0_3491,plain,
( c_Divides_Odiv__class_Omod(X1,X2,c_Groups_Oone__class_Oone(X1)) = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Divides_Osemiring__div(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2121]),
[final] ).
cnf(i_0_3492,plain,
( X1 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(X2,X1) = hAPP(c_Nat_OSuc,c_Polynomial_Odegree(X2,X1))
| ~ class_Groups_Ozero(X2) ),
inference(split_conjunct,[status(thm)],[i_0_2122]),
[final] ).
cnf(i_0_3493,plain,
( X2 = c_Groups_Ozero__class_Ozero(X1)
| c_Divides_Odiv__class_Odiv(X1,X2,X2) = c_Groups_Oone__class_Oone(X1)
| ~ class_Divides_Osemiring__div(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2123]),
[final] ).
cnf(i_0_3494,plain,
( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),c_Groups_Ozero__class_Ozero(X1)) = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Rings_Odivision__ring__inverse__zero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2124]),
[final] ).
cnf(i_0_3495,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),c_Groups_Ozero__class_Ozero(X1)) = c_Groups_Ozero__class_Ozero(X1)
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2125]),
[final] ).
cnf(i_0_3496,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),c_Groups_Ozero__class_Ozero(X1)) = c_Groups_Ozero__class_Ozero(X1)
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2126]),
[final] ).
cnf(i_0_3497,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),c_Groups_Ozero__class_Ozero(X1)) = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Rings_Omult__zero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2127]),
[final] ).
cnf(i_0_3498,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),c_Groups_Ozero__class_Ozero(X1)) = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2128]),
[final] ).
cnf(i_0_3499,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(X2),X3),X1) = c_Groups_Oone__class_Oone(X2)
| X1 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ class_Power_Opower(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1596]),
[final] ).
cnf(i_0_3500,plain,
( hAPP(c_Polynomial_Opoly(X2,X1),X3) = c_Groups_Ozero__class_Ozero(X2)
| X1 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| ~ class_Rings_Oidom(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1894]),
[final] ).
cnf(i_0_3501,plain,
( X1 = X2
| ~ hBOOL(hAPP(c_fequal(X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_2129]),
[final] ).
cnf(i_0_3502,plain,
( X3 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2),X3),X1)
| X1 != c_Groups_Ozero__class_Ozero(X2)
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X2) ),
inference(split_conjunct,[status(thm)],[i_0_2050]),
[final] ).
cnf(i_0_3503,plain,
( X1 = c_Groups_Ozero__class_Ozero(X2)
| hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X2),X1),X1) = c_Groups_Oone__class_Oone(X2)
| ~ class_Rings_Odivision__ring__inverse__zero(X2) ),
inference(split_conjunct,[status(thm)],[i_0_2116]),
[final] ).
cnf(i_0_3504,plain,
( X2 = c_Groups_Ozero__class_Ozero(X1)
| hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X2) = c_Groups_Oone__class_Oone(X1)
| ~ class_Rings_Odivision__ring(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2130]),
[final] ).
cnf(i_0_3505,plain,
( c_Divides_Odiv__class_Odiv(X1,X2,c_Groups_Oone__class_Oone(X1)) = X2
| ~ class_Divides_Osemiring__div(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2131]),
[final] ).
cnf(i_0_3506,plain,
( c_Divides_Odiv__class_Omod(X1,X2,c_Groups_Ozero__class_Ozero(X1)) = X2
| ~ class_Divides_Osemiring__div(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2132]),
[final] ).
cnf(i_0_3507,plain,
( hAPP(c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X1)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))
| ~ class_Groups_Oab__group__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2133]),
[final] ).
cnf(i_0_3508,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X2),X1) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| X1 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(split_conjunct,[status(thm)],[i_0_2001]),
[final] ).
cnf(i_0_3509,plain,
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(X3),X1),X2) = c_Groups_Ozero__class_Ozero(X3)
| X1 != X2
| ~ class_Groups_Ogroup__add(X3) ),
inference(split_conjunct,[status(thm)],[i_0_2042]),
[final] ).
cnf(i_0_3510,plain,
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(X3),X1),X2) = c_Groups_Ozero__class_Ozero(X3)
| X1 != X2
| ~ class_Groups_Oab__group__add(X3) ),
inference(split_conjunct,[status(thm)],[i_0_2043]),
[final] ).
cnf(i_0_3511,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(X1)
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2134]),
[final] ).
cnf(i_0_3512,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(X1)
| ~ class_Power_Opower(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2135]),
[final] ).
cnf(i_0_3513,plain,
( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),c_Groups_Oone__class_Oone(X1)) = X2
| ~ class_Rings_Odivision__ring(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2136]),
[final] ).
cnf(i_0_3514,plain,
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X2),c_Groups_Ozero__class_Ozero(X1)) = X2
| ~ class_Groups_Ogroup__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2137]),
[final] ).
cnf(i_0_3515,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),c_Groups_Oone__class_Oone(X1)) = X2
| ~ class_Groups_Ocomm__monoid__mult(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2138]),
[final] ).
cnf(i_0_3516,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),c_Groups_Oone__class_Oone(X1)) = X2
| ~ class_Groups_Omonoid__mult(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2139]),
[final] ).
cnf(i_0_3517,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),c_Groups_Oone__class_Oone(X1)) = X2
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2140]),
[final] ).
cnf(i_0_3518,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),c_Groups_Ozero__class_Ozero(X1)) = X2
| ~ class_Groups_Omonoid__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2141]),
[final] ).
cnf(i_0_3519,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),c_Groups_Ozero__class_Ozero(X1)) = X2
| ~ class_Groups_Ocomm__monoid__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2142]),
[final] ).
cnf(i_0_3520,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),c_Groups_Ozero__class_Ozero(X1)) = X2
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2143]),
[final] ).
cnf(i_0_3521,plain,
( hAPP(c_Rings_Oinverse__class_Oinverse(X1),hAPP(c_Rings_Oinverse__class_Oinverse(X1),X2)) = X2
| ~ class_Rings_Odivision__ring__inverse__zero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2144]),
[final] ).
cnf(i_0_3522,plain,
( hAPP(c_Groups_Ouminus__class_Ouminus(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)) = X2
| ~ class_Lattices_Oboolean__algebra(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2145]),
[final] ).
cnf(i_0_3523,plain,
( hAPP(c_Groups_Ouminus__class_Ouminus(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)) = X2
| ~ class_Groups_Ogroup__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2146]),
[final] ).
cnf(i_0_3524,plain,
( c_Divides_Odiv__class_Omod(X1,X2,X2) = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Divides_Osemiring__div(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2147]),
[final] ).
cnf(i_0_3525,plain,
hAPP(c_Nat_OSuc,X1) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X1),
inference(split_conjunct,[status(thm)],[i_0_2148]),
[final] ).
cnf(i_0_3526,plain,
( hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,X1)) = c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,X2)
| X1 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(split_conjunct,[status(thm)],[i_0_2081]),
[final] ).
cnf(i_0_3527,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X2
| ~ class_Groups_Omonoid__mult(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2149]),
[final] ).
cnf(i_0_3528,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X2
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2150]),
[final] ).
cnf(i_0_3529,plain,
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X2),X2) = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Groups_Ogroup__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2151]),
[final] ).
cnf(i_0_3530,plain,
( hAPP(c_Groups_Ouminus__class_Ouminus(X1),X3) = X2
| hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2) != X3
| ~ class_Groups_Ogroup__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2152]),
[final] ).
cnf(i_0_3531,plain,
( hAPP(c_Groups_Ouminus__class_Ouminus(X1),X3) = X2
| hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2) != X3
| ~ class_Groups_Ogroup__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2152]),
[final] ).
cnf(i_0_3532,plain,
( X3 = hAPP(c_Groups_Ouminus__class_Ouminus(X2),X1)
| X1 != hAPP(c_Groups_Ouminus__class_Ouminus(X2),X3)
| ~ class_Groups_Ogroup__add(X2) ),
inference(split_conjunct,[status(thm)],[i_0_2153]),
[final] ).
cnf(i_0_3533,plain,
( X3 = hAPP(c_Groups_Ouminus__class_Ouminus(X2),X1)
| X1 != hAPP(c_Groups_Ouminus__class_Ouminus(X2),X3)
| ~ class_Groups_Ogroup__add(X2) ),
inference(split_conjunct,[status(thm)],[i_0_2153]),
[final] ).
cnf(i_0_3534,plain,
( c_Orderings_Oord__class_Oless__eq(X1,X2,X2)
| ~ class_Orderings_Opreorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2154]),
[final] ).
cnf(i_0_3535,plain,
hAPP(c_Nat_OSuc,X1) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),c_Groups_Oone__class_Oone(tc_Nat_Onat)),
inference(split_conjunct,[status(thm)],[i_0_2155]),
[final] ).
cnf(i_0_3536,plain,
( X2 = X3
| c_Polynomial_Opoly(X1,X2) != c_Polynomial_Opoly(X1,X3)
| ~ class_Int_Oring__char__0(X1)
| ~ class_Rings_Oidom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2156]),
[final] ).
cnf(i_0_3537,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| X1 != c_Groups_Oone__class_Oone(tc_Nat_Onat)
| X2 != c_Groups_Oone__class_Oone(tc_Nat_Onat) ),
inference(split_conjunct,[status(thm)],[i_0_2089]),
[final] ).
cnf(i_0_3538,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X1 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(split_conjunct,[status(thm)],[i_0_2090]),
[final] ).
cnf(i_0_3539,plain,
( c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2)
| X1 != c_Groups_Oone__class_Oone(tc_Nat_Onat)
| X2 != c_Groups_Oone__class_Oone(tc_Nat_Onat) ),
inference(split_conjunct,[status(thm)],[i_0_2091]),
[final] ).
cnf(i_0_3540,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X2) = X2
| ~ class_Lattices_Oab__semigroup__idem__mult(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2157]),
[final] ).
cnf(i_0_3541,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X2) = X2
| ~ class_Lattices_Oab__semigroup__idem__mult(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2158]),
[final] ).
cnf(i_0_3542,plain,
( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1) ),
inference(split_conjunct,[status(thm)],[i_0_2052]),
[final] ).
cnf(i_0_3543,plain,
( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1) ),
inference(split_conjunct,[status(thm)],[i_0_2159]),
[final] ).
cnf(i_0_3544,plain,
( X1 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X1) = c_Groups_Oone__class_Oone(tc_Int_Oint) ),
inference(split_conjunct,[status(thm)],[i_0_2160]),
[final] ).
cnf(i_0_3545,plain,
c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),
inference(split_conjunct,[status(thm)],[fact_int__0__less__1]),
[final] ).
cnf(i_0_3546,plain,
( ~ class_Rings_Olinordered__idom(X1)
| ~ c_Polynomial_Opos__poly(X1,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))) ),
inference(split_conjunct,[status(thm)],[i_0_2161]),
[final] ).
cnf(i_0_3547,plain,
c_Divides_Odiv__class_Odiv(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[i_0_2162]),
[final] ).
cnf(i_0_3548,plain,
c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[i_0_2163]),
[final] ).
cnf(i_0_3549,plain,
c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[i_0_2164]),
[final] ).
cnf(i_0_3550,plain,
c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = X1,
inference(split_conjunct,[status(thm)],[i_0_2164]),
[final] ).
cnf(i_0_3551,plain,
( c_Groups_Osgn__class_Osgn(tc_Polynomial_Opoly(X2),X1) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| X1 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| ~ class_Rings_Olinordered__idom(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1905]),
[final] ).
cnf(i_0_3552,plain,
c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X1) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[i_0_2165]),
[final] ).
cnf(i_0_3553,plain,
hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[i_0_2166]),
[final] ).
cnf(i_0_3554,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[i_0_2167]),
[final] ).
cnf(i_0_3555,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X2),X1) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| X1 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(split_conjunct,[status(thm)],[i_0_1628]),
[final] ).
cnf(i_0_3556,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X1 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(split_conjunct,[status(thm)],[i_0_1476]),
[final] ).
cnf(i_0_3557,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X1 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(split_conjunct,[status(thm)],[i_0_2083]),
[final] ).
cnf(i_0_3558,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X1 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(split_conjunct,[status(thm)],[i_0_2083]),
[final] ).
cnf(i_0_3559,plain,
( X2 = X3
| c_Nat_Osemiring__1__class_Oof__nat(X1,X2) != c_Nat_Osemiring__1__class_Oof__nat(X1,X3)
| ~ class_Nat_Osemiring__char__0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2168]),
[final] ).
cnf(i_0_3560,plain,
( X2 = X3
| c_Polynomial_Ocoeff(X1,X2) != c_Polynomial_Ocoeff(X1,X3)
| ~ class_Groups_Ozero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2169]),
[final] ).
cnf(i_0_3561,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1) = X1,
inference(split_conjunct,[status(thm)],[i_0_2170]),
[final] ).
cnf(i_0_3562,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X1) = X1,
inference(split_conjunct,[status(thm)],[i_0_2171]),
[final] ).
cnf(i_0_3563,plain,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1) = X1,
inference(split_conjunct,[status(thm)],[i_0_2172]),
[final] ).
cnf(i_0_3564,plain,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1) = X1,
inference(split_conjunct,[status(thm)],[i_0_2173]),
[final] ).
cnf(i_0_3565,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2) = X2
| X1 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(split_conjunct,[status(thm)],[i_0_1499]),
[final] ).
cnf(i_0_3566,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[i_0_2174]),
[final] ).
cnf(i_0_3567,plain,
( c_Groups_Ozero__class_Ozero(X1) = X2
| c_Groups_Ozero__class_Ozero(X1) != hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)
| ~ class_Groups_Ogroup__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2175]),
[final] ).
cnf(i_0_3568,plain,
( X2 = c_Groups_Oone__class_Oone(X1)
| hAPP(c_Rings_Oinverse__class_Oinverse(X1),X2) != c_Groups_Oone__class_Oone(X1)
| ~ class_Fields_Ofield__inverse__zero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2176]),
[final] ).
cnf(i_0_3569,plain,
( X2 = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Rings_Odivision__ring(X1)
| hAPP(c_Rings_Oinverse__class_Oinverse(X1),X2) != c_Groups_Ozero__class_Ozero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2177]),
[final] ).
cnf(i_0_3570,plain,
( X2 = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Rings_Odivision__ring(X1)
| hAPP(c_Rings_Oinverse__class_Oinverse(X1),X2) != c_Groups_Ozero__class_Ozero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2178]),
[final] ).
cnf(i_0_3571,plain,
( X2 = c_Groups_Ozero__class_Ozero(X1)
| hAPP(c_Rings_Oinverse__class_Oinverse(X1),X2) != c_Groups_Ozero__class_Ozero(X1)
| ~ class_Rings_Odivision__ring__inverse__zero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2179]),
[final] ).
cnf(i_0_3572,plain,
( X2 = c_Groups_Ozero__class_Ozero(X1)
| hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2) != c_Groups_Ozero__class_Ozero(X1)
| ~ class_Groups_Ogroup__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2180]),
[final] ).
cnf(i_0_3573,plain,
( ~ hBOOL(hAPP(c_fNot,X1))
| ~ hBOOL(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2181]),
[final] ).
cnf(i_0_3574,plain,
hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X1,
inference(split_conjunct,[status(thm)],[i_0_2182]),
[final] ).
cnf(i_0_3575,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),c_Groups_Oone__class_Oone(tc_Int_Oint)) = X1,
inference(split_conjunct,[status(thm)],[i_0_2183]),
[final] ).
cnf(i_0_3576,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X1,
inference(split_conjunct,[status(thm)],[i_0_2184]),
[final] ).
cnf(i_0_3577,plain,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = X1,
inference(split_conjunct,[status(thm)],[i_0_2185]),
[final] ).
cnf(i_0_3578,plain,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X1,
inference(split_conjunct,[status(thm)],[i_0_2186]),
[final] ).
cnf(i_0_3579,plain,
hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X1)) = X1,
inference(split_conjunct,[status(thm)],[i_0_2187]),
[final] ).
cnf(i_0_3580,plain,
hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),X1) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[i_0_2188]),
[final] ).
cnf(i_0_3581,plain,
( c_Polynomial_OAbs__poly(X1,c_Polynomial_Ocoeff(X1,X2)) = X2
| ~ class_Groups_Ozero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2189]),
[final] ).
cnf(i_0_3582,plain,
( hBOOL(hAPP(c_fequal(X1),X2))
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_2190]),
[final] ).
cnf(i_0_3583,plain,
( X2 = c_Groups_Ozero__class_Ozero(X1)
| hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2) != X2
| ~ class_Groups_Olinordered__ab__group__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2191]),
[final] ).
cnf(i_0_3584,plain,
( X1 = c_Groups_Ozero__class_Ozero(X2)
| X1 != hAPP(c_Groups_Ouminus__class_Ouminus(X2),X1)
| ~ class_Groups_Olinordered__ab__group__add(X2) ),
inference(split_conjunct,[status(thm)],[i_0_2192]),
[final] ).
cnf(i_0_3585,plain,
( X2 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))
| c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(X1,X2) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ class_Groups_Ozero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2193]),
[final] ).
cnf(i_0_3586,plain,
c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = c_Groups_Oone__class_Oone(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[fact_int__Suc0__eq__1]),
[final] ).
cnf(i_0_3587,plain,
( c_Polynomial_Odegree(X1,c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(X1))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2194]),
[final] ).
cnf(i_0_3588,plain,
( c_Polynomial_Odegree(X1,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ class_Groups_Ozero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2195]),
[final] ).
cnf(i_0_3589,plain,
( c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(X2,X1) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X1 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| ~ class_Groups_Ozero(X2) ),
inference(split_conjunct,[status(thm)],[i_0_2122]),
[final] ).
cnf(i_0_3590,plain,
( c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(X2,X1) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X1 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| ~ class_Groups_Ozero(X2) ),
inference(split_conjunct,[status(thm)],[i_0_2193]),
[final] ).
cnf(i_0_3591,plain,
( X1 = X2
| c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,X1) != c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,X2) ),
inference(split_conjunct,[status(thm)],[i_0_2196]),
[final] ).
cnf(i_0_3592,plain,
( X1 = X2
| c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,X1) != c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,X2) ),
inference(split_conjunct,[status(thm)],[i_0_2197]),
[final] ).
cnf(i_0_3593,plain,
( X1 = X2
| hAPP(c_Nat_OSuc,X1) != hAPP(c_Nat_OSuc,X2) ),
inference(split_conjunct,[status(thm)],[i_0_2198]),
[final] ).
cnf(i_0_3594,plain,
( X1 = X2
| hAPP(c_Nat_OSuc,X1) != hAPP(c_Nat_OSuc,X2) ),
inference(split_conjunct,[status(thm)],[i_0_2199]),
[final] ).
cnf(i_0_3595,plain,
( hAPP(c_Rings_Oinverse__class_Oinverse(X2),X1) = c_Groups_Oone__class_Oone(X2)
| X1 != c_Groups_Oone__class_Oone(X2)
| ~ class_Fields_Ofield__inverse__zero(X2) ),
inference(split_conjunct,[status(thm)],[i_0_2176]),
[final] ).
cnf(i_0_3596,plain,
( hAPP(c_Rings_Oinverse__class_Oinverse(X2),X1) = c_Groups_Ozero__class_Ozero(X2)
| X1 != c_Groups_Ozero__class_Ozero(X2)
| ~ class_Rings_Odivision__ring__inverse__zero(X2) ),
inference(split_conjunct,[status(thm)],[i_0_2179]),
[final] ).
cnf(i_0_3597,plain,
( hAPP(c_Groups_Ouminus__class_Ouminus(X2),X1) = c_Groups_Ozero__class_Ozero(X2)
| X1 != c_Groups_Ozero__class_Ozero(X2)
| ~ class_Groups_Ogroup__add(X2) ),
inference(split_conjunct,[status(thm)],[i_0_2180]),
[final] ).
cnf(i_0_3598,plain,
( c_Groups_Ozero__class_Ozero(X1) = hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)
| c_Groups_Ozero__class_Ozero(X1) != X2
| ~ class_Groups_Ogroup__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2175]),
[final] ).
cnf(i_0_3599,plain,
( hAPP(c_Rings_Oinverse__class_Oinverse(X1),c_Groups_Oone__class_Oone(X1)) = c_Groups_Oone__class_Oone(X1)
| ~ class_Rings_Odivision__ring(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2200]),
[final] ).
cnf(i_0_3600,plain,
( hAPP(c_Rings_Oinverse__class_Oinverse(X1),c_Groups_Ozero__class_Ozero(X1)) = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Fields_Ofield__inverse__zero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2201]),
[final] ).
cnf(i_0_3601,plain,
( hAPP(c_Rings_Oinverse__class_Oinverse(X1),c_Groups_Ozero__class_Ozero(X1)) = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Rings_Odivision__ring__inverse__zero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2202]),
[final] ).
cnf(i_0_3602,plain,
( hAPP(c_Groups_Ouminus__class_Ouminus(X1),c_Groups_Ozero__class_Ozero(X1)) = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Groups_Ogroup__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2203]),
[final] ).
cnf(i_0_3603,plain,
( class_Orderings_Oord(tc_fun(X2,X1))
| ~ class_Orderings_Oord(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2204]),
[final] ).
cnf(i_0_3604,plain,
( class_Orderings_Oorder(tc_fun(X2,X1))
| ~ class_Orderings_Oorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2205]),
[final] ).
cnf(i_0_3605,plain,
( class_Orderings_Opreorder(tc_fun(X2,X1))
| ~ class_Orderings_Opreorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2206]),
[final] ).
cnf(i_0_3606,plain,
( class_Groups_Ouminus(tc_fun(X2,X1))
| ~ class_Groups_Ouminus(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2207]),
[final] ).
cnf(i_0_3607,plain,
( class_Lattices_Oboolean__algebra(tc_fun(X2,X1))
| ~ class_Lattices_Oboolean__algebra(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2208]),
[final] ).
cnf(i_0_3608,plain,
( class_Groups_Ominus(tc_fun(X2,X1))
| ~ class_Groups_Ominus(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2209]),
[final] ).
cnf(i_0_3609,plain,
( hAPP(c_Groups_Ouminus__class_Ouminus(X2),X1) = X1
| X1 != c_Groups_Ozero__class_Ozero(X2)
| ~ class_Groups_Olinordered__ab__group__add(X2) ),
inference(split_conjunct,[status(thm)],[i_0_2191]),
[final] ).
cnf(i_0_3610,plain,
( X1 = hAPP(c_Groups_Ouminus__class_Ouminus(X2),X1)
| X1 != c_Groups_Ozero__class_Ozero(X2)
| ~ class_Groups_Olinordered__ab__group__add(X2) ),
inference(split_conjunct,[status(thm)],[i_0_2192]),
[final] ).
cnf(i_0_3611,plain,
( hBOOL(X1)
| hBOOL(hAPP(c_fNot,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_2210]),
[final] ).
cnf(i_0_3612,plain,
( c_Nat_Osemiring__1__class_Oof__nat(X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(X1)
| ~ class_Rings_Osemiring__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2211]),
[final] ).
cnf(i_0_3613,plain,
( c_Nat_Osemiring__1__class_Oof__nat(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Rings_Osemiring__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2212]),
[final] ).
cnf(i_0_3614,plain,
( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,X1) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
inference(split_conjunct,[status(thm)],[i_0_2213]),
[final] ).
cnf(i_0_3615,plain,
hAPP(c_Nat_OSuc,X1) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[i_0_2214]),
[final] ).
cnf(i_0_3616,plain,
hAPP(c_Nat_OSuc,X1) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[i_0_2215]),
[final] ).
cnf(i_0_3617,plain,
hAPP(c_Nat_OSuc,X1) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[i_0_2216]),
[final] ).
cnf(i_0_3618,plain,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,X1),
inference(split_conjunct,[status(thm)],[i_0_2217]),
[final] ).
cnf(i_0_3619,plain,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,X1),
inference(split_conjunct,[status(thm)],[i_0_2218]),
[final] ).
cnf(i_0_3620,plain,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,X1),
inference(split_conjunct,[status(thm)],[i_0_2219]),
[final] ).
cnf(i_0_3621,plain,
hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[fact_zminus__0]),
[final] ).
cnf(i_0_3622,plain,
hAPP(c_Nat_OSuc,X1) != X1,
inference(split_conjunct,[status(thm)],[i_0_2220]),
[final] ).
cnf(i_0_3623,plain,
X1 != hAPP(c_Nat_OSuc,X1),
inference(split_conjunct,[status(thm)],[i_0_2221]),
[final] ).
cnf(i_0_3624,plain,
hAPP(c_COMBI(X1),X2) = X2,
inference(split_conjunct,[status(thm)],[i_0_2222]),
[final] ).
cnf(i_0_3625,plain,
( c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,X1) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| X1 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(split_conjunct,[status(thm)],[i_0_2213]),
[final] ).
cnf(i_0_3626,plain,
( ~ class_Rings_Ozero__neq__one(X1)
| c_Groups_Oone__class_Oone(X1) != c_Groups_Ozero__class_Ozero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2223]),
[final] ).
cnf(i_0_3627,plain,
( ~ class_Rings_Ozero__neq__one(X1)
| c_Groups_Ozero__class_Ozero(X1) != c_Groups_Oone__class_Oone(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2224]),
[final] ).
cnf(i_0_3628,plain,
c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[fact_int__1]),
[final] ).
cnf(i_0_3629,plain,
c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[fact_int__0]),
[final] ).
cnf(i_0_3630,plain,
c_Groups_Oone__class_Oone(tc_Int_Oint) = c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Nat_Onat)),
inference(split_conjunct,[status(thm)],[fact_transfer__int__nat__numerals_I2_J]),
[final] ).
cnf(i_0_3631,plain,
c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(split_conjunct,[status(thm)],[fact_One__nat__def]),
[final] ).
cnf(i_0_3632,plain,
c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(split_conjunct,[status(thm)],[fact_transfer__int__nat__numerals_I1_J]),
[final] ).
cnf(i_0_3633,plain,
( class_Groups_Ocancel__comm__monoid__add(tc_Polynomial_Opoly(X1))
| ~ class_Groups_Ocancel__comm__monoid__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2225]),
[final] ).
cnf(i_0_3634,plain,
( class_Rings_Oordered__ring(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2226]),
[final] ).
cnf(i_0_3635,plain,
( class_Orderings_Oord(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2227]),
[final] ).
cnf(i_0_3636,plain,
( class_Orderings_Oorder(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2228]),
[final] ).
cnf(i_0_3637,plain,
( class_Orderings_Olinorder(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2229]),
[final] ).
cnf(i_0_3638,plain,
( class_Orderings_Opreorder(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2230]),
[final] ).
cnf(i_0_3639,plain,
( class_Groups_Oordered__cancel__ab__semigroup__add(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2231]),
[final] ).
cnf(i_0_3640,plain,
( class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2232]),
[final] ).
cnf(i_0_3641,plain,
( class_Groups_Oordered__ab__group__add(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2233]),
[final] ).
cnf(i_0_3642,plain,
( class_Rings_Olinordered__idom(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2234]),
[final] ).
cnf(i_0_3643,plain,
( class_Groups_Oordered__comm__monoid__add(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2235]),
[final] ).
cnf(i_0_3644,plain,
( class_Rings_Olinordered__ring(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2236]),
[final] ).
cnf(i_0_3645,plain,
( class_Rings_Olinordered__semiring__strict(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2237]),
[final] ).
cnf(i_0_3646,plain,
( class_Rings_Olinordered__comm__semiring__strict(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2238]),
[final] ).
cnf(i_0_3647,plain,
( class_Rings_Olinordered__semidom(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2239]),
[final] ).
cnf(i_0_3648,plain,
( class_Rings_Osemiring__1(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2240]),
[final] ).
cnf(i_0_3649,plain,
( class_Nat_Osemiring__char__0(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2241]),
[final] ).
cnf(i_0_3650,plain,
( class_Divides_Oring__div(tc_Polynomial_Opoly(X1))
| ~ class_Fields_Ofield(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2242]),
[final] ).
cnf(i_0_3651,plain,
( class_Divides_Osemiring__div(tc_Polynomial_Opoly(X1))
| ~ class_Fields_Ofield(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2243]),
[final] ).
cnf(i_0_3652,plain,
( class_Rings_Odvd(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2244]),
[final] ).
cnf(i_0_3653,plain,
( class_Groups_Ouminus(tc_Polynomial_Opoly(X1))
| ~ class_Groups_Oab__group__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2245]),
[final] ).
cnf(i_0_3654,plain,
( class_Groups_Ominus(tc_Polynomial_Opoly(X1))
| ~ class_Groups_Oab__group__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2246]),
[final] ).
cnf(i_0_3655,plain,
( class_Rings_Oring__1(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Ocomm__ring__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2247]),
[final] ).
cnf(i_0_3656,plain,
( class_Rings_Oring(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Ocomm__ring(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2248]),
[final] ).
cnf(i_0_3657,plain,
( class_Groups_Ogroup__add(tc_Polynomial_Opoly(X1))
| ~ class_Groups_Oab__group__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2249]),
[final] ).
cnf(i_0_3658,plain,
( class_Rings_Ocomm__ring(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Ocomm__ring(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2250]),
[final] ).
cnf(i_0_3659,plain,
( class_Groups_Oab__group__add(tc_Polynomial_Opoly(X1))
| ~ class_Groups_Oab__group__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2251]),
[final] ).
cnf(i_0_3660,plain,
( class_Rings_Oring__no__zero__divisors(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Oidom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2252]),
[final] ).
cnf(i_0_3661,plain,
( class_Rings_Ocomm__ring__1(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Ocomm__ring__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2253]),
[final] ).
cnf(i_0_3662,plain,
( class_Rings_Osemiring(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Ocomm__semiring__0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2254]),
[final] ).
cnf(i_0_3663,plain,
( class_Rings_Ocomm__semiring(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Ocomm__semiring__0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2255]),
[final] ).
cnf(i_0_3664,plain,
( class_Groups_Olinordered__ab__group__add(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2256]),
[final] ).
cnf(i_0_3665,plain,
( class_Groups_Omonoid__add(tc_Polynomial_Opoly(X1))
| ~ class_Groups_Ocomm__monoid__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2257]),
[final] ).
cnf(i_0_3666,plain,
( class_Groups_Oone(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2258]),
[final] ).
cnf(i_0_3667,plain,
( class_Groups_Ocancel__ab__semigroup__add(tc_Polynomial_Opoly(X1))
| ~ class_Groups_Ocancel__comm__monoid__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2259]),
[final] ).
cnf(i_0_3668,plain,
( class_Groups_Ocancel__semigroup__add(tc_Polynomial_Opoly(X1))
| ~ class_Groups_Ocancel__comm__monoid__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2260]),
[final] ).
cnf(i_0_3669,plain,
( class_Groups_Oab__semigroup__add(tc_Polynomial_Opoly(X1))
| ~ class_Groups_Ocomm__monoid__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2261]),
[final] ).
cnf(i_0_3670,plain,
( class_Groups_Oab__semigroup__mult(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Ocomm__semiring__0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2262]),
[final] ).
cnf(i_0_3671,plain,
( class_Rings_Olinordered__ring__strict(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2263]),
[final] ).
cnf(i_0_3672,plain,
( class_Groups_Ocomm__monoid__mult(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2264]),
[final] ).
cnf(i_0_3673,plain,
( class_Rings_Oring__1__no__zero__divisors(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Oidom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2265]),
[final] ).
cnf(i_0_3674,plain,
( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Oidom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2266]),
[final] ).
cnf(i_0_3675,plain,
( class_Int_Oring__char__0(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2267]),
[final] ).
cnf(i_0_3676,plain,
( class_Groups_Ocomm__monoid__add(tc_Polynomial_Opoly(X1))
| ~ class_Groups_Ocomm__monoid__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2268]),
[final] ).
cnf(i_0_3677,plain,
( class_Rings_Ozero__neq__one(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2269]),
[final] ).
cnf(i_0_3678,plain,
( class_Rings_Ono__zero__divisors(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Oidom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2270]),
[final] ).
cnf(i_0_3679,plain,
( class_Rings_Omult__zero(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Ocomm__semiring__0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2271]),
[final] ).
cnf(i_0_3680,plain,
( class_Groups_Omonoid__mult(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2272]),
[final] ).
cnf(i_0_3681,plain,
( class_Rings_Ocomm__semiring__1(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2273]),
[final] ).
cnf(i_0_3682,plain,
( class_Rings_Osemiring__0(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Ocomm__semiring__0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2274]),
[final] ).
cnf(i_0_3683,plain,
( class_Power_Opower(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2275]),
[final] ).
cnf(i_0_3684,plain,
( class_Rings_Ocomm__semiring__0(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Ocomm__semiring__0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2276]),
[final] ).
cnf(i_0_3685,plain,
( class_Groups_Ozero(tc_Polynomial_Opoly(X1))
| ~ class_Groups_Ozero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2277]),
[final] ).
cnf(i_0_3686,plain,
( class_Rings_Oidom(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Oidom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2278]),
[final] ).
cnf(i_0_3687,plain,
( class_Groups_Ocancel__comm__monoid__add(X1)
| ~ class_Rings_Oidom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2279]),
[final] ).
cnf(i_0_3688,plain,
( class_Rings_Osemiring__1(X1)
| ~ class_Rings_Oidom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2280]),
[final] ).
cnf(i_0_3689,plain,
( class_Rings_Odvd(X1)
| ~ class_Rings_Oidom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2281]),
[final] ).
cnf(i_0_3690,plain,
( class_Groups_Ouminus(X1)
| ~ class_Rings_Oidom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2282]),
[final] ).
cnf(i_0_3691,plain,
( class_Groups_Ominus(X1)
| ~ class_Rings_Oidom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2283]),
[final] ).
cnf(i_0_3692,plain,
( class_Rings_Oring__1(X1)
| ~ class_Rings_Oidom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2284]),
[final] ).
cnf(i_0_3693,plain,
( class_Rings_Oring(X1)
| ~ class_Rings_Oidom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2285]),
[final] ).
cnf(i_0_3694,plain,
( class_Groups_Ogroup__add(X1)
| ~ class_Rings_Oidom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2286]),
[final] ).
cnf(i_0_3695,plain,
( class_Rings_Ocomm__ring(X1)
| ~ class_Rings_Oidom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2287]),
[final] ).
cnf(i_0_3696,plain,
( class_Groups_Oab__group__add(X1)
| ~ class_Rings_Oidom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2288]),
[final] ).
cnf(i_0_3697,plain,
( class_Rings_Oring__no__zero__divisors(X1)
| ~ class_Rings_Oidom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2289]),
[final] ).
cnf(i_0_3698,plain,
( class_Rings_Ocomm__ring__1(X1)
| ~ class_Rings_Oidom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2290]),
[final] ).
cnf(i_0_3699,plain,
( class_Rings_Osemiring(X1)
| ~ class_Rings_Oidom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2291]),
[final] ).
cnf(i_0_3700,plain,
( class_Rings_Ocomm__semiring(X1)
| ~ class_Rings_Oidom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2292]),
[final] ).
cnf(i_0_3701,plain,
( class_Groups_Omonoid__add(X1)
| ~ class_Rings_Oidom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2293]),
[final] ).
cnf(i_0_3702,plain,
( class_Groups_Oone(X1)
| ~ class_Rings_Oidom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2294]),
[final] ).
cnf(i_0_3703,plain,
( class_Groups_Ocancel__ab__semigroup__add(X1)
| ~ class_Rings_Oidom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2295]),
[final] ).
cnf(i_0_3704,plain,
( class_Groups_Ocancel__semigroup__add(X1)
| ~ class_Rings_Oidom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2296]),
[final] ).
cnf(i_0_3705,plain,
( class_Groups_Oab__semigroup__add(X1)
| ~ class_Rings_Oidom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2297]),
[final] ).
cnf(i_0_3706,plain,
( class_Groups_Oab__semigroup__mult(X1)
| ~ class_Rings_Oidom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2298]),
[final] ).
cnf(i_0_3707,plain,
( class_Groups_Ocomm__monoid__mult(X1)
| ~ class_Rings_Oidom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2299]),
[final] ).
cnf(i_0_3708,plain,
( class_Rings_Oring__1__no__zero__divisors(X1)
| ~ class_Rings_Oidom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2300]),
[final] ).
cnf(i_0_3709,plain,
( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X1)
| ~ class_Rings_Oidom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2301]),
[final] ).
cnf(i_0_3710,plain,
( class_Groups_Ocomm__monoid__add(X1)
| ~ class_Rings_Oidom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2302]),
[final] ).
cnf(i_0_3711,plain,
( class_Rings_Ozero__neq__one(X1)
| ~ class_Rings_Oidom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2303]),
[final] ).
cnf(i_0_3712,plain,
( class_Rings_Ono__zero__divisors(X1)
| ~ class_Rings_Oidom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2304]),
[final] ).
cnf(i_0_3713,plain,
( class_Rings_Omult__zero(X1)
| ~ class_Rings_Oidom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2305]),
[final] ).
cnf(i_0_3714,plain,
( class_Groups_Omonoid__mult(X1)
| ~ class_Rings_Oidom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2306]),
[final] ).
cnf(i_0_3715,plain,
( class_Rings_Ocomm__semiring__1(X1)
| ~ class_Rings_Oidom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2307]),
[final] ).
cnf(i_0_3716,plain,
( class_Rings_Osemiring__0(X1)
| ~ class_Rings_Oidom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2308]),
[final] ).
cnf(i_0_3717,plain,
( class_Power_Opower(X1)
| ~ class_Rings_Oidom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2309]),
[final] ).
cnf(i_0_3718,plain,
( class_Rings_Ocomm__semiring__0(X1)
| ~ class_Rings_Oidom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2310]),
[final] ).
cnf(i_0_3719,plain,
( class_Groups_Ozero(X1)
| ~ class_Rings_Oidom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2311]),
[final] ).
cnf(i_0_3720,plain,
c_Groups_Ozero__class_Ozero(tc_Int_Oint) != c_Groups_Oone__class_Oone(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[fact_int__0__neq__1]),
[final] ).
cnf(i_0_3721,plain,
class_Groups_Ocancel__comm__monoid__add(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Groups_Ocancel__comm__monoid__add]),
[final] ).
cnf(i_0_3722,plain,
class_Groups_Ocancel__comm__monoid__add(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Groups_Ocancel__comm__monoid__add]),
[final] ).
cnf(i_0_3723,plain,
class_Rings_Oordered__ring(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Oordered__ring]),
[final] ).
cnf(i_0_3724,plain,
class_Orderings_Oord(tc_HOL_Obool),
inference(split_conjunct,[status(thm)],[arity_HOL__Obool__Orderings_Oord]),
[final] ).
cnf(i_0_3725,plain,
class_Orderings_Oord(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Orderings_Oord]),
[final] ).
cnf(i_0_3726,plain,
class_Orderings_Oord(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Orderings_Oord]),
[final] ).
cnf(i_0_3727,plain,
class_Orderings_Oorder(tc_HOL_Obool),
inference(split_conjunct,[status(thm)],[arity_HOL__Obool__Orderings_Oorder]),
[final] ).
cnf(i_0_3728,plain,
class_Orderings_Oorder(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Orderings_Oorder]),
[final] ).
cnf(i_0_3729,plain,
class_Orderings_Oorder(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Orderings_Oorder]),
[final] ).
cnf(i_0_3730,plain,
class_Orderings_Olinorder(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Orderings_Olinorder]),
[final] ).
cnf(i_0_3731,plain,
class_Orderings_Olinorder(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Orderings_Olinorder]),
[final] ).
cnf(i_0_3732,plain,
class_Orderings_Opreorder(tc_HOL_Obool),
inference(split_conjunct,[status(thm)],[arity_HOL__Obool__Orderings_Opreorder]),
[final] ).
cnf(i_0_3733,plain,
class_Orderings_Opreorder(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Orderings_Opreorder]),
[final] ).
cnf(i_0_3734,plain,
class_Orderings_Opreorder(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Orderings_Opreorder]),
[final] ).
cnf(i_0_3735,plain,
class_Groups_Oordered__cancel__ab__semigroup__add(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Groups_Oordered__cancel__ab__semigroup__add]),
[final] ).
cnf(i_0_3736,plain,
class_Groups_Oordered__cancel__ab__semigroup__add(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Groups_Oordered__cancel__ab__semigroup__add]),
[final] ).
cnf(i_0_3737,plain,
class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Groups_Oordered__ab__semigroup__add__imp__le]),
[final] ).
cnf(i_0_3738,plain,
class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Groups_Oordered__ab__semigroup__add__imp__le]),
[final] ).
cnf(i_0_3739,plain,
class_Groups_Oordered__ab__group__add(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Groups_Oordered__ab__group__add]),
[final] ).
cnf(i_0_3740,plain,
class_Rings_Olinordered__idom(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Olinordered__idom]),
[final] ).
cnf(i_0_3741,plain,
class_Groups_Oordered__comm__monoid__add(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Groups_Oordered__comm__monoid__add]),
[final] ).
cnf(i_0_3742,plain,
class_Groups_Oordered__comm__monoid__add(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Groups_Oordered__comm__monoid__add]),
[final] ).
cnf(i_0_3743,plain,
class_Rings_Olinordered__ring(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Olinordered__ring]),
[final] ).
cnf(i_0_3744,plain,
class_Rings_Olinordered__semiring__strict(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Olinordered__semiring__strict]),
[final] ).
cnf(i_0_3745,plain,
class_Rings_Olinordered__semiring__strict(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Rings_Olinordered__semiring__strict]),
[final] ).
cnf(i_0_3746,plain,
class_Rings_Olinordered__comm__semiring__strict(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Olinordered__comm__semiring__strict]),
[final] ).
cnf(i_0_3747,plain,
class_Rings_Olinordered__comm__semiring__strict(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Rings_Olinordered__comm__semiring__strict]),
[final] ).
cnf(i_0_3748,plain,
class_Rings_Olinordered__semidom(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Olinordered__semidom]),
[final] ).
cnf(i_0_3749,plain,
class_Rings_Olinordered__semidom(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Rings_Olinordered__semidom]),
[final] ).
cnf(i_0_3750,plain,
class_Rings_Osemiring__1(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Osemiring__1]),
[final] ).
cnf(i_0_3751,plain,
class_Rings_Osemiring__1(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Rings_Osemiring__1]),
[final] ).
cnf(i_0_3752,plain,
class_Nat_Osemiring__char__0(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Nat_Osemiring__char__0]),
[final] ).
cnf(i_0_3753,plain,
class_Nat_Osemiring__char__0(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Nat_Osemiring__char__0]),
[final] ).
cnf(i_0_3754,plain,
class_Divides_Oring__div(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Divides_Oring__div]),
[final] ).
cnf(i_0_3755,plain,
class_Divides_Osemiring__div(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Divides_Osemiring__div]),
[final] ).
cnf(i_0_3756,plain,
class_Divides_Osemiring__div(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Divides_Osemiring__div]),
[final] ).
cnf(i_0_3757,plain,
class_Orderings_Owellorder(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Orderings_Owellorder]),
[final] ).
cnf(i_0_3758,plain,
class_Rings_Odvd(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Odvd]),
[final] ).
cnf(i_0_3759,plain,
class_Rings_Odvd(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Rings_Odvd]),
[final] ).
cnf(i_0_3760,plain,
class_Groups_Ouminus(tc_HOL_Obool),
inference(split_conjunct,[status(thm)],[arity_HOL__Obool__Groups_Ouminus]),
[final] ).
cnf(i_0_3761,plain,
class_Groups_Ouminus(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Groups_Ouminus]),
[final] ).
cnf(i_0_3762,plain,
class_Lattices_Oboolean__algebra(tc_HOL_Obool),
inference(split_conjunct,[status(thm)],[arity_HOL__Obool__Lattices_Oboolean__algebra]),
[final] ).
cnf(i_0_3763,plain,
class_Groups_Ominus(tc_HOL_Obool),
inference(split_conjunct,[status(thm)],[arity_HOL__Obool__Groups_Ominus]),
[final] ).
cnf(i_0_3764,plain,
class_Groups_Ominus(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Groups_Ominus]),
[final] ).
cnf(i_0_3765,plain,
class_Groups_Ominus(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Groups_Ominus]),
[final] ).
cnf(i_0_3766,plain,
class_Rings_Oring__1(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Oring__1]),
[final] ).
cnf(i_0_3767,plain,
class_Rings_Oring(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Oring]),
[final] ).
cnf(i_0_3768,plain,
class_Groups_Ogroup__add(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Groups_Ogroup__add]),
[final] ).
cnf(i_0_3769,plain,
class_Rings_Ocomm__ring(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Ocomm__ring]),
[final] ).
cnf(i_0_3770,plain,
class_Groups_Oab__group__add(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Groups_Oab__group__add]),
[final] ).
cnf(i_0_3771,plain,
class_Rings_Oring__no__zero__divisors(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Oring__no__zero__divisors]),
[final] ).
cnf(i_0_3772,plain,
class_Rings_Ocomm__ring__1(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Ocomm__ring__1]),
[final] ).
cnf(i_0_3773,plain,
class_Rings_Osemiring(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Osemiring]),
[final] ).
cnf(i_0_3774,plain,
class_Rings_Osemiring(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Rings_Osemiring]),
[final] ).
cnf(i_0_3775,plain,
class_Rings_Ocomm__semiring(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Ocomm__semiring]),
[final] ).
cnf(i_0_3776,plain,
class_Rings_Ocomm__semiring(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Rings_Ocomm__semiring]),
[final] ).
cnf(i_0_3777,plain,
class_Groups_Olinordered__ab__group__add(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Groups_Olinordered__ab__group__add]),
[final] ).
cnf(i_0_3778,plain,
class_Groups_Omonoid__add(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Groups_Omonoid__add]),
[final] ).
cnf(i_0_3779,plain,
class_Groups_Omonoid__add(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Groups_Omonoid__add]),
[final] ).
cnf(i_0_3780,plain,
class_Groups_Oone(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Groups_Oone]),
[final] ).
cnf(i_0_3781,plain,
class_Groups_Oone(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Groups_Oone]),
[final] ).
cnf(i_0_3782,plain,
class_Groups_Ocancel__ab__semigroup__add(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Groups_Ocancel__ab__semigroup__add]),
[final] ).
cnf(i_0_3783,plain,
class_Groups_Ocancel__ab__semigroup__add(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Groups_Ocancel__ab__semigroup__add]),
[final] ).
cnf(i_0_3784,plain,
class_Groups_Ocancel__semigroup__add(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Groups_Ocancel__semigroup__add]),
[final] ).
cnf(i_0_3785,plain,
class_Groups_Ocancel__semigroup__add(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Groups_Ocancel__semigroup__add]),
[final] ).
cnf(i_0_3786,plain,
class_Groups_Oab__semigroup__add(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Groups_Oab__semigroup__add]),
[final] ).
cnf(i_0_3787,plain,
class_Groups_Oab__semigroup__add(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Groups_Oab__semigroup__add]),
[final] ).
cnf(i_0_3788,plain,
class_Groups_Oab__semigroup__mult(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Groups_Oab__semigroup__mult]),
[final] ).
cnf(i_0_3789,plain,
class_Groups_Oab__semigroup__mult(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Groups_Oab__semigroup__mult]),
[final] ).
cnf(i_0_3790,plain,
class_Rings_Olinordered__ring__strict(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Olinordered__ring__strict]),
[final] ).
cnf(i_0_3791,plain,
class_Groups_Ocomm__monoid__mult(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Groups_Ocomm__monoid__mult]),
[final] ).
cnf(i_0_3792,plain,
class_Groups_Ocomm__monoid__mult(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Groups_Ocomm__monoid__mult]),
[final] ).
cnf(i_0_3793,plain,
class_Rings_Oring__1__no__zero__divisors(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Oring__1__no__zero__divisors]),
[final] ).
cnf(i_0_3794,plain,
class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct]),
[final] ).
cnf(i_0_3795,plain,
class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct]),
[final] ).
cnf(i_0_3796,plain,
class_Int_Oring__char__0(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Int_Oring__char__0]),
[final] ).
cnf(i_0_3797,plain,
class_Groups_Ocomm__monoid__add(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Groups_Ocomm__monoid__add]),
[final] ).
cnf(i_0_3798,plain,
class_Groups_Ocomm__monoid__add(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Groups_Ocomm__monoid__add]),
[final] ).
cnf(i_0_3799,plain,
class_Rings_Ozero__neq__one(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Ozero__neq__one]),
[final] ).
cnf(i_0_3800,plain,
class_Rings_Ozero__neq__one(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Rings_Ozero__neq__one]),
[final] ).
cnf(i_0_3801,plain,
class_Rings_Ono__zero__divisors(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Ono__zero__divisors]),
[final] ).
cnf(i_0_3802,plain,
class_Rings_Ono__zero__divisors(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Rings_Ono__zero__divisors]),
[final] ).
cnf(i_0_3803,plain,
class_Rings_Omult__zero(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Omult__zero]),
[final] ).
cnf(i_0_3804,plain,
class_Rings_Omult__zero(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Rings_Omult__zero]),
[final] ).
cnf(i_0_3805,plain,
class_Groups_Omonoid__mult(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Groups_Omonoid__mult]),
[final] ).
cnf(i_0_3806,plain,
class_Groups_Omonoid__mult(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Groups_Omonoid__mult]),
[final] ).
cnf(i_0_3807,plain,
class_Rings_Ocomm__semiring__1(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Ocomm__semiring__1]),
[final] ).
cnf(i_0_3808,plain,
class_Rings_Ocomm__semiring__1(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Rings_Ocomm__semiring__1]),
[final] ).
cnf(i_0_3809,plain,
class_Rings_Osemiring__0(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Osemiring__0]),
[final] ).
cnf(i_0_3810,plain,
class_Rings_Osemiring__0(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Rings_Osemiring__0]),
[final] ).
cnf(i_0_3811,plain,
class_Power_Opower(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Power_Opower]),
[final] ).
cnf(i_0_3812,plain,
class_Power_Opower(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Power_Opower]),
[final] ).
cnf(i_0_3813,plain,
class_Rings_Ocomm__semiring__0(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Ocomm__semiring__0]),
[final] ).
cnf(i_0_3814,plain,
class_Rings_Ocomm__semiring__0(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Rings_Ocomm__semiring__0]),
[final] ).
cnf(i_0_3815,plain,
class_Groups_Ozero(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Groups_Ozero]),
[final] ).
cnf(i_0_3816,plain,
class_Groups_Ozero(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Groups_Ozero]),
[final] ).
cnf(i_0_3817,plain,
class_Rings_Oidom(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Oidom]),
[final] ).
cnf(i_0_3818,hypothesis,
class_Rings_Oidom(t_a),
inference(split_conjunct,[status(thm)],[tfree_0]),
[final] ).
cnf(i_0_3819,axiom,
X1 = X1 ).
cnf(i_0_3820,axiom,
( X1 = X2
| X2 != X1 ) ).
cnf(i_0_3821,axiom,
( X1 = X2
| X1 != X3
| X3 != X2 ) ).
cnf(i_0_3822,axiom,
( X1 != X2
| c_Polynomial_Oorder(X1,X3,X4) = c_Polynomial_Oorder(X2,X3,X4) ) ).
cnf(i_0_3823,axiom,
( X1 != X2
| c_Polynomial_Oorder(X3,X1,X4) = c_Polynomial_Oorder(X3,X2,X4) ) ).
cnf(i_0_3824,axiom,
( X1 != X2
| c_Polynomial_Oorder(X3,X4,X1) = c_Polynomial_Oorder(X3,X4,X2) ) ).
cnf(i_0_3825,axiom,
( X1 != X2
| c_Groups_Oone__class_Oone(X1) = c_Groups_Oone__class_Oone(X2) ) ).
cnf(i_0_3826,axiom,
( X1 != X2
| c_Groups_Ozero__class_Ozero(X1) = c_Groups_Ozero__class_Ozero(X2) ) ).
cnf(i_0_3827,axiom,
( X1 != X2
| c_Polynomial_Opcompose(X1,X3,X4) = c_Polynomial_Opcompose(X2,X3,X4) ) ).
cnf(i_0_3828,axiom,
( X1 != X2
| c_Polynomial_Opcompose(X3,X1,X4) = c_Polynomial_Opcompose(X3,X2,X4) ) ).
cnf(i_0_3829,axiom,
( X1 != X2
| c_Polynomial_Opcompose(X3,X4,X1) = c_Polynomial_Opcompose(X3,X4,X2) ) ).
cnf(i_0_3830,axiom,
( X1 != X2
| c_Polynomial_Opoly__rec(X1,X3,X4,X5,X6) = c_Polynomial_Opoly__rec(X2,X3,X4,X5,X6) ) ).
cnf(i_0_3831,axiom,
( X1 != X2
| c_Polynomial_Opoly__rec(X3,X1,X4,X5,X6) = c_Polynomial_Opoly__rec(X3,X2,X4,X5,X6) ) ).
cnf(i_0_3832,axiom,
( X1 != X2
| c_Polynomial_Opoly__rec(X3,X4,X1,X5,X6) = c_Polynomial_Opoly__rec(X3,X4,X2,X5,X6) ) ).
cnf(i_0_3833,axiom,
( X1 != X2
| c_Polynomial_Opoly__rec(X3,X4,X5,X1,X6) = c_Polynomial_Opoly__rec(X3,X4,X5,X2,X6) ) ).
cnf(i_0_3834,axiom,
( X1 != X2
| c_Polynomial_Opoly__rec(X3,X4,X5,X6,X1) = c_Polynomial_Opoly__rec(X3,X4,X5,X6,X2) ) ).
cnf(i_0_3835,axiom,
( X1 != X2
| c_Orderings_Oord__class_OLeast(X1,X3) = c_Orderings_Oord__class_OLeast(X2,X3) ) ).
cnf(i_0_3836,axiom,
( X1 != X2
| c_Orderings_Oord__class_OLeast(X3,X1) = c_Orderings_Oord__class_OLeast(X3,X2) ) ).
cnf(i_0_3837,axiom,
( X1 != X2
| c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X1,X3,X4) = c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X2,X3,X4) ) ).
cnf(i_0_3838,axiom,
( X1 != X2
| c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X3,X1,X4) = c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X3,X2,X4) ) ).
cnf(i_0_3839,axiom,
( X1 != X2
| c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X3,X4,X1) = c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X3,X4,X2) ) ).
cnf(i_0_3840,axiom,
( X1 != X2
| c_Divides_Odiv__class_Omod(X1,X3,X4) = c_Divides_Odiv__class_Omod(X2,X3,X4) ) ).
cnf(i_0_3841,axiom,
( X1 != X2
| c_Divides_Odiv__class_Omod(X3,X1,X4) = c_Divides_Odiv__class_Omod(X3,X2,X4) ) ).
cnf(i_0_3842,axiom,
( X1 != X2
| c_Divides_Odiv__class_Omod(X3,X4,X1) = c_Divides_Odiv__class_Omod(X3,X4,X2) ) ).
cnf(i_0_3843,axiom,
( X1 != X2
| c_Polynomial_Ocoeff(X1,X3) = c_Polynomial_Ocoeff(X2,X3) ) ).
cnf(i_0_3844,axiom,
( X1 != X2
| c_Polynomial_Ocoeff(X3,X1) = c_Polynomial_Ocoeff(X3,X2) ) ).
cnf(i_0_3845,axiom,
( X1 != X2
| c_Polynomial_Odegree(X1,X3) = c_Polynomial_Odegree(X2,X3) ) ).
cnf(i_0_3846,axiom,
( X1 != X2
| c_Polynomial_Odegree(X3,X1) = c_Polynomial_Odegree(X3,X2) ) ).
cnf(i_0_3847,axiom,
( X1 != X2
| c_Polynomial_Omonom(X1,X3,X4) = c_Polynomial_Omonom(X2,X3,X4) ) ).
cnf(i_0_3848,axiom,
( X1 != X2
| c_Polynomial_Omonom(X3,X1,X4) = c_Polynomial_Omonom(X3,X2,X4) ) ).
cnf(i_0_3849,axiom,
( X1 != X2
| c_Polynomial_Omonom(X3,X4,X1) = c_Polynomial_Omonom(X3,X4,X2) ) ).
cnf(i_0_3850,axiom,
( X1 != X2
| c_Polynomial_OAbs__poly(X1,X3) = c_Polynomial_OAbs__poly(X2,X3) ) ).
cnf(i_0_3851,axiom,
( X1 != X2
| c_Polynomial_OAbs__poly(X3,X1) = c_Polynomial_OAbs__poly(X3,X2) ) ).
cnf(i_0_3852,axiom,
( X1 != X2
| hAPP(X1,X3) = hAPP(X2,X3) ) ).
cnf(i_0_3853,axiom,
( X1 != X2
| hAPP(X3,X1) = hAPP(X3,X2) ) ).
cnf(i_0_3854,axiom,
( X1 != X2
| c_Nat_Osemiring__1__class_Oof__nat(X1,X3) = c_Nat_Osemiring__1__class_Oof__nat(X2,X3) ) ).
cnf(i_0_3855,axiom,
( X1 != X2
| c_Nat_Osemiring__1__class_Oof__nat(X3,X1) = c_Nat_Osemiring__1__class_Oof__nat(X3,X2) ) ).
cnf(i_0_3856,axiom,
( X1 != X2
| c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(X1,X3) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(X2,X3) ) ).
cnf(i_0_3857,axiom,
( X1 != X2
| c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(X3,X1) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(X3,X2) ) ).
cnf(i_0_3858,axiom,
( X1 != X2
| c_Polynomial_Opoly(X1,X3) = c_Polynomial_Opoly(X2,X3) ) ).
cnf(i_0_3859,axiom,
( X1 != X2
| c_Polynomial_Opoly(X3,X1) = c_Polynomial_Opoly(X3,X2) ) ).
cnf(i_0_3860,axiom,
( X1 != X2
| c_Polynomial_Osynthetic__div(X1,X3,X4) = c_Polynomial_Osynthetic__div(X2,X3,X4) ) ).
cnf(i_0_3861,axiom,
( X1 != X2
| c_Polynomial_Osynthetic__div(X3,X1,X4) = c_Polynomial_Osynthetic__div(X3,X2,X4) ) ).
cnf(i_0_3862,axiom,
( X1 != X2
| c_Polynomial_Osynthetic__div(X3,X4,X1) = c_Polynomial_Osynthetic__div(X3,X4,X2) ) ).
cnf(i_0_3863,axiom,
( X1 != X2
| c_Divides_Odiv__class_Odiv(X1,X3,X4) = c_Divides_Odiv__class_Odiv(X2,X3,X4) ) ).
cnf(i_0_3864,axiom,
( X1 != X2
| c_Divides_Odiv__class_Odiv(X3,X1,X4) = c_Divides_Odiv__class_Odiv(X3,X2,X4) ) ).
cnf(i_0_3865,axiom,
( X1 != X2
| c_Divides_Odiv__class_Odiv(X3,X4,X1) = c_Divides_Odiv__class_Odiv(X3,X4,X2) ) ).
cnf(i_0_3866,axiom,
( X1 != X2
| c_Polynomial_Opoly__gcd(X1,X3,X4) = c_Polynomial_Opoly__gcd(X2,X3,X4) ) ).
cnf(i_0_3867,axiom,
( X1 != X2
| c_Polynomial_Opoly__gcd(X3,X1,X4) = c_Polynomial_Opoly__gcd(X3,X2,X4) ) ).
cnf(i_0_3868,axiom,
( X1 != X2
| c_Polynomial_Opoly__gcd(X3,X4,X1) = c_Polynomial_Opoly__gcd(X3,X4,X2) ) ).
cnf(i_0_3869,axiom,
( X1 != X2
| c_Nat_Osemiring__1__class_Oof__nat__aux(X1,X3,X4,X5) = c_Nat_Osemiring__1__class_Oof__nat__aux(X2,X3,X4,X5) ) ).
cnf(i_0_3870,axiom,
( X1 != X2
| c_Nat_Osemiring__1__class_Oof__nat__aux(X3,X1,X4,X5) = c_Nat_Osemiring__1__class_Oof__nat__aux(X3,X2,X4,X5) ) ).
cnf(i_0_3871,axiom,
( X1 != X2
| c_Nat_Osemiring__1__class_Oof__nat__aux(X3,X4,X1,X5) = c_Nat_Osemiring__1__class_Oof__nat__aux(X3,X4,X2,X5) ) ).
cnf(i_0_3872,axiom,
( X1 != X2
| c_Nat_Osemiring__1__class_Oof__nat__aux(X3,X4,X5,X1) = c_Nat_Osemiring__1__class_Oof__nat__aux(X3,X4,X5,X2) ) ).
cnf(i_0_3873,axiom,
( X1 != X2
| c_Power_Opower_Opower(X1,X3,X4) = c_Power_Opower_Opower(X2,X3,X4) ) ).
cnf(i_0_3874,axiom,
( X1 != X2
| c_Power_Opower_Opower(X3,X1,X4) = c_Power_Opower_Opower(X3,X2,X4) ) ).
cnf(i_0_3875,axiom,
( X1 != X2
| c_Power_Opower_Opower(X3,X4,X1) = c_Power_Opower_Opower(X3,X4,X2) ) ).
cnf(i_0_3876,axiom,
( X1 != X2
| c_Transcendental_Odiffs(X1,X3,X4) = c_Transcendental_Odiffs(X2,X3,X4) ) ).
cnf(i_0_3877,axiom,
( X1 != X2
| c_Transcendental_Odiffs(X3,X1,X4) = c_Transcendental_Odiffs(X3,X2,X4) ) ).
cnf(i_0_3878,axiom,
( X1 != X2
| c_Transcendental_Odiffs(X3,X4,X1) = c_Transcendental_Odiffs(X3,X4,X2) ) ).
cnf(i_0_3879,axiom,
( X1 != X2
| c_Nat_Onat_Onat__case(X1,X3,X4) = c_Nat_Onat_Onat__case(X2,X3,X4) ) ).
cnf(i_0_3880,axiom,
( X1 != X2
| c_Nat_Onat_Onat__case(X3,X1,X4) = c_Nat_Onat_Onat__case(X3,X2,X4) ) ).
cnf(i_0_3881,axiom,
( X1 != X2
| c_Nat_Onat_Onat__case(X3,X4,X1) = c_Nat_Onat_Onat__case(X3,X4,X2) ) ).
cnf(i_0_3882,axiom,
( X1 != X2
| c_Groups_Osgn__class_Osgn(X1,X3) = c_Groups_Osgn__class_Osgn(X2,X3) ) ).
cnf(i_0_3883,axiom,
( X1 != X2
| c_Groups_Osgn__class_Osgn(X3,X1) = c_Groups_Osgn__class_Osgn(X3,X2) ) ).
cnf(i_0_3884,axiom,
( X1 != X2
| c_Power_Opower__class_Opower(X1) = c_Power_Opower__class_Opower(X2) ) ).
cnf(i_0_3885,axiom,
( X1 != X2
| ~ class_Rings_Oidom(X1)
| class_Rings_Oidom(X2) ) ).
cnf(i_0_3886,axiom,
( X1 != X2
| ~ c_Deriv_Oderiv(X1,X3,X4,X5)
| c_Deriv_Oderiv(X2,X3,X4,X5) ) ).
cnf(i_0_3887,axiom,
( X1 != X2
| ~ c_Deriv_Oderiv(X3,X1,X4,X5)
| c_Deriv_Oderiv(X3,X2,X4,X5) ) ).
cnf(i_0_3888,axiom,
( X1 != X2
| ~ c_Deriv_Oderiv(X3,X4,X1,X5)
| c_Deriv_Oderiv(X3,X4,X2,X5) ) ).
cnf(i_0_3889,axiom,
( X1 != X2
| ~ c_Deriv_Oderiv(X3,X4,X5,X1)
| c_Deriv_Oderiv(X3,X4,X5,X2) ) ).
cnf(i_0_3890,axiom,
( X1 != X2
| ~ class_RealVector_Oreal__normed__field(X1)
| class_RealVector_Oreal__normed__field(X2) ) ).
cnf(i_0_3891,axiom,
( X1 != X2
| ~ class_RealVector_Oreal__normed__algebra(X1)
| class_RealVector_Oreal__normed__algebra(X2) ) ).
cnf(i_0_3892,axiom,
( X1 != X2
| ~ c_Polynomial_Opdivmod__rel(X1,X3,X4,X5,X6)
| c_Polynomial_Opdivmod__rel(X2,X3,X4,X5,X6) ) ).
cnf(i_0_3893,axiom,
( X1 != X2
| ~ c_Polynomial_Opdivmod__rel(X3,X1,X4,X5,X6)
| c_Polynomial_Opdivmod__rel(X3,X2,X4,X5,X6) ) ).
cnf(i_0_3894,axiom,
( X1 != X2
| ~ c_Polynomial_Opdivmod__rel(X3,X4,X1,X5,X6)
| c_Polynomial_Opdivmod__rel(X3,X4,X2,X5,X6) ) ).
cnf(i_0_3895,axiom,
( X1 != X2
| ~ c_Polynomial_Opdivmod__rel(X3,X4,X5,X1,X6)
| c_Polynomial_Opdivmod__rel(X3,X4,X5,X2,X6) ) ).
cnf(i_0_3896,axiom,
( X1 != X2
| ~ c_Polynomial_Opdivmod__rel(X3,X4,X5,X6,X1)
| c_Polynomial_Opdivmod__rel(X3,X4,X5,X6,X2) ) ).
cnf(i_0_3897,axiom,
( X1 != X2
| ~ class_RealVector_Oreal__field(X1)
| class_RealVector_Oreal__field(X2) ) ).
cnf(i_0_3898,axiom,
( X1 != X2
| ~ class_Rings_Ocomm__ring__1(X1)
| class_Rings_Ocomm__ring__1(X2) ) ).
cnf(i_0_3899,axiom,
( X1 != X2
| ~ class_Divides_Osemiring__div(X1)
| class_Divides_Osemiring__div(X2) ) ).
cnf(i_0_3900,axiom,
( X1 != X2
| ~ class_Rings_Ocomm__ring(X1)
| class_Rings_Ocomm__ring(X2) ) ).
cnf(i_0_3901,axiom,
( X1 != X2
| ~ class_Rings_Odvd(X1)
| class_Rings_Odvd(X2) ) ).
cnf(i_0_3902,axiom,
( X1 != X2
| ~ class_Rings_Oordered__ring(X1)
| class_Rings_Oordered__ring(X2) ) ).
cnf(i_0_3903,axiom,
( X1 != X2
| ~ class_Rings_Ocomm__semiring__0(X1)
| class_Rings_Ocomm__semiring__0(X2) ) ).
cnf(i_0_3904,axiom,
( X1 != X2
| ~ class_Rings_Ocomm__semiring__1(X1)
| class_Rings_Ocomm__semiring__1(X2) ) ).
cnf(i_0_3905,axiom,
( X1 != X2
| ~ class_Groups_Oab__group__add(X1)
| class_Groups_Oab__group__add(X2) ) ).
cnf(i_0_3906,axiom,
( X1 != X2
| ~ class_Groups_Ocomm__monoid__add(X1)
| class_Groups_Ocomm__monoid__add(X2) ) ).
cnf(i_0_3907,axiom,
( X1 != X2
| ~ class_Rings_Odivision__ring(X1)
| class_Rings_Odivision__ring(X2) ) ).
cnf(i_0_3908,axiom,
( X1 != X2
| ~ class_Rings_Oring(X1)
| class_Rings_Oring(X2) ) ).
cnf(i_0_3909,axiom,
( X1 != X2
| ~ class_Rings_Osemiring(X1)
| class_Rings_Osemiring(X2) ) ).
cnf(i_0_3910,axiom,
( X1 != X2
| ~ c_Orderings_Oord__class_Oless__eq(X1,X3,X4)
| c_Orderings_Oord__class_Oless__eq(X2,X3,X4) ) ).
cnf(i_0_3911,axiom,
( X1 != X2
| ~ c_Orderings_Oord__class_Oless__eq(X3,X1,X4)
| c_Orderings_Oord__class_Oless__eq(X3,X2,X4) ) ).
cnf(i_0_3912,axiom,
( X1 != X2
| ~ c_Orderings_Oord__class_Oless__eq(X3,X4,X1)
| c_Orderings_Oord__class_Oless__eq(X3,X4,X2) ) ).
cnf(i_0_3913,axiom,
( X1 != X2
| ~ class_Rings_Osemiring__0(X1)
| class_Rings_Osemiring__0(X2) ) ).
cnf(i_0_3914,axiom,
( X1 != X2
| ~ class_Rings_Osemiring__1(X1)
| class_Rings_Osemiring__1(X2) ) ).
cnf(i_0_3915,axiom,
( X1 != X2
| ~ class_Rings_Olinordered__ring__strict(X1)
| class_Rings_Olinordered__ring__strict(X2) ) ).
cnf(i_0_3916,axiom,
( X1 != X2
| ~ hBOOL(X1)
| hBOOL(X2) ) ).
cnf(i_0_3917,axiom,
( X1 != X2
| ~ class_Rings_Olinordered__ring(X1)
| class_Rings_Olinordered__ring(X2) ) ).
cnf(i_0_3918,axiom,
( X1 != X2
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X1)
| class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X2) ) ).
cnf(i_0_3919,axiom,
( X1 != X2
| ~ class_Divides_Oring__div(X1)
| class_Divides_Oring__div(X2) ) ).
cnf(i_0_3920,axiom,
( X1 != X2
| ~ class_Fields_Olinordered__field(X1)
| class_Fields_Olinordered__field(X2) ) ).
cnf(i_0_3921,axiom,
( X1 != X2
| ~ class_Fields_Ofield__inverse__zero(X1)
| class_Fields_Ofield__inverse__zero(X2) ) ).
cnf(i_0_3922,axiom,
( X1 != X2
| ~ class_Rings_Oring__1(X1)
| class_Rings_Oring__1(X2) ) ).
cnf(i_0_3923,axiom,
( X1 != X2
| ~ class_Groups_Omonoid__mult(X1)
| class_Groups_Omonoid__mult(X2) ) ).
cnf(i_0_3924,axiom,
( X1 != X2
| ~ class_Fields_Olinordered__field__inverse__zero(X1)
| class_Fields_Olinordered__field__inverse__zero(X2) ) ).
cnf(i_0_3925,axiom,
( X1 != X2
| ~ class_Rings_Olinordered__semidom(X1)
| class_Rings_Olinordered__semidom(X2) ) ).
cnf(i_0_3926,axiom,
( X1 != X2
| ~ class_Groups_Ocomm__monoid__mult(X1)
| class_Groups_Ocomm__monoid__mult(X2) ) ).
cnf(i_0_3927,axiom,
( X1 != X2
| ~ c_Orderings_Oord__class_Oless(X1,X3,X4)
| c_Orderings_Oord__class_Oless(X2,X3,X4) ) ).
cnf(i_0_3928,axiom,
( X1 != X2
| ~ c_Orderings_Oord__class_Oless(X3,X1,X4)
| c_Orderings_Oord__class_Oless(X3,X2,X4) ) ).
cnf(i_0_3929,axiom,
( X1 != X2
| ~ c_Orderings_Oord__class_Oless(X3,X4,X1)
| c_Orderings_Oord__class_Oless(X3,X4,X2) ) ).
cnf(i_0_3930,axiom,
( X1 != X2
| ~ class_Rings_Ocomm__semiring(X1)
| class_Rings_Ocomm__semiring(X2) ) ).
cnf(i_0_3931,axiom,
( X1 != X2
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X1)
| class_Groups_Oordered__ab__semigroup__add__imp__le(X2) ) ).
cnf(i_0_3932,axiom,
( X1 != X2
| ~ class_Groups_Ominus(X1)
| class_Groups_Ominus(X2) ) ).
cnf(i_0_3933,axiom,
( X1 != X2
| ~ class_Rings_Olinordered__semiring__strict(X1)
| class_Rings_Olinordered__semiring__strict(X2) ) ).
cnf(i_0_3934,axiom,
( X1 != X2
| ~ class_Rings_Olinordered__comm__semiring__strict(X1)
| class_Rings_Olinordered__comm__semiring__strict(X2) ) ).
cnf(i_0_3935,axiom,
( X1 != X2
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(X1)
| class_Groups_Oordered__cancel__ab__semigroup__add(X2) ) ).
cnf(i_0_3936,axiom,
( X1 != X2
| ~ class_Groups_Oab__semigroup__mult(X1)
| class_Groups_Oab__semigroup__mult(X2) ) ).
cnf(i_0_3937,axiom,
( X1 != X2
| ~ class_Groups_Oab__semigroup__add(X1)
| class_Groups_Oab__semigroup__add(X2) ) ).
cnf(i_0_3938,axiom,
( X1 != X2
| ~ class_Power_Opower(X1)
| class_Power_Opower(X2) ) ).
cnf(i_0_3939,axiom,
( X1 != X2
| ~ class_Groups_Oordered__comm__monoid__add(X1)
| class_Groups_Oordered__comm__monoid__add(X2) ) ).
cnf(i_0_3940,axiom,
( X1 != X2
| ~ class_Orderings_Oorder(X1)
| class_Orderings_Oorder(X2) ) ).
cnf(i_0_3941,axiom,
( X1 != X2
| ~ c_Polynomial_Opos__poly(X1,X3)
| c_Polynomial_Opos__poly(X2,X3) ) ).
cnf(i_0_3942,axiom,
( X1 != X2
| ~ c_Polynomial_Opos__poly(X3,X1)
| c_Polynomial_Opos__poly(X3,X2) ) ).
cnf(i_0_3943,axiom,
( X1 != X2
| ~ class_Rings_Olinordered__idom(X1)
| class_Rings_Olinordered__idom(X2) ) ).
cnf(i_0_3944,axiom,
( X1 != X2
| ~ class_Groups_Olinordered__ab__group__add(X1)
| class_Groups_Olinordered__ab__group__add(X2) ) ).
cnf(i_0_3945,axiom,
( X1 != X2
| ~ class_Groups_Oordered__ab__group__add(X1)
| class_Groups_Oordered__ab__group__add(X2) ) ).
cnf(i_0_3946,axiom,
( X1 != X2
| ~ class_Groups_Ogroup__add(X1)
| class_Groups_Ogroup__add(X2) ) ).
cnf(i_0_3947,axiom,
( X1 != X2
| ~ class_Rings_Odivision__ring__inverse__zero(X1)
| class_Rings_Odivision__ring__inverse__zero(X2) ) ).
cnf(i_0_3948,axiom,
( X1 != X2
| ~ class_Orderings_Opreorder(X1)
| class_Orderings_Opreorder(X2) ) ).
cnf(i_0_3949,axiom,
( X1 != X2
| ~ class_Lattices_Oab__semigroup__idem__mult(X1)
| class_Lattices_Oab__semigroup__idem__mult(X2) ) ).
cnf(i_0_3950,axiom,
( X1 != X2
| ~ class_Groups_Ouminus(X1)
| class_Groups_Ouminus(X2) ) ).
cnf(i_0_3951,axiom,
( X1 != X2
| ~ class_Orderings_Owellorder(X1)
| class_Orderings_Owellorder(X2) ) ).
cnf(i_0_3952,axiom,
( X1 != X2
| ~ c_Orderings_Oorder_Ostrict__mono(X1,X3,X4,X5)
| c_Orderings_Oorder_Ostrict__mono(X2,X3,X4,X5) ) ).
cnf(i_0_3953,axiom,
( X1 != X2
| ~ c_Orderings_Oorder_Ostrict__mono(X3,X1,X4,X5)
| c_Orderings_Oorder_Ostrict__mono(X3,X2,X4,X5) ) ).
cnf(i_0_3954,axiom,
( X1 != X2
| ~ c_Orderings_Oorder_Ostrict__mono(X3,X4,X1,X5)
| c_Orderings_Oorder_Ostrict__mono(X3,X4,X2,X5) ) ).
cnf(i_0_3955,axiom,
( X1 != X2
| ~ c_Orderings_Oorder_Ostrict__mono(X3,X4,X5,X1)
| c_Orderings_Oorder_Ostrict__mono(X3,X4,X5,X2) ) ).
cnf(i_0_3956,axiom,
( X1 != X2
| ~ class_Orderings_Olinorder(X1)
| class_Orderings_Olinorder(X2) ) ).
cnf(i_0_3957,axiom,
( X1 != X2
| ~ class_Groups_Ocancel__semigroup__add(X1)
| class_Groups_Ocancel__semigroup__add(X2) ) ).
cnf(i_0_3958,axiom,
( X1 != X2
| ~ class_Groups_Ocancel__ab__semigroup__add(X1)
| class_Groups_Ocancel__ab__semigroup__add(X2) ) ).
cnf(i_0_3959,axiom,
( X1 != X2
| ~ c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(X1,X3,X4)
| c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(X2,X3,X4) ) ).
cnf(i_0_3960,axiom,
( X1 != X2
| ~ c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(X3,X1,X4)
| c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(X3,X2,X4) ) ).
cnf(i_0_3961,axiom,
( X1 != X2
| ~ c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(X3,X4,X1)
| c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(X3,X4,X2) ) ).
cnf(i_0_3962,axiom,
( X1 != X2
| ~ class_Rings_Oring__1__no__zero__divisors(X1)
| class_Rings_Oring__1__no__zero__divisors(X2) ) ).
cnf(i_0_3963,axiom,
( X1 != X2
| ~ class_Rings_Omult__zero(X1)
| class_Rings_Omult__zero(X2) ) ).
cnf(i_0_3964,axiom,
( X1 != X2
| ~ class_Rings_Ono__zero__divisors(X1)
| class_Rings_Ono__zero__divisors(X2) ) ).
cnf(i_0_3965,axiom,
( X1 != X2
| ~ class_Rings_Ozero__neq__one(X1)
| class_Rings_Ozero__neq__one(X2) ) ).
cnf(i_0_3966,axiom,
( X1 != X2
| ~ class_Rings_Oring__no__zero__divisors(X1)
| class_Rings_Oring__no__zero__divisors(X2) ) ).
cnf(i_0_3967,axiom,
( X1 != X2
| ~ class_Int_Oring__char__0(X1)
| class_Int_Oring__char__0(X2) ) ).
cnf(i_0_3968,axiom,
( X1 != X2
| ~ c_Orderings_Oorder_Omono(X1,X3,X4,X5)
| c_Orderings_Oorder_Omono(X2,X3,X4,X5) ) ).
cnf(i_0_3969,axiom,
( X1 != X2
| ~ c_Orderings_Oorder_Omono(X3,X1,X4,X5)
| c_Orderings_Oorder_Omono(X3,X2,X4,X5) ) ).
cnf(i_0_3970,axiom,
( X1 != X2
| ~ c_Orderings_Oorder_Omono(X3,X4,X1,X5)
| c_Orderings_Oorder_Omono(X3,X4,X2,X5) ) ).
cnf(i_0_3971,axiom,
( X1 != X2
| ~ c_Orderings_Oorder_Omono(X3,X4,X5,X1)
| c_Orderings_Oorder_Omono(X3,X4,X5,X2) ) ).
cnf(i_0_3972,axiom,
( X1 != X2
| ~ class_Lattices_Oboolean__algebra(X1)
| class_Lattices_Oboolean__algebra(X2) ) ).
cnf(i_0_3973,axiom,
( X1 != X2
| ~ class_Groups_Omonoid__add(X1)
| class_Groups_Omonoid__add(X2) ) ).
cnf(i_0_3974,axiom,
( X1 != X2
| ~ class_Nat_Osemiring__char__0(X1)
| class_Nat_Osemiring__char__0(X2) ) ).
cnf(i_0_3975,axiom,
( X1 != X2
| ~ class_Orderings_Oord(X1)
| class_Orderings_Oord(X2) ) ).
cnf(i_0_3976,axiom,
( X1 != X2
| ~ class_Groups_Ocancel__comm__monoid__add(X1)
| class_Groups_Ocancel__comm__monoid__add(X2) ) ).
cnf(i_0_3977,axiom,
( X1 != X2
| ~ class_Groups_Oone(X1)
| class_Groups_Oone(X2) ) ).
cnf(i_0_3978,axiom,
( X1 != X2
| ~ class_Fields_Ofield(X1)
| class_Fields_Ofield(X2) ) ).
cnf(i_0_3979,axiom,
( X1 != X2
| ~ class_Groups_Ozero(X1)
| class_Groups_Ozero(X2) ) ).
cnf(i_0_4013,plain,
X1 = X1,
inference(equality_inference,[],[2963]) ).
cnf(i_0_4044,plain,
X1 = X1,
inference(equality_inference,[],[3251]) ).
cnf(i_0_4045,plain,
X1 = X1,
inference(equality_inference,[],[3252]) ).
cnf(i_0_4051,plain,
X1 = X1,
inference(equality_inference,[],[3285]) ).
cnf(i_0_4055,plain,
hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),X1)),
inference(equality_inference,[],[3375]) ).
cnf(i_0_4056,plain,
hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),X1)),
inference(equality_inference,[],[3377]) ).
cnf(i_0_4067,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(equality_inference,[],[3417]) ).
cnf(i_0_4070,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X1),
inference(equality_inference,[],[3431]) ).
cnf(i_0_4071,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X1),
inference(equality_inference,[],[3432]) ).
cnf(i_0_4075,plain,
c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,hAPP(c_Nat_OSuc,X1)),
inference(equality_inference,[],[3451]) ).
cnf(i_0_4103,plain,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1) = X1,
inference(equality_inference,[],[3565]) ).
cnf(i_0_4104,plain,
hBOOL(hAPP(c_fequal(X1),X1)),
inference(equality_inference,[],[3582]) ).
cnf(i_0_4106,plain,
X1 = X1,
inference(equality_inference,[],[3592]) ).
cnf(i_0_4107,plain,
X1 = X1,
inference(equality_inference,[],[3594]) ).
cnf(i_0_4116,plain,
~ c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(t_a,t_a,c_Polynomial_Opoly(t_a,v_p)),
inference(scs_inference,[],[i_0_3818,i_0_3316]) ).
cnf(i_0_4130,plain,
c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,hAPP(c_Nat_OSuc,X1)),
inference(rename_variables,[],[i_0_3460]) ).
cnf(i_0_4145,plain,
hAPP(c_COMBI(X1),X2) = X2,
inference(rename_variables,[],[i_0_3624]) ).
cnf(i_0_4148,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X1),
inference(rename_variables,[],[i_0_3439]) ).
cnf(i_0_4157,plain,
hAPP(c_COMBI(X1),X2) = X2,
inference(rename_variables,[],[i_0_3624]) ).
cnf(i_0_4163,plain,
c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,hAPP(c_Nat_OSuc,X1)),
inference(rename_variables,[],[i_0_3460]) ).
cnf(i_0_4169,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X1),
inference(rename_variables,[],[i_0_3439]) ).
cnf(i_0_4172,plain,
hAPP(c_COMBI(X1),X2) = X2,
inference(rename_variables,[],[i_0_3624]) ).
cnf(i_0_4186,plain,
hAPP(c_Nat_OSuc,X1) != X1,
inference(rename_variables,[],[i_0_3622]) ).
cnf(i_0_4265,plain,
c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,hAPP(c_Nat_OSuc,X1)),
inference(rename_variables,[],[i_0_3460]) ).
cnf(i_0_4274,plain,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = X1,
inference(rename_variables,[],[i_0_3577]) ).
cnf(i_0_4280,plain,
X1 != hAPP(c_Nat_OSuc,X1),
inference(rename_variables,[],[i_0_3623]) ).
cnf(i_0_4284,plain,
X1 != hAPP(c_Nat_OSuc,X1),
inference(rename_variables,[],[i_0_3623]) ).
cnf(i_0_4297,plain,
hAPP(c_Nat_OSuc,X1) != X1,
inference(rename_variables,[],[i_0_3622]) ).
cnf(i_0_4344,plain,
hAPP(c_COMBI(X1),X2) = X2,
inference(rename_variables,[],[i_0_3624]) ).
cnf(i_0_4346,plain,
hAPP(c_COMBI(X1),X2) = X2,
inference(rename_variables,[],[i_0_3624]) ).
cnf(i_0_4388,plain,
hAPP(c_COMBI(X1),X2) = X2,
inference(rename_variables,[],[i_0_3624]) ).
cnf(i_0_4426,plain,
hAPP(c_Nat_OSuc,X1) != X1,
inference(rename_variables,[],[i_0_3622]) ).
cnf(i_0_4467,plain,
hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X1)),
inference(rename_variables,[],[i_0_3347]) ).
cnf(i_0_4470,plain,
hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(rename_variables,[],[i_0_3364]) ).
cnf(i_0_4473,plain,
hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X1)),
inference(rename_variables,[],[i_0_3347]) ).
cnf(i_0_4476,plain,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1) = X1,
inference(rename_variables,[],[i_0_3564]) ).
cnf(i_0_4477,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X1),
inference(rename_variables,[],[i_0_3439]) ).
cnf(i_0_4480,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(rename_variables,[],[i_0_3421]) ).
cnf(i_0_4493,plain,
hAPP(c_Nat_OSuc,X1) != X1,
inference(rename_variables,[],[i_0_3622]) ).
cnf(i_0_4494,plain,
c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,hAPP(c_Nat_OSuc,X1)),
inference(rename_variables,[],[i_0_3460]) ).
cnf(i_0_4497,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X1),
inference(rename_variables,[],[i_0_3439]) ).
cnf(i_0_4506,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X1),
inference(rename_variables,[],[i_0_3439]) ).
cnf(i_0_4516,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(rename_variables,[],[i_0_3421]) ).
cnf(i_0_4524,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(rename_variables,[],[i_0_3421]) ).
cnf(i_0_4531,plain,
hAPP(c_COMBI(X1),X2) = X2,
inference(rename_variables,[],[i_0_3624]) ).
cnf(i_0_4534,plain,
hAPP(c_COMBI(X1),X2) = X2,
inference(rename_variables,[],[i_0_3624]) ).
cnf(i_0_4537,plain,
hAPP(c_COMBI(X1),X2) = X2,
inference(rename_variables,[],[i_0_3624]) ).
cnf(i_0_4540,plain,
hAPP(c_COMBI(X1),X2) = X2,
inference(rename_variables,[],[i_0_3624]) ).
cnf(i_0_4543,plain,
hAPP(c_COMBI(X1),X2) = X2,
inference(rename_variables,[],[i_0_3624]) ).
cnf(i_0_4548,plain,
hAPP(c_Nat_OSuc,X1) != X1,
inference(rename_variables,[],[i_0_3622]) ).
cnf(i_0_4551,plain,
hAPP(c_COMBI(X1),X2) = X2,
inference(rename_variables,[],[i_0_3624]) ).
cnf(i_0_4557,plain,
hAPP(c_Nat_OSuc,X1) != X1,
inference(rename_variables,[],[i_0_3622]) ).
cnf(i_0_4560,plain,
hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X1)),
inference(rename_variables,[],[i_0_3347]) ).
cnf(c_0_3824,plain,
( ~ class_Rings_Oidom(t_a)
| ~ c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(t_a,t_a,c_Polynomial_Opoly(t_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)))) ),
i_0_3218 ).
cnf(c_0_3825,hypothesis,
class_Rings_Oidom(t_a),
i_0_3818 ).
cnf(c_0_3826,plain,
( c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(X1,X2,X3)
| hAPP(X3,esk2_1(X3)) != hAPP(X3,esk3_1(X3)) ),
i_0_3310 ).
cnf(c_0_3827,plain,
( hAPP(c_Polynomial_Opoly(X1,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))),X2) = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Rings_Ocomm__semiring__0(X1) ),
i_0_3427 ).
cnf(c_0_3828,plain,
~ c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(t_a,t_a,c_Polynomial_Opoly(t_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_3824,c_0_3825])]) ).
cnf(c_0_3829,plain,
( c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(X1,X2,c_Polynomial_Opoly(X3,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3))))
| ~ class_Rings_Ocomm__semiring__0(X3) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_3826,c_0_3827]),c_0_3827]) ).
cnf(c_0_3830,plain,
~ class_Rings_Ocomm__semiring__0(t_a),
inference(spm,[status(thm)],[c_0_3828,c_0_3829]) ).
cnf(c_0_3831,plain,
( class_Rings_Ocomm__semiring__0(X1)
| ~ class_Rings_Oidom(X1) ),
i_0_3718 ).
cnf(c_0_3832,plain,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_3830,c_0_3831]),c_0_3825])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWW246+1 : TPTP v9.2.1. Released v5.2.0.
% 0.00/0.12 % Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.15/0.33 % Computer : n029.cluster.edu
% 0.15/0.33 % Model : x86_64 x86_64
% 0.15/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.33 % Memory : 8042.1875MB
% 0.15/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.33 % CPULimit : 300
% 0.15/0.33 % WCLimit : 300
% 0.15/0.33 % DateTime : Tue May 5 06:29:14 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.35 % start to proof: theBenchmark
% 145.80/112.06 % Version : CSE_E---1.7
% 145.80/112.06 % Problem : theBenchmark.p
% 145.80/112.06 % SZS status Theorem for theBenchmark.p
% 145.80/112.06 % SZS output start CNFRefutation
% See solution above
% 219.80/186.11 % Total time : 109.984s
%------------------------------------------------------------------------------